damage mechanisms associated with kink-band formation in

Damage Mechanisms Associated with

Kink-Band Formation in Unidirectional

Fibre Composites

A Thesis

submitted to the University of Manchester for the degree of

Doctor of Philosophy

in the Faculty of Engineering and Physical Sciences

2015

YING WANG

School of Materials

2

Contents

Contents ................................................................................................................................. 2

List of Figures ........................................................................................................................ 9

List of Tables........................................................................................................................ 20

Abstract ................................................................................................................................ 21

Declaration ........................................................................................................................... 22

Copyright ............................................................................................................................. 23

Acknowledgements .............................................................................................................. 24

1. Introduction ................................................................................................................... 25

1.1. Background ........................................................................................................ 25

1.2. Aims and objectives ........................................................................................... 26

1.3. Structure of thesis .............................................................................................. 27

2. Literature Review .......................................................................................................... 29

2.1. Composite materials .......................................................................................... 29

2.2. Manufacture of composite materials.................................................................. 32

2.2.1. Pultrusion ....................................................................................................... 32

2.2.2. Vacuum Assisted Resin Infusion ................................................................... 33

2.2.3. Prepreg processing ......................................................................................... 34

2.3. Compressive failure of FRPs ............................................................................. 35

2.3.1. Compression test ............................................................................................ 36

3

2.3.2. Macroscopic failure modes ............................................................................ 37

2.3.2.1. In-plane shear failure mode .................................................................... 38

2.3.2.2. Brooming failure mode ........................................................................... 39

2.3.2.3. Through-the-thickness shear failure mode ............................................. 39

2.3.3. Microscopic damage mechanisms.................................................................. 39

2.3.3.1. Fibre micro-buckling .............................................................................. 41

2.3.3.2. Fibre kinking ........................................................................................... 42

2.3.3.3. Fibre failure............................................................................................. 44

2.3.3.4. Longitudinal splitting .............................................................................. 46

2.3.4. Factors affecting the compressive failure ...................................................... 47

2.4. Kink bands ......................................................................................................... 49

2.4.1. Kink-band morphology .................................................................................. 50

2.4.2. Kink-band formation ...................................................................................... 50

2.4.2.1. Characterisation methods ........................................................................ 50

2.4.2.2. Kink-band initiation ................................................................................ 52

2.4.2.3. Kink-band propagation ........................................................................... 55

2.5. X-ray computed tomography ............................................................................. 59

2.5.1. The physics of X-ray computed tomography ................................................. 59

2.5.2. X-ray computed tomography processing ....................................................... 60

2.5.2.1. Acquisition .............................................................................................. 61

4

2.5.2.2. Reconstruction ........................................................................................ 62

2.5.2.3. Analysis .................................................................................................. 62

2.5.3. Artefacts ......................................................................................................... 63

2.5.4. Approaches to enhance feature visibility in X-ray CT................................... 66

2.5.4.1. Staining ................................................................................................... 66

2.5.4.2. Phase contrast ......................................................................................... 67

2.5.5. Application of X-ray computed tomography in composite materials ............ 68

2.5.5.1. Post mortem tomography ........................................................................ 69

2.5.5.2. Ex situ tomography ................................................................................. 70

2.5.5.3. Interrupted in situ tomography ............................................................... 71

2.5.5.4. Continuous in situ tomography ............................................................... 73

2.6. Chapter summary ............................................................................................... 74

3. Failure of unidirectional CFRP rods under axial compression ..................................... 75

3.1. Introduction ........................................................................................................ 75

3.2. Experimental ...................................................................................................... 77

3.2.1. Materials ......................................................................................................... 77

3.2.1.1. Fibre ........................................................................................................ 77

3.2.1.2. Resin ....................................................................................................... 78

3.2.2. Manufacturing of UD carbon fibre-epoxy composite rods ............................ 78

3.2.2.1. Preparation .............................................................................................. 78

5

3.2.2.2. Manufacturing method ............................................................................ 80

3.2.2.3. Curing and demolding process ............................................................... 84

3.2.3. Sample preparation......................................................................................... 84

3.2.3.1. Machining ............................................................................................... 84

3.2.3.2. Adding tabs ............................................................................................. 85

3.2.4. Quality control ............................................................................................... 86

3.2.4.1. Fibre volume fraction.............................................................................. 86

3.2.4.2. Initial fibre misalignment angle .............................................................. 86

3.2.4.3. Uniformity of reinforcement distribution ............................................... 88

3.2.5. Axial compression testing .............................................................................. 88

3.2.5.1. Compression testing of waisted samples ................................................ 89

3.2.5.2. In situ compression testing of waisted and circular-notched samples .... 89

3.2.6. Scanning electron microscopy ....................................................................... 91

3.2.7. X-ray micro-computed tomography ............................................................... 91

3.2.7.1. Post mortem X-ray μCT ......................................................................... 91

3.2.7.2. Interrupted in situ X-ray μCT ................................................................. 93

3.2.7.3. Continuous in situ X-ray μCT ................................................................ 94

3.3. Results and discussion ....................................................................................... 96

3.3.1. Material quality .............................................................................................. 96

3.3.1.1. Fibre volume fraction.............................................................................. 96

6

3.3.1.2. Initial fibre misalignment angle .............................................................. 96

3.3.1.3. Resin-rich regions ................................................................................... 97

3.3.1.4. Voids ....................................................................................................... 98

3.3.2. Compressive failure of UD CFRP rods ........................................................ 102

3.3.3. Kink bands on fracture surfaces – 2D observations ..................................... 103

3.3.4. Kink bands in the damage zone – 3D observations ..................................... 105

3.3.4.1. Kink-band geometry ............................................................................. 108

3.3.4.2. Kink-band boundaries ........................................................................... 109

3.3.4.3. Splits ..................................................................................................... 110

3.3.4.4. Matrix micro-cracks .............................................................................. 111

3.3.4.5. Curvature of unbroken fibres ................................................................ 112

3.3.5. Multiple kink bands ..................................................................................... 112

3.3.6. High-speed in situ observations ................................................................... 113

3.4. Conclusions ...................................................................................................... 115

4. Failure of UD CFRP beams under four-point bending ............................................... 117

4.1. Introduction ...................................................................................................... 117

4.2. Experimental .................................................................................................... 118

4.2.1. Materials ....................................................................................................... 119

4.2.2. Composite manufacture ............................................................................... 120

4.2.2.1. B8 UD laminate .................................................................................... 120

7

4.2.2.2. B7 UD laminate .................................................................................... 123

4.2.2.3. B3 UD laminate .................................................................................... 126

4.2.3. Sample preparation....................................................................................... 126

4.2.3.1. Samples for preliminary four-point bending test .................................. 126

4.2.3.2. Samples for in situ four-point bending test ........................................... 127

4.2.4. Fibre volume fraction ................................................................................... 129

4.2.5. Four-point bending test ................................................................................ 131

4.2.5.1. Preliminary four-point bending test ...................................................... 131

4.2.5.2. In situ four-point bending test ............................................................... 132

4.2.6. X-ray micro-tomographic imaging .............................................................. 133

4.2.6.1. Interrupted in situ X-ray μCT ............................................................... 133

4.2.6.2. Post mortem X-ray μCT ....................................................................... 134

4.2.6.3. Reconstruction ...................................................................................... 135

4.2.6.4. Data analysis ......................................................................................... 136

4.3. Results and discussion ..................................................................................... 136

4.3.1. Fibre volume fraction ................................................................................... 136

4.3.2. Preliminary four-point bending behaviour ................................................... 137

4.3.3. In situ four-point bending behaviour............................................................ 141

4.3.4. Damage mechanisms .................................................................................... 152

4.3.4.1. Fibre micro-buckling and fibre kinking ................................................ 153

8

4.3.4.2. Fibre fracture......................................................................................... 159

4.3.4.3. Splitting ................................................................................................. 160

4.3.4.4. Through-the-thickness cracks ............................................................... 166

4.3.5. Kink bands ................................................................................................... 168

4.3.5.1. Kink bands at different stages ............................................................... 168

4.3.5.2. Kink bands with parallel and non-parallel boundaries ......................... 168

4.3.5.3. In-plane and out-of-plane kink bands ................................................... 170

4.3.5.4. Kink-band geometry ............................................................................. 171

4.3.5.5. Multiple kink bands .............................................................................. 173

4.3.5.6. Conjugate kink bands............................................................................ 180

4.3.6. Effect of material system on the initial bucking location ............................ 181

4.3.7. Effect of unloading on damage morphology ................................................ 182

4.3.8. Sequence of events leading to failure........................................................... 183

4.4. Conclusions ...................................................................................................... 184

5. Conclusions and future work ...................................................................................... 187

5.1. Conclusions ...................................................................................................... 187

5.2. Future work ...................................................................................................... 191

References .......................................................................................................................... 193

Appendix ............................................................................................................................ 206

Word count: 45416

9

List of Figures

Figure 2.1: Specific tensile strength as a function of specific modulus of composite materials,

metals and ceramics. (Kutz, 2002) ....................................................................................... 30

Figure 2.2: Schematic diagram demonstrating the use of FRPs in the Airbus 380. (Mallick,

2007) .................................................................................................................................... 31

Figure 2.3: Schematic diagram of the pultrusion process – from dry fibres to cured

composites. (Joshi, 2012) ..................................................................................................... 33

Figure 2.4: Schematic of the VARI process. (Goren and Atas, 2008) ................................. 34

Figure 2.5: Methods to introduce load to specimens for compression tests. (Hodgkinson,

2000) .................................................................................................................................... 36

Figure 2.6: Typical acceptable failure modes for composites under compression. (a) in-plane

shear, (b) brooming and (c) through-the-thickness shear..................................................... 38

Figure 2.7: In-plane shear failure modes under compression: (a) transverse, (b) branched

transverse, (c) split transverse. (Odom and Adams, 1990) .................................................. 38

Figure 2.8: Schematic diagram of two fibre instability buckling modes discussed in this

thesis: (a) fibre micro-buckling and (b) fibre kinking. ......................................................... 40

Figure 2.9: Typical X-ray CT slice image of kink bands in CFRP from my own work for

illustration of the kink-band width ω, the kink-band angle β, and the angle of fibre rotation

within the kink bands Φ= φ+φo. .......................................................................................... 41

Figure 2.10: Two modes of fibre elastic micro-buckling: (a) shear mode, and (b) extensional

mode. .................................................................................................................................... 42

Figure 2.11: Schematic showing the fibre kinking of initially misaligned fibres forming an

inclined kink band. (Jumahat et al., 2010b) ......................................................................... 44

10

Figure 2.12: Schematic illustration of typical fibre failure modes in FRPs: shear failure,

kinking of fibrils and bending (buckling) failure. (Hahn and Williams, 1986) ................... 45

Figure 2.13: SEM images showing failure modes of carbon fibre in CFRP failed under axial

compression, (a) shear induced fibre compressive failure and (b) fibre buckling failure.

(Ewins et al., 1980) .............................................................................................................. 45

Figure 2.14: Optical micrographs exhibiting the transition of failure pattern from shear

driven fibre compressive failure to kink bands in a notched cross-ply T800/924 specimen

failed under compression along 0º fibre direction. Surface 90º layer was polished off before

observation while maintaining the load on the specimen. (Gutkin et al., 2010) .................. 46

Figure 2.15: SEM image showing micro-cracks along the interface at the top edge of a kink

band in a notched UD T800/924 specimen under load. (Gutkin et al., 2011) ..................... 47

Figure 2.16: Kink-band propagation observed by optical microscopy on the surface of a

notched UD T800/924 specimen loaded under compression. (Pimenta, 2008) ................... 51

Figure 2.17: SEM images showing damage patterns in the sub-surface plies in notched UD

T700/977-2 carbon fibre/epoxy composite specimen observed under load by FIB milling of

the surface layers. (Hapke et al., 2011) ................................................................................ 52

Figure 2.18: Schematic illustration of specimen geometry designed for inducing shear stress

with axial compression load for in situ SEM studies by (a) Pimenta (2008) and (b) Hapke et

al. (2011). ............................................................................................................................. 53

Figure 2.19: SEM images of the surface of a notched UD T700/977-2 carbon fibre/epoxy

composite specimen under compression load. (a) The last frame before kink band

propagation starts. (b) Taken 0.2 s later, a kink band already having propagated over more

than 100 μm. (Hapke et al., 2011) ....................................................................................... 54

Figure 2.20: Typical load-end shortening curve with the illustration of different stages in

kink-band formation in notched IM7/PEEK composite under axial compression load.

(Moran et al., 1995) ............................................................................................................. 56

11

Figure 2.21: Photomicrograph of kink bands after band broadening in UD AS4/APC-2

composite. (Vogler and Kyriakides, 1997) .......................................................................... 57

Figure 2.22: Number of individual kink bands as a function of the distance behind the micro-

buckle tip in UD T800/924C composite. (Fleck, 1997) ....................................................... 58

Figure 2.23: Schematic illustration of CT acquisition and reconstruction processes. (Landis

and Keane, 2010) ................................................................................................................. 61

Figure 2.24: Illustration of different X-ray CT acquisition configurations: (a) fan beam, (b)

cone beam, and (c) parallel beam (synchrotron radiation). (Salvo et al., 2003) .................. 62

Figure 2.25: Slice image of a limestone core sample showing the difference before (upper

half) and after (bottom half) beam-hardening correction. (Davis and Elliott, 2006) ........... 64

Figure 2.26: Incorrect centre-of-rotation induced artefact with double edges in the image.

(Davis and Elliott, 2006) ...................................................................................................... 64

Figure 2.27: An example of ring artefacts in a CT slice image. (Davis and Elliott, 2006).. 65

Figure 2.28: X-ray µCT reconstructed cross-section of a graphite/epoxy sample (a) without

using the dye penetrant (zinc iodide solution), and (b) using the dye penetrant. (Schilling et

al., 2005) .............................................................................................................................. 66

Figure 2.29: Radiographic images corresponding to a. absorption radiography, and b. phase

sensitive radiography of Al/SiC composite. (Cloetens et al., 1997) .................................... 68

Figure 2.30: (a) Post mortem, (b) Ex situ, (c) Interrupted in situ, and (d) Continuous in situ

X-ray CT process. σ means mechanical testing and T refers to heat treatment. S1 (S2, S3 or

S4) is abbreviated for Sample 1 (2, 3 or 4). (Salvo et al., 2010) ......................................... 69

Figure 2.31: X-ray μCT cross-sectional view of stitched CFRP specimens damaged by low-

velocity impact. (Tan et al., 2011) ....................................................................................... 70

Figure 2.32: X-ray μCT cross-sections of CFRP showing new damage propagation due to

12

compressive load after impact damage. (Bull et al., 2014) .................................................. 71

Figure 2.33: 3D extraction and segmentation of progressive damage accumulation in cross-

ply CFRP composite under progressive tensile straining. (Scott et al., 2011) .................... 72

Figure 2.34: Schematic of in situ load frame. (Wright et al., 2010) .................................... 73

Figure 2.35: Pure Al compact heated to slightly above the melting point. Images show state

at, (a) 0 s, (b) 48 s, (c) 60 s, (d) 72 s, (e) 92 s and (f) 200 s after the beginning of heating.

(Babcsán et al., 2007)........................................................................................................... 74

Figure 3.1: Photographs of the preparation of fibres. (a) Step-like stacking of fibre tows at

the top. (b) Binding of the fibre tows using a flexible film.................................................. 79

Figure 3.2: Fibre wetting step in the pultrusion process (a) in a paper cup and (b) in a flat

tray........................................................................................................................................ 80

Figure 3.3: Photograph of the SSRI experiment set-up. ...................................................... 81

Figure 3.4: Photograph demonstrating the connections between parts. The three ends of the

Y connector correspond to fibre fixing end, resin inlet and resin outlet, respectively. ....... 82

Figure 3.5: Schematic of the SSRI manufacturing method developed to make UD composite

rods. ...................................................................................................................................... 83

Figure 3.6: Schematic of the specimen geometry, in which the carbon fibre rod is in black

while metal tabs are in white. The diameter of the rod was 2.4 mm and the waisted gauge

section was 1.5 mm in diameter. (Unit: mm) ....................................................................... 85

Figure 3.7: Photograph of the modified Daresbury tension-compression loading rig (rig tube

outside diameter = 66 mm). ................................................................................................. 90

Figure 3.8: Photograph of the INSA-Lyon tension-compression loading machine (rig tube

outside diameter: 76 mm)..................................................................................................... 90

13

Figure 3.9: Photograph of the sample preparation for post-failure µCT imaging. .............. 92

Figure 3.10: The Zeiss Xradia Micro-XCT system. ............................................................ 92

Figure 3.11: Photograph of the in situ experiment set-up in the MicroXCT hutch. ............ 94

Figure 3.12: Photograph of the in situ experiment set-up at the TOMCAT beamline. ....... 95

Figure 3.13: Initial fibre misalignment angle distribution in carbon fibre/epoxy rods made

by the SSRI method. ............................................................................................................ 97

Figure 3.14: Optical microscopic cross-sectional view of a composite rod made by the SSRI

method with the resin-rich regions highlighted in yellow ellipses. ..................................... 98

Figure 3.15: Lab-based X-ray µCT XY slice image giving the cross-sectional view of the

composite rod made by the SSRI method (Pixel size: 2.1 μm). .......................................... 99

Figure 3.16: Extracted volume of the voids in a composite rod made by the SSRI method

before sample preparation. ................................................................................................... 99

Figure 3.17: YZ slice images from high-resolution region-of-interest µCT scan showing the

same elongated void at different positions along the X axis. (a) Micro-voids are formed close

to left side of the macro-void, and (b) micro-voids are formed at the tip of the macro-void

(Pixel size: 0.6 μm). ........................................................................................................... 101

Figure 3.18: Photographs showing typical failure of the composite samples. Samples

fractured into two parts: (a) both fracture surfaces are inclined, and (b) one fracture surface

is inclined while the other is flat at the outside (inside part is inclined). (c) Intact sample after

failure with an inclined damage zone across the sample. .................................................. 102

Figure 3.19: A typical SEM image of the fracture surface showing multiple kink bands with

varied kink-band widths. .................................................................................................... 103

Figure 3.20: A typical SEM image of the fracture surface showing matrix failure, splitting

and different modes of fibre failure associated with kink-band formation. ....................... 104

14

Figure 3.21: A typical high-magnification SEM image showing the failure pattern of

individual fibres. The fracture surface of one fibre consists of a compressive zone and a

tensile zone. ........................................................................................................................ 104

Figure 3.22: The designated origin and axes for the discussion of the kink bands in this

section. The compressive loading and the fibre direction are along the Z axis. The X axis

was chosen to include kink bands in the XZ planes........................................................... 106

Figure 3.23: A typical X-ray μCT XZ slice image in the middle of the sample showing kink

bands and associated damage mechanisms. Most of the bands lie in the XZ plane, thus the

kink-band width, kink-band boundary angle and fibre rotation angle can be measured as

indicated. ............................................................................................................................ 106

Figure 3.24: X-ray μCT XZ slice images of the sample at different distance from the origin

along the Y axis: (a) 100 μm, (b) 300 μm, (c) 500 μm, (d) 700 μm, (e) 900 μm, (f) 1100 μm

and (g) 1300 μm. ................................................................................................................ 107

Figure 3.25: Side view of the segmented X-ray µCT image showing planes of fibre breakage

(purple) normal to, and three splits (yellow) parallel to, the fibre direction. The upper and

lower fibre-fracture planes delineate a wide kink band, within which multiple narrow bands

that are similarly inclined lie. ............................................................................................. 109

Figure 3.26: Top view of the segmented kink-band boundaries defined by fibre breakage,

categorised in three groups according to their location and morphology: (a) upper, (b) middle

and (c) lower. ..................................................................................................................... 110

Figure 3.27: Angled views of the three segmented splits at different locations in the specimen,

numbered I, II and III. The small split highlighted in the red circle corresponds to the

highlighted position in Figure 3.26 (a). .............................................................................. 110

Figure 3.28: Adjacent X-ray CT XZ slice images of the specimen (two sequential images in

between were not shown) showing the transition between split, micro-cracks and fibre

breakage. ............................................................................................................................ 111

15

Figure 3.29: Radiographs showing the progressive damage evolution in notched and waisted

rod sample forming kink bands. (a), (b), (c) and (d) are sequential radiographs, each of which

is taken in 0.1 ms and is rotated by 0.78º with respect to the last. The interval between (c)

and (e) is 1 ms, and that between (e) and (f) is 10 ms. The number at the bottom left corner

of each image indicates the number of radiograph taken. .................................................. 114

Figure 4.1: Photograph of the plies of prepreg material after cutting from the roll. .......... 121

Figure 4.2: Recommended bagging arrangement to manufacture laminates from the prepreg

manufacturer. ..................................................................................................................... 122

Figure 4.3: Photograph showing the debulking procedure, in which the plies of prepreg

materials were compacted under vacuum to eliminate enclosed air. ................................. 122

Figure 4.4: Photograph of the vacuum bagged panel from prepregs. ................................ 123

Figure 4.5: Photograph showing the pin-mould used for the preparation of UD T700 carbon

fibre preform. ..................................................................................................................... 125

Figure 4.6: Schematic diagram of the vacuum bagging arrangement for the VARI

manufacturing method. ...................................................................................................... 125

Figure 4.7: UD T300 carbon fabric with glass binder yarns. ............................................. 126

Figure 4.8: Radiograph image of sample IB8-4, illustrating the measurement of notch

geometry. ............................................................................................................................ 127

Figure 4.9: Schematic diagram of the sample geometry for in situ FPB test (wider notch).

(Unit: mm) .......................................................................................................................... 128

Figure 4.10: Photograph of the electronic balance for density measurement. ................... 130

Figure 4.11: Photograph showing the preliminary FPB test set-up on the Instron machine.

............................................................................................................................................ 131

16

Figure 4.12: Photograph of the bottom part of the in situ loading rig with the sample placed

on the supporting rollers..................................................................................................... 132

Figure 4.13: µCT scan set-up in the Zeiss Xradia Versa machine with the Deben CT5000

loading rig. ......................................................................................................................... 134

Figure 4.14: Photograph of the sample arrangement for post-failure µCT scan................ 135

Figure 4.15: Photographs of (a) specimen EB8-2 after unloaded, specimen EB8-1 (b) after

unloaded and (c) under load, presenting unacceptable failure modes. .............................. 137

Figure 4.16: Load-displacement curve of sample EB8-3 under preliminary 4PB test. ..... 139

Figure 4.17: Photographs of specimen EB8-3 at different stages during the loading process.

Images (a), (b), (c) and (d) correspond to a, b, c and d points highlighted on the loading curve

in Figure 4.16, respectively. ............................................................................................... 139

Figure 4.18: Load-displacement curve of sample IB8-4 (see Table 4.3) under in situ FPB

test. CT scans were taken at steps 0, 1, 2, 3 and 4 marked in red on the curve, corresponding

to cross-head displacement of 0 mm, 0.31 mm, 0.38 mm, 0.44 mm and 0.51mm. ........... 141

Figure 4.19: X-ray µCT XZ slice images from the same through thickness location (see

schematic at bottom of the figure) in specimen IB8-4 (notch width 800 μm) at different

loading steps. Images (a), (b), (c) and (d) correspond to steps 1, 2, 3 and 4 highlighted on the

loading curve in Figure 4.18, respectively. ........................................................................ 144

Figure 4.20: X-ray µCT XZ slice images from the same position in specimen IB7-1 (notch

width 800 μm) at different loading steps. Images (a), (b), (c) and (d) correspond to steps 1,

2, 3 and 4. ........................................................................................................................... 146

Figure 4.21: X-ray µCT XY slice images of specimen IB7-1 (notch width 800 μm) at the

position illustrated as the XY Plane in Figure 4.20 at (a) step 3 and (b) step 4 showing the

formation of kink bands from fibre micro-buckling in the XY plane. ............................... 147

17


width 400 μm) at different loading steps. Images (a), (b) and (c) correspond to steps 1, 2 and

3. ......................................................................................................................................... 148


position illustrated as the XY Plane in Figure 4.22 (c) at step 3 showing the formation of

intersecting kink bands from fibre micro-buckling in the XY plane. ................................ 149

Figure 4.24: X-ray µCT XZ slice images from the same position in specimen IB3-1 at

different loading steps. Images (a), (b) and (c) correspond to steps 1, 2 and 3. ................ 150

Figure 4.25: X-ray µCT XY slice images of specimen IB3-1 (notch width 800 μm) at two

locations at step 3, showing (a) kink bands and (b) fibre kinking. .................................... 151

Figure 4.26: X-ray µCT XZ slice images near side surface in specimen IB3-1 (notch width

800 μm) at step 1, showing two micro-buckling waves. .................................................... 152

Figure 4.27: Schematic diagram demonstrating the amplitude and half-wavelength of the

fibre buckle wave in the case of fibre micro-buckling. ...................................................... 154

Figure 4.28: Schematic diagram demonstrating the amplitude and quarter-wavelength of the

fibre buckle wave in the case of fibre kinking. .................................................................. 155

Figure 4.29: X-ray μCT XZ slice image of specimen IB8-4 (notch width 800 μm) near the

side surface at step 4, presenting the morphology of multiple fibre buckling along one fibre.

............................................................................................................................................ 156


other side surface at step 4, presenting the morphology of fibre micro-buckling with an entire

waveform............................................................................................................................ 157

Figure 4.31: X-ray μCT XZ slice image of specimen IB7-2 (notch width 400 μm) at step 1

showing fibre micro-buckling (kinking) contained within the splitting region. ................ 158

18

Figure 4.32: X-ray μCT XZ slice images of the same position in specimen IB8-4 (notch

width 800 μm) at (a) step 3 and (b) step 4. Fibre micro-buckling (kinking) is contained within

the splitting region. ............................................................................................................ 158


showing individual fibre fracture at the notch surface due to buckling. ............................ 159

Figure 4.34: Sequential X-ray radiographs of specimen IB7-1 (notch width 800 μm) taken

before the scan at step 1 showing the opening of additional splits. ................................... 160

Figure 4.35: X-ray μCT XZ slice images of specimen IB3-1 (notch width 800 μm) at (a) step

1 and (b) step 2 showing the interaction between fibre micro-buckling and splitting. Resin-

rich region is found to arrest the propagation of fibre microbuckling. .............................. 161

Figure 4.36: Unique feature observed inside a failed AS4/APC-2 composite sample, which

was regarded as a manufacturing defect. (Kyriakides and Ruff, 1997) ............................. 163

Figure 4.37: X-ray μCT XZ slice images of specimen IB8-4 (notch width 800 μm) at (a) step

3 and (b) step 4 showing the broadening of a split originated from a kink band. .............. 164

Figure 4.38: Side view of the segmented and extracted splits in specimen IB8-4 (notch width

800 μm) at step 3 and step 4. .............................................................................................. 165

Figure 4.39: Top view of the segmented and extracted splits in specimen IB8-4 (notch width

800 μm) at step 3 and step 4. .............................................................................................. 166

Figure 4.40: X-ray μCT YZ slice images of specimen IB8-4 (notch width 800 μm) at (a) step

3 and (b) step 4 showing through-the-thickness cracks. .................................................... 167

Figure 4.41: Schematic diagram of fibre fracture due to fibre kinking, forming parallel-

boundary kink bands. ......................................................................................................... 169

Figure 4.42: Schematic diagram of progressive fibre fracture due to fibre micro-buckling,

forming kink bands with non-parallel boundaries. ............................................................ 170

19

Figure 4.43: Sequential X-ray radiographs of specimen IB8-4 (notch width 800 μm) after

loading to step 4 showing the sequential adding of narrow kink bands resulting in the

morphology of multiple kink bands. .................................................................................. 175

Figure 4.44: X-ray μCT XZ slice images of the same location in specimen IB8-4 (notch

width 800 μm) at step 3 (a), step 4 (b) and after unloading (c). The fibre rotation angle, band-

boundary angle and band width of the primary kink band are all kept the same once formed.

The fibre rotation angle is reduced after unloading, while the boundary angle is maintained.

............................................................................................................................................ 176

Figure 4.45: Schematic diagram illustrating the segmented kink bands with two distinct band

boundaries defined by fibre breaks. ................................................................................... 176

Figure 4.46: Two views of the extracted volumes of the primary kink band in specimen IB8-

4 (notch width 800 μm) at step 3 and 4 demonstrating the propagation in 3D. ................. 179

Figure 4.47: Extracted volumes of the five fully developed individual kink bands in

specimen IB8-4 (notch width 800 μm) at step 4 as illustrated in Figure 4.45. The kink bands

are shown in different colours. ........................................................................................... 179

Figure 4.48: Schematic diagram of conjugating kink bands: (a) π-shaped and (b) zigzag

shaped. ................................................................................................................................ 180

Figure 4.49: X-ray μCT XZ slice image of specimen IB8-4 near the side surface after

unloading. The two regions exhibiting the straightening of buckled fibres are highlighted in

red boxes. The white box demonstrates the region in which the rotation of fibres out of the

XZ plane is released. .......................................................................................................... 183

Figure A.1: Load-displacement curve of sample IB7-1 under in situ FPB test................ 206

Figure A.2: Load-displacement curve of sample IB7-2 under in situ FPB test................. 206

Figure A.3: Load-displacement curve of sample IB3-1 under in situ FPB test................. 207

20

List of Tables

Table 3.1: Properties of T700-12000-50C carbon fibre yarns. ............................................ 77

Table 3.2: Properties of cured Araldite® LY 564/ Aradur® XB 3486 epoxy matrix. ........... 77

Table 3.3: Setting parameters for lab-based CT scans in the Zeiss Xradia MicroXCT system.

.............................................................................................................................................. 93

Table 3.4: Scanning parameters for synchrotron radiation experiments at the TOMCAT

beamline. .............................................................................................................................. 95

Table 3.5: Fibre volume fraction of the samples calculated according to formula (3.1). .... 96

Table 4.1: Properties of the carbon fibres and the composites according to the datasheets

from the fibre manufacture................................................................................................. 119

Table 4.2: Curing cycles for the matrix systems. ............................................................... 120

Table 4.3: Details of the samples discussed in this chapter. .............................................. 128

Table 4.4: Setting parameters of X-ray µCT scans in the Zeiss Xradia Versa machine. ... 135

Table 4.5: Fibre volume fractions of the composite laminates measured by acid digestion.

............................................................................................................................................ 136

Table 4.6: Summary of the kink-band geometry observed in all the material systems within

the field of view. ................................................................................................................ 172

Table 4.7: The distance between buckling peak and notch side surface in different specimens.

............................................................................................................................................ 181

21

Abstract

The University of Manchester

Ying Wang

Doctor of Philosophy

Damage Mechanisms Associated with Kink-Band Formation in Unidirectional Fibre

Composites

September, 2015

The compressive strength of unidirectional (UD) carbon fibre reinforced plastics (CFRPs)

is often only 60-70% of their tensile strength owing to premature failure associated with

kink-band formation. The sudden and complex nature of kink-band formation has been

hindering the progress in experimental studies on the evolution of damage in compressive

failure. A better understanding of the damage mechanisms associated with kink-band

formation can help to design more reliable composite structures. Therefore, the principal aim

of this project is to identify, in three dimensions (3D), the key damage mechanisms

underlying the initiation and propagation of kink bands in UD carbon fibre/epoxy composite.

A new manufacturing method is developed to fabricate high-quality UD T700/epoxy

cylindrical rods for axial compression tests and high-resolution imaging of kink bands by

post mortem and in situ X-ray computed tomography (CT). The morphology of kink bands

is visualised in 3D by segmenting fibre breaks at kink-band boundaries and representative

longitudinal splits. The geometrical parameters of each fully developed kink band are

consistent through the specimen. Radiographs obtained from ultra-fast synchrotron imaging

show that a kink band initiates and propagates across the specimen in less than 1.2 ms. A

scenario of kink-band failure is proposed: fibre buckling and longitudinal splitting occur

prior to fibre breakage, which forms kink-band boundaries and eventually the morphology

of multiple kink bands develops suddenly.

3D tomographs of the fast and unstable kink-band formation could not be captured in the

axial compression experiments. Therefore, a testing method of loading notched UD carbon

fibre (T800, T700 and T300)/epoxy beams using a four-point bending (FPB) fixture is

developed to enable monitoring of more stable initiation and propagation of kink bands by

in situ X-ray CT. Kink-band formation is significantly slowed in the FPB tests. Fibre micro-

buckling accompanied by splitting, could initiate the formation of kink bands. In the

T700/epoxy system, the early initiation stage of fibre micro-buckling without fracture is

captured, and the critical radius of curvature of unbroken fibres prior to fracture is ～130μm.

Unloading causes significant recovery of fibre curvature (radius of curvature ～280 μm)

and a reduction of 10-20º in fibre rotation angle within the kink band. The results show that

in situ 3D characterisation of kink bands is essential as fibre buckling is a 3D phenomenon,

resulting in development of both in-plane and out-of-plane kink bands.

Understanding of kink-band formation in 3D will help to establish strategies to improve the

compressive strength of CFRP composites by depressing kink-band formation; in this

respect lateral constraint conferred by strong interfaces is a key aspect.

22

Declaration

I declare that no portion of the work referred to in the thesis has been submitted in support

of an application for another degree or qualification of this or any other university or other

institute of learning.

23

Copyright

i. The author of this thesis (including any appendices and/or schedules to this thesis) owns

certain copyright or related rights in it (the “Copyright”) and s/he has given The University

of Manchester certain rights to use such Copyright, including for administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy,

may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as

amended) and regulations issued under it or, where appropriate, in accordance with licensing

agreements which the University has from time to time. This page must form part of any

such copies made.

iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual

property (the “Intellectual Property”) and any reproductions of copyright works in the thesis,

for example graphs and tables (“Reproductions”), which may be described in this thesis, may

not be owned by the author and may be owned by third parties. Such Intellectual Property

and Reproductions cannot and must not be made available for use without the prior written

permission of the owner(s) of the relevant Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy (see

http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant Thesis

restriction declarations deposited in the University Library, The University Library’s

regulations (see http://www.manchester.ac.uk/library/aboutus/regulations) and in The

University’s policy on presentation of Theses.

24

Acknowledgements

I would like to express my sincere gratitude to my supervisor Professor Philip Withers for

his patience, encouragement and continuous support through my PhD study. I would also

like to thank my co-supervisor Professor Costas Soutis for the inspiring discussions on my

project. I am gratitude to Professor Paul Hogg, who introduced me to Manchester and the

field of composite materials.

My sincere thanks also go to Mark, Tom and Susan for helping me to machine numerous

samples through my study. I would like to thank everyone in the Northwest Composites

Centre for all the help in my research, special thanks to Bill Godwin for his sharing of

invaluable experience in composite manufacturing and testing with me.

I would like to thank all the staff in the Henry Moseley X-ray Imaging Facility, especially

Tristan Lowe, Rob Bradley, Sam Mcdonald, Julia Benhsen for teaching me to use various

CT machines and helping me to solve imaging problems. Without their precious support it

would not be possible to conduct this research.

I thank my colleagues and friends for all the helpful discussions and all the fun we had in

the past four years. Special thanks go to Kate Meade, Shengnan Min, Serafina Garcea,

Paulina Hoyos for the help in the days I struggled with writing.

Last but not the least, I would like to thank my parents and Yuan for supporting me spiritually

throughout writing this thesis. This thesis is a gift to my 26th birthday.

Chapter 1 Introduction

25

1. Introduction

1.1. Background

Fibre reinforced plastics (FRPs) consist of high performance fibres in a polymer matrix,

which is usually a thermosetting polymer. CFRPs are an important category of FRPs widely

used in high-performance aerospace, aircraft and automotive structures, due to their high

specific strength and specific stiffness, which offer an attractive approach to substantially

reduce the weight of these structures. However, one crucial factor limiting the design of

structures composed of CFRPs is the susceptibility of the material to compressive load.

Experiments on CFRPs have indicated compressive strengths that are 60-70% of the reported

tensile strengths (Ahn and Waas, 1999; Berbinau et al., 1999b; Budiansky and Fleck, 1993).

As compressive loads naturally arise in many mechanical structures deliberately or

accidentally, large safety margins are incorporated in current composite designs, resulting in

overweight and inefficient structures (Soutis, 2005b). Thus, the advantage of high specific

strengths of composite materials cannot be fully exploited.

From the materials development point of view, the most basic and effective approach to

strengthen the reliability of composite materials under compressive load is to control the

damage evolution. An understanding of the correlation between microscopic structure and

the triggering mechanisms involved in damage initiation and propagation is then required.

As a result, the compressive failure of FRPs has been a subject of extensive research over

the past fifty years (Rosen, 1965), and today a great number of experimental, theoretical and

numerical results have enriched our knowledge in this field. Compressive failure of UD

carbon fibre/epoxy composite tends to be instantaneous and catastrophic due to the

occurrence of kink bands (Hapke et al., 2011; Jumahat et al., 2010b) . The sudden nature

and complexity of kink-band formation have hindered the progress in experimental studies

on the evolution of damage in compressive failure.

In an effort to investigate the micromechanics of kink-band formation, both post mortem

and in situ characterisation using a combination of optical microscopy and scanning electron

microscopy (SEM) have been undertaken (Hapke et al., 2011; Pimenta, 2008; Sivashanker


26

et al., 1996; Sutcliffe and Fleck, 1994; Vogler and Kyriakides, 1997; 1999). Post-failure

cross-sections cut so as to include the fibre direction have been carefully studied revealing

the two-dimensional (2D) geometry of the kink bands. Monitoring of surface change under

different load levels has been used to reveal the sequence of events in the evolution of kink

bands (Hapke et al., 2011; Pimenta, 2008). Unfortunately these techniques are destructive

in nature and/or only provide a 2D view of the microstructure at a given instant in time.

Moreover, the failure mechanisms interact with each other in 3D, resulting in the observation

using conventional 2D techniques not being truly representative of the deformed

microstructure. Some fundamental issues concerning the initiation and propagation of kink

bands still remain open, which promotes the idea of investigating kink bands in 3D and even

in four dimensions (4D – 3D and time).

Non-destructive X-ray CT has been increasingly applied to the field of materials science for

better understanding of the 3D material microstructure and its effect on properties. Recently,

X-ray micro-CT (μCT) has been employed to image the 3D damage morphology and

distribution of the tensile failure (Scott et al., 2011), impact damage (McCombe et al., 2012),

compression after impact (CAI) damage (Bull et al., 2014) and fatigue failure (Garcea et al.,

2014) in CFRPs; however, the analysis of compressive failure with the formation of kink

bands has not been reported and will be addressed in this thesis.

1.2. Aims and objectives

The main aim of this project is to map the 3D morphology of kink bands, and to establish

the relationships between damage mechanisms associated with the formation of kink bands

in the compressive failure of UD carbon fibre/epoxy composite, thus providing experimental

basis for potential development in analytical and numerical modelling on compressive

failure of CFRPs. Specific research objectives are:

to characterise kink bands developed in the compressive failure of UD carbon

fibre/epoxy composite by X-ray μCT, and to propose the 3D morphology and

distribution of damage mechanisms in the kink zone;


27

to monitor the evolution of kink bands in UD carbon fibre/epoxy composite under in

situ compressive loading by X-ray μCT;

to observe catastrophic kink-band formation in real time with ultra-fast synchrotron

radioscopic imaging and to identify the sequence of events leading to the failure;

to develop a methodology which allows the tracking of the 3D damage evolution during

slow and stable kink-band formation in UD carbon fibre/epoxy composite;

to establish damage mechanisms underlying the initiation and propagation of kink bands

in UD carbon fibre/epoxy composite.

1.3. Structure of thesis

Following the introduction of this thesis in Chapter 1, the background and the literature

relating to the basics and compressive failure mechanisms of fibre reinforced polymer matrix

composites including the formation of kink bands in CFRPs are reviewed. In addition the X-

ray tomography method is described and its application to damage characterisation in

composites is presented.

Chapter 3 describes a study on the compressive collapse and failure of UD carbon

fibre/epoxy composite rods with the formation of kink bands under axial compressive

loading. The manufacturing, compression testing and X-ray tomographic imaging methods

are introduced. Both high-resolution post mortem and in situ X-ray μCT are employed in the

study. The 3D kink-band morphology is presented by segmenting features in the damage

zone in post failure CT data. The use of ultra-fast synchrotron radiation CT enables studying

the kink band formation process at a very high radiographic rate of 10,000 frames per second,

delivering 22 tomographs per second. The lower bound of kink propagation velocity is

estimated and the sequence of events leading to failure is discussed based on observation in

radiographs.

Because axial kink-band formation of UD composites is too fast and unstable, in Chapter 4

a FPB testing configuration on notched UD carbon fibre/epoxy composite beams is used for

the study on progressive damage evolution in 3D by in situ X-ray μCT. The role of damage


28

mechanisms, including fibre micro-buckling, fibre kinking and splitting, in kink-band

formation are identified and the relationships between these mechanisms are discussed. The

maximum curvature of buckled fibre prior to fracture is measured under load. The formation

of multiple kink bands is analysed based on both radiographs and segmented kinking

volumes in 3D. By comparing μCT data obtained under load and after unloading, the effect

of unloading on the 3D morphology of kink bands is discussed.

Chapter 5 presents the main conclusions drawn from the work in this project and future work

recommendations.

Chapter 2 Literature Review

29

2. Literature Review

This chapter provides an overview of composite materials, damage mechanisms associated

with the compressive failure and the experimental damage characterisation techniques. The

background and manufacturing of fibre composite materials are presented before exploring

the compressive failure mechanisms of fibre reinforced composite materials, especially the

formation of kink bands. The computed tomography technique and its application to

composite materials are detailed.

2.1. Composite materials

Composites are multi-phase materials with the constituent phases acting cooperatively on

the microscopic scale (Hull and Clyne, 1996). Nature produced the original composite

materials such as wood and bone. Man-made composites generally consist of a strong and

brittle reinforcing phase dispersed in a tougher and more ductile phase termed the matrix

(Hull and Clyne, 1996). Modern composite materials often use polymer, ceramic or metal as

the matrix. The reinforcing phase may take the form of long or short fibres, whiskers or

particles. Composite materials can be categorised into metal-matrix composites (MMCs),

ceramic-matrix composites (CMCs) and polymer-matrix composites (PMCs) according to

the type of matrix material.

Figure 2.1 compares the specific properties of a range of composite materials, metals and

ceramics. FRPs are regarded as advanced composite materials because of their high specific

strength (strength divided by density) and specific modulus (Young’s modulus divided by

density). FRPs have gained popularity in a number of fields in the past decades, such as the

sports, automotive, military, aircraft and aerospace industries, to replace conventional metal

materials (Soutis, 2005a). Since the introduction of carbon fibres into the aircraft industry in

the 1960s, CFRPs, especially carbon fibre/epoxy composites, have become increasingly

important in the design of both military and commercial aircrafts. Figure 2.2 shows the use

of composite materials in Airbus 380, in which the total usage is ～25% by weight. For the

Boeing 787 Dreamliner, this value can be as high as 50% (Marsh, 2005). The primary reason


30

promoting the use of CFRPs in aircrafts is weight reduction, which contributes to increase

in fuel efficiency and payload. The increase in the use of composite materials in aircrafts

could lead to 40% reduction in weight of secondary structures and 20% of primary structures

(Soutis, 2005a). Other reasons for its increasing use include the flexibility for moulding

CFRPs into complex shapes and the ease in tailoring the properties by designing the

composite system. CFRPs are also extensively used in Formula 1 racing cars where speed

instead of cost is the major concern. While in the commercial automotive industry, the use

of CFRP is limited due to its high cost and the difficulty in manufacturing large numbers of

units.

Figure 2.1: Specific tensile strength as a function of specific modulus of composite

materials, metals and ceramics. (Kutz, 2002)


31

Figure 2.2: Schematic diagram demonstrating the use of FRPs in the Airbus 380. (Mallick,

2007)

The properties of composite material depend on its constituents. The intention of designing

composite materials is to attain a suite of properties superior to those of the individual

constituent. FRPs can be tailored to meet specific requirements by adopting the appropriate

reinforcement and matrix, by optimising the interface, and by designing the geometric

arrangement of the reinforcement in the matrix (Goutianos, 2004). Generally, in FRPs fibres

carry most of the load while the surrounding polymer matrix holds the fibres in designated

position and transfers the load, which also protects fibres from environmental damage

(Mallick, 2007). Therefore, although fibres reinforce the matrix, the polymer matrix is of

vital importance in determining the matrix-related properties of FRPs, including the

compressive strength, inter-laminar strength, damage resistance and damage tolerance

(Kinsey et al., 1995; Soutis, 1997).

Long fibre reinforced composites are widely used in the form of laminated sheet in the

aerospace and automotive industries (Soutis et al., 1993). UD composite laminates are rarely

used on their own in structural components but are usually used together with plies of

varying orientation to form a multidirectional laminate. However, it is the 0° layers in such


32

a laminate that carry most of the load, and in compression failure of the laminate occurs due

to the micro-buckling of these 0° plies (Berbinau et al., 1999b). It is therefore important to

understand the damage mechanism in UD composite laminates.

2.2. Manufacture of composite materials

The quality of composite materials largely depends on the manufacturing method by which

they are fabricated. This is because that the manufacture of the composite material and

fabrication of the final composite component are usually performed at the same time. The

proper manufacturing technique should be chosen according to the properties of the fibre

and the matrix, the shape of the component and the required mechanical properties (Hull and

Clyne, 1996). In the meantime, the production cost and efficiency are key factors in

industrial composite manufacturing.

A number of methods can be employed to manufacture FRPs. Typical methods include hand

lay-up, pultrusion, filament winding, resin transfer moulding, resin infusion and prepreg

processing (Rudd et al., 1997). For the manufacturing of unidirectionally reinforced

thermoset composites, pultrusion (Campbell and Maji, 2006; Soutis, 2000), vacuum assisted

rein infusion (VARI) (Arshad, 2014) and prepreg processing (Jumahat et al., 2010b; Pinho

et al., 2006) are widely used. The manufacturing methods used in this thesis are based on

these three methods.

2.2.1. Pultrusion

Pultrusion is an effective method to manufacture FRP components with a constant cross-

section. The term pultrusion combines the meaning of the two words – ‘pull’ and ‘extrusion’

(Joshi, 2012). In the pultrusion process, continuous dry fibres pulled through a resin bath are

then fed into a heated die and extruded in the desired shape of cured composite part. Figure

2.3 shows the schematic of the pultrusion process.


33

Figure 2.3: Schematic diagram of the pultrusion process – from dry fibres to cured

composites. (Joshi, 2012)

With the advancing of this relatively old technique, pultrusion can be used to manufacture

almost any composite components with uniform cross-sectional geometry (Joshi 2012), such

as channels, tubes, rods, beams and bars. It is extensively used in the composite

manufacturing industry because of its continuous, low-cost and highly productive nature.

The length of the parts manufactured is very flexible and ranges from several centimetres

(cms) to several kilometres (kms). However, the pultrusion process is not suitable for

composite parts with a complex shape, and the accuracy of the dimensions is not as high as

that of some other techniques. Moreover, defects caused by non-uniform heating and

entrapped air can lower the reliability of the composites (Majumdar et al., 2009).

2.2.2. Vacuum Assisted Resin Infusion

The VARI manufacturing method is one of the modern liquid composite moulding

composite manufacturing processes and has been increasingly adapted in the production of

advanced composites for ships, wind turbines and aircrafts (Tzetzis and Hogg, 2008). A

number of different terms are used to interpret the vacuum infusion process, including

vacuum assisted resin transfer moulding (VARTM) (Kuentzer et al., 2007), Seemann

composites resin infusion moulding process (SCRIMP™) (Boh et al., 2005), and vacuum

assisted resin infusion moulding (VARIM) (Sánchez et al., 2013). The principle of these

methods is basically the same, which is the impregnation of dry fabrics with liquid resin

driven by vacuum.


34

Figure 2.4: Schematic of the VARI process. (Goren and Atas, 2008)

In the VARI process, resin is infused into a sealed vacuum bag with dry fabrics laid-up on

the mould by a vacuum pump. After infusion is finished, the whole part is cured in the oven.

Figure 2.4 shows the schematic of a typical VARI set-up. The processing is relatively easier

to handle without the use of complicated equipment. The VARI method has the advantages

of adaptability to the manufacture of complex shaped parts and large-scale components,

relatively high fibre volume fraction and low production cost. Additionally, the lay-up

orientation and sequence of fabrics can be tailored depending on the desired mechanical

properties of the final composite. However, it also has limitations such as non-uniform

thickness and susceptibility to leakage in the vacuum bag.

2.2.3. Prepreg processing

Other than the impregnation of fibres during the manufacturing of composites, the use of

pre-impregnated continuous reinforcement, also referred to as prepregs, has gained

popularity in the manufacture of advanced composites and are described in detail by Long

(2005). Prepregs often consist of a single layer of fibres (UD or woven carbon, glass or

aramid fibres) embedded in partially cured resin (epoxy is mostly used) in the form of rolled

sheets. The prepregs are typically stored in a freezer, processed at room temperature and

then cured at elevated temperatures, in order to ensure a reasonable shelf-life of the prepregs.

The curing of prepregs can be carried out in the autoclave (in which pressure as high as

several atmospheres can be applied) or in the oven. While the autoclave gives very high

quality products, it is a very expensive piece of equipment and its contribution to the bulk


35

composite performance is still uncertain. Thus prepregs and processing techniques without

the need of autoclave have been developed. For these materials, the part can be cured in an

oven once vacuumed.

Prepreg processing is intensively used in the aircraft industry and is extensively employed

to manufacture wind turbines, racing cars and sports equipment (Long, 2005). It has

advantages over liquid moulding techniques in that the fibre volume fraction can be

controlled and optimised and fibres can be precisely placed in the desired orientation due to

the fixed positon of fibres in each ply of the prepreg (Rudd et al., 1997). Moreover, the

composite components manufactured from prepregs have high quality with little variation.

The main disadvantages are the high cost and the low-temperature storing requirement. The

cost of prepreg materials can be twice that of the separate fibre and resin systems, while the

difference in cost of the finished composite part can be small (Long, 2005).

Except the military and Formula 1 industries, where cost is not an issue, prepregs are more

suitable for small-scale components where quality is key as only a small quantity of prepreg

material is needed. For large composite structures, liquid moulding techniques may be more

appropriate, due to the relatively low cost for a large quantity of raw materials. The

manufacturing method of composite components with a medium size should be determined

balancing the quality and cost requirement (Rudd et al., 1997).

2.3. Compressive failure of FRPs

Compression failure is of particular concern as a design-limiting feature of unidirectionally

reinforced fibrous composites. This is due to the fact that compressive loads inherently exist

in many mechanical structures, directly or indirectly, and that the compressive strengths of

long, aligned fibre composites can be as low as 60%-70% of their tensile strength and

therefore failure of composites may be initiated due to compressive stresses (Soutis, 1991).

Thus, the understanding of failure behaviour of composites under compression is of great

importance.


36

2.3.1. Compression test

The compressive strength is one of the most difficult mechanical properties of fibre

reinforced composite materials to measure. Ideally, the full capacity of the composites would

be attained under compressive loading until failure. However, due to the sensitivity of fibre

reinforced composites to manufacturing defects, specimen preparation and testing conditions,

premature failure tends to occur because of geometric instability. It was noted that the

compressive strength of the same composite material tested in seven different laboratories

around Europe varied by a factor of two, even if experienced technicians followed standard

test methods in each centre (Hodgkinson, 2000). The effect of composite manufacturing was

excluded so the scatter of results revealed the high dependency of compressive strength on

the testing conditions and individuals. Therefore, extensive studies have been made on

developing reliable compression testing methods that will lead to classic compressive failure,

give consistent compressive strengths and make it easier to reveal the damage mechanisms

triggering the failure of fibrous composites.

Figure 2.5: Methods to introduce load to specimens for compression tests. (Hodgkinson,

2000)

In the compression testing of fibre reinforced composites, compressive loading can be

introduced to a specimen by direct end loading, shear, and combined direct and shear loading

(see Figure 2.5). A variety of testing fixtures have been developed based on the above three

basic loading principles, including the Celanese jig, the Illinois Institute of Technology

Research Institute (IITRI) fixture and the former Royal Aircraft Establishment (RAE) fixture.


37

Standard test methods have been established based on these testing configurations, such as

the ASTM D3410 (shear loading), the ASTM D695 (end loading) and the ASTM D6641

(combined shear and end loading) standards. In order to obtain satisfactory results, great care

must be taken during the whole process of testing, no matter which test method is used.

In order to easily observe the damage mechanisms, various unstandardised tests to induce

and monitor compressive failure have been developed which will be detailed in section 2.4.2.

Aspects such as specimen size and geometry, loading mode (axial compression or bending,

compressive end loading or shear loading), lateral constraints to prevent macro-buckling, the

use of notches and end tabs have been considered and tailored in these test methods

(Schultheisz and Waas, 1996).

2.3.2. Macroscopic failure modes

As mentioned previously, failure of unidirectional CFRPs is usually catastrophic and sudden.

On the macro-scale, the failure mode of the composite specimen under compression is

determined by many factors, including the specimen geometry, the loading conditions and

stress concentrations (Yang et al., 2000). A number of failure modes have been observed in

CFRPs due to compressive loading, such as macro-buckling, end-crushing, brooming,

longitudinal splitting and in-plane or through-the-thickness shear failures (Lee and Soutis,

2005; Lee and Soutis, 2007; Odom and Adams, 1990; Parry and Wronski, 1982; Port, 1982;

Soutis and Lee, 2008; Soutis and Turkmen, 1997; Waas and Schultheisz, 1996; Weaver and

Williams, 1975). As stated in ASTM D3410, the macro-buckling mode, end-crushing mode

and failures outside the gauge region are considered as unacceptable failure modes. Multiple

failure modes can be observed in one sample and kink bands are found to occur along with

various failure modes leading to the global instability (Schultheisz and Waas, 1996). Several

typical macroscopic failure modes in UD CFRPs are described in the following paragraphs.


38

Figure 2.6: Typical acceptable failure modes for composites under compression. (a) in-

plane shear, (b) brooming and (c) through-the-thickness shear.

Figure 2.7: In-plane shear failure modes under compression: (a) transverse, (b) branched

transverse, (c) split transverse. (Odom and Adams, 1990)

2.3.2.1. In-plane shear failure mode

The in-plane shear failure, also referred to as the transverse failure, forms parallel to the

thickness direction, but at an angle to the width direction of the sample. Figure 2.6 (a) shows

(a) (b) (c)


39

the schematic of a typical in-plane shear failure near the inner edge of the tab. Odom and

Adams (1990) observed three different in-plane shear failure modes in UD carbon

fibre/epoxy composite specimens tested using the IITRI compression test fixture, which

were transverse, branched transverse (in which a part of the sample is missing if the failed

two halves are placed back together) and split transverse (in which separated splits can be

seen along the fibre direction). Figure 2.7 shows these three sub-failure modes representing

in-plane shear failure.

2.3.2.2. Brooming failure mode

The brooming failure mode, as illustrated in Figure 2.6 (b) has been attributed to post-failure

effect (Adams and Hyer, 1994). It occurs when two halves of the failed sample spread open

and are then pushed together by slight movement of the loading machine after the loading

software senses the load drop (indicating failure).

2.3.2.3. Through-the-thickness shear failure mode

The through-the-thickness shear failure mode is observed oriented at an angle to the

thickness direction, but can be either parallel to or at an angle to the width direction of the

sample (see Figure 2.6 (c)). Macroscopic shear failure usually involves fracture or gross

deformation of fibres from fibre flaws (Hull and Clyne, 1996). The fracture tends to occur

on a plane of near-maximum shear stress (Ewins et al., 1980).

2.3.3. Microscopic damage mechanisms

Experiments show that the macroscopic compressive failure of UD fibre reinforced

composites under axial compression is often associated with the formation of kink bands

(Fleck, 1997; Hahn et al., 1986; Schultheisz and Waas, 1996; Soutis, 1991; Weaver and

Williams, 1975). In multi-directional composites the development of kink bands in the 0°

plies is the initial damage mode triggering the global failure (Berbinau et al., 1999a). The

formation of kink bands will be explored in detail in section 2.4.

Microscopic damage mechanisms associated with compressive failure have been an active


40

research field for decades. The main damage mechanisms include fibre micro-buckling, fibre

kinking, fibre crushing, matrix failure, longitudinal splitting, shear banding and buckle

delamination (Couque et al., 1993; Cox et al., 1994; Evans and Adler, 1978; Fleck, 1997;

Piggott and Harris, 1980; Pimenta et al., 2009; Prabhakar and Waas, 2013; Vogler and

Kyriakides, 2001).

The terms fibre micro-buckling and fibre kinking are both extensively used to describe the

deformation of fibres under compression (Schultheisz and Waas, 1996). Some researchers

consider fibre kinking as the final stage of fibre micro-buckling and these two terms can be

used interchangeably, while others argue that these two are separate damage mechanisms

(Hahn et al., 1986; Hapke et al., 2011). Fibre micro-buckling or fibre kinking refers to the

buckling instability on the fibre scale. In this thesis, these two terms are differentiated

regarding end conditions, as shown in Figure 2.8. Fibre micro-buckling refers to the bending

of fibres where no relative lateral displacement occurs, while fibre kinking means the

deflection of fibres accompanied by relative lateral displacement across the damage zone.

So far, fibre kinking is considered to be the critical failure mechanism in polymeric matrix

composites (Argon, 1972; Jelf and Fleck, 1992). Typical damage mechanisms are described

in this section.

Figure 2.8: Schematic diagram of two fibre instability buckling modes discussed in this

thesis: (a) fibre micro-buckling and (b) fibre kinking.


41

Figure 2.9: Typical X-ray CT slice image of kink bands in CFRP from my own work for

illustration of the kink-band width ω, the kink-band angle β, and the angle of fibre rotation

within the kink bands Φ= φ+φo.

For ease of discussion, the important geometric parameters relating to kink bands are

illustrated in Figure 2.9, including the kink-band width ω, the kink-band angle β, and the

angle of fibre rotation within the kink bands Φ= φ+φo (φ is the additional fibre rotation under

load and φo is the initial fibre misalignment angle).

2.3.3.1. Fibre micro-buckling

Early attempts to model fibre micro-buckling failure were based on the assumptions of

elastic fibre bending and elastic shear in the matrix. The most quoted analysis of fibre micro-

buckling in aligned-fibre composites was proposed by Rosen (1965), who considered the

elastic bifurcation buckling of a continuum containing perfectly aligned fibres under axial

compression, resulting in kink-band angle β = 0, and derived a critical compressive stress

for micro-buckling given by

(2.1)

, where G is the effective longitudinal shear modulus of the composite. If the shear modulus

of the fibre is significantly large in comparison with the shear modulus of the matrix Gm,


42

then

(2.2)

, where Vf is the fibre volume fraction.

Figure 2.10: Two modes of fibre elastic micro-buckling: (a) shear mode, and (b)

extensional mode.

Considering the composite to be 2D, Rosen (1965) assumed that there are two possible

modes of failure (as illustrated in Figure 2.10): the shear mode in which the matrix shears

parallel to the fibre direction, and the extension mode in which the matrix undergoes

extensional straining transverse to the fibre direction. In other words, fibres buckle in-phase

in shear mode and out-of-phase in extension mode (Naik and Kumar, 1999). In composites

with high fibre volume fraction, the shear mode is considered as the predominant buckling

mode which predicts lower failure strengths than that of the extension mode (Jelf and Fleck,

1992). Even though the shear mode gives relatively lower strength, this theoretical value still

overestimates the compressive failure strength.

2.3.3.2. Fibre kinking

An alternative view, that long-fibre composites undergo fibre kinking was first proposed by

Argon (1972). He assumed that kinking occurs in a band where β = 0 and fibres suffer an

initial misalignment angle φo. The fibres are presumed to be inextensible and a remote

compressive axial stress is applied. Under the compressive stress, fibres suffer an additional

rotation φ, which gives rise to large matrix shear deformation in the kink band. In a rigid-

perfectly plastic composite with shear yield stress of τy, the critical stress for kinking


43

initiation is given by

. (2.3)

The development of additional rotation cannot be triggered until the critical compressive

stress is reached, after which the compressive stress reduces with increasing φ. The Argon

formula (2.3) demonstrates that the most important parameters are initial fibre misalignment

angle and shear yield strength.

The Argon formula (2.3), giving the kinking stress, was broadened to fit an elastic-perfectly

plastic composite by Budiansky (1983), in which the shear yield strain is γy = τy / G, then the

critical kinking stress is

. (2.4)

This formula gives the Rosen micro-buckling stress (2.1) when φo = 0, and approaches the

Argon kinking stress (2.3) as φo grows.

The Rosen and Argon models are both based on the simple assumptions of kink-band angle

β = 0 and ideal plasticity. In fact, kink bands are generally observed to be oriented inclined

to the transverse direction at 5-30° (Budiansky et al., 1998; Narayanan and Schadler, 1999;

Wadee et al., 2004). Figure 2.11 shows the schematic of the kink band with inclined band-

boundaries. Budiansky (1983) postulated an explanation for the tendency to form inclined

kink bands, which suggested that localised edge fibre misalignments tend to arrange

themselves into inclined bands under axial loading. These rotations will further induce

inclined kink bands and the angle of pre-kinking bands will determine the kink-band angle

(Budiansky, 1983). In his analysis, the kink band angle is related to the compressive strength,

the shear modulus and the transverse elastic modulus of the laminate. Soutis (1991) and

Berbinau (1997) evidenced that experimentally observed β lies close to the range 12-27º

defined by the upper and lower limit predicted from extreme cases of short-wave and long-


44

wave imperfections using Budiansky’s analysis.

Figure 2.11: Schematic showing the fibre kinking of initially misaligned fibres forming an

inclined kink band. (Jumahat et al., 2010b)

However, the models discussed so far work on the assumption that fibres have no bending

stiffness; that is to say, they break at the kink band boundaries. An alternative model

considering finite fibre bending stiffness, which is referred to as the couple stress model,

was developed (Fleck et al., 1995; Slaughter and Fleck, 1994; Slaughter et al., 1996).

Budiansky and Fleck (1993) analysed available experimental data of various aligned FRPs

under compression. They found that the compressive strength of composites suffers

considerable scatter, which is consistent with fibre kinking. This is due to the high sensitivity

to imperfection, as shown in the formula (2.3). Thus they concluded that fibre kinking is the

dominant failure mode in these composites.

2.3.3.3. Fibre failure

The final failure of FRPs under axial compression is associated with fracture of fibres. Hahn

(1984) studied the compressive failure of fibres by embedding fibre bundles in transparent

resins, and three fibre failure modes have been identified: shear failure, kinking of fibrils

(Baley, 2004) and bending (buckling) failure, as shown in Figure 2.12. The fracture surface

of fibres in CFRP samples failed under compression shows that both shear-driven fibre

compressive failure and fibre buckling (bending) failure can occur (Ewins et al., 1980).

Figure 2.13 (a) shows the shear failure pattern on fracture surface, in which a large amount


45

of debris is left on the fracture surfaces as sliding occurs. In bucking failure, fibre ends show

two distinct regions representing compressive failure and tensile failure as shown in Figure

2.13 (b).

Figure 2.12: Schematic illustration of typical fibre failure modes in FRPs: shear failure,

kinking of fibrils and bending (buckling) failure. (Hahn and Williams, 1986)

Figure 2.13: SEM images showing failure modes of carbon fibre in CFRP failed under

axial compression, (a) shear induced fibre compressive failure and (b) fibre buckling

failure. (Ewins et al., 1980)


46

Figure 2.14: Optical micrographs exhibiting the transition of failure pattern from shear

driven fibre compressive failure to kink bands in a notched cross-ply T800/924 specimen

failed under compression along 0º fibre direction. Surface 90º layer was polished off before

observation while maintaining the load on the specimen. (Gutkin et al., 2010)

Gutkin et al. (2010) reported the transition between these two modes in notched CFRP

laminates failed under axial compression. Failure initiates from shear-driven fibre

compressive failure at the notch which facilitates fibre bending and formation of kink bands,

as shown in Figure 2.14.

2.3.3.4. Longitudinal splitting

Longitudinal splitting along the fibre direction is commonly observed within the kink-band

damage zone due to compression induced transverse tensile stress or shear stress (Gutkin et

al., 2011; Guynn et al., 1992; Lankford, 1997; Lee et al., 2000). This damage mode can be

located either in the matrix or at the fibre-matrix interface in systems with weak matrix or

low interfacial strength. Gutkin et al. (2010) recently proposed that splits were formed by

accumulation of micro-cracks at the fibre/matrix interface based on observation of the failed

specimen surface under load, as shown in Figure 2.15.


47

Figure 2.15: SEM image showing micro-cracks along the interface at the top edge of a kink

band in a notched UD T800/924 specimen under load. (Gutkin et al., 2011)

Longitudinal splitting plays a vital role in the formation of kink bands (Prabhakar and Waas,

2013). Hapke et al. (2011) and Soutis (2012) suggested fibre kinking originated from axial

splitting near a notch or a hole in carbon fibre/epoxy composite, which was drawn from

observations in which both damage mechanisms already occurred. However, it has not been

evidenced whether large splitting bordering (outside) kink bands triggers or arrests fibre

micro-buckling/kinking. In addition, the sequence of splitting inside kink bands, formed

from initial micro-cracks, and fibre micro-buckling is still an open question. The sequential

relationship of the damage modes needs to be validated with in situ experiments.

2.3.4. Factors affecting the compressive failure

A number of factors influence the macroscopic and microscopic compressive response of

FRPs. Therefore it is difficult to predict the compressive failure mode and strength of

composite materials without understanding the effects of these factors.

Compressive failure mode of fibrous composites has been found to vary with fibre volume

fraction, shape of the specimen, testing fixture, and loading temperature (Ewins et al., 1980).

With the above conditions kept constant, experimental results indicate that failure mode is

also influenced by the tabbing material, tab geometry, and the effectiveness of the fixture

gripping (Odom and Adams, 1990).


48

Effect of fibre

The increase in fibre diameter increases the bending stiffness of the fibre, thus the buckling

load of fibres is raised (Hahn et al., 1986). However, the larger probability of flaws in larger

diameter fibres decreases the buckling load of fibres after exceeding the critical fibre

diameter (Schultheisz and Waas, 1996). Hancox (1975) proposed the linear variation of

compressive strength with fibre volume fraction in carbon fibre/epoxy composite tested in a

Celanease type fixture. However, in different material systems non-linear correlation has

also been observed (Soutis, 1997).

Effect of matrix

Loading CFRPs under compression the full capacity of fibre strength cannot be used, as

failure occurs by fibre micro-buckling/kinking, which is found to be dominated by matrix

properties (Soutis, 1997). The matrix provides lateral support to the fibres to avoid buckling

of the fibres. A number of studies have proven that the matrix shear modulus and shear yield

strength affect the compressive strength of UD composites (Berbinau et al., 1999b; Ewins

et al., 1980; Lankford, 1995; Steif, 1990; Tankasala et al., 2014).

Effect of interface

The fibre/matrix interface is also of great importance to the mechanical properties of

composite materials. The interfacial bonding strength can be increased by applying surface

treatment to fibres (Song et al., 2011; Yuan et al., 1991). In composites with a stronger

interface, fibre micro-buckling/kinking is the dominant failure mode; while in composites

with weaker interface, longitudinal splitting is favoured. Madhukar and Drzal (1992) found

that the compressive strength also depends on the interface, as a strong interface helps to

hinder fibre micro-buckling/kinking.

Effect of manufacturing defects

As mentioned previously, the compressive strength is largely concerned with the initial fibre

waviness (Potter et al., 2008; Wang et al., 2012; Wang et al., 2013; Wisnom and Atkinson,


49

2000), which is an inevitable defect induced in the manufacturing process. The thermal

expansion mismatch between fibre and matrix during the curing process is the main cause

(Jochum et al., 2008; Parlevliet et al., 2007). The increase in fibre misalignment angle

significantly reduces the compressive strength of the composites. Mrse and Piggott (1993)

observed the reduction of compressive strength from 1.9 GPa to 1.5 GPa with the increase

in fibre misalignment angle from 1° to 6° in carbon fibre/PEEK composite. A significant

reduction in compressive strength was also observed in carbon fibre/epoxy composite, where

the compressive strength of composite with 5° misalignment angle is 61% lower than that

with 1° fibre misalignment (Jumahat et al., 2010b).

Another manufacturing defect affecting the compressive failure is the void. The effect of

void content, as an imperfection, on compressive strength has been studied (de Almeida and

Neto, 1994; Guo et al., 2009; Lo and Chim, 1992). Voids in the matrix considerably decrease

the compressive strength. Part of the decrease is due to poorer bonding between the fibre

and resin, which reduces the lateral support for the fibres. Also at higher void contents

serious fibre misalignment is visible in the specimen and this gives rise to fibre kinking at

lower stress (Hancox, 1975). Bazhenov et al. (1992) reported that the compressive strength

of glass fibre/epoxy composites decreased proportional to the square root of void content. A

similar relationship has also been proposed based on the carbon fibre/epoxy data reported in

literatures (Bazhenov and Kozey, 1991). Other than the effect of void content, the initiation

of failure from a specific void has recently been numerically modelled by Liebig et al. (2015).

2.4. Kink bands

The term, kink band, was introduced by Orowan (1942) to describe deformation of axially

compressed cadmium single-crystal wires. It is also observed in various materials such as

slates (Anderson, 1974), paper (Wadee et al., 2004), wood (Benabou, 2010) and fibre

reinforced polymer composites. The understanding of geometry and evolution of kink bands

from literatures to date is presented as follows.


50

2.4.1. Kink-band morphology

The important geometric parameters relating to kink bands were defined in section 2.3.3.

For geometrical reasons, together with the assumption of zero volumetric strain in the kink-

band region, it is proposed that the fibres within the kink band rotate by an angle of twice

the kink-band angle

Φ = 2β (2.5)

and then lock-up (Weaver and Williams, 1975). A wide range of kink inclination angles and

fibre rotation angles has been reported in different composite systems. In CFRP, typical

values are reported as β ≈ 0º to 30º, Φ ≈ 30º to 45º and ω ≈ 5df (fibre diameter) to 300df. The

post-failure measurements are generally in agreement with the proposed relation (see

formula 2.5), so this premise has been accepted and used in many studies (Evans and Adler,

1978; Fleck and Budiansky, 1991; Moran et al., 1995; Moran and Shih, 1998; Sivashanker

et al., 1996). However, the fact that fibre rotation angle is larger than 2β under load has been

reported (Vogler and Kyriakides, 1997), which was also predicted by Steif (1990)

analytically. All the measurements in literatures have been made on certain 2D planes, but

the formation of fibre micro-buckling/kinking and kink bands is evidenced to be a 3D

phenomenon (Waas et al., 1990). Therefore, the use of 2D characterisation techniques limits

the accuracy and will somehow mislead the development of analytical and numerical models.

In this case, the 3D morphology of kink bands needs to be determined.

2.4.2. Kink-band formation

The investigation of the evolution of kink bands in FRPs is difficult, since the initiation of

kink bands is sudden followed by unstable propagation.

2.4.2.1. Characterisation methods

Optical microscopy and SEM are two conventional methods to characterise and visualise

microscopic damage in composite materials. 2D information of damage can be obtained in

great detail. Experimental characterisation of kink bands in literatures to date is almost all


51

based on these two techniques.

Post mortem studies

In early studies on compressive failure of composite materials, damage mechanisms

associated with kink-band formation were proposed based on post mortem observations on

the sample surface, or on sectioned planes along the fibre direction inside the sample by

optical microscopy or SEM (Evans and Adler, 1978; Guynn and Bradley, 1989; Sutcliffe

and Fleck, 1997). On one hand, the material relaxation after unloading might give rise to

change in damage morphology; on the other hand, serial sectioning is a destructive method

which can generate new damage to the sectioning plane. Therefore, post-failure observations

are not ideal for providing experimental data guiding the establishment of models analysing

and predicting the formation of kink bands.

Figure 2.16: Kink-band propagation observed by optical microscopy on the surface of a

notched UD T800/924 specimen loaded under compression. (Pimenta, 2008)

In situ studies

With the use of dedicated in situ loading rigs in optical microscopy and SEM, the

development of kink bands on ground sample surface could be tracked (Hapke et al., 2011;

Moran et al., 1995; Pimenta, 2008; Vogler and Kyriakides, 2001). Out-of-plane fibre micro-

buckling or kinking is often associated with the development of kink bands, which provokes

problems identifying the geometry of kink bands, especially in optical micrographs. As

shown in Figure 2.16, out-of-plane kink bands are shown as dark regions, the detail of which

cannot be seen (Pimenta, 2008). In order to exclude the effect of surface on damage

morphology, dual beam SEM together with a focused ion beam (FIB) microscope have been


52

applied to observe the sub-surface damage pattern (Hapke et al., 2011). While it is found

that surface and sub-surface damage patterns appear the same (see Figure 2.17 (b)), it

remains unclear whether failure originates below the surface or from the surface. Such

identification of failure initiation will require non-destructive, in situ monitoring of the

composite structure in 3D, which could be accomplished through in situ X-ray CT studies.

Figure 2.17: SEM images showing damage patterns in the sub-surface plies in notched UD

T700/977-2 carbon fibre/epoxy composite specimen observed under load by FIB milling of

the surface layers. (Hapke et al., 2011)

2.4.2.2. Kink-band initiation

Although there is a general agreement that abrupt failure of polymer composites under

compression is due to the formation kink bands developed from fibre micro-buckling or fibre

kinking (Pinho et al., 2012; Schultheisz and Waas, 1996; Sivashanker and Osiyemi, 1999),

the understanding on the initiation of fibre micro-buckling/kinking varies among researchers.

This is due to the lack of experimental observation of the failure onset caused by the sudden

and catastrophic nature of instability type of failure. Post-failure examination is not a reliable

method to validate the sequence of events giving rise to the onset of failure. Moreover, it is

challenging to arrest the initiation stage of failure.


53

Figure 2.18: Schematic illustration of specimen geometry designed for inducing shear

stress with axial compression load for in situ SEM studies by (a) Pimenta (2008) and (b)

Hapke et al. (2011).

In recent years, with the progress in in situ experimental techniques using optical microscopy

and SEM and the improvement in acquisition speed of images, the evolution of kink bands

has been observed from the surface of composite samples. The initiation of kink bands has

been observed in CFRPs to a certain extent in samples with notches or holes acting as stress

risers (Sutcliffe and Fleck, 1994), and in samples under combined compression and shear

loading (Vogler and Kyriakides, 2001). Pimenta (2008) (see Figure 2.18 (a)) and Hapke et

al. (2011) (see Figure 2.18 (b)) combined these two strategies and employed a sample

geometry having a notch with its normal at an angle to the fibre direction, so that shear stress

was induced when the sample was loaded under compression. Hapke et al. (2011) took two

SEM images with an interval of 0.2 s at the onset of kink band on UD carbon fibre/epoxy

sample surface. In the first frame (see Figure 2.19 (a)), kink band did not form; while in the

second frame (see Figure 2.19 (b)), the kink band formed and propagated for more than

100μm. They believed that the large matrix shearing evidenced by the ‘shear cups’ was the

first feature prior to the formation of kink bands. Fibre micro-buckling was not observed

before fibre kinking. Even in their study, there was not enough evidence to explain the

initiation of kink bands. In the meantime, large out-of-plane displacement of fibres is often

present at the initiation site (Pimenta, 2008). As optical microscopy and SEM studies can

only provide time-lapse information from the front surface of the samples, if failure initiates

from the other surface or the internal structure of the sample then the onset of failure cannot


54

be captured.

Figure 2.19: SEM images of the surface of a notched UD T700/977-2 carbon fibre/epoxy

composite specimen under compression load. (a) The last frame before kink band

propagation starts. (b) Taken 0.2 s later, a kink band already having propagated over more

than 100 μm. (Hapke et al., 2011)

Together with the progress in experimental work, great efforts have been made to establish

numerical models of micro-buckling/kinking initiation in composites using finite element

modelling (FEM). Since imperfection sensitivity plays an important role in the compressive

micro-buckling of composites. Initial research was based on the assumption that the

initiation sites for fibre deflection are regions of fibre waviness, accompanied with resin-rich

regions or free edges (Vogler et al., 2001). The role of matrix shear yield properties is also

addressed in the study by Pimenta et al. (2009). Several FE models have been used to

simulate the formation of kink bands, and results show that under compression the composite

deforms elastically globally until the matrix starts to yield and the composite softens locally

in a narrow band, leading to the deflection of fibres followed by the onset of fibre failure

near edges. An alternative view has been proposed, which suggests that fibre fracture is the

key to the initiation of micro-buckling (Garland et al., 2001; Lankford, 1995). Even though

results from model composites have shown that fibre fracture is not necessary for the

initiation of micro-buckling/kinking (Jelf and Fleck, 1992; Sutcliffe and Yuwono, 2001), it


55

is still a competing mechanism due to the fact that actual failure mechanism for a given

composite is the weakest one in that particular system. As mentioned previously, in notched

carbon fibre/epoxy composite loaded under compression, shear-driven fibre fracture

originated from notch is found to promote fibre buckling (Gutkin et al., 2010). Despite that

the critical initiation mechanism proposed is varied, in all the studies the catastrophic

characteristic of kink-band initiation has been confirmed.

2.4.2.3. Kink-band propagation

Kink bands with the global deformation of fibres perpendicular to the ply plane are defined

as out-of-plane kink bands (Berbinau, 1997). If fibre rotation is within the ply plane, then

the formed kink band is referred to as an in-plane kink band. The growing path leading to

either type is determined by the lateral constraints imposed on the free surfaces (Sutcliffe

and Fleck, 1997). Sutcliffe and Fleck (1994) employed large-scale bridging models to

describe both in-plane and out-of-plane kink-band propagation in unidirectional composites.

For composite laminates with much smaller thickness than width, the constraint in the

though-the-thickness direction is much less, so out-of-plane kink bands are more likely to

occur rather than in-plane kink bands (Sivashanker et al., 1996).

As for the experiments on monitoring kink-band propagation, progress has been made in

notched composite samples under axial compressive loading or combined compressive and

shear loading. Once formed, the kink band in UD CFRPs is found to propagate in two steps

in the kinking plane (where kink bands lie in): lateral propagation (along the band boundary)

and axial propagation (Moran et al., 1995; Vogler and Kyriakides, 2001). Axial propagation

is the broadening of kink band along the direction defined by Φ, after the full propagation

along the boundary direction.

By successively sectioning a partially failed glass/epoxy specimen, Chaplin (1977) showed

that the kink band does not change its orientation during propagation. Once started from a

notch or a pre-existing defect, the kink band keeps the same orientation and width. This is

compatible with the observations in graphite/epoxy composites in which sequential micro-


56

buckling of fibres in the early stage of failure sets the kink band angle (Hahn and Williams,

1984).

Figure 2.20: Typical load-end shortening curve with the illustration of different stages in

kink-band formation in notched IM7/PEEK composite under axial compression load.

(Moran et al., 1995)

Moran et al. (1995) and Moran and Shih (1998) used a video coupled microscope to monitor

the initiation and propagation of a kink band in a notched unidirectional IM7/PEEK

composite compressed axially. As the sample was clamped between two plates with a

transparent window, only in-plane kink bands occurred, allowing the real time formation of

a kink band to be observed. Figure 2.20 shows the typical load-end shortening curve. Matrix

yielding originated around the notch (termed incipient kinking) prior to the peak load and a

kink band suddenly propagated from the notch across the sample width. At the initial stage

fibre rotation was shallow and as loading continued it was increased slowly to 15º to 20º.

This was then followed by sudden and unstable fibre rotation to 40º to 45º, accompanied by

an increase in kink-band angle to 20º to 25º, until the fibres were locked-up at large matrix


57

shear strains. After this transient phase, the band started to broaden at a steady state with

progressive increase in kink-band width by bending adjacent fibres to align with fibres

within the band. The final band width was determined by fibre fracture.

Figure 2.21: Photomicrograph of kink bands after band broadening in UD AS4/APC-2

composite. (Vogler and Kyriakides, 1997)

Vogler and Kyriakides (1997; 1999; 2001) managed to follow the propagation of kink bands

in AS4/PEEK composite in a multi-step loading experiment. After the initiation of kink

bands, the samples were loaded under shear at constant axial compression load to study the

propagation stage. They found that along with the propagation of kink bands, the fibre

rotated progressively to Φ = 25º, while the inclination angle (β = 12º) and width (25df) of

the kink band were kept constant. The lateral propagation was followed by the formation of

multiple kink bands caused by broadening, as shown in Figure 2.21. The mechanism was

proposed as the progressive adding of narrow bands of broken fibres at the kink-band

boundaries, which is known as the ‘bend-break-rotate’ process. After the formation of the

primary kink band, the straight fibres outside the band tended to bend at a lower stress in

contact with the rotated fibres inside the band. A narrow band of fibres then broke along the


58

boundaries due to excessive bending, followed by further rotation to align with the fibres

inside the primary kink band. It was also found that the ‘bend-break-rotate’ process occurred

more rapidly in some regions along the boundary, which resulted the uneven front of the

broadening kink band. This morphology has been observed by Sutcliffe and Fleck (1994),

Sivashanker et al. (1996), Kyriakides and Ruff (1997), S. Pimenta (2008) and Hapke et al.

(2011) in composites composed of T700, T800 or AS4 carbon fibres.

Figure 2.22: Number of individual kink bands as a function of the distance behind the

micro-buckle tip in UD T800/924C composite. (Fleck, 1997)

The number of kink bands was counted in SEM images of the side faces in T800/924C

sample (Sivashanker et al., 1996). It was found that the number of individual kink bands

within the large kink zone increases from 1 to 6 with increasing distance from the kink-band

tip, illustrated in Figure 2.22. The width of the kink band ranges from 70 μm to 800 μm, with

a constant single band width of around 100 μm (～20df). The width of individual narrow

kink band is found to be between 5df to 13df in the AS4/APC-2 composite (Vogler and

Kyriakides, 1997), and around 8df in laminate fabricated from commercially available

carbon fibre-epoxy prepregs (Kumar et al., 2005). These measurements are in reasonable

agreement with the individual band width of 10-15df as predicted by (Fleck et al., 1995).

In composite systems reinforced with fibres with higher bending strength, such as the IM7

(Moran et al., 1995) and IM8 (Sivashanker et al., 1996) fibres, the fibres tend to remain


59

intact during kinking (micro-buckling). Thus multiple kink bands have not been observed

during kink-band broadening in these composite systems. However, the broadening

phenomenon is similar in all the conditions. The broadening process is found to be a steady-

state propagation at a constant stress. During fibre micro-buckling or kinking in the primary

kink band, the matrix undergoes large shear straining, which hardens the matrix so that it is

not energetically favourable for fibres to rotate further. Thus the broadening of the band into

the adjacent softer region takes place (Moran and Shih, 1998). The final width of the

broadened kink band is of the order of 100df.

2.5. X-ray computed tomography

High-resolution X-ray CT, or µCT, is an advanced radiographic imaging technique used to

obtain the 3D microstructure of materials at a spatial resolution on the scale of a few microns

(Landis and Keane, 2010). Since the 1970s, X-ray CT was once mainly employed in medical

fields to derive non-invasive images of the bones and tissues in human body (Flannery et al.,

1987). It has now gained popularity as a non-destructive testing (NDT) technique to assess

defects and damage in materials and mechanical structures, so that the macroscopic

properties of the materials can be better understood and predicted with the knowledge of the

microstructural behaviour inside the 3D volume.

2.5.1. The physics of X-ray computed tomography

X-ray radiography is the basis of X-ray CT and it is based on the Beer-Lambert law, or

attenuation law (Baruchel et al., 2000). When an incident X-ray beam passes through an

object, the X-ray photons can be absorbed, scattered or transmitted. The attenuation of the

X-ray beam is the difference between the incident and transmitted photons, which is due to

the absorption and scattering interaction with the material. According to the Beer-Lambert

law, the ratio between the number of transmitted photons and the number of incident photons

is related to the attenuation capability of the material, and the X-ray beam travelling distance

as it passes through the object (Stock, 1999). Formula 2.6 is a basic expression of the Beer-


60

Lambert law,

(2.6)

where I0 is the intensity of the incident X-ray beam, and I is the beam intensity after it travels

through a thickness x of the material with a linear attenuation coefficient μ. To be specific,

the attenuation coefficient of a material depends on the local density and atomic number of

the material, and the photon energy. As μ varies along the path in the material, the more

general form can be obtained by calculating the integral of the attenuation along the X-ray

propagation path,

(2.7)

where f(x,y) is the linear attenuation coefficient at position (x, y) along the X-ray path.

The Beer-lambert law can be used to explain the contrast in a radiograph between different

constituents in a bulk material, since each point in the radiograph corresponds to different

X-ray beam travel paths. X-ray CT is realised by acquiring a finite number of radiographs

(projections) while the sample is rotated 180° or 360°. The obtained X-ray CT data exhibits

cross-sectional information of the object volume according to the linear attenuation

coefficients computed for each point in the slice from the radiographs.

2.5.2. X-ray computed tomography processing

The processing stages of X-ray CT data generally include data acquisition, reconstruction

and visualisation, which are detailed in the following paragraphs. Figure 2.23 shows the

schematic of the acquisition and reconstruction processes.


61

Figure 2.23: Schematic illustration of CT acquisition and reconstruction processes. (Landis

and Keane, 2010)

2.5.2.1. Acquisition

Figure 2.24 shows the schematic of three different CT systems with different acquisition

speed. In the CT systems with a micro-focus X-ray source, the detector used can either be a

one-dimensional (1D) linear detector (corresponding to a fan beam configuration (see Figure

2.24 (a)), in which the sample needs to be translated in the vertical direction during the scan),

or a 2D planar detector (corresponding to the cone beam configuration (see Figure 2.24 (b)),

which gives rise to less scanning time). The sample is fixed on the stage between the source

and detector, and the distance between them can be adjusted to obtain different resolution.

In practice, a compromise has to be made between the sample size and the resolution,

considering the limited field of view of the detector (Salvo et al., 2003). The optimum

resolution of the system is limited by the spot size of the micro-focus source. With a smaller

spot size, the penumbral blurring is less, which results in less noise in the reconstructed

image. The beam emitted from the micro-focus source is cone shaped polychromatic X-ray

beam, which might result in cone-beam and beam hardening (see section 2.5.3) artefacts if

not correctly reconstructed.

Considerable enhancement of imaging capability in X-ray µCT has been achieved with the

application of synchrotron radiation as an intense parallel X-ray source (see Figure 2.24(c)).

The synchrotron radiation source can emit a higher flux of many orders of magnitude greater

than that of laboratory sources, which contributes to higher sensitivity to marginal material


62

difference and much less data acquisition time. In addition, the parallel beam configuration

simplifies the reconstruction algorithm, and enables X-ray energy to be constrained within a

narrow energy band, which allows accurate reconstruction of the attenuation coefficient for

quantitative study (Landis and Keane, 2010).

Figure 2.24: Illustration of different X-ray CT acquisition configurations: (a) fan beam, (b)

cone beam, and (c) parallel beam (synchrotron radiation). (Salvo et al., 2003)

2.5.2.2. Reconstruction

Once a series of radiographs are obtained, the next step is to reconstruct a 3D map of X-ray

attenuation in the volume using proper reconstruction algorithms. Then the 3D volume will

be presented as a stack of 2D cross-sectional slice images or a single volume.

The radiographs can be reconstructed using the following methods: filtered back projection

(FBP) algorithm (Herman, 1979) and algebraic reconstruction technique (ART) (Pan et al.,

2009) for parallel beam and the Feldkamp-Davis-Kress (FDK) algorithm (Feldkamp et al.,

1984) for small angle cone beam systems. The reader is referred to the references above for

details about reconstruction algorithms.

2.5.2.3. Analysis

After the CT data has been reconstructed, the data needs to be analysed and visualised to

obtain useful information for the study of material behaviour. Segmentation according to the

grey value is used to extract features of interest from the 2D slices or 3D volume. Filters are

often applied to reduce noise, enabling easier segmentation. The visualisation of features in


63

the 3D volume is very helpful to the understanding of the sequence and interaction of

different features in real structures. The reconstructed data can also be used to generate

meshes for numerical modelling.

2.5.3. Artefacts

Although the X-ray CT scanners and the reconstruction algorithms have been advanced

rapidly in the past decades, the existence of artificial features is still inevitable. Artefacts are

anything displayed in the reconstructed image that does not correspond to features in the

original object. Various artefacts can result from different set-up geometry and materials

scanned, degrading the quality of CT images. Some of them can be removed from the images,

while others are inherent with CT imaging and cannot be avoided. The major artefacts and

the methods to alleviate their effects are discussed in this section.

The beam-hardening artefact is one of the most common artefact in data obtained from

laboratory X-ray CT instruments, which is induced by the polychromatic nature of the micro-

focus X-ray beam. As the X-ray beam passes through an object, the low-energy photons are

preferably absorbed. Thus the beam spectrum shifts to an increasing mean energy along the

X-ray path through the object (Brooks and Di Chiro, 1976). Beam-hardening artefacts are

displayed as cupping, streaking or shading effects in the reconstructed volume. This artefact

can be avoided by adding a filter to the incident beam during the scan or corrected after scan

in the reconstruction software. Figure 2.25 shows an example of shading effect caused by

beam hardening, and the effect of applying correction in reconstruction software.


64

Figure 2.25: Slice image of a limestone core sample showing the difference before (upper

half) and after (bottom half) beam-hardening correction. (Davis and Elliott, 2006)

Figure 2.26: Incorrect centre-of-rotation induced artefact with double edges in the image.

(Davis and Elliott, 2006)

Reconstruction algorithm is performed with reference to the centre-of-rotation axis of the

object. The incorrect determination of centre-of-rotation of the projection data can result in

artefacts in the reconstructed volume in the form of distortions. Double edges of the features

will be observed in the images of large errors and blurring for small errors. Figure 2.27 shows

an example of the centre-error artefact. This artefact can be corrected either during setup

prior to acquisition by careful positioning the sample and checking the rotation centre by


65

taking several projections or during the reconstruction setup stage in the reconstruction

software.

Ring artefact is another typical artefact, and is generally displayed as circles centred on the

rotation axis in the image (Davis and Elliott, 2006), as shown in Figure 2.27. Faulty detector

elements and nonlinear spread of the signal intensity level in the sensitive elements will

cause this artefact. Two solutions are mostly used in the acquisition stage to eliminate ring

artefacts. The first is realised by shifting the object with small and pre-determined

movements between projections in order to reduce the effect from bad elements. The second

is to calibrate the detector before scanning to linearly spread the signal level.

Figure 2.27: An example of ring artefacts in a CT slice image. (Davis and Elliott, 2006)

Partial volume effect is an artefact that is inherent with the CT imaging technique. When a

voxel in the object consists of a variety of materials with different attenuation coefficients,

the average of these values is considered as the attenuation coefficient of this voxel. This

problem is referred to as the partial volume effect. In this case, material boundaries or thin

cracks are blurred due to the limitation in resolution, which will influence the accuracy of

quantification.


66

2.5.4. Approaches to enhance feature visibility in X-ray CT

For weakly absorbing materials, such as bio-materials, polymers or CFRP composites, there

is little absorption and thereby low image contrast. Meanwhile, the observation of cracks

tends to be difficult by CT imaging, due to the fact that cracks can only be detected when

they are open to a certain extent. Therefore, the assessment of defects and damage in CFRP

composites is challenging. Efforts have been made to enhance the visibility of features in

low absorbing materials by staining and phase contrast as discussed in the following sections.

2.5.4.1. Staining

The application of radio-opaque staining in X-ray CT imaging can vary the local material

density. Thus in regions where staining agent has reached, better contrast can be obtained

from differential attenuation of X-rays.

For the imaging of various animal tissues, the most broadly used contrast stains are inorganic

iodine and phosphotungstic acid (Metscher, 2009). For the imaging of micro-damage in

bones, iodinated molecules, lead sulfide, barium sulfate, and functionalised gold

nanoparticles are most widely used as contrast agents (Landrigan et al., 2011).

Figure 2.28: X-ray µCT reconstructed cross-section of a graphite/epoxy sample (a) without

using the dye penetrant (zinc iodide solution), and (b) using the dye penetrant. (Schilling et

al., 2005)


67

For fibre reinforced polymer composites, zinc iodide solution is preferably employed as the

dye penetrant highlighting cracks and micro-cracks (Schilling et al., 2005; Tan et al., 2011).

Schilling et al. (2005) studied the effect of dye penetrant in micro-crack determination in

carbon fibre/epoxy laminates. The same micro-cracks were observed before and after the

addition of dye penetrant, as shown in Figure 2.28. The crack appears dark after staining and

becomes more detectable. The sensitivity to micro-cracks, with an opening of 20% of the

pixel size, has been reported in their study. Moreover, this sub-pixel detectability can be

further improved to 5% if dye penetrant is used for staining (Schilling et al., 2005). With the

aid of dye penetrant, the 3D morphology of cracks can be successfully extracted. However,

the accuracy of the result depends on the connectivity of the damage and the extent of

penetration of the dye through the whole volume of the damage. In this case, staining is

suitable for materials with connected damage and should be limitedly used in quantitative

analysis.

2.5.4.2. Phase contrast

In recent years, phase contrast imaging has been increasingly used to enhance detecting

capability of X-ray CT (Cloetens et al., 1997). As an X-ray beam travels through an object,

the phase of the beam is shifted because of the interaction with the electrons in the material

(Baruchel et al., 2000). The interaction cross-section of the X-ray phase shift could be much

larger than that of absorption, which contributes to enhanced contrast in the image due to the

occurrence of phase contrast (Withers and Preuss, 2012).

Phase sensitive imaging can be performed by many approaches, but can be generally

classified as interferometric technique (Momose, 2003), projection methods (Cloetens et al.,

1996), and analyser methods (Davis et al., 1995). Among them, projection methods are more

suitable for imaging boundaries, such as cracks (Withers, 2007). The differences in refractive

index between materials with low attenuation contrast can induce Fresnel diffraction patterns

at interface regions in the form of light and dark fringes. These Fresnel fringes can enhance

edge contrast and aid the detection of cracks (Cloetens et al., 1997), as illustrated in Figure

2.29. Using phase contrast enhanced CT, Wright et al. (2008) reported a sensitivity of 14%


68

of the pixel size for a carbon fibre-epoxy composite system.

.

Figure 2.29: Radiographic images corresponding to a. absorption radiography, and b. phase

sensitive radiography of Al/SiC composite. (Cloetens et al., 1997)

2.5.5. Application of X-ray computed tomography in composite materials

X-ray CT has been applied to solve a variety of problems in the area of materials science, as

reviewed by (Stock, 1999). With regard to fibre reinforced polymer matrix composite

materials, μCT has been used to inspect damage and defects such as matrix cracks (Bull et

al., 2013b; Moffat et al., 2008; Moffat et al., 2010), fibre fractures (Aroush et al., 2006),

delamination (Bull et al., 2013a; Sket et al., 2014; Wright et al., 2008), voids (Lambert et

al., 2012; Nikishkov et al., 2013) and very recently kink bands (Ueda et al., 2014).

In research on material damage mechanisms, other than the identification of damage

mechanisms in 3D the aim is often to follow the damage evolution on micro-scale during

heating and/or mechanical testing. Several methods can be employed to perform this type of

tomography study in materials science as summarised by Salvo et al. (2010). Figure 2.30

shows the experiment scenario for (a) post mortem, (b) ex situ, (c) interrupted in situ and (d)

continuous in situ studies. In this thesis, post mortem, interrupted and continuous in situ

tomography are used to follow the evolution of compressive failure in CFRP.


69

Figure 2.30: (a) Post mortem, (b) Ex situ, (c) Interrupted in situ, and (d) Continuous in situ

X-ray CT process. σ means mechanical testing and T refers to heat treatment. S1 (S2, S3 or

S4) is abbreviated for Sample 1 (2, 3 or 4). (Salvo et al., 2010)

2.5.5.1. Post mortem tomography

In post mortem tomography studies, scan is performed on a sample after heat treatment or

mechanical testing. In order to study the effect of heating or mechanical loading on the

microstructure of the material, several samples can be used.

The failure of fibre reinforced polymer matrix composite laminates is very complex and

difficult to characterise, especially for the extensive damage induced under impact and

compression after impact. Progress has been achieved to understand impact damage in 3D

by post mortem X-ray CT (Bull et al., 2014; Bull et al., 2013c; McCombe et al., 2012; Tan

et al., 2011). Tan et al. (2011) observed low-velocity impact behaviour of stitched carbon

fibre reinforced composite laminates with X-ray μCT. Cross-sectional views obtained from

μCT shows detailed through-the-thickness matrix cracks distribution and 3D delamination

damage pattern. As demonstrated in Figure 2.31, the white regions represent impact damage

areas that are infiltrated with radio-opaque zinc iodide dye penetrant. It has been noted that

the delamination pattern in densely stitched laminates is more cylindrical, while in

moderately stitched composite it is more conical.


70

Figure 2.31: X-ray μCT cross-sectional view of stitched CFRP specimens damaged by

low-velocity impact. (Tan et al., 2011)

2.5.5.2. Ex situ tomography

The procedure of ex situ tomography is the same as that of post mortem tomography, and

the only difference is that the same sample is scanned. This process involves cooling and

reheating or unloading and reloading of the specimen, which may affect the damage

mechanisms to be observed. This technique has been preferably used for the investigation

into the damage tolerance or fatigue properties of composite structures, as the standard

testing specimens are relatively too large to fit in in situ loading rigs.


71

Figure 2.32: X-ray μCT cross-sections of CFRP showing new damage propagation due to

compressive load after impact damage. (Bull et al., 2014)

Bull et al. (2014) studied the development of damage mechanisms leading up to CAI failure

in CFRP laminates. Monitoring of the internal damage development in 3D was achieved by

taking X-ray μCT scans after impact, after applying near-failure compression load and after

CAI failure. Damage propagation including delamination growth into undamaged region and

increase in crack-opening was identified after applying a near-failure load, as shown in

Figure 2.32. Ex situ tomography is an ideal method to study the evolution of damage in large

samples or samples under complex loadings.

2.5.5.3. Interrupted in situ tomography

Interrupted in situ tomography is similar to ex situ tomography except that this technique

requires mounting specific in situ testing devices (furnaces and loading rigs) directly on the

CT sample stage. For scans with in situ loading, the mechanical loading needs to be

interrupted during the scan which may affect the mechanisms under load relaxation.

Moffat et al. (2008) used synchrotron radiation computed tomography (SRCT) to study 0o

ply splits in a double-notched 4 mm wide [90/0]s carbon fibre/epoxy laminate during

incrementally increased tensile loading. It was noted that in resin-rich regions, crack pinning,

retardation, and bridging mechanisms were present; while in fibre-rich regions the splits


72

advanced more freely with less constraint. Scott et al. (2011) further analysed the progressive

failure involved by incrementally straining laminates to failure. The sequential occurrence

of transverse ply cracks, 0o splits and finally delamination is shown in Figure 2.33. It is

suggested that failure of fibres is the dominant damage mechanism controlling the fracture

stress for the sample geometry tested. Fibre breaks were initially observed at isolated

locations. At higher loads the accumulation of broken fibres was observed, which occurred

within a narrow stress range rather than accumulating progressively with increased loading.

In these studies, a screw-driven load frame was employed to incrementally load samples to

failure, as illustrated in Figure 2.34.

Figure 2.33: 3D extraction and segmentation of progressive damage accumulation in cross-

ply CFRP composite under progressive tensile straining. (Scott et al., 2011)


73

Figure 2.34: Schematic of in situ load frame. (Wright et al., 2010)

2.5.5.4. Continuous in situ tomography

In continuous in situ tomography, the same sample is scanned continuously without

interrupting the heat treatment or the mechanical loading. In order to obtain a correct

tomographic reconstruction the sample needs to remain unchanged until all the projections

for one dataset are acquired. If this is not satisfied, motion artefacts can occur, making it

difficult to perform quantitative analysis of the data. There are two methods to ensure the

image quality. The first is to slow down the deformation of the sample and the second is to

acquire the tomographic dataset faster (Mokso et al., 2011). Frame rate at fast as 10,000

frames per second can be achieved by ultra-fast synchrotron radioscopic imaging at

TOMCAT beamline based in Swiss Light Source. Although several ultra-fast imaging

experiments have been explored so far (Buffiere et al., 2010; Maire et al., 2007), there is

still no progress in its application to FRPs. In experiments where 3D datasets with sufficient

image quality cannot be captured, X-ray radiography can also be used to study fast evolution

process. Figure 2.35 shows an example of using radiographs to study the fast evolution of

liquid metal foams (Babcsán et al., 2007).


74

Figure 2.35: Pure Al compact heated to slightly above the melting point. Images show state

at, (a) 0 s, (b) 48 s, (c) 60 s, (d) 72 s, (e) 92 s and (f) 200 s after the beginning of heating.

(Babcsán et al., 2007)

2.6. Chapter summary

In this chapter, the literature concerning the areas of composite materials, compressive

failure of composite materials, the formation of kink bands and the 3D characterisation

technique X-ray CT have been reviewed.

Fibre micro-buckling or fibre kinking is proposed to be the main failure mechanism in

unidirectional CFRPs under compression, and the resulting kink bands have been

extensively experimentally in 2D. However, the 3D visualisation of failure features has not

yet been achieved, especially at the onset of the failure, which can be realised with the aid

of X-ray μCT. On the basis of the progressive accumulating of damages and the 3D geometry

of the kink band, a better understanding of the damage mechanisms leading to kink bands

can be established.

Chapter 3 Failure of unidirectional CFRP rods under axial compression

75

3. Failure of unidirectional CFRP rods under axial compression

3.1. Introduction

In this chapter, an experimental study on the axial compressive failure of UD CFRP rods is

performed to delineate the compressive damage mechanisms associated with the formation

of kink bands. Although the first report on the low compressive strength of fibre composites

resulting from fibre micro-buckling (kinking) and kink bands appeared in 1960 (Dow and

Gruntfest, 1960), this subject is still an active field of research in recent years. This is because

that the fully understanding of the damage mechanisms has not been achieved yet due to the

sudden and uncontrolled nature of compressive failure.

The tensile properties of UD fibre composites are generally dominated by the reinforcing

fibres. However, under compression, the matrix and the interface also play a vital role by

providing the lateral support and constraint to fibres. Compressive failure of fibre composites

takes a variety of forms at the micro-scale, including fibre micro-buckling, fibre kinking ,

fibre compressive failure, fibre shear failure , matrix shear deformation and splitting along

the interface or in the matrix (Chaplin, 1977; Hahn et al., 1986; Pimenta et al., 2009; Vogler

and Kyriakides, 1999). The different damage modes could occur simultaneously or

sequentially across the composite structure in a short time, making the identification of the

correlation between different damage modes and the sequence of events leading to failure

by 2D examination difficult. Therefore, it is important to characterise the entire damage zone

in 3D experimentally to comprehensively understand the geometric and sequential

interaction between different damage modes.

In order to characterise the 3D volume of the damage zone, X-ray CT is employed in this

thesis. However, considering the intrinsic low contrast between carbon fibre and epoxy

matrix in CT data, the main challenge of this experiment was to design a specimen geometry

for kink bands to be observed by X-ray CT. Standard unidirectionally reinforced composite

samples for compression testing are beams with a rectangular cross-section (high ratio

between width and thickness), which are prepared from laminates manufactured using the

composite laminating technique. From an X-ray imaging viewpoint the high aspect ratio


76

would limit penetration of the X-rays, which can lead to artefacts lowering the image quality.

In addition, generally the use of anti-buckling devices preventing the Euler buckling of

samples is required, which is not feasible for the in situ studies. Thus the specimens for this

work are designed to be cylindrical composite rods to optimise the image quality for analysis

on micro-scale damage mechanisms. Direct end loading is often chosen for testing of un-

standardised specimens due to its simplicity. Composite cylinders without end constraint

tend to fail by brooming, while the failure mode changes to the formation of kink bands in

end-constrained composite cylinders (Weaver and Williams, 1975). Considering the factors

above, small-diameter cylinder composite rods were chosen for the tests here to obtain very

high resolution (≤ 2μm) CT images. In order to manufacture high quality (high fibre volume

fraction, good fibre alignment and few manufacturing defects) cylindrical composite rods

with designated small-diameter, a new manufacturing method, small-scale resin infusion

(SSRI), has been developed in this work.

The study of kink bands in this chapter is focused on two aspects. The first is to investigate

in the compressive failure mechanisms based on post-failure examinations. SEM is used to

observe in 2D the kink bands on fractured surfaces. In order to obtain the detailed 3D

morphology of kink bands and the associated damage mechanisms, X-ray CT is used to

assess the damage zone. With the better understanding of geometry of kink bands inside the

UD composite structure, the second part aims to study the evolution of kink bands by X-ray

CT with in situ loading. Interrupted in situ studies have been carried out on lab-based

instruments, and each scan is optimised to take 4 hours. Continuous in situ tests have been

performed on synchrotron beamline, and the scan time is significantly reduced to sub-second.

The ultra-high speed imaging allows the identification of the time-scale of the failure process.

The specific objectives of the study in this chapter are:

To identify the damage mechanisms associated with the formation of kink bands;

To characterise the post-failure geometry of kink bands in 3D;


77

To propose the mechanisms of kink-band formation caused by axial compressive

loading based on post-failure and in situ observations;

3.2. Experimental

This section details the manufacturing process of composite material, the preparation of the

testing specimens, the compression test method, and the post mortem and in situ X-ray

imaging processes of UD carbon fibre/epoxy composite.

3.2.1. Materials

The composite material used in this chapter was composed of carbon fibre and epoxy resin.

3.2.1.1. Fibre

Untwisted carbon fibre yarn T700S-12000-50C supplied by Torayca was used as the

reinforcing UD carbon fibres. It is a high-strength carbon fibre with surface treatment. The

individual tow is flat and rigid compared with untreated fibre tows. The major properties of

the T700S fibres are listed in Table 3.1.

Table 3.1: Properties of T700-12000-50C carbon fibre yarns.

Filament

diameter (μm)

Fibre

count

Density

(g/cm3)

Tensile

strength

(MPa)

Tensile

modulus

(GPa)

Strain (%)

7 12k 1.80 4900 230 2.1

Table 3.2: Properties of cured Araldite® LY 564/ Aradur® XB 3486 epoxy matrix.

Tensile

strength

(MPa)

Tensile

modulus

(GPa)

Flexural

strength

(MPa)

Flexural

modulus

(GPa)

Fracture

toughness

(MPa√m)

Fracture

energy

(J/m2)

70-74 2.86-3 118-130 2.9-3.05 0.95-1.05 260-310


78

3.2.1.2. Resin

The matrix material used was an epoxy system based on Araldite® LY 564 resin and Aradur®

XB 3486 hardener supplied by Huntsman. The mix ratio by weight was 100:34 respectively,

giving a pot life of 560-620 minutes at 23 oC. The mechanical properties of the cured resin,

following the curing cycle of 8 hours at 80 oC, are presented in Table 3.2.

3.2.2. Manufacturing of UD carbon fibre-epoxy composite rods

As the compressive failure of UD composites is sensitive to manufacturing defects, it is of

great importance to ensure the quality of the composite samples by using the appropriate

manufacturing method. The manufacturing process of cylindrical UD carbon fibre-epoxy

composite rods is described in the following paragraphs.

3.2.2.1. Preparation

Preparation of the mould

Two types of glass tubes with inner diameter of 3 mm and 2.4 mm supplied by Glass-

solutions were employed as the mould for the cylindrical composite rods. The length of the

glass tube was 10 cm. The inner surface of the glass tubes was coated with release agent

(Toctile® 700NC, Frekote), for ease of demoulding after curing.

Preparation of carbon fibre tows

The consumables used in the manufacturing process were purchased from Aerovac Systems

Ltd. unless stated otherwise. Several fibre tows were closely bound together, making them

rigid enough to be pulled through the glass tube. The fibre tows were arranged in a step-like

shape at the top (see Figure 3.1 (a)) and then rolled into a cylinder; thus the top part of the

fibre tows was thinner than the bottom. A stripe of thin film with high flexibility was then

used to wrap, in a helical formation, the straight fibre tows approximately 20 cm from the

top, as shown in Figure 3.1 (b). The flexibility of the film contributed to a more compacted

fibre arrangement. Twisting should be avoided in this step.


79

Figure 3.1: Photographs of the preparation of fibres. (a) Step-like stacking of fibre tows at

the top. (b) Binding of the fibre tows using a flexible film.

In initial trials, it was noted that the film tended to stick on the inside surface of the glass

tube. Therefore, blue tape was used to cover the film for a smooth contact with the glass tube.

The difficulties lay in optimising the fibre alignment and improving fibre volume fraction

by putting as many fibres as possible into the glass tube.

As the film and the tape layers added to the diameter of the fibre tows, the fibre volume

fraction in the final composite was limited to around 60% using this method.

Preparation of epoxy resin

Typically 100 g of epoxy resin and 34 g of hardener were weighed and mixed in a paper cup.

The mixed liquid was degassed in a vacuum oven at 23 oC for 1 hour. The degassing process

aimed to eliminate air bubbles introduced into the resin system in order to reduce the void

content in the cured composite, which may affect the mechanical properties of the composite.


80

3.2.2.2. Manufacturing method

Manual pultrusion

The overall process of the manual pultrusion method was as follows. Bound fibres were

placed in the degassed resin for 20 minutes, enabling fibres to be fully wetted-out. The fibre

tows were then gradually pulled through the glass tube with an inner diameter of 3 mm. The

two ends were then closed with tape. Finally, the glass tube and the fibres were placed in an

oven for curing.

Figure 3.2: Fibre wetting step in the pultrusion process (a) in a paper cup and (b) in a flat

tray.

A series of modifications were made in order to optimise the manufacturing process. Initially,

when fibres were placed into degassed resin in a paper cup, a lot of air bubbles were

introduced into the resin turning the resin cloudy, as shown in Figure 3.2 (a). The use of a

flat tray greatly improved the process, limiting the introduction of new air bubbles (Figure

3.2 (b)).

In addition, efforts were made to increase the fibre volume fraction. In the pultrusion process,

resin occupied a large amount of space in the limited cross-section of the glass tube, making

it difficult to put in more fibres. To overcome this, heat-shrink tubing was used as the mould

instead of the glass tube. The aim was to make the fibres more compacted as the tube shrank


81

at elevated temperature. However, the tube did not uniformly shrink causing the composite

rod to slightly bend. This method was therefore not chosen for making composite rods for

the axial compression test, as under compression the bent rod was more likely to fail under

macro-buckling instead of forming kink bands.

In general, the pultrusion process was quite messy with a large amount of resin dissipated

around the sample. Therefore, an alternative method based on conventional resin infusion

was pursued.

Small-scale resin infusion

In an attempt to make the manufacturing process more reliable and repeatable, the

conventional resin infusion approach to make composite laminates was introduced to

produce small-scale specimens. This manufacturing process, termed small-scale resin

infusion (SSRI) here, was modified and optimised through a number of trials.

Figure 3.3: Photograph of the SSRI experiment set-up.

After a series of modifications to prevent fibre movement, increase infusion speed and obtain

rods with a uniform diameter, the SSRI process proved to be a reliable manufacturing

method.

In this process, the glass tube was used as a closed mould with the two ends connected to

plastic tubes acting as the resin inlet and outlet. Dry fibres were placed into the glass tube


82

(inner diameter 2.4 mm) before resin infusion. As the cross-section of the glass tube is

determined, the fibre volume fraction can be easily tailored by changing the amount of fibres.

A resin trap made with a plastic bag and cotton breather was attached to the outlet tubing,

preventing extra resin from flowing into the vacuum pump. Figure 3.3 shows the

experimental set-up of the SSRI method.

Fixing the position of fibres

With a vacuum pump drawing resin through the whole experiment set-up, fibres tended to

move towards the vacuum pump direction when wetted-out with resin. In order to ensure

that the fibre position was fixed during infusion, a Y- or T-connector (outer diameter 6mm)

was added between the glass tube (inner diameter 2.4 mm and outer diameter 4mm) and the

inlet tubing. One end of the connector was connected to the glass tube via a short length of

plastic tubing (inner diameter 6mm); the second end was used for the fibres to pass through

and was fixed with sealing tape; the third end was connected to the resin inlet tube, as

illustrated in Figure 3.4. The addition of a connector was effective in preventing fibre

movement during infusion.

Figure 3.4: Photograph demonstrating the connections between parts. The three ends of the

Y connector correspond to fibre fixing end, resin inlet and resin outlet, respectively.


83

Accelerating the infusion process

In initial trial experiments, the resin flowed very slowly though the closely packed fibres

without the aid of flow media, taking 3 to 4 hours to progress through the 10 cm long glass

tube. Considering that resin will become less viscous with a small increase in temperature

and taking into account the curing temperature, resin infusion was conducted at around 40oC

on a heating table (Elkom GmbH Vakutherm), effectively speeding up the process to 1 hour.

Obtaining a uniform diameter

After the infusion process was completed, the two ends of the tubing were sealed with tape.

Initially the whole system was placed flat in the oven, but measurement of the diameter of

the final composite showed that the cross-section of the cured rod was not a perfect circle

due to the resin flow into the connecting plastic tubing during curing. To optimise the

uniformity of the diameter, in the curing process the sample was hung straight in the oven

with the inlet tubing (filled with resin) facing downwards.

Glass tubes with a relatively small inner diameter (2.4 mm compared with 3 mm) in the SSRI

method were used for achieving a higher resolution whilst ensuring the whole sample

remained in the field of view during X-ray CT imaging. The schematic of the SSRI method

used to make composite rods in this work is illustrated in Figure 3.5.

Figure 3.5: Schematic of the SSRI manufacturing method developed to make UD

composite rods.


84

3.2.2.3. Curing and demolding process

The composite was cured in an oven (Thermo Scientific Heraeus Function Line

programmable oven) according to the curing cycle on the datasheet. The curing temperature

was increased from room temperature to 80 oC in an hour, and then kept steady for 8 hours

followed by natural cooling in the oven. When fully cured, the other parts were cut off using

a diamond saw, leaving just the glass tube section. After that, the glass was carefully

squeezed off using a vise, exposing the carbon fibre/epoxy composite rod.

3.2.3. Sample preparation

The UD composite rods were prepared into samples for axial compression tests following

the steps below.

3.2.3.1. Machining

The cylindrical UD carbon fibre/epoxy specimens were cut from the composite rods using a

precision cutting machine (ATM Brilliant 221). The length of each composite specimen was

20 mm. The two ends were ground using grinding paper to ensure the flatness, which is

essential to the alignment of the sample under compressive load.

Waisted specimens for post mortem studies

In the uniaxial compression study of CFRP rods by Couque et al. (1993), the specimens with

a reduced gauge section were inserted in chamfered steel bases to a snug fit for better load

transfer. A waisted specimen geometry modified from that used by Couque et al. (1993) was

employed here, as schematically shown in Figure 3.7. The nominal diameter of the

composite rod was 2.4 mm (inside diameter of the glass tube). The middle section was

ground down to a diameter of around 1.5 mm over a 3 mm long gauge section, with smooth

radii at the transition regions.


85

Figure 3.6: Schematic of the specimen geometry, in which the carbon fibre rod is in black

while metal tabs are in white. The diameter of the rod was 2.4 mm and the waisted gauge

section was 1.5 mm in diameter. (Unit: mm)

Waisted and circular-notched specimens for in situ studies

It was found that in side-notched samples, kink bands tend to form in a plane angled to the

plane perpendicular to the base of the cylinder. It was difficult to locate the kinking plane in

the CT data, which would raise problems for further data analysis, so an alternative specimen

geometry based on the waisted specimen was used. A circular notch around the

circumference of the rod was made at the centre of the waisted gauge section using a razor

blade. The depth of the notch was intentionally made around 150 µm. However, as the

sample was rotated 360° while machining, a slight misalignment of the rod axis would result

in a variation in the depth. The final notch depth was measured in radiographs of the samples

as ranging between 100 µm and 200 µm.

3.2.3.2. Adding tabs

The surface of the rods near two ends were ground using grinding paper (P800) in order to

obtain a rough surface for better adhesion. The two ends of the specimen were then stuck

with an epoxy adhesive (Araldite® Strength in Bonding 2000+) into chamfered metal end

caps having small holes drilled to remove any surplus epoxy, as shown in Figure 3.7. Initially

aluminium tabs were used, but wrinkles were found on the surface of the tabs after


86

compression. In this case, high-strength steel was used to make the end caps.

3.2.4. Quality control

The quality of the composites made using the SSRI method was validated to confirm the

superiority of the newly developed manufacturing method.

3.2.4.1. Fibre volume fraction

The weight of each 8 cm composite rod manufactured was 0.70 g±0.06 g with 1 cm sections

removed at each end. The acid digestion method widely used for measuring the fibre volume

fraction of CFRP materials is not suitable for the rod sample here, as each individual sample

was too long and too light. Thus the fibre volume fraction was calculated according to the

area fraction of fibres in the circular cross-section.

Each T700 carbon fibre tow contained 12,000 filaments and the diameter of each individual

fibre was 7 μm. The number of tows within in each sample was recorded during the

manufacturing process and the nominal diameter of the rod equalled the inside diameter of

the glass tubes. Therefore, the area ratio of fibres in the cross-section could be calculated,

which gave the fibre volume fraction Vf,

(3.1)

where Af is the area of fibres in the cross-section, A is the cross-section area of the rod. As

the fibres could fracture whilst being bound, resulting in fewer fibre filaments, the calculated

value might be slightly higher than the actual Vf in the sample.

3.2.4.2. Initial fibre misalignment angle

The initial fibre misalignment angle, introduced in the manufacturing process, is an

important factor affecting the formation of kink bands and the compressive strength (Argon,

1972). The initial fibre misalignment angle of the composite rods was measured using a

method proposed by Yurgartis (1987). Two assumptions were made using this method: (1)


87

the fibres were straight over a certain distance (≥20df) and (2) the cross-section of all the

fibres were circular with the same diameter. The bias towards counting fibres with larger

misalignment angle can be corrected based on the stereological relationship as detailed by

Yurgartis (1987) . The measurement of the fibre misalignment angle involved the following

procedures:

1. The composite rods were cut at approximately 5° to the nominal 0° fibre direction. Five

samples were cut and mounted in epoxy resin. The specimens were ground (following the

order P200, P400, P800 and P1200) and polished (following the order 4 μm, 1 μm and

0.25μm) for optical microscopy. The fibres were elliptically shaped as they were cut at an

angle to the fibre direction.

2. The major axis and the short axis (which equalled the fibre diameter) of the elliptical

surface of the fibres were directly measured in the Fiji ImageJ software. 400 measurements

were recorded for each specimen and in total 5 specimens were analysed for the composite

system.

3. The actual cutting angle for each fibre θ was calculated using the following equation:

(3.2)

where df is the fibre diameter and a is the length of the major axis of elliptical fibre section.

4. The calculated cut angles were classified into bins with width of 0.5°. The volume fraction

of the fibres at angle θi was calculated using the following equation:

(3.3)

where θi is the mean angle in the ith bin, Ni is the number of values within the ith bin and n is

the number of bins.


88

5. The average angle representing the mean of distribution �̅� was calculated using the

following equation:

(3.4)

6. The angle of intersection of each individual fibre φj was calculated using the following

transformation:

(3.5)

where the plane-cut angle φpc equals the mean of distribution angle �̅�.

7. Finally, standard deviation, σ, was calculated based on the following equation:

(3.6)

A large standard deviation would indicate poor overall alignment whereas a smaller one

would characterise a narrower angle distribution.

3.2.4.3. Uniformity of reinforcement distribution

In order to assess the reinforcement distribution in the composites, short pieces of the rod

samples were cut off and mounted in resin, followed by grinding and polishing as described

above. The samples were mounted with the fibre direction perpendicular to the observation

surface, thus presenting the cross-sectional view. Then the samples were inspected under

optical microscopy.

3.2.5. Axial compression testing

Compression tests were conducted on the waisted samples for post-failure studies, while in

situ compression tests were performed on the waisted and notched samples so that the onset


89

of kink bands could be located near the notched region within the field of view during

progressive loading.

3.2.5.1. Compression testing of waisted samples

Axial compressive end loading was applied to the specimens via the platens of an Instron

5569 machine under a constant displacement rate of 0.02 mm/min. These specimens were

then prepared for post-failure X-ray CT imaging.

3.2.5.2. In situ compression testing of waisted and circular-notched samples

Interrupted in situ tests on lab-based X-ray CT machine

Specimens with circular notch were compressed in a tension-compression in situ loading rig

(manufactured in the Daresbury Laboratory) accommodated on the rotating sample stage of

the X-ray CT scanner. The rig was modified to achieve the higher compression load required

to fail the CFRP composites. The polycarbonate tube of the rig would be stretched while

compression was applied to the sample, which would cause fracture of the tube. Bolts were

used together with epoxy adhesive at the joint parts of the plastic tube and the aluminium

top and bottom to avoid the fracture of the tube. The load was applied manually under

displacement control at approximately 1 µm/s. The loading was interrupted at different

displacement for X-ray CT scanning. Figure 3.7 shows the modified Daresbury rig.

Continuous in situ tests on synchrotron beamline

Specimens with the circular notch were also compressed in a tension-compression in situ

loading rig manufactured by INSA-Lyon (see Figure 3.8), which could be accommodated

on the ultra-high speed TOMCAT beamline at the Swiss Light Source. The compression

tests were conducted under displacement control at the rate of 1 µm/s. The rig was suitable

for ultra-high speed imaging, which would require rotation speed of as high as 22 rotations

per second.


90

Figure 3.7: Photograph of the modified Daresbury tension-compression loading rig (rig

tube outside diameter = 66 mm).

Figure 3.8: Photograph of the INSA-Lyon tension-compression loading machine (rig tube

outside diameter: 76 mm).


91

3.2.6. Scanning electron microscopy

SEM was employed to observe the fracture surfaces of samples failed into two parts after

compression tests. The fracture surfaces were coated with gold palladium. The SEM images

were taken on Sirion EVO60 at accelerating voltage 10 kV at various magnifications. The

high resolution of SEM could reveal the failure of individual fibres, which was relatively

difficult to be achieved in X-ray CT imaging.

3.2.7. X-ray micro-computed tomography

All the lab-based X-ray µCT scans were conducted in the Henry Moseley X-ray Imaging

Facility (HMXIF) at the University of Manchester. The synchrotron radiation experiments

were performed at the Swiss Light Source. Both post-failure imaging on waisted sample and

in situ imaging on notched and waisted sample were carried out.

3.2.7.1. Post mortem X-ray μCT

The failed rod samples which did not fail into two parts were scanned by µCT. The sample

was wrapped by blue tape as shown in Figure 3.9 to avoid further failure while being rotated

during the scan. The sample was then glued to the head of a nail, the bottom of which could

fit into the sample holder. The X-ray µCT scans were performed on the Zeiss Xradia

MicroXCT machine (Figure 3.10) housed in a walk-in hutch. Table 3.3 summarises the

setting parameters. Reconstruction of the imaging data was performed in the TXM

Reconstructor software. The reconstructed data was then imported to the Avizo 8.0 software

(FEI Visualisation Sciences Group) for 3D data analysis.


92

Figure 3.9: Photograph of the sample preparation for post-failure µCT imaging.

Figure 3.10: The Zeiss Xradia Micro-XCT system.


93

Table 3.3: Setting parameters for lab-based CT scans in the Zeiss Xradia MicroXCT

system.

Experiment Post-failure In situ

Accelerating Voltage (kV) 40 80

Power (W) 10 7

Optical Magnification 10x 4x

Source to sample distance (mm) 40 72

Sample to detector distance (mm) 12 48

Exposure time (s) 40 20

Number of Projections 1001 501

Pixel size (µm) 1.1 2.0

3.2.7.2. Interrupted in situ X-ray μCT

Interrupted in situ X-ray µCT was performed on waisted samples with razor blade notch in

order to ensure the kink bands were developed within the field of view. The modified

Daresbury rig was fixed on the sample stage as shown in Figure 3.11. The cables and wires

were kept out of the imaging window during the rotation. Scan time was an important issue

for interrupted in situ test, since the material tended to deform with time. Moreover, with the

use of rig the X-ray beam needs to travel through thicker material (rig tubing) and longer

distance (the source and detector were placed further away from the sample compared to

post-failure scans allowing the free rotation of the rig), which resulted in the need for longer

exposure time for each projection or higher accelerating voltage. The choice of exposure

time and voltage was determined after comparing the noise-to-signal ratios of the data

obtained using different settings. The setting parameters shown in Table 3.3 were used.

Multiple scans were taken while the loading was paused with displacement maintained.

Reconstruction of the imaging data was performed in the TXM Reconstructor software. The

reconstructed data was then imported to the Avizo 8.0 software for 3D data analysis.


94

Figure 3.11: Photograph of the in situ experiment set-up in the MicroXCT hutch.

3.2.7.3. Continuous in situ X-ray μCT

The continuous in situ X-ray imaging was conducted at the TOMCAT synchrotron beamline

based at the Swiss Light Source. Ultra-fast X-ray imaging could be performed at relatively

high resolution. Figure 3.12 shows the experiment set-up of the synchrotron radiation

experiment with in situ loading rig. Due to the trade-off between image quality and imaging

speed, X-ray CT scanning parameters were optimised to obtain 3D volumes at (1) 1 dataset

per second at pixel size of 1.1 µm and (2) 20 datasets per second at pixel size of 3µm.

Interrupted static scans were performed at relatively low load and continuous dynamic scans

were taken when approaching the expected failure load. Table 3.4 shows the scanning

parameters. The data was reconstructed by the Pagnin algorithm developed at the Swiss

Light Source and analysed in Avizo 8.0 software.


95

Figure 3.12: Photograph of the in situ experiment set-up at the TOMCAT beamline.

Table 3.4: Scanning parameters for synchrotron radiation experiments at the TOMCAT

beamline.

Data acquisition 1 dataset/second 22 datasets/second

X-ray Beam Monochromatic White

Mean beam energy (keV) 20 15.5

Exposure time (ms) 2 0.1


Pixel size (µm) 1.1 3


96

3.3. Results and discussion

3.3.1. Material quality

The quality of the carbon fibre-epoxy composites manufactured by the SSRI method is

assessed in this section. Typical defects include fibre misalignment, resin-rich regions and

voids, which are characterised below. The SSRI method is easier to handle and, with the

modifications, the fibre volume fraction and fibre alignment of the composite are improved.

SSRI proves to be a suitable method for making UD small-diameter cylindrical composite

rods.

3.3.1.1. Fibre volume fraction

As discussed in section 3.2.1.1, each fibre tow contained 12,000 filaments and the diameter

of each individual fibre was 7 μm. By pultrusion, the 3 mm-diameter rod contained 8 tows

of carbon fibres; by SSRI, the 2.4 mm-diameter rod contains 6 tows of carbon fibres. Using

the formula presented in section 3.2.4.1, fibre volume fractions were calculated for the

samples made using the two different methods, as shown in Table 3.5. The fibre volume

fraction of the composite rods is largely increased by using the SSRI method.

Table 3.5: Fibre volume fraction of the samples calculated according to formula (3.1).

Manufacturing method Pultrusion SSRI

Vf (%) 54 63

3.3.1.2. Initial fibre misalignment angle

Fibre misalignment is inevitable in the manufacturing of long fibre reinforced composite

materials. During the manual pulling of fibre tows into the glass tube, fibres were not held

with force at the other end; therefore, fibre twists tended to occur, introducing fibre

misalignment and waviness. Initial fibre misalignment angle is used to describe the severity

of this manufacturing defect. Using the Yurgartis (1987) technique described in section

3.2.4.2, the measured fibre volume fraction as a function of φo is shown in Figure 3.13. It


97

can be drawn from the graph that 95% of fibres lie within ±1.5° of the 0° fibre axis. The

initial fibre misalignment angle in specimens fabricated using the SSRI method is less than

the typical values in UD CFRP laminates (Jelf and Fleck, 1992) and rods (Soutis, 2000).

Figure 3.13: Initial fibre misalignment angle distribution in carbon fibre/epoxy rods made

by the SSRI method.

3.3.1.3. Resin-rich regions

Fibres cannot be perfectly distributed uniformly in the glass tube, thus giving rise to resin-

rich regions. Figure 3.14 shows a typical optical microscopic image of the composite cross-

section with several resin-rich regions distributed across the sample cross-section. In general,

due to the relatively high fibre volume fraction in the composite rods, fibres are compacted

with few resin-rich regions. As can be seen in Figure 3.15, resin-rich regions are also

identifiable in the CT slice image of the rod cross-section, although the contrast between

fibres and matrix is low. However, in CT slice images along the fibre direction, it is difficult

to distinguish between fibres and matrix.


98

Figure 3.14: Optical microscopic cross-sectional view of a composite rod made by the

SSRI method with the resin-rich regions highlighted in yellow ellipses.

3.3.1.4. Voids

Although the resin has been degassed in advance, in the pultrusion process, air will be drawn

into the glass tube when pulling the fibre tows. Although this is partly avoided in the SSRI

method, it is still difficult for air bubbles to be expelled through the closely packed fibres

without the aid of flow media. After being cured, the air bubbles left in the composite become

voids, demonstrated as relatively dark regions in Figure 3.15. The voids in a SSRI composite

rod before machining were segmented, and the extracted void volume is shown in 3D in

Figure 3.16. These elongated voids along the fibre direction are mostly located near the rod

circumference, which will be machined off at the gauge section, thus not affecting the

compressive failure in most of the samples tested.


99

Figure 3.15: Lab-based X-ray µCT XY slice image giving the cross-sectional view of the

composite rod made by the SSRI method (Pixel size: 2.1 μm).

Figure 3.16: Extracted volume of the voids in a composite rod made by the SSRI method

before sample preparation.


100

Figure 3.17 shows the CT slice images from a high-resolution (pixel size is 0.6 µm) scan of

a composite rod made by the SSRI method. Compared with the slice image from the lower-

resolution (pixel size is 2.1 µm) scan in Figure 3.15, the contrast between the void region

(highlighted in yellow rectangular) and the bulk composite is lower. This is partly due to the

noise and artefacts caused by the region-of-interest scan at higher resolution, in which the

composite rod is larger than the field-of-view. Nevertheless, micro-voids have been observed

both beside and at the tip of the elongated void. The micro-voids are discontinuously located

between the fibres, being separated by resin ligaments. It can also be observed that fibres are

more severely misaligned near the voids than at the other parts.


101

Figure 3.17: YZ slice images from high-resolution region-of-interest µCT scan showing

the same elongated void at different positions along the X axis. (a) Micro-voids are formed

close to left side of the macro-void, and (b) micro-voids are formed at the tip of the macro-

void (Pixel size: 0.6 μm).


102

3.3.2. Compressive failure of UD CFRP rods

All the samples discussed in the following sections were prepared from composite rods

manufactured by the SSRI method.

The failure of the waisted carbon fibre-epoxy composite under compression was sudden and

without preceding visible damage. Catastrophic compressive failure occurred at the average

failure stress of 910 MPa±60 MPa, averaging the results of ten samples. Seven specimens

fractured into two parts while being removed from the testing machine after failure, which

was not ideal for X-ray µCT imaging. Generally the fracture surface was inclined at around

20o to the loading direction and was close to the machined transient region. There are two

typical failure geometries; one is that both the failure surfaces are inclined (see Figure 3.18

(a)), and the other is that the short section appears flat from the outside, but in fact the fracture

surface is depressed apart from the outer surface at the same angle as the fracture surface of

the longer section (see Figure 3.18 (b)). The debonding of the outer layer is partly due to

fibre fracture at the transient region after machining. Figure 3.18 (c) shows a typical intact

sample after failure. The intact sample was scanned by X-ray µCT to analyse the damage

zone.

Figure 3.18: Photographs showing typical failure of the composite samples. Samples

fractured into two parts: (a) both fracture surfaces are inclined, and (b) one fracture surface

is inclined while the other is flat at the outside (inside part is inclined). (c) Intact sample

after failure with an inclined damage zone across the sample.


103

3.3.3. Kink bands on fracture surfaces – 2D observations

In order to observe the damage at the fibre scale, the fracture surfaces of the samples

fractured into two parts were imaged under SEM. Results show that the formation of kink

bands is the dominating failure pattern, and the geometrical parameters of the kink bands do

not vary in different samples. The damage mechanisms associated with kink bands are

presented in typical SEM images from different samples.

Figure 3.19: A typical SEM image of the fracture surface showing multiple kink bands

with varied kink-band widths.


104

Figure 3.20: A typical SEM image of the fracture surface showing matrix failure, splitting

and different modes of fibre failure associated with kink-band formation.

Figure 3.21: A typical high-magnification SEM image showing the failure pattern of

individual fibres. The fracture surface of one fibre consists of a compressive zone and a

tensile zone.


105

The morphology of multiple kink bands was observed, as shown in Figure 3.19. The narrow

bands were 25-60 µm wide, while the wider band was 80-90 µm wide. Fibres in the adjacent

two narrow bands were aligned in the same direction. The fibre rotation angle and kink-band

boundary angle could not be measured directly from SEM images, as the view was angled

with respect to the kinking plane. Figure 3.20 shows a SEM image at a higher-magnification,

in which micro-cracks in the matrix, splitting between fibres and fibre breakage can be seen.

Most of the fibres fractured into two parts either perpendicular or angled to the fibre axis.

Feature 5 in Figure 3.20 shows fibre failure into three sections with the formation of a small

wedge. Meanwhile, it is noted that the failure surfaces of individual fibres can be divided

into two zones, which are associated with tensile and compressive failure of the fibre, as

shown in Figure 3.21, indicating fibre bending failure originated from instability.

3.3.4. Kink bands in the damage zone – 3D observations

Although kink bands could be observed on the fracture surface, the extent of damage below

the fracture surface could not be revealed using SEM. In this part of the work, the 3D

morphology of the kinking damage zone is determined and analysed. A failed sample, which

remained in one-piece, was analysed by X-ray µCT (see Figure 3.18 (c)) with a voxel size

of 1.1 µm×1.1 µm×1.1µm. An inclined damage zone could be observed on the specimen

surface, located near the end of the gauge section possibly due to local stress concentration

induced by machining. Figure 3.22 shows the designated origin and axes of this sample for

convenience to present the results. Compression loading was applied along the Z direction.

The CT dataset was rotated in reference to the Z axis, so that the kink bands were lying in

the XZ plane. Figure 3.25 exhibits a typical µCT XZ slice image of the kinked region

highlighted in the yellow box in Figure 3.18 (c). In the planes where the kink bands lie, the

geometric parameters of the kink bands can be measured directly. Unlike the angled view in

the SEM images, the measurement in CT images could be made more accurately by looking

through multiple XZ slice images along the Y direction.


106

Figure 3.22: The designated origin and axes for the discussion of the kink bands in this

section. The compressive loading and the fibre direction are along the Z axis. The X axis

was chosen to include kink bands in the XZ planes.

Figure 3.23: A typical X-ray μCT XZ slice image in the middle of the sample showing

kink bands and associated damage mechanisms. Most of the bands lie in the XZ plane, thus

the kink-band width, kink-band boundary angle and fibre rotation angle can be measured

as indicated.


107

Figure 3.24: X-ray μCT XZ slice images of the sample at different distance from the origin

along the Y axis: (a) 100 μm, (b) 300 μm, (c) 500 μm, (d) 700 μm, (e) 900 μm, (f) 1100 μm

and (g) 1300 μm.


108

3.3.4.1. Kink-band geometry

The geometric parameters of the kink bands were: ω ≈ 20-320 μm, β ≈ 11-40° and Φ (φ+φo)

≈ 18-52° in the sample scanned. The damage zone has almost propagated through the whole

sample with undamaged regions around the circumference holding the sample together. Six

individual narrow kink bands at maximum were seen on the left inclined part of the sample,

as shown in Figure 3.23. The fibres in the middle four bands were roughly aligned at the

same angle, while small angular change in fibre direction was observed in the top and bottom

narrow bands.

Figure 3.24 shows the sequential XZ slice images of the sample at different locations along

the Y axis. The boundaries of the wide kink band in Figure 3.24 (c), (d) and (e) were clearly

defined by fibre breakage, indicating the fully development of kink bands. While in Figure

3.24 (a), (b), (f) and (g), some of the fibres at the boundary of the wide kink band buckled

but not fractured. The discontinuous boundaries at the outer layer of the rod indicate that in

these regions, the material is at an earlier stage before that in the centre of the sample. The

geometry of each fully developed kink band was found to be consistent through the specimen

along the Y axis. In the compressive failure of laminates with high aspect ratio, due to the

lack of constraint in the thickness direction, out-of-plane kink bands are dominant (Sutcliffe

and Fleck, 1994). The specimen tested in the current study is cylindrical, with its surface

unsupported, thus the lateral support is similar in all directions. Nevertheless the kink bands

predominantly lay within the same plane across the sample (determined as the XZ plane)

except for a few isolated regions.

All the kink-band boundaries and three representative splits along the fibre direction were

segmented and visualised, as shown in Figure 3.25, the details of which are discussed in the

following section.


109

Figure 3.25: Side view of the segmented X-ray µCT image showing planes of fibre

breakage (purple) normal to, and three splits (yellow) parallel to, the fibre direction. The

upper and lower fibre-fracture planes delineate a wide kink band, within which multiple

narrow bands that are similarly inclined lie.

3.3.4.2. Kink-band boundaries

Fully developed kink-band boundaries were defined by fibre breaks. For the wide band, the

fibre angle changed abruptly at the boundary, while for the narrow bands, fibre rotation was

not observed. From the side view in Figure 3.25, all the band-boundary planes were found

to be inclined at ～25° to the X direction, with slight bending in 3D. The middle fibre-

fracture planes were developed due to the formation of multiple narrower kink bands and

the width of each kink band ranges between 25 μm and 100 μm. As depicted in Figure 3.26,

the planes of fibre breaks were shaped differently. The upper and lower boundaries,

delineating the wide band, have almost propagated across the entire specimen; while the


110

middle planes, representing the boundaries for narrower bands, are sickle-shaped around the

circumference of the rod at the left side. The difference in the planar shape indicates different

triggering and propagating mechanisms of damage.

Figure 3.26: Top view of the segmented kink-band boundaries defined by fibre breakage,

categorised in three groups according to their location and morphology: (a) upper, (b)

middle and (c) lower.

Figure 3.27: Angled views of the three segmented splits at different locations in the

specimen, numbered I, II and III. The small split highlighted in the red circle corresponds

to the highlighted position in Figure 3.26 (a).

3.3.4.3. Splits

The splits parallel to the fibre direction in the 2D slices formed 3D curved planes in the

kinked volume, as shown in Figure 3.27. The morphology of these planes changes with


111

position along the X direction. Three typical splits were segmented near two maximum-

bending surfaces and at the centre of the specimen, as shown in Figure 3.25. Figure 3.27

demonstrates that splits I and III were curved as the circumference of the specimen; while

the waviness of split II was because the fibre rotation angle varied through the sample along

the Y direction. The morphology of the splitting planes suggests that its propagating

direction is roughly along the Y axis. It can be seen in Figure 3.25 that split I has stopped

the propagation of fibre breakage at the lower kink-band boundary by releasing the stored

strain energy. It is also found that split III corresponds to the indentation highlighted in

Figure 3.26 (a). It is possible that the upper boundary originates from the split.

3.3.4.4. Matrix micro-cracks

By careful analysing sequential XZ slice through the sample, the transition between different

damage mechanisms can be identified. Figure 3.28 shows close-up views of small region-

of-interest in three adjacent XZ planes along the Y axis. The matrix micro-cracks appeared

to be localised between a split and fibre breakage. The morphology of the micro-cracks is

similar to that reported by Gutkin et al. (2010). They proposed that the micro-cracks would

eventually coalesce into a split, which can be validated by the observation here that the split

and the micro-cracks are connected in sequential images. The fibre fracture plane was

inclined at ～45º to the fibre axis, indicating the presence of shear stress.

Figure 3.28: Adjacent X-ray CT XZ slice images of the specimen (two sequential images

in between were not shown) showing the transition between split, micro-cracks and fibre

breakage.


112

3.3.4.5. Curvature of unbroken fibres

As mentioned in section 3.3.4.1, some of the fibres at the boundary of the wide kink band

heavily buckled but not fractured (see Figure 3.24). The discontinuous boundaries with both

broken and unbroken fibres indicate that curvature of unbroken fibres should be close to the

maximum bending curvature that the fibres can attain before fracture. The smallest radius of

curvature, corresponding the maximum curvature, of the unbroken fibres measured in

ImageJ using the ThreePointCircularROI plugin was ～280 µm. Weaver and Williams

(1975) observed larger radius of curvature (～530 µm) of unbroken fibres in Modmur Type

II carbon fibre/epoxy composite rods failed under axial compression with hydrostatic

pressure. As these values were measured in unloaded specimens, elastic recovery would take

place following unloading the compressive load. Therefore, even larger curvature (higher

strains) would have been sustained in the fibre during buckling.

3.3.5. Multiple kink bands

Although only post mortem µCT qualitative analysis was conducted, damage information

could be obtained from orthogonal slices at different positions along the damage propagation

direction. This provides some clues as to the materials’ behaviour at different stages during

the loading process. Hapke et al. (2011) found that only the initial band is ever found to

propagate through the whole width of the specimen, and secondary bands terminate when

the shared boundary with the initial bands stop. In terms of this finding, it is appropriate to

consider the top and bottom narrow bands that define the points of maximum curvature as

the primary bands with the middle narrow bands as secondary ones. As shown in Figure 3.25

at the upper concave side, split III occurs due to transverse tensile stress induced by axial

compressive load, and then reduces the lateral support of the fibres, which bend and break

to form the top narrow band. At the lower convex side, fibre rotation has exceeded the

maximum bending angle the fibre can bear so that fibres break and the bottom narrow band

is developed. Meanwhile, the fibres in the top and bottom bands abruptly change angle from

outside to the inside of the bands, whereas for the middle bands the change in fibre angle is

slight. This might be explained by the band broadening mechanism of progressive addition


113

of narrow zones of broken fibres to form a broadened band (Vogler and Kyriakides, 1997).

Nevertheless, it is not possible to determine from the post-failure image the evolution of

multiple kink bands in this experiment, which requires further verification with in situ

observation.

3.3.6. High-speed in situ observations

In un-notched samples, kink bands might form at either of the two transient regions at the

ends of the waisted gauge section, but the field of view could not cover the whole length if

reasonable resolution is assured. Thus the specimen geometry with waisted gauge section

and a circular notch around the circumference was developed. In these samples, the damage

zone was constrained near the notch, which was ideal for in situ imaging with limited field

of view.

However, the lab-based in situ tests showed no sign of deformation before the sudden

formation of kink bands in the final dataset at failure. Even in the data obtained at 1 dataset

per second at the synchrotron beamline, it was found that the progressive development of

kink bands could not be captured in any of the samples tested. The initiation and propagation

of kink bands were observed to occur within one projection, which took 2 ms.

Figure 3.29 shows the radiographs taken at 10,000 frames per second (exposure time 0.1

ms), including the damage process in the notched and waisted rod sample. As the

radiographs were captured while the specimen was rotating, the angle between each two

frames was 0.78º. In Figure 3.29 (a) the specimen was intact with an elongated void, while

in the next radiograph (b) fibre buckling occurred and a split was formed. The fibre buckling

curvature was then increased accompanied with the broadening of the split, as shown in (c).

In (d) and (e) the buckled fibres broke and formed the boundaries of the kink band across

the sample. The morphology of multiple kink bands occurred eventually with multiple splits

opened due to the buckling of fibres at the boundaries. The initiation and full propagation of

a kink band (across the specimen) were found to occur in less than 1.2 ms.


114

Figure 3.29: Radiographs showing the progressive damage evolution in notched and

waisted rod sample forming kink bands. (a), (b), (c) and (d) are sequential radiographs,

each of which is taken in 0.1 ms and is rotated by 0.78º with respect to the last. The

interval between (c) and (e) is 1 ms, and that between (e) and (f) is 10 ms. The number at

the bottom left corner of each image indicates the number of radiograph taken.

The sequence of events can be roughly proposed based on the 2D radiographs (3D

information stacked in the 2D image). The buckling of fibres and the splits occurred at the


115

initial stage of damage in less than 0.2 ms. Excessive rotation of fibres resulted in fibre

fracture, which then propagated to form the boundary of the kink band in less than 1 ms,

significantly less than the reported 200 ms (Hapke et al., 2011). Therefore, a lower bound of

the kink propagation velocity could be estimated from the radiographs, which was 1.5 m/s.

The formation of multiple kink bands is not accidental, but the progressive adding of narrow

kink bands could not be observed from the radiographs. This might be attributed to the poor

image quality of the radiographs for the observation of fibre breakage within the sample.

3.4. Conclusions

The development of the SSRI manufacturing method proves to be effective in improving the

quality of UD cylindrical composite rods with a small diameter. As can be evidenced by

both 2D and 3D observations the formation of kink bands is the dominate failure mode in

all the wasited UD CFRP samples tested under axial compression. The damage morphology

has been visualised in 3D by segmenting the post-failure CT data, focusing on the boundaries

of the kink-band and splits along the fibre direction. 2D slice images lying in the kinking

plane also serve to the better understanding of the failure pattern. The main findings

regarding the post-failure kink bands include:

Kink-band boundaries are essentially planar being inclined at ～25° with slight bending

in 3D. The boundary planes of the narrow kink bands are sickle-shaped, while those of

the wide kink band have grown across the specimen;

In 3D, split along the fibre direction forms curved planes, with its shape similar to the

circumference at locations near the outer layers and aligned with the rotated fibres inside

the specimen;

Matrix micro-cracks are expected to coalesce into splits;

The morphology of multiple kink bands has been observed and two narrow bands at the

top and bottom are assumed to be the primary kink bands;

With the introduction of a circular notch at the centre of the waisted gauge section, the

location of kink bands can be located in the vicinity of the notched region. The initiation and


116

propagation of kink bands in samples under axial compressive loading occur in a very short

time (at the ms level). 3D volumes showing the progressive evolution of kink bands cannot

be captured using this test method. The general sequence of damage can be drawn from

radiographs: (1) fibre buckling and splits, (2) fibre breakage forming kink-band boundary

and (3) multiple kink bands. A lower bound of the kink propagation velocity could be

estimated from the radiographs, which was 1.5 m/s. The detailed micro-scale evolution of

failure associated with kink-band formation still needs to be revealed in further studies.

Chapter 4 Failure of unidirectional CFRP beams under four-point bending

117

4. Failure of UD CFRP beams under four-point bending

4.1. Introduction

In the previous chapter, it was difficult to monitor the evolution of kink bands in the axial

compression test of UD CFRP because the failure was sudden without much prior warning.

However, the establishment of the correlation and sequence of damage mechanisms leading

to the formation of kink bands in the 3D volume is essential for the development of accurate

analytical and numerical models predicting the compressive failure of CFRPs.

This chapter describes the monitoring of the evolution of kink bands in UD CFRP laminates

using in situ FPB with X-ray μCT. The aim of this part of the work was to qualitatively

identify the damage mechanisms associated with kink-band formation and the sequential

events occurring in the initiation and propagation of fibre buckling/deflection and kink bands.

Fully understanding the damage mechanisms associated with kink bands will help to

improve the design of composite structures employed in compressive load.

The dynamic nature of kink band development under axial compression makes it unfeasible

to identify the microscopic damage sequence leading to the final failure except at ultra-fast

synchrotron X-ray CT. According to our recent synchrotron experiments conducted on the

TOMCAT beamline at Swiss Light Source, it was found that the damage process occurs in

less than 1.2 ms, which is too fast to be recorded at sufficient resolution for analysis even on

ultra-high speed synchrotron beamlines.

A 4D study on the micro-mechanisms of kink bands requires 3D microscopic observation of

composite material under progressive loading along the timescale. As the imaging capability

of state-of-art X-ray CT is limited in the characterisation of dynamic failures, the evolution

of kink bands must be slowed by modifying the specimen geometry and loading

configurations. The use of biaxial loading (combined shear and axial compression loading)

stabilises the kink-band propagation process in UD CFRP for in situ observation on sample

surface (Vogler et al., 2001). Pimenta et al. (2009) utilised samples with off-axis fibre

orientation to induce shear under compressive loading. Study of the development of kink


118

bands through arresting its propagation may also be achieved by introducing a notch, or by

testing in bending (Chaplin, 1977; Schultheisz and Waas, 1996; Wind et al., 2015) to achieve

a gradient in the stress field. In this case, the kink band that initiates in the part with high

compressive stress must propagate into the less compressively stressed regions, resulting in

a more stable failure process. Under FPB load, the specimen stress state is divided into a

compressive zone and a tensile zone separated with a neutral axis (Hodgkinson, 2000). In

the compressive zone, compression along the fibre direction is induced by the bending

moment within the bending region, which generates the similar condition of axial

compression loading in UD FRP.

To stabilise the development of kink bands and constrain their formation into limited field

of view of X-ray CT imaging, single-edge notched rectangular beam specimens with UD

carbon fibres reinforced along the specimen length are used for FPB tests in the work

presented in this chapter. Three different carbon fibre (T800, T700 and T300)/epoxy

composite systems are used in an attempt to obtain a generalised understanding of the

evolution of kink bands. The notch width is varied for one specimen type to study the effect

of notch shape on the initiation of fibre buckling/deflection. The failed specimens are also

scanned after unloading, so that the influence of unloading on damage morphology can be

explored.

The general aim of this chapter is to identify the incipient damage mechanism and the

sequence of events leading to failure in UD CFRPs under FBP load, by capturing the early

initiation stage and progressive propagation process of kink bands in 3D; thereby

complementing the lack of knowledge in damage evolution from axial compressive failure.

4.2. Experimental

In the following sections, the experimental details on studying the kinking mechanisms by

four-point bending tests will be presented. The manufacture of composite materials, the

preparation of samples, the mechanical tests and the µCT imaging tests are detailed.


119

4.2.1. Materials

In this part of the project, three different material systems were employed to manufacture

UD composite laminates.

1. (B8) UD T800H/MTM28-1 prepreg

2. (B7) UD T700S preform (fabricated from UD T700 carbon fibre yarns on

a pin-mould) /Araldite LY564+Ardur XB3486

3. (B3) UD T300 fabric with glass binder yarns/ Araldite LY564+Ardur

XB3486

Table 4.1: Properties of the carbon fibres and the composites according to the datasheets

from the fibre manufacture.

Fibre Type

Fibre Properties

T800H T700S T300

Tensile Strength (MPa) 5490 4900 3530

Tensile Modulus (GPa) 294 230 230

Strain (%) 1.9 2.1 1.5

Filament Diameter (µm) 5 7 7

Density (g/cm3) 1.81 1.8 1.76

Composite Properties (Toray 120°C epoxy resin, normalised to Vf = 60%)

Tensile Strength (MPa) 2650 2550 1860

Tensile Modulus (GPa) 170 135 135

Tensile Strain (%) 1.5 1.7 1.3

Compressive Strength (MPa) 1570 1470 1470

Flexural Strength (MPa) 1620 1670 1810

Flexural Modulus (GPa) 150 120 125

Table 4.1 shows the properties of the carbon fibres and the epoxy matrix composites

according to the datasheets from Toray Carbon Fibres America, Inc. These information can

provide guidance for understanding the relations between fibre properties and the damage


120

mechanisms.

The matrix material was different for the B8 laminate, which was made from UD

T800H/MTM28-1 prepregs supplied by Umeco structural materials Ltd. UD T800H carbon

fibres were impregnated in a toughened epoxy resin system MTM-28. While in the other

two composites, matrix was the two-part epoxy resin system composed of Araldite LY564

and hardener Ardur XB3486. This resin system was the same as that used in Chapter 3,

which was a warm epoxy system without toughening. The curing cycles were different for

the two matrix systems, as shown in Table 4.2.

Table 4.2: Curing cycles for the matrix systems.

Matrix System MTM28

Araldite LY564

Ardur XB3486

Curing Cycle

Heat from room temperature

to 120 °C at 1 °C/min

Maintain at 120 °C for 1

hour

Heat from room temperature

to 80 °C at 1 °C/min

Maintain at 80 °C for 8 hours

4.2.2. Composite manufacture

Three types of UD carbon fibre/epoxy composites were manufactured using different

methods, according to the availability and characteristics of the raw material. The B8

laminate was manufactured from prepregs, while the B7 and B3 laminates were

manufactured by the VARI method. The consumables used in the manufacturing process

were purchased from Aerovac Systems.

4.2.2.1. B8 UD laminate

The prepreg material was stored in the freezer to avoid the curing of the resin. The roll of

prepreg was taken out of the freezer and stored at room temperature for 12 hours before


121

removing the sealing bag in order to avoid the build-up of condensation. The prepreg was

supplied in a roll with the width of 300 mm and the nominal ply thickness is 0.125 mm. 32

plies of 300 mm×300 mm were cut from the prepreg roll (see Figure 4.1) and laminated into

a ~4 mm thick UD panel, according to the recommended vacuum bagging arrangement from

the manufacturer, as shown in Figure 4.2.

Figure 4.1: Photograph of the plies of prepreg material after cutting from the roll.

The materials were placed onto a flat steel mould, the surface of which was covered with a

polytetrafluoroethylene (PTFE) release film. The plies were laid up manually all oriented in

0° direction and care was taken to keep the fibre aligned properly.

During the lay-up process, a reusable silicon vacuum membrane was used after the first ply

and then every subsequent third ply to debulk the laminate. The debulking procedure was

employed to remove the air enclosed between layers and promote laminate compaction, as

shown in Figure 4.3. A perforated PTFE release film, a nylon peel ply and breather material

were placed on the stack of plies before covering it with the vacuum membrane. The

membrane was then connected to a vacuum hose for 10 minutes. After the lay-up of the 32

plies, the laminate was covered with the assisting vacuum bagging materials as shown in

Figure 4.2. The vacuum condition was checked with a gauge connected to the vacuum port


122

to assure that the laminate was exposed to vacuum. Figure 4.4 shows the panel after the

vacuum bagging process.

The vacuum bagged panel was then cured in an oven according to the curing cycle in Table

4.2. After cooling, the laminate was removed from the vacuum bag and the mould.

Figure 4.2: Recommended bagging arrangement to manufacture laminates from the

prepreg manufacturer.

Figure 4.3: Photograph showing the debulking procedure, in which the plies of prepreg

materials were compacted under vacuum to eliminate enclosed air.


123

Figure 4.4: Photograph of the vacuum bagged panel from prepregs.


Preparation of the fabric preform

Constrained by the availability of materials, UD T700H preform was prepared from UD

T700H carbon fibre yarns using a pin-mould, as shown in Figure 4.5. The yarns were placed

around the pins through a guiding tool to avoid crimp and breakage. The fibres were kept

under tension in order to prevent fibre misalignment. After each layer, sealant tape was used

at the inner ends to fix the position of the fibres. The final preform was 300 mm (along the

fibre direction) ×150 mm in size and was composed of 8 layers of UD carbon fibres. The

dry preform was then carefully transferred to the top of a flat steel mould, which had been

treated with release agent. Distortion of the preform should be avoided during the move to

assure the fibre alignment.

Vacuum bagging process

The composite laminate was then manufactured using the VARI method. Figure 4.6 shows

the schematic diagram of the vacuum bagging arrangement. Resin inlet and outlet tubes were

placed at the top and bottom of the fabric preform with a gap for ease of demoulding. The


124

part of the tubes inside the vacuum bag was a spiral tube to spread the resin evenly along the

fabric top edge. A Nylon peel ply, a PTFE perforated release film and a loosely warp knitted

Nylon6 mesh were placed on top of the fabric preform. The peel ply provides a smooth

surface of the laminate, and the perforated release film aids the separation between mesh and

the peel ply. The mesh is a resin flow media promoting the resin flow through the dry fabric.

The materials were then sealed in a vacuum bagging film with tacky tape. The outlet tube

was connected to a resin trap to absorb extra resin, avoiding blocking the vacuum pump.

After closing the inlet tube with a clamp, the system was connected to the vacuum hose. The

vacuum condition was then checked using a gauge.

Resin infusion process

As mentioned in section 3.2.2.1, the epoxy resin system was mixed at the weight ratio of

100:34 between resin and hardener. The mixed resin was degassed in a vacuum oven at room

temperature for one hour to remove air bubbles introduced in the mixing process. The

degassed epoxy resin was then infused into the vacuum bag through the inlet tube by pressure

gradient with the aid of a vacuum pump connected to the outlet tube. The inlet tube was

closed with a clamp after discontinuous resin came out through the outlet tube. At that

moment, the part near to the inlet tube is thicker than the part near the outlet tube. After the

thickness of the laminate became uniform and continuous resin came out of the outlet tube,

the infusion process was stopped by closing the outlet tube with a clamp. The tubes were

then cut and closed with sealing tape at the ends, followed by switching off the vacuum

pump.

Curing and demoulding of the laminate

The infused panel was then transferred into the oven to cure the matrix material. The curing

process followed the recommended curing cycle by the manufacture, as listed in Table 4.2.

After curing, the panel was cooled naturally in the oven to room temperature. The composite

laminate was then demoulded carefully from the steel plate.


125

Figure 4.5: Photograph showing the pin-mould used for the preparation of UD T700

carbon fibre preform.

Figure 4.6: Schematic diagram of the vacuum bagging arrangement for the VARI

manufacturing method.


126


The third category of samples was reinforced with UD T300 carbon fabric (450GSM/PW-

BUD/T300C 12k) supplied by Sigmatex. 22 tex glass fibre yarns were woven at 6 mm

interval into the UD fabric to hold the carbon fibre tows in position, as shown in Figure 4.7.

The fabric was crimped at the regions with binder yarns, which would result in initial fibre

waviness and resin rich regions in the composite laminate. 10 layers of the T300 fabric with

the dimensions of 150 mm×100 mm were cut and laid up with fibres lying in the 0° direction.

The B3 composite laminate was manufactured by the VARI method following the same

procedures as described in the manufacturing of the B7 laminate in section 4.2.2.2.

Figure 4.7: UD T300 carbon fabric with glass binder yarns.

4.2.3. Sample preparation

Composite samples were prepared for both preliminary and in situ 4PB tests. The samples

were cut from the laminates and then notched.

4.2.3.1. Samples for preliminary four-point bending test

Three bar samples with the nominal dimensions of 25 mm in length, 4 mm in width and 4.2

mm in thickness were cut from the B8 laminate using a diamond saw. The exact dimensions

of the samples were measured with an electronic calliper and averaged at three positions.


127

Care was taken to ensure that the length direction was the fibre direction to alleviate the

effect of initial fibre misalignment. In addition, the thickness direction of the sample was

along the laminate thickness direction.

Each sample was notched at the centre of its length with disc cutting wheels (two cutting

wheels with a thickness of 0.35 mm were used together to make a wider notch) on a precision

cutting machine (ATM Brilliant 221). The notch dimensions were measured with an

electronic calliper. The notch width was 0.8mm and the depth was 0.8 mm (EB8-1), 1.6 mm

(EB8-2) and 2.4 mm (EB8-3), respectively.

Figure 4.8: Radiograph image of sample IB8-4, illustrating the measurement of notch

geometry.

4.2.3.2. Samples for in situ four-point bending test

Bar samples with nominal dimensions of 25 mm in length, 2 mm in width and 4.2 mm in

thickness were cut from the laminates using a diamond saw, following the same procedures

as described above. The width of the sample was reduced to half of that of the samples for

preliminary tests in order to reduce the scan time for in situ CT imaging. A notch was also


128

made on these samples. The notch was about 0.8 mm wide and 2 mm deep. The exact

dimensions of the notch of each sample were measured in the radiographs taken of the

samples before in situ imaging, as shown in Figure 4.8. Figure 4.9 shows the schematic

diagram of the sample geometry.

In order to study the effect of notch width on the damage mechanisms, a narrower notch was

also made on the B7 samples. The notch was made with one disk cutting wheel, and the

notch width was 0.4 mm. The other dimensions were kept the same as shown in Figure 4.9.

Figure 4.9: Schematic diagram of the sample geometry for in situ FPB test (wider notch).

(Unit: mm)

Due to the long CT scanning time and limited access to the CT machines, one sample of

each specification was scanned by in situ X-ray imaging (IB8-4, IB7-1, IB7-2 and IB3-1).

Table 4.3 shows the details of the samples discussed in the results section. Before the step-

imaging, three B8 samples were scanned with lower image quality and shorter time to ensure

the reproducibility of the damage mechanisms and similarity in failure process between in

situ and preliminary tests.

Table 4.3: Details of the samples discussed in this chapter.

Sample Sample Dimensions Notch Dimensions Number of

CT scans


129

(length×width×thickness) /mm (depth×width)/mm

EB8-1 25.8×3.8×4.2 0.8×0.8 -

EB8-2 25.8×4.0×4.2 1.6×0.8 -

EB8-3 25.7×3.9×4.2 2.4×0.8 -

IB8-4 25.7×2.2×4.2 1.9×0.8 5

IB7-1 25.4×2.0×4.2 1.9×0.8 4

IB7-2 25.3×2.0×4.2 1.9×0.4 3

IB3-1 25.8×2.0×4.4 1.9×0.8 3

EB – preliminary bending

IB – in situ bending

8 – T800, 7 – T700 and 3 – T300

4.2.4. Fibre volume fraction

The fibre volume fraction of the laminates was measured by the acid digestion method

according to ASTM D3171. The epoxy matrices were digested using sulfuric acid/hydrogen

peroxide. Three specimens of each laminate were tested to obtain averaged values.

The specimens were dried at 70°C in the oven for five days prior to density measurements

to assure that moisture in the specimens was dried up. The weight and density of the dried

specimens were measured using a Mettler Toledo XP205 Delta Range® electronic balance

with the density measurement kit, as shown in Figure 4.10. The glass filters that would be

used in the next stage were also dried and weighed.


130

Figure 4.10: Photograph of the electronic balance for density measurement.

Every composite specimen was placed into an individual beaker and 25 mL of 100 % sulfuric

acid was added. The beakers were placed into a sand bath and heated to 160 °C. The

temperature was maintained while adding drops of 30% hydrogen peroxide as the oxidising

agent. Once the matrix was fully digested, the mixture was transferred into a glass filter,

filtered and washed with distilled water. The remaining was dried at 120 °C overnight and

its weight was measured. The weight of fibres was then calculated by subtracting the weight

of the glass filters.

The fibre volume fraction was calculated based on the following equation:

(4.1)

where 𝑀𝑓 is the weight of fibres in the composite specimen, 𝑀𝑐 is the weight of the

composite specimen, 𝜌𝑓 is the density of the fibre, and 𝜌𝑐 is the density of the composite.


131

4.2.5. Four-point bending test

Both preliminary and in situ FBP tests were conducted to ensure that the failure mechanisms

are not affected by the different loading conditions.

Figure 4.11: Photograph showing the preliminary FPB test set-up on the Instron machine.

4.2.5.1. Preliminary four-point bending test

The preliminary FPB tests were conducted on an Instron 5569 mechanical testing machine

with the bending fixtures shown in Figure 4.11. The span distances were the same as those

of the in situ loading fixtures. The supporting span was 20 mm and the loading span was 7.5

mm. As in this project the qualitative analysis of the damage mechanisms was the aim, the

loading fixtures were not specifically designed and made. The sample was loaded at a cross-

head speed of 0.1 mm/minute by displacement control. Photographs of the sample front

surface were taken at specific points on the loading curve to record the sequence of damage

on the sample surface.


132

4.2.5.2. In situ four-point bending test

In situ FPB tests were performed in the tension/compression Deben CT5000 rig,

manufactured by Deben UK Ltd. The loading was controlled from the MICROTEST control

software in the Windows system. The rig was mounted onto the sample stage of the Zeiss

Xradia Versa machine via an adapting plate. The control cables were fed into the machine

to connect the rig with the control software, so that loading can be controlled safely from

outside during µCT imaging.

Figure 4.12: Photograph of the bottom part of the in situ loading rig with the sample placed

on the supporting rollers.

The supporting tube of the rig was made of glassy carbon with a wall thickness of 3 mm.

The rollers of the FPB clamps were made of glassy carbon with a diameter of 5 mm. The

supporting span was 20 mm and the loading span was 7.5 mm. The un-notched side of the

sample was glued to the supporting rollers with a double sided tape to fix the position of the

sample while reassembling the top part of the loading rig. The mid-line of the notch was

ensured to be at the centre of the span. Figure 4.12 shows the bottom part of the loading

fixture with the sample inside the Deben rig.


133

The sample was loaded at 0.1 mm/minute by displacement control and the loading process

monitored by radiography. The loading was interrupted when damage was observed in the

radiograph. The µCT scan was started after the load became relatively stable, which was

normally 10 minutes after each load stop. During each scan, the displacement was

maintained, but the load was relaxed to some extent because of the inherent material property.

4.2.6. X-ray micro-tomographic imaging

The X-ray µCT imaging of the samples were all conducted in the Henry Moseley X-ray

Imaging Facility. Two Zeiss Xradia CT systems were used in this part of the project. In situ

scans were conducted on the Versa system due to its faster scan capability at a higher

resolution, while post-failure scans were conducted on the Micro-XCT system due to its

larger field of view to include the side surfaces of the sample.

4.2.6.1. Interrupted in situ X-ray μCT

The in situ X-ray µCT scans were conducted on the Zeiss Xradia Versa machine. With in

situ loading the 4D (3D and time) material behaviour could be obtained, facilitating the study

of damage mechanisms. Figure 4.13 shows the scan set-up in the machine. Special care was

taken to ensure that any part of the rig and the cables would not hit the source or the detector

during the scan.

It was also ensured that at 0° the long side of the sample was in the view (perpendicular to

the source-detector line). With the rig tube in the way between the source/detector and the

sample, the energy level and exposure time needs to be higher than preliminary experiments,

in order to obtain imaging data with satisfactory quality to examine the features at the fibre

scale. The sample was scanned at 80 kV with the power of 7 W, and the voxel size was

1.8µm with the 4 times optical magnification. 1001 projections were taken during the 360°

rotation, and the exposure time for each projection was 22 s, which resulted in a total scan

time of about 8 hours. The number of scans for each sample were shown in Table 4.3.

Radiographic images of the samples at 0° were also taken while waiting for the load to


134

become stable. These radiographs could help to explain the damage propagation mechanisms,

which could not be captured in the 3D datasets.

Figure 4.13: µCT scan set-up in the Zeiss Xradia Versa machine with the Deben CT5000

loading rig.

4.2.6.2. Post mortem X-ray μCT

The four samples loaded in the rig were removed from the rig after the in situ scans. Each of

the samples was then mounted on a sample holder vertically, as shown in Figure 4.14. In this

case, the X-ray travel distance through the sample was not varied much during rotation, and

it was ensured that the sample cross-section was within the field of view. The sample was

then scanned on the Zeiss Xradia Micro-XCT machine, without the rig tubing material. The

scan time was significantly reduced when the sample was scanned on its own. The sample

was scanned at 40 kV with the power of 10 W, and the voxel size was 2.2 µm with the 4

times optical magnification. 1501 projections were taken during the 360° rotation, and the

exposure time for each projection was 10 s, which resulted in a scan time of about 5 hours.

Table 4.4 shows the summary of the setting parameters for both the in situ and post-failure

scans.

Source Detector

Loading rig

(sample inside)


135

Figure 4.14: Photograph of the sample arrangement for post-failure µCT scan.

Table 4.4: Setting parameters of X-ray µCT scans in the Zeiss Xradia Versa machine.

Experiment In situ Post-failure

CT Machine Zeiss Xradia Versa Zeiss Xradia Micro-XCT

Accelerating Voltage (kV) 80 40

Power (W) 7 10

Optical Magnification 4x 4x

Exposure time (s) 22 10


Voxel size (µm) 1.8 2.2

4.2.6.3. Reconstruction

Reconstruction was performed in the TXM Reconstructor software. The correct centre of

shift was selected for reconstruction. As the sample was larger than the field of view and the

X-ray travel distance through the sample was varied as the sample rotated, the image quality


136

was not perfect using commercial reconstruction algorithms due to artefacts. However, the

data quality was still acceptable for measuring distance and angle, and qualitative analysis

of the damage mechanisms.

4.2.6.4. Data analysis

The reconstructed data was then imported into the Avizo 8.0 software for 3D data analysis.

Upon loading and rotation, slight sample movement was inevitable although the sample was

not removed from the machine during the entire imaging process. The datasets for one

sample at different steps were registered, so that the 2D slice images at the same location

were correlated. 2D slice images at different locations in the samples were used to study the

initiation and propagation of damage. Segmentation and extraction of the 3D volumes of the

features were conducted in sample IB8-4. The splits were segmented using an automatic

local region-growing segmentation tool – magic wand and modified with the manual brush

tool. The kink bands were segmented with the manual brush tool for the rough indication of

the 3D morphology of kink bands.

4.3. Results and discussion

4.3.1. Fibre volume fraction

The fibre volume fractions for the three laminates measured by the acid digestion method

are given in Table 4.5. The results show that the fibre volume fractions of the laminates are

all above 50% and are in the range of typical values for unidirectional composite materials

(50-65%). Although the fibre volume fraction is different in each panel, it is expected that

failure is caused by kink bands in these composites with relatively high fibre volume

fractions (Budiansky and Fleck, 1993).

Table 4.5: Fibre volume fractions of the composite laminates measured by acid digestion.

Composite Laminate Fibre volume fraction (%)

B8 51.1


137

B7 58.2

B3 54.0

4.3.2. Preliminary four-point bending behaviour

The geometry of the samples discussed here are summarised in Table 4.3.

Sample design

The design of the specimen geometry concerns two aspects: to ensure the formation of kink

bands is the predominant damage mechanism and to constrain the location of kink bands to

within the observation window.

Figure 4.15: Photographs of (a) specimen EB8-2 after unloaded, specimen EB8-1 (b) after

unloaded and (c) under load, presenting unacceptable failure modes.

Preliminary testing

As various damage mechanisms might occur under the FPB load, preliminary FPB tests were

first conducted to determine the sample geometry so that the development of kink bands


138

would be the dominant failure mechanism. Wind et al. (2015) found that the depth of notch

could influence the dominant failure mechanism (either micro-buckling or splitting) in

IM7/8852 CFRP samples under FPB. Thus, the effect of the variation of notch depth on the

failure process has been studied prior to the in situ tests in this project. Figure 4.15 (a) shows

sample EB8-2 with a notch depth of 1.6 mm. Kink bands formed from both roots of the

notch, along with debonding at the top left part of the sample. The occurrence of debonding

redistributes the stress at the tip of the kink bands, which will influence the propagation of

kink bands. In order to study the evolution of kink bands, debonding in the tensile zone of

the bending sample should be avoided.

It is also important to ensure that kink bands form within a region near the notch, so that the

failure process can be captured in the limited field of view during in situ X-ray CT imaging.

Figure 4.15 (b) and (c) show sample EB8-1 with a 0.8 mm deep notch after unloaded and

under load, respectively. As can be seen, the fibres at the loading points have been severely

crushed before any damage occurs in the notched region. Loading was stopped as damage

initiated from the bottom pins propagated through halfway of the sample thickness. The

small radius of the bottom pins is thought to be the main cause for damage. Although the

diameter (5 mm) of the rollers in the in situ rig is larger, there is still the chance that damage

zones will start from rollers at a lower load than damage from the notch, which will then

affect the observed damage mechanisms.


139

Figure 4.16: Load-displacement curve of sample EB8-3 under preliminary 4PB test.

Figure 4.17: Photographs of specimen EB8-3 at different stages during the loading process.

Images (a), (b), (c) and (d) correspond to a, b, c and d points highlighted on the loading

curve in Figure 4.16, respectively.


140

The failure process of sample EB8-3 (2.4 mm deep notch) is depicted in Figure 4.16 and

Figure 4.17. Four photographs of the sample side surface corresponding to the four points

highlighted on the load-displacement curve (see Figure 4.16) are shown. Due to the bending

moment, lower part of the sample was under compressive load parallel to the fibre direction.

Thus, in this region the condition was similar to the axial compressive failure in UD

composite.

At stage a, the sample was slightly bent;

At stage b, the sample was more severely bent without visible damage on the

sample surface;

At stage c, damage was seen to initiate from the left notch root forming a kink

band;

At stage d, kink bands were observed to have formed from both notch roots

symmetrically. However, the notch flanks were touching at the tip, which would

change the stress distribution and influence the propagation of kink bands.

Conclusions form the preliminary tests

Considering the behaviour of the above three samples under 4PB tests, it was determined

that the notch depth should be between 1.6 mm and 2.4 mm, avoiding debonding or closing

of the notch before sufficient propagation of kink bands. 2 mm was then chosen as the notch

depth for samples for in situ tests, which equalled almost half of the sample thickness.

It has been observed that the failure process is significantly slowed down in the FPB tests

compared with that in the axial compression tests. This test configuration is therefore ideal

for studying the progressive failure process, with the formation of kink bands constrained

within the notched compressive zone of the sample.


141

4.3.3. In situ four-point bending behaviour

As mentioned in section 4.2.3, four composites (see Table 4.3) in total were scanned by CT

in the in situ FPB fixture. Therefore, based on the optimal geometry identified in the previous

section, a notch depth of 2 mm was used, while the sample width was further reduced, from

4 mm to 2 mm in order to shorten the scan time.

The damage processes of the four composites are presented in the following paragraphs. In

specimen IB8-4, the cooperative interaction between different damage mechanisms

promoting the development of kink bands was captured and all the kink bands formed in the

XZ plane. In other specimens, kink bands were observed in both the XY and XZ planes as

defined in Figure 4.9.

Figure 4.18: Load-displacement curve of sample IB8-4 (see Table 4.3) under in situ FPB

test. CT scans were taken at steps 0, 1, 2, 3 and 4 marked in red on the curve,

corresponding to cross-head displacement of 0 mm, 0.31 mm, 0.38 mm, 0.44 mm and

0.51mm.

For specimen IB8-4, five scans were taken at cross-head displacement of 0 mm, 0.31 mm,

0.38 mm, 0.44 mm and 0.51 mm, corresponding to the steps 0, 1, 2, 3 and 4 marked in red

on the load-displacement curve respectively, as shown in Figure 4.18. The peak between


142

step 3 and 4 is due to the signal error in the controller, which should be noise instead of

increased load on the sample. The load relaxed at constant displacement while the scans

were taken in the Zeiss Xradia Versa machine using the settings summarised in Table 4.4 (8

hours per scan). As the dropping load was relatively small in respect to the peak load applied,

this load dropping would not affect the deformation to such an extent that the mechanisms

were changed. Similar to the conditions in the preliminary tests, the fibres in region

immediately below the notch were under compressive load.

Figure 4.19 shows the X-ray µCT XZ slice images at the same position in the centre of the

sample at steps 1, 2, 3 and 4. The sequence of damage modes observed is as follows:

At step 1, fibre fracture due to buckling was observed close to the left corner of

the notch. Fibre breakage at two points formed the kink band;

At step 2, the fibre failure propagated from the free notch surface layer to the sub-

layers;

At step 3, the fibre failure on the left side locked-up, while a primary kink band

formed lower than the significant fibre kinking at the right notch corner

accompanied by a split;

At step 4, multiple kink bands formed from the primary kink band and the

compressive misfit near the notch was alleviated by forcing out a wedge thus

opening the split into a parallelogram shape. The elongation in the X direction

was marginal.


143


144

Figure 4.19: X-ray µCT XZ slice images from the same through thickness location (see

schematic at bottom of the figure) in specimen IB8-4 (notch width 800 μm) at different

loading steps. Images (a), (b), (c) and (d) correspond to steps 1, 2, 3 and 4 highlighted on

the loading curve in Figure 4.18, respectively.


145

The failure process of T800/epoxy specimen IB8-4 tested in situ is similar to that of

specimen EB8-3 (see Figure 4.17). In general, one set of kink bands initiates at a certain

distance from one notch root similar to the fix-end Euler buckling mode, followed by the

development of the second set of kink bands from the other notch root. The similarity in the

failure process validates that the in situ loading condition and the X-rays should not affect

the damage mechanisms studied in this project.

The load-displacement curves of specimens IB7-1, IB7-2 and IB3-1 (see Table 4.3) are

provided in the Appendix. The X-ray µCT XZ slice images from the centre of the specimens

at different steps, and certain XY slices showing interesting features are presented in Figure

4.20-25.

In the T700/epoxy system (samples labelled IB7), fibres buckled to a large extent before

fracture, facilitating the observation of the damage initiation stage in both XZ plane (Figure

4.20 (a)) and XY plane (Figure 4.21 (a)) from fibre micro-buckling. Although the notch

width was changed, the sequence of events observed in specimen IB7-1 and IB7-2 was

essentially the same, as shown in Figure 4.20 and Figure 4.22. The difference in behaviour

between these two specimens was the micro-buckling of fibres in the XY plane. In specimen

IB7-1 the fibres buckled favourably in one direction (see Figure 4.21), while in specimen

IB7-2 fibres buckled simultaneously in two opposite directions (see Figure 4.23), towards

the side surfaces of the specimen. In spite of the divergence in fibre micro-buckling direction,

the overall direction was along the sample width. The fibres fractured due to excessive

bending at the maximum curvature points in XY planes below the kink bands in the XZ

plane, and the fibre breakage formed a crack along the Y direction. Kink bands have formed

from the meeting point of the two buckling ‘waves’ in XY planes of specimen IB7-2.


146


width 800 μm) at different loading steps. Images (a), (b), (c) and (d) correspond to steps 1,

2, 3 and 4.


147


position illustrated as the XY Plane in Figure 4.20 at (a) step 3 and (b) step 4 showing the

formation of kink bands from fibre micro-buckling in the XY plane.


148


width 400 μm) at different loading steps. Images (a), (b) and (c) correspond to steps 1, 2

and 3.


149


position illustrated as the XY Plane in Figure 4.22 (c) at step 3 showing the formation of

intersecting kink bands from fibre micro-buckling in the XY plane.

In specimen IB3-1, the effect of resin-rich regions near binder yarns on damage propagation

could be studied. The propagation of fibre micro-buckling was arrested by resin-rich region.

The fibre buckling in XZ plane and XY plane was separated by the resin-rich region (see

Figure 4.24 (c)), which was highly deformed with no fracture observable. In the XY plane,

fibres kinked into two opposite directions, thus opening a split. Near the side surfaces of the

specimen, fibre fractured at the point with maximum curvature due to buckling. In the region

inside the specimen, the fibres broke at two points due to combined compression with shear

stress from fibre kinking, forming kink bands from the split. Fibre kinking without fracture

was arrested in regions further below the notch, as shown in Figure 4.25 (b)

In the XZ planes near one side surface of specimen IB3-1, another fibre micro-buckling

failure was observed near the left notch root, as shown in Figure 4.26. The lengths of the

fibres between the buckling wave peaks to the notch flank were the same for the two micro-

buckling regions.


150

Figure 4.24: X-ray µCT XZ slice images from the same position in specimen IB3-1 at

different loading steps. Images (a), (b) and (c) correspond to steps 1, 2 and 3.


151

Figure 4.25: X-ray µCT XY slice images of specimen IB3-1 (notch width 800 μm) at two

locations at step 3, showing (a) kink bands and (b) fibre kinking.


152

Figure 4.26: X-ray µCT XZ slice images near side surface in specimen IB3-1 (notch width

800 μm) at step 1, showing two micro-buckling waves.

4.3.4. Damage mechanisms

As presented in the previous section, the formation of kink bands is the major failure

mechanism of UD CFRPs in the compressive zone under FPB loading. The initiation and

propagation of kink bands are associated with various damage mechanisms, including fibre

micro-buckling, fibre kinking, splitting (matrix or interface failure) and fibre fracture. These

damage modes can combine and interact with each other in the same specimen or one

damage mode can dominate at a certain stage. In order to clarify the correlation between the

mechanisms in the evolution of kink bands, each damage mode is discussed in the following

paragraphs.


153

4.3.4.1. Fibre micro-buckling and fibre kinking

From the observations in the specimens above, it is found that in-plane (XY plane) and out-

of-plane (XZ plane) that fibre micro-buckling and fibre kinking are both the incipient

damage mechanism causing the formation of kink bands.

It has been found that fibre micro-buckling or fibre kinking often occurs without warning

and immediately leads to fracture of fibres (Hahn et al., 1986; Hapke et al., 2011). Therefore,

it has always been challenging to capture the stage of failure at which the fibres have buckled

but not yet broken. Previous studies in literatures employed serial sectioning to find a

position in the sample where the fibres did not break, while in most parts of the sample fibre

fracture and even kink bands already existed (Vogler and Kyriakides, 1997). Thus it is not

convincing to establish the initiation mechanism of kink bands based on these observations.

Initiation of kink bands via fibre micro-buckling

In this study, the onset of failure in UD CFRP under compressive load has been captured at

the fibre micro-buckling stage, that is before fibre failure, in T700/epoxy specimens IB7-1

and IB7-2. As shown in Figure 4.20 (a), fibres heavily buckled sequentially along a band

which was lying in the range of 15° to 25° to the X axis. The amplitude and half-wavelength

of the sinusoidal shaped fibre wave, as indicated in Figure 4.27, were 30-35 µm and 250-

350 µm respectively. The values were measured in ten XZ slice images through specimen

IB7-1. Although several fibres broke at the surface of the notch, the majority of the damage

zone was contained at the fibre micro-buckling stage just before fibre breakage. The

curvature of the fibres therefore is considered to be approaching the critical radius of

curvature for the onset of fibre breakage, which was ～130 µm as measured in ImageJ using

the ThreePointCircularROI plugin. The notion of critical curvature in fibre buckling was

proposed by Yin (1992), in which the criterion for kink-band formation was obtained from

a buckling model, which occurred when fibres’ curvature attained a critical value. This value

is significantly smaller than that in the post mortem rod specimen composed of the same

material system in Chapter 3, which was ～280 µm, indicating large relaxation of fibre


154

rotation after unloading. Thus these in situ parameters could be considered representative of

the characteristics of the micro-buckling of fibres causing failure in this material system.

Figure 4.20 (b) shows the same position of the specimen IB7-1 at step 2, in which the buckled

fibres were all broken. A kink band with non-parallel boundaries formed with one boundary

perpendicular to the initial fibre direction, and the other one at 20-25° in reference to the Z

axis. The boundaries were determined by fibre fracture at the mostly curved points. The

kink-band width was 50-100 µm, and the fibres within the band were further rotated to 40-

60° to the X axis. The orientation of these fibres measured at this stage highly depends on

how early the test is stopped after fibre fracture (Hahn et al., 1986).

Figure 4.27: Schematic diagram demonstrating the amplitude and half-wavelength of the

fibre buckle wave in the case of fibre micro-buckling.

In other samples, this early stage of failure has not been captured, which can be attributed to

many factors. For example, the loading was not stopped as immediately as in the case of the

T700/epoxy specimens. In addition, the difference in ultimate tensile strain of the fibres

might also be one of the causes. As shown in Table 4.1, the tensile strain of T700 fibre is the

highest among these three types of carbon fibres, which may also contribute to delayed fibre

breakage observed.

Initiation of kink bands via fibre kinking

As mentioned previously, fibre kinking is fibre buckling/deflection accompanied by lateral

displacement. Figure 4.28 shows the schematic diagram of fibre kinking with the illustration

of quarter-wavelength and amplitude. It was observed that fibre micro-buckling (see Figure

4.19 (a)) and fibre kinking (see Figure 4.19 (c)) were both involved at the onset of kink bands.

It is challenging to determine the correlation and distinction between these two incipient


155

damage mechanisms due to relatively slow imaging capability of lab-based CT instruments.

Figure 4.28: Schematic diagram demonstrating the amplitude and quarter-wavelength of

the fibre buckle wave in the case of fibre kinking.

In specimen IB8-4, it is evident that the primary kink band at the right corner of the notch

was initiated by fibre kinking. In the XZ slice images in Figure 4.19 (b) during step 2, the

onset of fibre kinking with a band of fibres oriented at less than 5ºto the original fibre

direction could be observed. The deflection of fibres was marginal but still distinguishable

which indicates that the captured stage was just at the beginning of fibre kinking. Under

further loading, the kinked fibres either broke at two points forming a kink band or deflected

more without fibre fracture.

Fibre kinking has also been observed in specimen IB3-1 in the XY plane below the glass

binder yarn in the damage zone, as shown in Figure 4.25. In XY planes closer to the notch,

fibres fractured at two points and the broken fibres rotated at 45-60ºto the original fibre

direction. In XY planes further below the notch, the fibres kinked at 25-35º to the X axis

without fracture. The increase in fibre rotation within the kink band indicates further rotation

after fibre fracture, which tends to occur after the kink-band boundaries are defined(Vogler

and Kyriakides, 2001). It should be noted that this tendency is followed by initiation from

both fibre micro-buckling and fibre-kinking

Fibre buckling waves

As shown in Figure 4.29, double-peak fibre waving has been observed in slice images near

the side surface of specimen IB8-4 at step 4. These two bands with buckled fibres correspond

to the two regions where kink bands formed at the central part of the specimen as shown in

Figure 4.19 (d). The amplitude and wavelength of the two peaks were similar and the buckled

fibres were 10º to 15º to the X axis. The section of fibre between these two peaks was slightly


156

lifted by ～10 μm (the accuracy is restricted by the voxel size) but still below the peaks,

which indicates a transitional stage from fibre micro-buckling to fibre kinking. Similar

transition from micro-buckling form to kinking form of failure has also been reported by

Chung and Weitsman (1995) based on results from numerical modelling considering initial

fibre misalignment and stochastic fibre spacings.


side surface at step 4, presenting the morphology of multiple fibre buckling along one

fibre.

Although quarter-wave shaped fibre kinking and half-wave shaped fibre micro-buckling are

dominant in the samples observed, fibre micro-buckling with one entire waveform has also

been captured near the other side surface of the same specimen at the same stage as in Figure

4.29. As shown in Figure 4.30, the crest and trough of the wave are highlighted with arrows.

The amplitude of the wave was ～5 μm and the wavelength was ～145 μm. The stress field

to contain this wavy pattern was complex with a narrow kink band located to the left of the

buckled fibres and fibre shear breaks (Gutkin et al., 2010) present to the right of this fibre-


157

buckling region.


other side surface at step 4, presenting the morphology of fibre micro-buckling with an

entire waveform.

Fibre deflection constrained within splits

Fibre micro-buckling (or fibre kinking) was observed in splits in all of the material systems.

Typical examples are presented in Figure 4.31 (a) and Figure 4.32. The buckling of fibre

captured in the split region indicates the initiation of split via fibre deflection, which will be

detailed in 4.3.4.3.


158


showing fibre micro-buckling (kinking) contained within the splitting region.

Figure 4.32: X-ray μCT XZ slice images of the same position in specimen IB8-4 (notch

width 800 μm) at (a) step 3 and (b) step 4. Fibre micro-buckling (kinking) is contained

within the splitting region.


159

4.3.4.2. Fibre fracture

In CFRPs, the intrinsic compressive strengths of carbon fibres are not fully utilised due to

the fact that failure of these fibres in composites is the consequence of micro-buckling or

kinking (Hahn et al., 1986). As can be seen in Figure 4.32 (b), under further loading the split

was opened along Z direction and the buckled fibre broke due to excessive bending. With

the formation of splits, less support from the matrix is given to the fibres from the

surrounding matrix, which facilitates fibre breakage within the split. The interaction of split

and fibre breakage on a larger scale has been studied by Mukhopadhyay et al. (2015) in

cross-ply carbon fibre/epoxy laminates with embedded wrinkles, in which delamination in

90ºlayer promotes failure of buckled fibres in 0ºlayer.


showing individual fibre fracture at the notch surface due to buckling.

Figure 4.33 shows an individual fibre failure at the notch surface in specimen IB7-2 at step

1. The free surface at the notch provides less constraint on the surface fibres, thus promoting

the micro-buckling of fibres and the final fibre fracture. The fibre failure induced by fibre

micro-buckling is actually a bending failure as a result of buckling (Jumahat et al., 2010a).

It is also possible that the fibre failure observed at the surface has been caused by machining

defect while introducing the notch.


160

4.3.4.3. Splitting

The term ‘splitting’ used here refers to a crack or void formed in the composite due to either

matrix or interface failure in shear or transverse tension.

Interactions between splitting and fibre micro-buckling

As mentioned in the previous section, in sample IB7-1 and IB7-2 at step 1, the initiation of

failure was from sequential micro-buckling of fibres from the free surface of the notch. Fibre

micro-buckling is often accompanied by splitting (Allix et al., 2014; Fleck et al., 2000; Fleck

et al., 1996; Soutis and Fleck, 1990). Figure 4.34 shows three X-ray radiographs of specimen

IB7-1 taken before the scan at step 1 showing the opening of additional splits. Thin splits

following the shape of the deflected fibres took place between fibres within the strip of

buckled fibres. While at the bottom of this stripe, a thick split corresponding to the volume

under the sinusoidal wave was generated by the transverse tensile stress induced by the

buckling.

Figure 4.34: Sequential X-ray radiographs of specimen IB7-1 (notch width 800 μm) taken

before the scan at step 1 showing the opening of additional splits.

Under further loading, the buckled fibres broke at the point of maximum curvature, and the

thick split was closed due to the further rotation of the broken fibre segments and the

propagation of fibre micro-buckling ahead of it, as shown in Figure 4.20 (b). It was also

observed that when the split was located adjacent to the resin-rich region, such as the resin

pocket caused by the nesting of woven binding yarns in Figure 4.35, the split remained open


161

because the propagation of micro-buckling was arrested by the matrix. In addition, the split

located here is a proof of fibre-matrix debonding.

Figure 4.35: X-ray μCT XZ slice images of specimen IB3-1 (notch width 800 μm) at (a)

step 1 and (b) step 2 showing the interaction between fibre micro-buckling and splitting.

Resin-rich region is found to arrest the propagation of fibre microbuckling.


162

Therefore, based on the observations above, the correlation between splitting and fibre

micro-buckling can be proposed further. The splits opened due to transverse tension from

fibre micro-buckling could at a later stage be closed due to the breakage of the buckled fibres

and the propagation of fibre micro-buckling. It is expected that with a stronger interface,

splitting would be suppressed, thus providing continuous lateral constraint on fibres to delay

fibre buckling failure.

Interactions between splitting and fibre kinking

Parallelogram or half-parallelogram shaped splits have also taken place in the composite

specimens due to combined shear and transverse tensile stresses induced by fibre kinking or

the occurrence of kink bands. As mentioned before, the formation of kink bands is often

associated with shear deformation of the matrix and relative displacement across the damage

zone (Wisnom and Atkinson, 1996). The short edge of the half-parallelogram or the short

edges of the parallelogram were formed by the kinked fibres.

Parallelogram shaped splits were also observed due to the intersecting of two fibre kinking

zones. Figure 4.25 shows XY slice images of specimen IB3-1 at step 3 at different positions

along the Z direction. As can be seen in these images, in-plane fibre kinking propagated from

both the side surfaces (in the XZ plane) of the sample towards the interior of the sample.

When these two fibre kinking zones met, a split was opened due to the relative displacement

of the fibres induced by fibre rotation within the kinking region. At positions relatively closer

to the notch, the four edges of the split were defined by broken fibre segments, two of which

belong to two fibre kink bands. At positions further below the notch the fibres were heavily

bent at the edges, but not yet broken. In the previous step, no defects or features were seen

in this region of the specimen. This indicates that the split is damage instead of a

manufacturing defect. Similar features were observed by Kyriakides and Ruff (1997) in

cylindrical AS4/APC-2 composite rods compressed along the fibre direction. By sectioning

the specimen after failure the interior of the specimen was examined to discover features not

observable on the sample surface, as shown in Figure 4.36. Due to the limitation of the post-

failure study and a single micrograph, they suggested this ‘unique feature’ to be a void,


163

interacting with a propagating kink band from its top and initiating a new kink band from its

bottom. According to the in situ observation in this study, the feature defined by Kyriakides

and Ruff (1997) as a pre-existing void could correspond to an opened split.

Figure 4.36: Unique feature observed inside a failed AS4/APC-2 composite sample, which

was regarded as a manufacturing defect. (Kyriakides and Ruff, 1997)

Figure 4.37 (a) is a XZ slice image of specimen IB8-4 at step 3 and clearly shows a split

formed in a half-parallelogram shape due to the kink band located at the right tip of the split.

The fibres at the left side of the kink band were shifted along the Z direction. The lifting of

these fibres induced the opening of the long split originating from the flank of the kink band.


164

Figure 4.37: X-ray μCT XZ slice images of specimen IB8-4 (notch width 800 μm) at (a)

step 3 and (b) step 4 showing the broadening of a split originated from a kink band.

Under further loading, this split propagated inside the specimen in 3D. Figure 4.37 (b)

presents the image at the same position in the sample at step 4. It can be seen that the split

opened along the Z direction due to the development of more kink bands and the transverse

tensile stress caused by the continuing compressive load. The propagation of this split in the


165

volume was analysed by segmenting and extracting the volume representing the split in the

CT data. Figure 4.38 and Figure 4.39 display the segmented split at step 3 and step 4 from

different view angles.

As shown in Figure 4.38, the split did not propagate along Y direction. Instead, two more

splits occurred at the left and right ends of the initial split. At the left, the new split was

connected to the original split via a through-the-thickness crack. The measured thicknesses

of the material above the new split and between the two splits do not correspond to the ply

thickness of the prepreg material, which indicates these splits do not belong to delamination

damage. At the right side of the original split, a new split took place below it and the starting

point of this split almost resembled the ending point of the original split along Y axis.

Figure 4.39 shows the top view of the splits at the two steps. The length of the initial split

did not significantly increase in X direction. The damage pattern indicates the potential roles

of splits as to either arrest propagating kink bands or initiate new kink bands.

Figure 4.38: Side view of the segmented and extracted splits in specimen IB8-4 (notch

width 800 μm) at step 3 and step 4.


166

Figure 4.39: Top view of the segmented and extracted splits in specimen IB8-4 (notch

width 800 μm) at step 3 and step 4.

4.3.4.4. Through-the-thickness cracks

Due to the limitation of 2D characterisation techniques, previous studies in literatures were

focused on the plane where the kink bands were located. Using X-ray CT, the information

in the plane perpendicular to the fibre direction can also be investigated in order to fully

understand the evolution of different damage mechanisms.

Looking through the YZ plane (transverse to the fibre direction) at different steps reveals

that transverse cracks through the thickness direction can only form at the later stage of the

failure process. This trend was observed in all the material systems. Figure 4.40 shows an

example of the same YZ slice image in specimen IB8-4 at step 3 and 4, where the cracks

developed at step 4.


167

Figure 4.40: X-ray μCT YZ slice images of specimen IB8-4 (notch width 800 μm) at (a)

step 3 and (b) step 4 showing through-the-thickness cracks.


168

4.3.5. Kink bands

From the observed sequence of damage events it is clear that kink-band formation is a post-

buckling event, as has been proposed based on modelling results by Vogler and Kyriakides

(2001). The formation of kink bands is the ultimate damage pattern leading to the failure of

UD fibre composites under compressive load. The morphology of kink bands has been a

major concern in experimental studies in this area. In this section, various morphologies of

kink bands are presented.

4.3.5.1. Kink bands at different stages

Although all the CFRP composites examined failed by fibre micro-buckling or fibre kinking,

different morphologies of kink bands could be identified for different material systems.

As can be seen in the X-ray CT slice images, kink bands at different stages have been

captured at different locations in the specimen at the same loading step; including kink bands

with unbroken fibres at both boundaries (initiation stage), broken fibres at one boundary

(transient stage) and broken fibres at both boundaries (final stage).

The stage of kink bands is addressed by the state of the fibres along the boundaries of the

band. Hahn et al. (1986) suggested that in the localised fibre micro-buckling region, fibres

undergo elastic micro-buckling followed by matrix plastic yielding, which eventually results

in fibre breakage forming boundaries.

4.3.5.2. Kink bands with parallel and non-parallel boundaries

As can be seen in all the samples, kink bands can be categorised into two types when

considering the kink-band boundaries: kink bands with parallel boundaries and kink bands

with non-paralleled boundaries. The variation in kink-band morphology can be attributed to

the difference in initiating mechanism.

It has been observed that the boundaries of kink bands caused by fibre kinking tend to be

parallel, thus resulting in uniform kink-band width across the band. As shown in Figure 4.41,


169

fibres break at the two maximum bending points due to fibre compressive failure

accompanied by shear. At the two ends of the rotated fibre segment, the angles between the

fibre within the band and outside the band are identical, thus the two cracks that coalesced

from fibre fracture surfaces are parallel with each other. However, the two boundaries may

not develop evenly, resulting in fibre breakage at one bending point prior to the fracture at

the other bending point. The asymmetric stress state at fibre level might be one of the causes

(Pimenta, 2008).

Figure 4.41: Schematic diagram of fibre fracture due to fibre kinking, forming parallel-

boundary kink bands.

Alternatively, the boundaries of kink bands produced by fibre micro-buckling may not be

parallel with each other. The kink-band width defined by the length of broken fibres changes

gradually along the propagating direction. Figure 4.42 demonstrates the sequential fracture

of fibres by fibre micro-buckling. The first breakage occurs at the maximum bending point

due to primary buckling. Under further compressive loading along the fibre direction, fibres

break at the secondary maximum bending point, forming a kink band. The cracks formed by

fibre breakage are the central lines of the buckling peaks. It is clearly shown that the initial

boundary is perpendicular to the fibre direction, while the secondary boundary is angled at

approximately half of the fibre rotation angle within the band.

In both cases, the fibre broke at two points with an interval of quarter-wavelength. Berbinau

et al. (1999b) proposed an analytical model predicting that the fibre micro-buckling half-

wavelength is equal to the kink-band width, which was also assumed by several other authors

(Guz, 1989; Jumahat et al., 2010a; Steif, 1990). However, in the current study, kink band

width should approximately equal quarter-wavelength of the buckling wave.


170

Figure 4.42: Schematic diagram of progressive fibre fracture due to fibre micro-buckling,

forming kink bands with non-parallel boundaries.

4.3.5.3. In-plane and out-of-plane kink bands

Fibres can either buckle in-plane within the ply (XY plane) or out-of-plane through the

thickness direction (XZ plane). As the buckling orientation of fibres sets the orientation of

kink bands, kink bands can be categorised into in-plane and out-of-plane kink bands. Out-

of-plane kink bands refer to the kink bands in which the global deformation of fibres is

perpendicular to the ply plane (Berbinau, 1997).

Both in-plane and out-of-plane kink bands have developed in the material systems tested in

this chapter. The tendency for the formation of in-plane or out-of-plane kink bands depends

on the extent of constraint on fibres in the width and thickness direction (Sivashanker et al.,

1996). If fibres are less supported by surrounding matrix and fibres within a certain plane,

fibres tend to buckle forming kink bands within the plane. The specimens tested in this

chapter are all approximately 4 mm thick and 2 mm wide. However, at the notched region,

the remaining thickness was ≈ 2 mm, similar to the width. Thus, it is difficult to determine

the preferable kinking plane from the difference in the amount of materials in X and Y

directions (Pinho et al., 2012).

As the notch was made with a cutting wheel, some of the fibres at the notch surface might

be broken due to machining. There was a tendency for fibres near the notch surface to buckle

out-of-plane towards the notch, as can be seen in Figure 4.33 where a single fibre buckled

out-of-plane and broke at the early loading stage. It is noted that below the stripe of fibres


171

buckled out-of-plane adjacent to the notch surface, in-plane fibre micro-buckling or kinking

tends to occur. This indicates that in this region the plies near the notch surface hinder the

rotation of fibres out-of-plane, thus it is energetically more favourable for fibre buckling to

propagate through the width direction to form in-plane kink bands. It is noted that the sharp

transition from out-of-plane to in-plane fibre buckling occurs within a small volume.

It is generally accepted that in CFRPs the preferred mode of failure is out-of-plane and the

development of an in-plane microbuckle appears to be sensitive to the initiation conditions

(Pinho et al., 2012; Sivashanker et al., 1996; Sutcliffe and Fleck, 1994). When the surfaces

of the plate specimens are constrained, in-plane kink bands can be generated as the major

mode. In the present study, both in-plane kink bands originating from the specimen side

surface and out-of-plane kink bands originating from the notch surface have been observed

at the early stage of failure. This indicates that lateral constraint is the major factor

determining the orientation of kinking plane.

4.3.5.4. Kink-band geometry

It is unreliable to characterise the geometry of kink bands that have not been fully developed,

as the boundaries cannot be accurately determined. Therefore, here, we discuss the geometry

of fully developed kink bands, for which the boundaries are formed by fibre breaks. As

discussed in the paragraphs above, the kink bands can be either in-plane or out-of-plane and

either with parallel boundaries or with non-paralleled boundaries.

The comparison of these parameters for kink bands in different stages reveals that the kink-

band geometry barely changes during propagation once it forms, which has also been

observed by Vogler and Kyriakides (2001) in AS4 carbon fibre/PEEK system. It should be

noted that for kink bands with non-parallel boundaries the band width varies along the

boundary, resulting in a broader range of width. In addition, the increase in Ф and decrease

in β due to crushing after the fully development of kink bands are considered as post-failure

deformation, which is not associated with the kinking mechanism. The geometrical

parameters of the various kink bands in different specimens are listed in Table 4.6. All of


172

these values were measured through the volume of the samples at the loaded state. Here, β

is in reference to the Z axis for out-of-plane kink bands and to the Y axis for the in-plane

kink bands.

Table 4.6: Summary of the kink-band geometry observed in all the material systems within

the field of view.

Specimen IB8-4 IB7-1 IB7-2 IB3-1

OK P ω (μm) 15-30 - - -

Ф 45-60º - - -

β 20-35º - - -

NP ω (μm) 15-115 60-150 80-150 60-130

Ф 30-50º 45-60º 45-70º 40-50º

β 0-20º 0-35º 0-20º 0-30º

IK P ω (μm) - - 40-50 40-90

Ф - - 40-45º 45-75º

β - - 0-10º 20-30º

NP ω (μm) - 40-350 40-100 60-120

Ф - 40-55º 40-45º 45-55º

β - 0-25º 0-25º 10-30º

OK – out-of-plane kink band

IK – in-plane kink band

P – kink band with parallel boundaries

NP – kink band with non-parallel boundaries


173

Not all types of kink bands mentioned above have been formed in a single specimen. In

specimen IB8-4, out-of-plane kink bands dominate, while in other samples in-plane kink

bands have also developed following the out-of-plane bands. The B8 laminate was

manufactured from prepregs (fibres were impregnated in the ply plane prior to lay-up),

which may lead to different fibre arrangements within the ply plane and in the through-the-

thickness direction. In the T700/epoxy system, the formation of non-parallel-boundary kink

bands due to the buckling failure of fibres is the principle damage mode. Only one in-plane

parallel-boundary kink band has formed in the IB7-2 specimen within several XY slice

images. In general, the individual parallel-boundary kink band is narrower than the non-

parallel band. The kink-band angle is less than 35º in all the composite samples, while the

fibre rotation angle varies, lying between 30º and 75º.

4.3.5.5. Multiple kink bands

Both in-plane and out-of-plane multiple kink bands have been observed in the samples failed

under 4PB load. The morphology of multiple kink bands observed here is similar to the

observation in the samples failed under axial compression as discussed in Chapter 3.

However, the 3D evolution of multiple kink bands has not been observed in the axial

compression experiments due to the catastrophic nature of failure. It is generally accepted

that the formation of multiple kink bands is caused by the broadening of the kinking region

along the fibre direction (axial propagation) after the propagation along the band boundary

(lateral propagation) (Fleck et al., 1996; Kumar et al., 2005; Sivashanker et al., 1996; Vogler

and Kyriakides, 2001; Vogler and Kyriakides, 1997; 1999).


174


175

Figure 4.43: Sequential X-ray radiographs of specimen IB8-4 (notch width 800 μm) after

loading to step 4 showing the sequential adding of narrow kink bands resulting in the

morphology of multiple kink bands.

Axial propagation (band broadening)

Although the axial propagation of kink bands was significantly slower in 4PB tests, it was

still not feasible to capture the detailed sequential development of multiple kink bands in 3D

CT datasets, the scanning time of which was 8 hours each. However, radiographs with short

exposure time can provide useful information to explain the sequence of events. As shown

in Figure 4.43, the evolution of multiple kink bands has been captured in radiographs of

sample IB8-4 taken after loading to step 4 to wait for the load to be stable before taking the

3D dataset. It is found that the narrow kink band on the right is the primary kink band while

the other narrow kinks and the wide kink zone are secondary ones. It can be seen that during

the broadening process, the boundaries of the primary kink band did not significantly

propagate along the boundary orientation in the XZ plane. The kink-band boundary

orientation was also found to be maintained during the axial propagation.


176

Figure 4.44: X-ray μCT XZ slice images of the same location in specimen IB8-4 (notch

width 800 μm) at step 3 (a), step 4 (b) and after unloading (c). The fibre rotation angle,

band-boundary angle and band width of the primary kink band are all kept the same once

formed. The fibre rotation angle is reduced after unloading, while the boundary angle is

maintained.

Figure 4.45: Schematic diagram illustrating the segmented kink bands with two distinct

band boundaries defined by fibre breaks.

Figure 4.44 (a) and (b) show the close XZ slice view of the region with multiple kink bands

in datasets obtained at step 3 and step 4. In highlighted region A, the broken fibres in each


177

individual band were aligned with the rotated fibres in the primary kink band. While in

highlighted region B, the fibres broke but not fully conformed to the deformation in the

primary kink bands. It can be inferred that the fibre rotation angle at the moment when the

fibre breaks due to bending is less than the final fibre rotation angle within the kink band,

thus further rotation takes place after the bending fracture of the fibres in the new band to

align with fibres in the primary kink band. This observation is in accordance with the ‘bend-

break-rotate’ mechanism proposed by Vogler and Kyriakides (1997). Three individual

narrow bands (numbered 1, 2 and 3 in Figure 4.45), each of which is between 15 to 25 µm

(~3-5df) wide, have developed within the wide band. The individual band-width is between

45 to 75 µm (~9-15df) for kink band 4, and between 100 to 115 µm (~20-23df) for kink band

5 (see Figure 4.45). The individual kink-band width ranges wider than the theoretical

prediction of 10-15df (Fleck et al., 1995). In addition, the narrow kink bands forming the

morphology of multiple kink bands possess shorter broken fibre segments than those in

previous observations which range from 5 to 20df (Kumar et al., 2005; Sivashanker et al.,

1996; Vogler and Kyriakides, 1997). This may be caused by the difference in the material

system, the loading conditions and the local stress distribution.

Transverse propagation

As shown in Figure 4.46, the 3D visualisation of the kinking volume enables the

understanding of the kink band propagation transverse to the kinking plane (through the

width of the specimen). The information of this dimension has not been considered before

in 2D kink-band propagation studies, as only the details of the propagation in the kinking

plane can be observed. Here the propagation in this dimension is termed the transverse

propagation in order to distinguish from the lateral propagation and axial propagation

discussed in 2D studies. The transverse propagation direction of the kink band was along the

Y direction from the origin of the axes. The width of the kink band, which is the width of

the strips in Figure 4.46 (b), remained the same as it propagated transversely.


178

3D arrangement of multiple kink bands

Figure 4.47 shows the extracted volumes of the five kink bands illustrated in Figure 4.45,

each of which is assigned a different colour. The morphology and relative position of the

kink bands are clearly visualised. The width and length of kink band 2 and kink band 3 are

almost the same. The transverse propagation of kink band 4 is further than that of kink band

2 and 3, and the propagation is arrested where kink band 1 laterally propagates.


179

Figure 4.46: Two views of the extracted volumes of the primary kink band in specimen

IB8-4 (notch width 800 μm) at step 3 and 4 demonstrating the propagation in 3D.

Figure 4.47: Extracted volumes of the five fully developed individual kink bands in

specimen IB8-4 (notch width 800 μm) at step 4 as illustrated in Figure 4.45. The kink

bands are shown in different colours.


180

4.3.5.6. Conjugate kink bands

In laterally confined specimens, the formation of a kink band could be followed by the

development of conjugate kink band in order to release the stresses induced by the lateral

displacement (Kyriakides et al., 1995; Pimenta, 2008; Schultheisz and Waas, 1996). As the

specimen cannot deform to accommodate fibre rotation within the initial kink band, a

conjugate kink band with fibres rotated in the opposite direction is then developed.

Figure 4.48: Schematic diagram of conjugating kink bands: (a) π-shaped and (b) zigzag

shaped.

As shown in Figure 4.43 (c), in specimen IB8-4 the conjugate kink bands have developed at

the left of the split after the formation of the multiple kink bands from the right notch corner.

The formation of multiple kink bands has also been observed in the conjugate kink bands

below the left tip of the split. As the sample has been restrained at the four loading rollers in

the Z direction, the large displacement in Z direction induced by the primary kink needs to

be accommodated, resulting in the formation of the conjugate kink band. This can be

evidenced by the observation that along with the formation of the conjugate kink bands, the

fibres in between the primary and conjugate kink zones have been realigned along the X

direction with the uplifting of the wedge volume. Figure 4.48 (a) shows the schematic

diagram of this type of π-shaped conjugate kink bands.


181

Conjugate kink bands forming a zigzag shape have been observed in specimens IB7-1 and

IB3-1. The zigzag shaped kink bands are formed due to the progressive fibre buckling failure

propagated along the fibre under continuous compressive load. The conjugating kink bands

are bordering each other, and the fibre rotation within two adjacent kink bands is opposite.

The boundaries tend to be rotated to perpendicular to the fibre axis under further loading, as

shown in Figure 4.24 (c). Figure 4.48 (b) shows the schematic diagram of the zigzag-shaped

conjugate kink bands.

4.3.6. Effect of material system on the initial bucking location

As discussed earlier, fibre micro-buckling from the notch surface is the incipient damage

mode observed in all the material systems, and the distance between the buckling peak and

the closest side surface of the notch is found to be consistent through the volume of the

specimen. Table 4.7 summarises the measured values demonstrating the buckling peak

position. Comparing the values for specimen IB7-1 and IB7-2 shows that this value in the

T700/epoxy system is relatively larger and not sensitive to the variation in notch width,

indicating the important role of material system on the buckling behaviour instead of the

notch geometry. In these two specimens, only one buckling wave has formed in the notched

region, while in specimens IB8-4 and IB3-1, with buckling peak closer to notch corner, two

buckling waves have formed near both notch corners. The position of the peak is closely

related to the buckling wavelength of the fibre, as the notch side surface acts as one end point

of the buckled section in the fix-end Euler buckling mode. Analytical and experimental

results denote that buckling wavelength is related to factors including fibre diameter and the

ratio between fibre and matrix modulus (Hahn et al., 1986), which would then affect the

number of buckling waves contained within a certain notch width.

Table 4.7: The distance between buckling peak and notch side surface in different

specimens.

Specimen IB8-4 IB7-1 IB7-2 IB3-1

Mean distance between buckling

peak to notch side surface (µm)

58.3 148.8 158.4 97.9


182

4.3.7. Effect of unloading on damage morphology

Until recently samples had to be either examined at the surface (lack of constraint) or after

removal from the loading device. As both elastic and plastic deformation occur during kink

band formation (Pimenta, 2008), one might expect that damage morphology will change

when load is removed from the specimen. The comparison of deformation under load and

after unloading can reveal the effect of unloading on the damage morphology associated

with kink-band formation.

Comparison between the final dataset obtained under load and the dataset taken after

unloading shows that the kink-band boundary angle and kink-band width tend to remain

unchanged by unloading, while the fibre rotation angle within the kink band tends to be

reduced by 10-20°. Figure 4.34 (b) and (c) represent a typical example of the kink-band

morphology before and after unloading. The recovery of fibre rotation within the kink bands

is evident, which is accompanied with the narrowing of the wide split adjacent to the kink

bands.

The recovery of fibre rotation can also occur in unbroken fibres, with the minimum radius

of curvature increased from ～130 μm to ～300 μm in specimen IB7-1. Figure 4.49 presents

the same slice image as that in Figure 4.29 from specimen IB8-4. The buckled fibres were

straightened when the load was removed (Sutcliffe and Fleck, 1994), and a split was opened

at the tip of the narrow kink band, which was located below the original fibre micro-buckling

region. It indicates that some of the splits observed in the post-failure studies might have

been opened due to the unloading process instead of being associated with the development

of kink bands.

Not only can the fibre rotation within the kinking plane be largely reduced, the recovery of

fibre rotation out of the kinking plane is also brought about by unloading, as shown in the

white box in Figure 4.49. Detailed examination of the fibres in this region at step 4 reveals

that the fibres are not lying in any of the three orthogonal planes (XY, XZ and YZ planes).

However, after unloading the fibres appear to lie almost in the XZ plane. In previous studies,


183

most of the kink bands were found to be lying either in-plane or out-of-plane, which

rationalised the 2D characterisation of kink bands. However, the formation of kink bands is

actually a 3D phenomenon, thus it is essential to carry out work on fibre micro-buckling and

kink bands in 4D if the objective is to better understand how a kink band is developed.

Figure 4.49: X-ray μCT XZ slice image of specimen IB8-4 near the side surface after

unloading. The two regions exhibiting the straightening of buckled fibres are highlighted in

red boxes. The white box demonstrates the region in which the rotation of fibres out of the

XZ plane is released.

4.3.8. Sequence of events leading to failure

Generally, the failure process in all specimens follow the same trend. The failure process of

UD CFRP under compressive load generated by bending moment is proposed as follows:


184

1. As the compressive load along the fibre direction is increased, the fibres with the

least lateral constraint (because of the free surface at the notch surface or specimen

side surface) will buckle. The micro-buckling of one fibre will result in a tensile

stress between the buckled fibre and adjacent straight fibre, which contributes to the

micro-buckling of the straight fibre at a lower stress. Splits will be opened by the

tensile stress during the propagation of fibre micro-buckling, which reduces lateral

support to the fibres, facilitating the propagation of fibre micro-buckling. The

fracture of the buckled fibres due to excessive buckling leads to the formation of kink

bands with non-parallel boundaries.

2. Following the development of non-parallel-boundary kink bands into the interior of

the sample, the fibre rotation orientation abruptly changes from out-of-plane to in-

plane. Parallel-boundary kink bands from fibre kinking and non-parallel-boundary

kink bands from fibre micro-buckling can both develop in-plane.

3. Due to the shape of the notch, the kinking zone observed here might not be localised

at one site as observed in samples under direct axial compressive loading. Kink bands

can develop away from the initial kinking region with the formation of an elongated

split along the fibre direction connecting the two regions of kink bands.

4.4. Conclusions

The use of a notched beam specimen geometry under FBP load in this work enables a better

understanding of the compressive failure mechanisms in UD composites to be built up,

because failure of the composite samples is well contained so that the failure process can be

monitored during loading as it progresses stably.

The deceleration of the evolution of kink bands in UD composites was achieved by

modifying the specimen geometry and loading configuration. The observations confirmed

the need to employ 3D characterisation technique such as the X-ray CT in the study on kink


185

bands, as both in-plane and out-of-plane kink bands can occur in the same composite sample.

The buckling of fibre is also found to be a 3D phenomenon.

The main findings are summarised as follows:

Splitting and fibre micro-buckling from the notch surface are the incipient damage

mechanism;

Both fibre micro-buckling and fibre kinking, with splitting, can occur at the onset of

kink bands; fibre micro-buckling leads to non-parallel-boundary kink bands and fibre

kinking leads to parallel-boundary kink bands;

Splits can be formed due to the transverse tensile stress induced by fibre micro-buckling

or the combined shear and transverse tensile stress induced by fibre kinking. The

formation of splits reduce the lateral constraint on fibres, thus promoting fibre buckling.

It is expected that with a stronger interface, splitting would be suppressed, thus

providing continuous lateral constraint on fibres to delay fibre buckling failure;

Through-the-thickness cracks are formed at the later stage of the failure process;

Propagation of kink bands is a 3D phenomenon, including lateral propagation, axial

propagation and transverse propagation;

The evolution of multiple kink bands has been captured in sequential radiographs. The

broadening of the primary kink band is by the ‘bend-break-rotate’ mechanism (Vogler

and Kyriakides, 1997). The morphology of multiple kink bands is a result of band

broadening;

Conjugating kink bands with fibres rotated in the opposite directions have been observed,

and they can be categorised into two types according to the relative position.

The location of the peak of the incipient buckling wave is found to vary in different

material systems; while notch width has little effect on the buckling wavelength of fibres

in the same composite;


186

The unloading process changes the damage morphology, which verifies the need to

characterise the compressive failure under load.

General sequence of events leading to failure is proposed based on observations.

Overall, the time-lapse X-ray CT study presented in this chapter is, to the best of the author’s

knowledge, the first detailed observation of the nucleation and growth of kink bands in 3D.

The understanding of the initiation and propagation of kink bands in 3D will provide

insightful contribution to the future establishment of strategies to improve the predictability

of the compressive properties of FRPs.

Chapter 5 Conclusions and future work

187

5. Conclusions and future work

5.1. Conclusions

The aims of this PhD thesis, as outlined in Chapter 1, were:

To map the 3D morphology and distribution of damage mechanisms in the kink zone

developed in the compressive failure of UD carbon fibre/epoxy composite;

To understand the evolution of kink bands in UD carbon fibre/epoxy composite via

ultra-fast synchrotron radioscopic imaging to observe catastrophic kink-band formation

in real time and via stabilising the kink-band formation process to enable progressive

damage propagation for lab-based interrupted in situ X-ray CT imaging;

To establish the relationship between damage mechanisms associated with the

formation of kink bands and propose sequence of events leading to failure.

The work presented in this thesis has significantly advanced the understanding of kink bands

formed in the compressive failure of UD carbon fibre/epoxy composites via experimental

observation by X-ray CT. Not only the 3D morphology of kink bands and the associated

damage mechanisms have been visualised, but also the evolution and interaction of damage

mechanisms leading to the formation of kink bands have been established based on time-

lapse X-ray CT results. The main outputs and conclusions of this project are summarised in

the following section.

In Chapter 3, with the aim to generate kink bands within the limited view of X-ray μCT, a

miniature waisted-rod shaped UD CFRP sample geometry was designed for post mortem

studies. Further modification by adding a circular notch around the circumference of the rod

sample was made for in situ experiments to predetermine the failure onset site. The samples

were axially compressed along the fibre direction. A new small-scale resin infusion

manufacturing method was developed to fabricate high-quality miniature UD carbon

fibre/epoxy rods for this study. Post-failure SEM on sample fracture surface validated the

formation of kink bands by this test method and indicated fibre failure by the buckling


188

mechanism.

In the post mortem X-ray CT study, damage morphology was visualised in 3D by

segmenting out cracks in the damage zone, focusing on the fibre breaks at kink-band

boundaries and representative longitudinal splits. Several findings have been proposed

regarding the 3D geometry of damage associated with kink bands. Matrix micro-cracks were

located connecting to splits in sequential kinking planes inside the sample, indicating the

coalescence of micro-cracks into splits. In 3D, splits formed curved planes, the shape of

which varied with distance from the specimen surface. Multiple kink bands (consisting of 6

individual kink bands) occurred within the damage zone and the boundary planes of the wide

kink band propagated to a larger extent than that of the narrow kink bands. The kink-band

boundaries were essentially planar (with slight bending) being inclined at ～25° to the

horizontal direction. Examining multiple 2D slice images of the kinking planes (in which

kink bands lie), it is found that the geometry of each fully developed kink band was

consistent through the specimen along the normal of the kinking plane. The geometric

parameters of the kink bands measured in the kinking planes were: ω ≈ 20-320 μm (3-45 df),

β ≈ 11-40° and Φ (φ+φo) ≈ 18-52°, similar to experimental observations in other CFRPs (see

section 2.4.1).

In situ X-ray μCT experiments were performed by loading samples in in situ loading rigs

that could be accommodated within the CT machines. Unsurprisingly, interrupted in situ

tomography on lab-based CT machine was too slow to capture the sudden and catastrophic

damage evolution in carbon fibre/epoxy composite under axial compression. Using ultra-

fast synchrotron imaging (10,000 frames per second), the initiation and full propagation of

kink bands (across the specimen) were found to occur in less than 1.2 ms. However, the

scenario of kink-band failure could be proposed based on multiple radiographs: fibre

buckling and splits occurred before fibres broke to form kink-band boundaries and

eventually the morphology of multiple kink bands was developed suddenly. The initiation

stage with fibre buckling and longitudinal splitting developed prior fibre fracture was less

than 0.2 ms. The kink band boundary defined by fibre fracture then propagated across the

entire sample in less than 1 ms, significantly less than that reported in literatures. Therefore,


189

a lower bound of the kink propagation velocity could be estimated from the radiographs,

which was 1.5 m/s.

Even though ultra-fast imaging as fast as 22 tomographs (461 frames each) per second was

achieved as mentioned above, volumes showing the progressive evolution of kink bands

under compression could still not be captured in 3D. A detailed picture of the microstructural

changes that precede and accompany kink-band formation could not be inferred from these

studies on axial compressive failure. Therefore, in Chapter 4 the aim of the study was to

extend the 3D study to a time-lapse 4D monitoring of the more stable and therefore more

progressive damage evolution inside the composite. A testing method of loading notched

UD carbon fibre/epoxy beam specimen using a FPB fixture was developed in this work, in

which kink bands were generated at a significantly slower speed. The initiation and

propagation of kink bands inside the composite samples were well contained so that the

failure process was successfully monitored under incrementally increased displacement.

Three different carbon fibre (T800, T700 and T300)/epoxy composite systems were tested

to obtain a generalised understanding of the evolution of kink bands in CFRPs.

Fibre micro-buckling, accompanied by splitting, from the notch surface was found to be the

incipient damage mechanism, followed by fibre breakage under bending and the formation

of kink bands with non-parallel boundaries. The initial fibre buckling wavelength varied in

different composite materials, and this value was not sensitive to notch width. The maximum

curvature of unbroken fibres prior to fracture in the loaded T700/epoxy beam (step1) (radius

of curvature ～130 μm) was found to be significantly larger than that in the post-failure

T700/epoxy rod specimen (radius of curvature ～280 μm). Fibre kinking (associated with

lateral displacement across the kinking region) could also occur at the onset of kink-band

formation, giving rise to kink bands with parallel boundaries. Splits could be formed due to

the transverse tensile stress induced by fibre micro-buckling or the combined shear and

transverse tensile stress induced by fibre kinking. The presence of splitting would promote

further fibre rotation leading to fibre fracture. Lateral constraint conferred by strong

interfaces is expected to be a key factor delaying kink-band formation. Moreover, in

T800/epoxy composite out-of-plane kink bands dominated, while in T700/epoxy and


190

T300/epoxy systems in-plane kink bands also developed following the out-of-plane bands.

The kink-band geometrical parameters for different types of kink bands were summarised

(see Table 4.6). In general, the individual parallel-boundary kink band was narrower than

the non-parallel-boundary kink band. The kink-band angle was less than 35º in all the

composite samples, while the fibre rotation angle varied from 30º to 75º.

The evolution of multiple kink bands was captured in sequential radiographs. The

broadening of the primary kink band was by the ‘bend-break-rotate’ mechanism (Vogler and

Kyriakides, 1997). The morphology of multiple kink bands was confirmed experimentally

to be a result of band broadening. The geometry of the primary kink band was observed to

be consistent during propagation. Conjugating kink bands with fibres rotated in the opposite

directions were formed following the primary set of kink bands.

By scanning failed specimens after unloading, it was confirmed that the damage morphology

across the sample was affected by the unloading process, which verified the need to

characterise the compressive failure under load. The recovery of fibre rotation was between

10º to 20º. The observations also confirmed the need to employ 3D characterisation

technique such as the X-ray CT in the study on kink bands, as both in-plane and out-of-plane

kink bands could occur at different regions in the same composite sample. The buckling of

fibre was also observed to be a 3D phenomenon.

Overall, the X-ray CT study on kink bands presented in this thesis is, to the best of the

author’s knowledge, the first detailed observation of the morphology and evolution of kink

bands in 3D. This work could also provide ideas for further work on improving the accuracy

of analytical and numerical models predicting compressive failure of FRPs.


191

5.2. Future work

As the synchrotron radioscopic imaging technique is advancing rapidly, in the near

future the acquisition speed could be even faster, enabling a more detailed monitoring

of kink-band formation. The design of specimen geometry and loading configuration

promoting in-plane kink bands could also be explored, so that the damage evolution

could be monitored with ultra-fast X-ray radiography.

The effect of manufacturing defects, such as fibre waviness and voids, on the onset

location and propagation path of kink bands in UD CFRPs could be explored by

intentionally adding various defects to the composite specimens. The deformation of the

defected region of interest could be monitored by in situ X-ray CT to reveal the

sensitivity of kink-band formation to defects. Tracing the deflection of individual fibre

is challenging in CFRP CT data due to the poor contrast between fibres and matrix. The

development of accurate automatic fibre tracing software will be very helpful.

A systematic study of CFRPs with various types of matrices or fibres could be

performed to better understand the relationships between material properties (matrix

shear property, interfacial strength and fibre bending stiffness etc.) and the kink-banding

behaviour. Providing experimental parameters for establishing analytical models to

better predict the kinking stress and kink-band geometry as a function of material

property.

Glass fibre reinforced polymer composites can be a better material system to study the

kinking mechanism, as the contrast between glass fibre and the polymer matrix is largely

better than that in CFRPs under X-ray beam. In addition, the diameter of glass fibre is

often larger. Therefore, the tracing of single glass fibre in CT data is supposed to be

more feasible and the kink banding process in GFRP could be studied by X-ray CT.

Other than the static compressive loading condition considered in this thesis, kink-band

formation has also been observed in composites failed under cyclic compression-

compression fatigue. It would be helpful to understand the effect of cyclic loading on


192

kink-band formation, such as the critical number or geometry of kink bands developed

to cause structure failure, thus the fatigue life can be better predicted. X-ray CT would

also be the most suitable characterisation technique for this issue.

References

193

References

ASTM D3171. Standard Test Methods for Constituent Content of Composite Materials.

ASTM D3410. Standard Test Method for Compressive Properties of Polymer Matrix

Composite Materials with Unsupported Gage Section by Shear Loading.

ASTM D6641. Standard Test Method for Compressive Properties of Polymer Matrix

Composite Materials Using a Combined Loading Compression (CLC) Test Fixture.

ASTM D695. Standard Test Method for Compressive Properties of Rigid Plastics.

Adams, D. O. and Hyer, M. W. 1994. Effects of layer waviness on the compression response

of laminates. ASTM Special Technical Publication, 1185, 65-6.

Ahn, J. and Waas, A. 1999. Finite Element Model for Compressive Failure of Notched

Uniply Composite Laminates under Remote Biaxial Loads. ASME Journal of Engineering

Materials and Technology, 121, 001-007.

Allix, O., Feld, N., Baranger, E., Guimard, J.-M. and Ha-Minh, C. 2014. The compressive

behaviour of composites including fiber kinking: modelling across the scales. Meccanica,

49 (11), 2571-2586.

Anderson, T. B. 1974. The relationship between kink–bands and shear fractures in the

experimental deformation of slate. Journal of the Geological Society, 130 (4), 367-382.

Argon, A. S. 1972. Fracture of composites. Treatise on materials science and technology, 1,

79-114.

Aroush, D. R. B., Maire, E., Gauthier, C., Youssef, S., Cloetens, P. and Wagner, H. 2006. A

study of fracture of unidirectional composites using in situ high-resolution synchrotron X-

ray microtomography. Composites science and technology, 66 (10), 1348-1353.

Arshad, M. 2014. Damage tolerance of 3D woven composites with weft binders. PhD thesis,

The University of Manchester.

Babcsán, N., Moreno, F. G. and Banhart, J. 2007. Metal foams—High temperature colloids:

Part II: In situ analysis of metal foams. Colloids and Surfaces A: Physicochemical and

Engineering Aspects, 309 (1), 254-263.

Baley, C. 2004. Influence of kink bands on the tensile strength of flax fibers. Journal of

materials science, 39 (1), 331-334.

Baruchel, J., Buffiere, J. Y. and Maire, E. 2000. X-ray tomography in material science.

Hermes Science Publications, Paris.

References

194

Bazhenov, S. and Kozey, V. 1991. Compression fracture of unidirectional carbon fibre-

reinforced plastics. Journal of materials science, 26 (24), 6764-6776.

Bazhenov, S., Kuperman, A., Zelenskii, E. and Berlin, A. 1992. Compression failure of

unidirectional glass-fibre-reinforced plastics. Composites science and technology, 45 (3),

201-208.

Benabou, L. 2010. Predictions of compressive strength and kink band orientation for wood

species. Mechanics of Materials, 42 (3), 335-343.

Berbinau, P., Soutis, C., Goutas, P. and Curtis, P. 1999a. Effect of off-axis ply orientation

on 0-fibre microbuckling. Composites Part A: Applied Science and Manufacturing, 30 (10),

1197-1207.

Berbinau, P., Soutis, C. and Guz, I. 1999b. Compressive failure of 0º unidirectional carbon-

fibre-reinforced plastic (CFRP) laminates by fibre microbuckling. Composites Science and

technology, 59 (9), 1451-1455.

Berbinau, P. J. 1997. A study of compression loading of composite laminates.PhD thesis,

Oregon State University.

Boh, J. W., Louca, L. A., Choo, Y. S. and Mouring, S. E. 2005. Damage modelling of

SCRIMP woven roving laminated beams subjected to transverse shear. Composites Part B:

Engineering, 36 (5), 427-438.

Brooks, R. A. and Di Chiro, G. 1976. Beam hardening in x-ray reconstructive tomography.

Physics in medicine and biology, 21 (3), 390.

Budiansky, B. 1983. Micromechanics. Computers & Structures, 16 (1), 3-12.

Budiansky, B., Fleck, N. and Amazigo, J. 1998. On kink-band propagation in fiber

composites. Journal of the Mechanics and Physics of Solids, 46 (9), 1637-1653.

Budiansky, B. and Fleck, N. A. 1993. Compressive failure of fibre composites. Journal of

the Mechanics and Physics of Solids, 41 (1), 183-211.

Buffiere, J. Y., Maire, E., Adrien, J., Masse, J. P. and Boller, E. 2010. In situ experiments

with X ray tomography: an attractive tool for experimental mechanics. Experimental

mechanics, 50 (3), 289-305.

Bull, D., Spearing, S. and Sinclair, I. 2014. Observations of damage development from

compression-after-impact experiments using ex situ micro-focus computed tomography.

Composites Science and Technology, 97, 106-114.

Bull, D. J., Helfen, L., Sinclair, I., Spearing, S. M. and Baumbach, T. 2013a. A comparison

of multi-scale 3D X-ray tomographic inspection techniques for assessing carbon fibre

References

195

composite impact damage. Composites Science and Technology, 75, 55-61.

Bull, D. J., Sinclair, I. and Spearing, S. M. 2013b. Partial volume correction for

approximating crack opening displacements in CFRP material obtained from micro-focus

X-ray CT scans. Composites Science and Technology, 81, 9-16.

Bull, D. J., Spearing, S. M., Sinclair, I. and Helfen, L. 2013c. Three-dimensional assessment

of low velocity impact damage in particle toughened composite laminates using micro-focus

X-ray computed tomography and synchrotron radiation laminography. Composites Part A:

Applied Science and Manufacturing, 52, 62-69.

Campbell, D. and Maji, A. 2006. Failure mechanisms and deployment accuracy of elastic-

memory composites. Journal of Aerospace Engineering, 19 (3), 184-193.

Chaplin, C. 1977. Compressive fracture in undirectional glass-reinforced plastics. Journal

of Materials Science, 12 (2), 347-352.

Chung, I. and Weitsman, Y. 1995. On the buckling/kinking compressive failure of fibrous

composites. International journal of solids and structures, 32 (16), 2329-2344.

Cloetens, P., Barrett, R., Baruchel, J., Guigay, J. P. and Schlenker, M. 1996. Phase objects

in synchrotron radiation hard x-ray imaging. Journal of Physics D: Applied Physics, 29 (1),

133.

Cloetens, P., Pateyron-Salomé, M., Buffiere, J., Peix, G., Baruchel, J., Peyrin, F. and

Schlenker, M. 1997. Observation of microstructure and damage in materials by phase

sensitive radiography and tomography. Journal of Applied Physics, 81 (9), 5878-5886.

Couque, H., Albertini, C. and Lankford, J. 1993. Failure mechanisms in a unidirectional

fibre-reinforced thermoplastic composite under uniaxial, in-plane biaxial and hydrostatically

confined compression. Journal of materials science letters, 12 (24), 1953-1957.

Cox, B., Dadkhah, M., Morris, W. and Flintoff, J. 1994. Failure mechanisms of 3D woven

composites in tension, compression, and bending. Acta Metallurgica et Materialia, 42 (12),

3967-3984.

Davis, G. and Elliott, J. 2006. Artefacts in X-ray microtomography of materials. Materials

science and technology, 22 (9), 1011-1018.

Davis, T., Gao, D., Gureyev, T., Stevenson, A. and Wilkins, S. 1995. Phase-contrast imaging

of weakly absorbing materials using hard X-rays. Nature, 373 (6515), 595-598.

de Almeida, S. F. M. and Neto, Z. d. S. N. 1994. Effect of void content on the strength of

composite laminates. Composite structures, 28 (2), 139-148.

Dow, N. F. and Gruntfest, I. J. 1960. Determination of most needed potentially possible

References

196

improvements in materials for ballistic and space vehicles. General Electric Company,

Space Science Laboratory, TIS R60SD389.

Evans, A. G. and Adler, W. F. 1978. Kinking as a mode of structural degradation in carbon

fiber composites. Acta Metallurgica, 26 (5), 725-738.

Ewins, P. D., Potter, R. T., Bishop, S. M. and Worthington, P. J. 1980. Some observations

on the nature of fibre reinforced plastics and the implications for structural design [and

discussion]. Philosophical Transactions of the Royal Society of London A: Mathematical,

Physical and Engineering Sciences, 294 (1411), 507-517.

Feldkamp, L. A., Davis, L. C. and Kress, J. W. 1984. Practical cone-beam algorithm. Journal

of Optical Society of America A, 1 (6), 612-619.

Flannery, B. P., Deckman, H. W., Roberge, W. G. and D'amico, K. L. 1987. Three-

dimensional X-ray microtomography. Science, 237 (4821), 1439-1444.

Fleck, N. 1997. Compresssive Failure of Fiber Composites. Advances in applied mechanics,

33, 43-119.

Fleck, N. and Budiansky, B. 1991. Compressive failure of fibre composites due to

microbuckling. Inelastic deformation of composite materials, Springer New York, 235-273.

Fleck, N., Deng, L. and Budiansky, B. 1995. Prediction of kink width in compressed fiber

composites. Journal of applied mechanics, 62 (2), 329-337.

Fleck, N., Liu, D. and Shu, J. 2000. Microbuckle initiation from a hole and from the free

edge of a fibre composite. International journal of solids and structures, 37 (20), 2757-2775.

Fleck, N., Sutcliffe, M., Sivashanker, S. and Xin, X. 1996. Compressive R-curve of a carbon

fibre-epoxy matrix composite. Composites Part B: Engineering, 27 (6), 531-541.

Garcea, S. C., Mavrogordato, M. N., Scott, A. E., Sinclair, I. and Spearing, S. M. 2014.

Fatigue micromechanism characterisation in carbon fibre reinforced polymers using

synchrotron radiation computed tomography. Composites Science and Technology, 99, 23-

30.

Garland, B. D., Beyerlein, I. J. and Schadler, L. S. 2001. The development of compression

damage zones in fibrous composites. Composites science and technology, 61 (16), 2461-

2480.

Goren, A. and Atas, C. 2008. Manufacturing of polymer matrix composites using vacuum

assisted resin infusion molding. Archives of materials Science and Engineering, 34 (2), 117-

120.

Goutianos, S. 2004. Micromechanics of compressive failure in carbon-fibre polymer

References

197

composites. PhD thesis, Queen Mary, University of London.

Guo, Z. S., Liu, L., Zhang, B. M. and Du, S. 2009. Critical void content for thermoset

composite laminates. Journal of Composite Materials, 43 (17), 1775-1790.

Gutkin, R., Pinho, S. T., Robinson, P. and Curtis, P. T. 2010. On the transition from shear-

driven fibre compressive failure to fibre kinking in notched CFRP laminates under

longitudinal compression. Composites Science and Technology, 70 (8), 1223-1231.

Gutkin, R., Pinho, S. T., Robinson, P. and Curtis, P. T. 2011. A finite fracture mechanics

formulation to predict fibre kinking and splitting in CFRP under combined longitudinal

compression and in-plane shear. Mechanics of Materials, 43 (11), 730-739.

Guynn, E. G. and Bradley, W. L. 1989. A detailed investigation of the micromechanisms of

compressive failure in open hole composite laminates. Journal of Composite Materials, 23

(5), 479-504.

Guynn, E. G., Ochoa, O. O. and Bradley, W. L. 1992. A Parametric Study of Variables That

Affect Fiber Microbuckling Initiation in Composite Laminates: Part 1-Analyses. Journal of

Composite Materials, 26 (11), 1594-1616.

Guz, I. A. 1989. Three-dimensional nonaxisymmetric problems of the theory of stability of

composite materials with a metallic matrix. International Applied Mechanics, 25 (12), 1196-

1201.

Hahn, H. T., Sohi, M. and Moon, S. 1986. Compression Failure Mechanisms of Composite

Structures. NASA Contractor Report 3988.

Hahn, H. T. and Williams, J. G. 1986. Compression failure mechanisms in unidirectional

composites. Composite Materials: Testing and Design, 115-139.

Hancox, N. L. 1975. The compression strength of unidirectional carbon fibre reinforced

plastic. Journal of Materials Science, 10 (2), 234-242.

Hapke, J., Gehrig, F., Huber, N., Schulte, K. and Lilleodden, E. T. 2011. Compressive failure

of UD-CFRP containing void defects: In situ SEM microanalysis. Composites Science and

Technology, 71 (9), 1242-1249.

Herman, G. T. 1979. Image reconstruction from projections. Image Reconstruction from

Projections: Implementation and Applications, 1.

Hodgkinson, J. M. 2000. Mechanical testing of advanced fibre composites, Elsevier.

Hull, D. and Clyne, T. W. 1996. An introduction to composite materials. Cambridge

university press, Cambridge.

References

198

Jelf, P. M. and Fleck, N. A. 1992. Compression failure mechanisms in unidirectional

composites. Journal of Composite Materials, 26 (18), 2706-2726.

Jochum, C., Grandidier, J. C. and Smaali, M. 2008. Proposal for a long-fibre microbuckling

scenario during the cure of a thermosetting matrix. Composites Part A: Applied Science and

Manufacturing, 39 (1), 19-28.

Joshi, S. C. 2012. The pultrusion process for polymer matrix composites. Manufacturing

Techniques for Polymer Matrix Composites (PMCs). Cambridge: Woodhead Publishing.

Jumahat, A., Soutis, C. and Hodzic, A. 2010a. A Graphical Method Predicting the

Compressive Strength of Toughened Unidirectional Composite Laminates. Applied


Jumahat, A., Soutis, C., Jones, F. and Hodzic, A. 2010b. Fracture mechanisms and failure

analysis of carbon fibre/toughened epoxy composites subjected to compressive loading.

Composite structures, 92 (2), 295-305.

Kinsey, A., Saunders, D. E. J. and Soutis, C. 1995. Post-impact compressive behaviour of

low temperature curing woven CFRP laminates. Composites, 26 (9), 661-667.

Kuentzer, N., Simacek, P., Advani, S. G. and Walsh, S. 2007. Correlation of void distribution

to VARTM manufacturing techniques. Composites Part A: applied science and

manufacturing, 38 (3), 802-813.

Kumar, S. B., Sivashanker, S., Bag, A. and Sridhar, I. 2005. Failure of aerospace composite

scarf-joints subjected to uniaxial compression. Materials Science and Engineering: A, 412

(1), 117-122.

Kutz, M. 2002. Handbook of materials selection. John Wiley & Sons, New York.

Kyriakides, S., Arseculeratne, R., Perry, E. J. and Liechti, K. M. 1995. On the compressive

failure of fiber reinforced composites. International Journal of Solids and Structures, 32 (6),

689-738.

Kyriakides, S. and Ruff, A. E. 1997. Aspects of the Failure and Postfailure of Fiber

Composites in Compression. Journal of Composite Materials, 31 (20), 2000-2037.

Lambert, J., Chambers, A. R., Sinclair, I. and Spearing, S. M. 2012. 3D damage

characterisation and the role of voids in the fatigue of wind turbine blade materials.

Composites Science and Technology, 72 (2), 337-343.

Landis, E. N. and Keane, D. T. 2010. X-ray microtomography. Materials Characterization,

61 (12), 1305-1316.

Landrigan, M. D., Li, J., Turnbull, T. L., Burr, D. B., Niebur, G. L. and Roeder, R. K. 2011.

References

199

Contrast-enhanced micro-computed tomography of fatigue microdamage accumulation in

human cortical bone. Bone, 48 (3), 443-450.

Lankford, J. 1995. Compressive failure of fibre-reinforced composites: buckling, kinking,

and the role of the interphase. Journal of materials science, 30 (17), 4343-4348.

Lankford, J. 1997. The compressive failure of polymeric composites under hydrostatic

confinement. Composites Part A: Applied Science and Manufacturing, 28 (5), 409-418.

Lee, J. and Soutis, C. 2005. Thickness effect on the compressive strength of T800/924C

carbon fibre–epoxy laminates. Composites Part A: Applied Science and Manufacturing, 36

(2), 213-227.

Lee, J. and Soutis, C. 2007. A study on the compressive strength of thick carbon fibre–epoxy

laminates. Composites Science and Technology, 67 (10), 2015-2026.

Lee, S., Yerramalli, C. S. and Waas, A. M. 2000. Compressive splitting response of glass-

fiber reinforced unidirectional composites. Composites Science and Technology, 60 (16),

2957-2966.

Liebig, W. V., Viets, C., Schulte, K. and Fiedler, B. 2015. Influence of voids on the

compressive failure behaviour of fibre-reinforced composites. Composites Science and

Technology, 117, 225-233.

Lo, K. and Chim, E. M. 1992. Compressive strength of unidirectional composites. Journal

of reinforced plastics and composites, 11 (8), 838-896.

Long, A. C. 2005. Design and manufacture of textile composites. Woodhead Publishing

Limited, Cambridge.

Madhukar, M. S. and Drzal, L. T. 1992. Fiber-matrix adhesion and its effect on composite

mechanical properties. III. Longitudinal (0) compressive properties of graphite/epoxy

composites. Journal of composite materials, 26 (3), 310-333.

Maire, E., Carmona, V., Courbon, J. and Ludwig, W. 2007. Fast X-ray tomography and

acoustic emission study of damage in metals during continuous tensile tests. Acta Materialia,

55 (20), 6806-6815.

Majumdar, P. K., Liu, Z., Lesko, J. J. and Cousins, T. E. 2009. Performance evaluation of

FRP composite deck considering for local deformation effects. Journal of Composites for

Construction, 13 (4), 332-338.

Mallick, P. K. 2007. Fiber-reinforced composites: materials, manufacturing, and design,

CRC press, Boca Raton.

Marsh, G. 2005. Airframers exploit composites in battle for supremacy. Reinforced Plastics,

References

200

49 (3), 26-32.

McCombe, G. P., Rouse, J., Trask, R. S., Withers, P. J. and Bond, I. P. 2012. X-ray damage

characterisation in self-healing fibre reinforced polymers. Composites Part A: Applied

Science and Manufacturing, 43 (4), 613-620.

Metscher, B. D. 2009. MicroCT for comparative morphology: simple staining methods allow

high-contrast 3D imaging of diverse non-mineralized animal tissues. BMC physiology, 9 (1),

11.

Moffat, A. J., Wright, P., Buffière, J. Y., Sinclair, I. and Spearing, S. M. 2008.

Micromechanisms of damage in 0 splits in a [90/0] s composite material using synchrotron

radiation computed tomography. Scripta Materialia, 59 (10), 1043-1046.

Moffat, A. J., Wright, P., Helfen, L., Baumbach, T., Johnson, G., Spearing, S. M. and

Sinclair, I. 2010. In situ synchrotron computed laminography of damage in carbon fibre–

epoxy [90/0] s laminates. Scripta Materialia, 62 (2), 97-100.

Mokso, R., Marone, F., Haberthür, D., Schittny, J. C., Mikuljan, G., Isenegger, A. and

Stampanoni, M. 2011. Following dynamic processes by X-ray tomographic microscopy with

sub-second temporal resolution. Proceedings of he 10th International Conference on X-ray

Microscopy, AIP Publishing, 38-41.

Momose, A. 2003. Phase-sensitive imaging and phase tomography using X-ray

interferometers. Optics Express, 11 (19), 2303-2314.

Moran, P. M., Liu, X. H. and Shih, C. F. 1995. Kink band formation and band broadening

in fiber composites under compressive loading. Acta metallurgica et Materialia, 43 (8),

2943-2958.

Moran, P. M. and Shih, C. F. 1998. Kink band propagation and broadening in ductile matrix

fiber composites: Experiments and analysis. International journal of solids and structures,

35 (15), 1709-1722.

Mrse, A. M. and Piggott, M. R. 1993. Compressive properties of unidirectional carbon fibre

laminates: II. The effects of unintentional and intentional fibre misalignments. Composites

science and technology, 46 (3), 219-227.

Mukhopadhyay, S., Jones, M. I. and Hallett, S. R. 2015. Compressive failure of laminates

containing an embedded wrinkle; experimental and numerical study. Composites Part A:

Applied Science and Manufacturing, 73, 132-142.

Naik, N. and Kumar, R. S. 1999. Compressive strength of unidirectional composites:

evaluation and comparison of prediction models. Composite structures, 46 (3), 299-308.

Narayanan, S. and Schadler, L. S. 1999. Mechanisms of kink-band formation in

References

201

graphite/epoxy composites: a micromechanical experimental study. Composites Science and

Technology, 59 (15), 2201-2213.

Nikishkov, Y., Airoldi, L. and Makeev, A. 2013. Measurement of voids in composites by X-

ray Computed Tomography. Composites Science and Technology, 89, 89-97.

Odom, E. M. and Adams, D. F. 1990. Failure modes of unidirectional carbon/epoxy

composite compression specimens. Composites, 21 (4), 289-296.

Orowan, E. 1942. A type of plastic deformation new in metals. Nature, 149 (3788), 643-644.

Pan, X., Sidky, E. Y. and Vannier, M. 2009. Why do commercial CT scanners still employ

traditional, filtered back-projection for image reconstruction? Inverse problems, 25 (12),

123009.

Parlevliet, P. P., Bersee, H. E. and Beukers, A. 2007. Residual stresses in thermoplastic

composites–a study of the literature. Part III: Effects of thermal residual stresses. Composites

Part A: applied science and manufacturing, 38 (6), 1581-1596.

Parry, T. V. and Wronski, A. S. 1982. Kinking and compressive failure in uniaxially aligned

carbon fibre composite tested under superposed hydrostatic pressure. Journal of Materials

Science, 17 (3), 893-900.

Piggott, M. R. and Harris, B. 1980. Compression strength of carbon, glass and Kevlar-49

fibre reinforced polyester resins. Journal of Materials Science, 15 (10), 2523-2538.

Pimenta, S. 2008. Micromechanics of kink-band formation. Master thesis, Imperial College

London.

Pimenta, S., Gutkin, R., Pinho, S. T. and Robinson, P. 2009. A micromechanical model for

kink-band formation: Part I—Experimental study and numerical modelling. Composites

Science and Technology, 69 (7), 948-955.

Pinho, S. T., Gutkin, R. and Pimenta, S. 2012. Fibre-dominated compressive failure in

polymer matrix composites. Failure Mechanisms in Polymer Matrix Composites: Criteria,

Testing and Industrial Applications, 183.

Pinho, S. T., Robinson, P. and Iannucci, L. 2006. Fracture toughness of the tensile and

compressive fibre failure modes in laminated composites. Composites science and

technology, 66 (13), 2069-2079.

Port, K. F. 1982. The Compressive Strength of Carbon Fibre Reinforced Plastics. Royal

Aircraft Establishment, Farnborough.

Potter, K., Khan, B., Wisnom, M., Bell, T. and Stevens, J. 2008. Variability, fibre waviness

and misalignment in the determination of the properties of composite materials and

References

202

structures. Composites Part A: Applied Science and Manufacturing, 39 (9), 1343-1354.

Prabhakar, P. and Waas, A. M. 2013. Interaction between kinking and splitting in the

compressive failure of unidirectional fiber reinforced laminated composites. Composite

Structures, 98, 85-92.

Rosen, B. W. 1965. Mechanics of composite strengthening, Fibre Composite Materials,

American Society for Metals, Ohio.

Rudd, C. D., Long, A.C., Kendall, K. N. and Mangin, C. G. E. 1997. Liquid moulding

technologies, Woodhead, Cambridge.

Salvo, L., Cloetens, P., Maire, E., Zabler, S., Blandin, J., Buffière, J. Y., Ludwig, W., Boller,

E., Bellet, D. and Josserond, C. 2003. X-ray micro-tomography an attractive characterisation

technique in materials science. Nuclear instruments and methods in physics research section

B: Beam interactions with materials and atoms, 200, 273-286.

Salvo, L., Suéry, M., Marmottant, A., Limodin, N. and Bernard, D. 2010. 3D imaging in

material science: Application of X-ray tomography. Comptes Rendus Physique, 11 (9-10),

641-649.

Sánchez, M., Campo, M., Jiménez-Suárez, A. and Ureña, A. 2013. Effect of the carbon

nanotube functionalization on flexural properties of multiscale carbon fiber/epoxy

composites manufactured by VARIM. Composites Part B: Engineering, 45 (1), 1613-1619.

Schilling, P. J., Karedla, B. R., Tatiparthi, A. K., Verges, M. A. and Herrington, P. D. 2005.

X-ray computed microtomography of internal damage in fiber reinforced polymer matrix

composites. Composites Science and Technology, 65 (14), 2071-2078.

Schultheisz, C. R. and Waas, A. M. 1996. Compressive failure of composites, part I: testing

and micromechanical theories. Progress in Aerospace Sciences, 32 (1), 1-42.

Scott, A. E., Mavrogordato, M., Wright, P., Sinclair, I. and Spearing, S. M. 2011. In situ

fibre fracture measurement in carbon–epoxy laminates using high resolution computed

tomography. Composites Science and Technology, 71 (12), 1471-1477.

Sivashanker, S., Fleck, N. A. and Sutcliffe, M. P. F. 1996. Microbuckle propagation in a

unidirectional carbon fibre-epoxy matrix composite. Acta Materialia, 44 (7), 2581-2590.

Sivashanker, S. and Osiyemi, S. 1999. Uniaxial compressive failure of unidirectional

composites with small imperfections. Metallurgical and Materials Transactions A, 30 (7),

1867-1876.

Sket, F., Enfedaque, A., Alton, C., González, C., Molina-Aldareguia, J. M. and Llorca, J.

2014. Automatic quantification of matrix cracking and fiber rotation by X-ray computed

tomography in shear-deformed carbon fiber-reinforced laminates. Composites Science and

References

203

Technology, 90, 129-138.

Slaughter, W. S. and Fleck, N. A. 1994. Microbuckling of fiber composites with random

initial fiber waviness. Journal of the Mechanics and Physics of Solids, 42 (11), 1743-1766.

Slaughter, W. S., Fan, J. and Fleck, N. A. 1996. Dynamic compressive failure of fiber

composites. Journal of the Mechanics and Physics of Solids, 44 (11), 1867-1890.

Song, W., Gu, A., Liang, G. and Yuan, L. 2011. Effect of the surface roughness on interfacial

properties of carbon fibers reinforced epoxy resin composites. Applied surface science, 257

(9), 4069-4074.

Soutis, C. 1991. Measurement of the static compressive strength of carbon-fibre/epoxy

laminates. Composites science and technology, 42 (4), 373-392.

Soutis, C. 1997. Compressive behaviour of composites, Rapra Technology Limited,

Shropshire.

Soutis, C. 2000. Compression testing of pultruded carbon fibre-epoxy cylindrical rods.

Journal of materials science, 35 (14), 3441-3446.

Soutis, C. 2005a. Carbon fiber reinforced plastics in aircraft construction. Materials Science

and Engineering: A, 412 (1-2), 171-176.

Soutis, C. 2005b. Fibre reinforced composites in aircraft construction. Progress in

Aerospace Sciences, 41 (2), 143-151.

Soutis, C. 2012. Compressive strength of composite laminates with an open hole: Effect of

ply blocking. Journal of Composite Materials, 47 (20-21), 2503-2512.

Soutis, C., Curtis, P. T. and Fleck, N. A. 1993. Compressive failure of notched carbon fibre

composites. Proceedings of the Royal Society of London A: Mathematical, Physical and

Engineering Sciences, 440 (1909), 241-256.

Soutis, C. and Fleck, N. A. 1990. Static Compression Failure of Carbon Fibre T800/924C

Composite Plate with a Single Hole. Journal of Composite Materials, 24 (5), 536-558.

Soutis, C. and Lee, J. 2008. Scaling effects in notched carbon fibre/epoxy composites loaded

in compression. Journal of Materials Science, 43 (20), 6593-6598.

Soutis, C. and Turkmen, D. 1997. Moisture and temperature effects of the compressive

failure of CFRP unidirectional laminates. Journal of Composite Materials, 31 (8), 832-849.

Steif, P. S. 1990. A model for kinking in fiber composites—I. Fiber breakage via micro-

buckling. International journal of solids and structures, 26 (5), 549-561.

References

204

Stock, S. 1999. X-ray microtomography of materials. International Materials Reviews, 44

(4), 141-164.

Sutcliffe, M. P. F. and Fleck, N. A.1997. Microbuckle propagation in fibre composites. Acta

materialia, 45 (3), 921-932.

Sutcliffe, M. P. F.and Yuwono, A. 2001. Experimental study of microbuckle initiation in a

model composite system. Scripta materialia, 45 (7), 831-837.

Sutcliffe, M. P. F. and Fleck, N. A. 1994. Microbuckle propagation in carbon fibre-epoxy

composites. Acta metallurgica et materialia, 42 (7), 2219-2231.

Tan, K. T., Watanabe, N. and Iwahori, Y. 2011. X-ray radiography and micro-computed

tomography examination of damage characteristics in stitched composites subjected to

impact loading. Composites Part B: Engineering, 42 (4), 874-884.

Tankasala, H., Fleck, N. A. and Deshpande, V. 2014. Toughening due to shear kinking in

composites. Society of Engineering Science 51st Annual Technical Meeting, Indiana, USA.

Tzetzis, D. and Hogg, P. 2008. Experimental and finite element analysis on the performance

of vacuum-assisted resin infused single scarf repairs. Materials and Design, 29 (2), 436-449.

Ueda, M., Mimura, K. and Jeong, T. K. 2014. In situ observation of kink-band formation in

a unidirectional carbon fiber reinforced plastic by X-ray computed tomography imaging.

Advanced Composite Materials, (ahead-of-print), 1-13.

Vogler, T., Hsu, S. Y. and Kyriakides, S. 2001. On the initiation and growth of kink bands

in fiber composites. Part II: analysis. International Journal of Solids and Structures, 38 (15),

2653-2682.

Vogler, T. J. and Kyriakides, S. 1997. Initiation and axial propagation of kink bands in fiber

composites. Acta Materialia, 45 (6), 2443-2454.

Vogler, T. J. and Kyriakides, S. 1999. On the axial propagation of kink bands in fiber

composites : Part i experiments. International Journal of Solids and Structures, 36 (4), 557-

574.

Vogler, T. J. and Kyriakides, S. 2001. On the initiation and growth of kink bands in fiber

composites: Part I. experiments. International journal of solids and structures, 38 (15),

2639-2651.

Waas, A. M., Babcock, C. D. and Knauss, W.G. 1990. An experimental study of

compression failure of fibrous laminated composites in the presence of stress gradients.

International Journal of Solids and Structures, 26 (9), 1071-1098.

Waas, A. M. and Schultheisz, C. R. 1996. Compressive failure of composites, part II:

experimental studies. Progress in Aerospace Sciences, 32 (1), 43-78.

Wadee, M. A., Hunt, G. and Peletier, M. 2004. Kink band instability in layered structures.

Journal of the Mechanics and Physics of Solids, 52 (5), 1071-1091.

References

205

Wang, J., Potter, K. D., Hazra, K. and Wisnom, M. R. 2012. Experimental fabrication and

characterization of out-of-plane fibre waviness in continuous fibre-reinforced composites.

Journal of Composite Materials, 46 (17), 2041-2053.

Wang, J., Potter, K. D., Wisnom, M. R. and Hazra, K. 2013. Failure mechanisms under

compression loading in composites with designed out-of-plane fibre waviness. Plastics,

Rubber and Composites, 42 (6), 231-238.

Weaver, C. W. and Williams, J. G. 1975. Deformation of a carbon-epoxy composite under

hydrostatic pressure. Journal of Materials Science, 10 (8), 1323-1333.

Wind, J. L., Waas, A. M. and Jensen, H. M. 2015. Initiation of failure at notches in

unidirectional fiber composites. Composite Structures, 122, 51-56.

Wisnom, M. R. and Atkinson, J. 2000. Fibre waviness generation and measurement and its

effect on compressive strength. Journal of reinforced plastics and composites, 19 (2), 96-

110.

Wisnom, M. R. and Atkinson, J. W. 1996. Compressive failure due to shear instability:

experimental investigation of waviness and correlation with analysis. Journal of reinforced

plastics and composites, 15 (4), 420-439.

Withers, P. J. 2007. X-ray nanotomography. Materials today, 10 (12), 26-34.

Withers, P. J. and Preuss, M. 2012. Fatigue and damage in structural materials studied by X-

ray tomography. Annual Review of Materials Research, 42, 81-103.

Wright, P., Fu, X., Sinclair, I. and Spearing, S. M. 2008. Ultra High Resolution Computed

Tomography of Damage in Notched Carbon Fiber--Epoxy Composites. Journal of


Wright, P., Moffat, A. E., Sinclair, I. and Spearing, S. M. 2010. High resolution tomographic

imaging and modelling of notch tip damage in a laminated composite. Composites Science

and Technology, 70 (10), 1444-1452.

Yang, B., Kozey, V., Adanur, S. and Kumar, S. 2000. Bending, compression, and shear

behavior of woven glass fiber–epoxy composites. Composites Part B: Engineering, 31 (8),

715-721.

Yin, W. L. 1992. A new theory of kink band formation. Proceedings of AIAA-92-2552-CP,

33rd Structures, Structural Dynamics and Materials Conference, 3028-3035.

Yuan, L., Shyu, S. and Lai, J. 1991. Plasma surface treatments on carbon fibers. II.

Mechanical property and interfacial shear strength. Journal of applied polymer science, 42

(9), 2525-2534.

Yurgartis, S. W. 1987. Measurement of small angle fiber misalignments in continuous fiber

composites. Composites Science and Technology, 30 (4), 279-293.

Appendix

206

Appendix

A. Load-displacement curves for specimens IB7-1, IB7-2 and IB3-1:

Figure A.1: Load-displacement curve of sample IB7-1 under in situ FPB test.


Appendix

207


damage mechanisms associated with kink-band formation in

Documents