fracture short report - j gopal

Jithin Gopal

Group2 Fracture Mechanics Short Report 0

IMPERIAL COLLEGE LONDON

Fracture Mechanics Short Report 4

Jithin Gopal

Demonstrator: Mr Mohammad Zainol Abdin

Technician: Mr Joeseph Meggyesi

Submitted on 23rd January 2012

Experiment carried out in mechanical lab Composite Centre

Imperial College London

Summary Inter-laminar fracture behaviour of ACG MTM 44-1 was studied using Mode I Double

Cantilever Beam method (DCB) and Mode II End Load Splitting (ELS). Fracture mechanism

like fibre bridging, crack splitting and friction were observed in the sample, which increased

the fracture energy. Correction factors were used to ensure the value obtained is more

matched with the actual testing. For mode I testing was done according to ISO 15024 but

mode II testing has no agreed international standard. The fracture energy obtained for two

DCB sample tested are GIC initiation energy was ~300Jm-2

and this was comparable with the

literature for epoxy matrix and there was an increase in the fracture energy with crack length

which and for mode II ELS testing the GIIC initiation energy was found to be ~450Jm-2

. There

were few problem associated with the testing in terms of data collection, the marking fluid

being thick and crack propagation not visible due to this. Overall, the experiment was success

in measuring the fracture energy for this ACG MTM 44-1 material and obtained comparable

data with published results.

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1. Introduction As laminated composites are widely used in aerospace applications, their failure mechanisms

under different loading conditions have been studied extensively by various research groups

(Naghipour, 2010). Different stacking sequences, fibre orientations and crack propagation

directions have considerable effects on the structural response, fracture resistance, and failure

mechanisms of the composite (Hashemi, 1990b). Laminated fibre composites made of high

strength fibres in a relatively weak matrix material are susceptible to delamination

(Hodgkinson J M, 2000). From a design point of view it is important to know how tough a

composite is to enable material developers to improve resistance to delamination and provide

failure criteria for designers.

Loading Modes

Delamination can be regarded as crack propagation and hence fracture mechanics can be

applied where the characterisation is via the energy per unit of crack area, GC(Department of

Aeronautics, Laboratories booklet 2011/2012 ., 2011/2012). The crack propagation will

usually be interlaminar, which leads to different modes of propagation under different

loading conditions (Taylor Ambrose Dr, 2011). The most obvious is mode I, the tensile

opening mode, giving GlC where the crack propagates by the crack faces opening normal to

the crack plane. In addition, the crack may propagate by a sliding or shear motion,

particularly in bending, which is characterized by GIIC. There is no reason for these to be the

same, and indeed combinations of opening and shear loadings can give mixed mode failure

that can only be characterized for each ratio of mode I to mode II loading(Hashemi, 1990a).

To characterise laminates it is necessary to devise testing methods to produce the various

modes, and hence determine GIC, GIIC and GIc/G11c under mixed mode loading(Taylor

Ambrose Dr, 2011). To fully understand fracture failure mechanism, the total strain energy

release rate, GI, the mode I component due to interlaminar tension, GI, the mode II

component due to interlaminar sliding shear, GII, and the mode III component, GIII, due to

interlaminar scissoring shear, need to be calculated(Williams, 1988). In order to accurately

predict delamination onset or growth for two-dimensional problems, these calculated G

components are compared to interlaminar fracture toughness properties experimentally

measured over a range from pure mode I loading to pure mode II loading.

Figure 1 Schematic diagram of the basic modes of crack loading, mode I( opening), mode II (

Shear), mode III (tearing) (Hodgkinson J M, 2000)

Double Cantilever Beam Test (DCB)

Standard test method used for mode one testing and it is the most common method used for

mode I testing. Sample of ACG MTM 44-1 was prepared in the lab in composite centre with

a release film at the mid thickness to create the initial delamination. End block are then bound

to the sample using a strong adhesive. The sample used have been shown in Figure 2 painted

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and marked with white pain as shown in the figure. The sample is pre-cracked to ensure a

sharp natural crack is obtained before the testing (this ensure the energy value measures is a

real value rather than the value of a resin rich area). The sample is subjected to tensile loading

at a constant rate and the crack length monitored using a video camera.

Figure 2 Mode I double cantilever beam (DCB) specimen (Hodgkinson J M, 2000)

Mode I standards are International Standard ISO 15024 ( also British Standard ISO 15024)

and American Society for Testing of Materials ASTM D5528. Technical details of the

testing are specified for DCB method but this standard is limited to uni directional (UD)

layup only and requires testing from insert and mode I pre-crack. There are different ways to

process the result obtained from the testing. The method used for analysis is via corrected

beam theory and modified compliance calibration method (MCC).Simple beam theory cannot

be applied here as assumption of built in beam is not strictly correct ( low shear modulus of

polymeric fibre composites leads to deflections and rotations occurring at the crack tip).Large

displacement so the beam cause shortening of the moment arm and because of the use of end

blocks the stiffness is a false stiffness and hence correction factors are derived. Crack length

is apparently longer due to deflections and rotation occurring at crack tip this is corrected by

introducing a correction factor χ. Shortening of the moment arm is corrected by introducing a

factor F derived using small displacement beam theory. Correction factor N is used to correct

the increased stiffness obtained by using the end blocks. These factors and there derivation is

outside the scope of this report and these have been used by referring to work done by S.

Hashemi; A. J. Kinloch; J. G. Williams(The Analysis of Interlaminar Fracture in Uniaxial

Fibre-Polymer Composites; Proceedings of the Royal Society of London. Series A,

Mathematical and Physical Sciences, Vol. 427, No. 1872. (Jan. 8, 1990), pp. 173-199.

End Loaded Split test (ELS)

Mode II testing covers the testing done for in-plane sliding and loading on a crack due to

bending, bending stresses on upper and lower arms induce opposing shear stresses on crack

faces. Loaded arrangement shown in Figure 3a this arrangement incorporates a small roller

which aims to eliminate friction between beam halves. There is no current ISO standard for

mode II testing and the work is still on-going other complication arises in this form of testing

in term of micro-cracking as observed by several researchers (O’Brien at NASA Langley).

Mode II testing is widely used to measure the mode II fracture energies despite the mentioned

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problems. Similar to mode one the correction factors were applied from S Hashemi et.al and

results analysed.

End Notch Flexure (ELF)

This is another version of the mode II test and this is more commonly used as this is simpler

to use in industry and is less complicated with the setup. This test as shown in Figure 3 b use

three point flexure arrangement. Due to the nature of this report (short ) not much detail about

the testing is included and has been mentioned for completeness.

Figure 3 Mode II specimens (a) Ended Loaded Split (ELS) specimen, (b) End notched flexure

(ENF)(Hashemi, 1990b)

Mixed mode test and Mode III testing

There are other two modes involved with fracture and energy, but is not discussed in this

report s it is outside the scope of the report.

2. Objective The purpose of this experiment is to perform fracture testing on ACG MTM 44-1composite

material. The experiment was carried according to International Standard ISO 15024 ( also

British Standard ISO 15024) for Mode I and as there is not an international standard for

Mode II End Loaded Split test (ELS) were performed and the analysis was performed based

on the literature available mainly by S. Hashemi; A. J. Kinloch; J. G. Williams(The Analysis

of Interlaminar Fracture in Uniaxial Fibre-Polymer Composites; Proceedings of the Royal

Society of London. Series A, Mathematical and Physical Sciences, Vol. 427, No. 1872. (Jan.

8, 1990), pp. 173-199.

The experiment performed were

Double cantilever beam test (Mode I) – 2 samples

End Loaded Split test (Mode II)- 2 samples

The main objective of this experiment is to measure the following properties

Interlaminar fracture energy GIC for Mode I

Interlaminar fracture energy GIIC for Mode II

Fracture energy GC non-linear initiation

Fracture energy GC max imitation

Fracture energy GC 5% max initiation

To Plot load vs displacement graph of both test

To Plot (C/N)1/3

vs ‘a’ plot where a is the crack length , N is a correction factor as

mentioned in introduction and C is compliance factor

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To understand the mechanics involved in Mode I and Mode II

Failure modes in both test is investigated

To measure these properties some other properties are measured like

o Load(N)

o Displacement (mm)

o Length, Width and Thickness (mm)

In order to carry out the objective different set of skills and equipment is required and it is

also important to analyse the failure mode and the expected failure mode. The equipment

used for this experiment is listed below

Instron 4505 Tensile testing machine (100kN)

Closed-circuit television

Data logger

Correction Fluid (Tipex)

Other measuring equipment

o Vernier calliper for width and length

o Screw gauge for thickness measurement

The technique required for this lab is to monitor the crack and machine

displacement , apply the correction fluid and making a scale on the edge

Collecting data from the data acquisition system

Two specimens per method tested and the data compared with published

literature

3. Procedure Manufacturing of specimen (Advanced Composite Group, 04/11/2011).

The pre-peg used for manufacture of the specimen was ACG MTM 44-1, is a high

performance, toughened epoxy matrix system optimised for low pressure vacuum-bag out of

Autoclave processing and cured(Advanced Composite Group, 04/11/2011). The cure cycle is

a single cycle with ramp rate of 1-2oC, with pressure from 3-7 bar and vacuum pressure

>0.75bar. For autoclave processing the temperature is 4 hours at 130oC.

Figure 4 Set up of Autoclave production of test (Advanced Composite Group)

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Sample for the testing were prepared in Imperial College Composite centre from ACG MTM

44-1 pre-peg and autoclave curing. ACG MTM 44-1 pre-peg was stacked in layers of 4 and

assembles to get a 12 stacked and a PTFE (0.25µm) thick release paper was incorporated into

the specimen 40 mm wide. So a 24 ply 3mm thick composite was produced for this test using

an autoclave to cure the sample as explained above. This sample was then machine to shape

using a diamond saw first to cut the excess and then using and wet saw to cut specimens of

size 150mm*20mm*3mm.Sample was then grit blasting at the one end and the aluminium

end block was attached using Araldite 2011 two component epoxy paste adhesive (50:50

mix) and left to cure at room temperature. 4 specimens are prepared to do the testing.

Sample preparation Sample prepares as above were measurement and the readings are

recorded in table and table 2 sample were then painted thinly with brittle white liquid

(correction fluid te-pex). This aids the visual location of the crack and it was monitored using

CCTV equipment. This setup is shown in Figure 5 .

Mode 2

DIMENSIONS:

Specimen Length Width Thickness Length Width Thickness Diameter

149.81 20.01 3.41 19.08 19.87 12.65 8

149.63 20 3.39 19.07 19.91 12.63 7.93

149.85 20.02 3.39 19.06 19.9 12.64 8.02

Average 149.76 20.01 3.4 19.07 19.89 12.64 7.98

149.22 19.88 3.33 19.02 20.03 12.31 7.93

149.24 19.97 3.32 19.06 20.01 12.32 7.85

149.16 20.02 3.3 19.07 19.98 12.3 8.01

Average 149.21 19.96 3.32 19.05 20.01 12.31 7.93

3

4

Material Load Block

Table 1 sample dimension for Mode II test Sample 3 and 4

mode 1

DIMENSIONS:

Specimen Length Width Thickness Diameter

T B T B T B

1 149.14 18.81 3.41 19.38 19.3 19.7 20.25 12.6 12.75 8.07

149.93 19.32 3.39 19.15 19.33 19.71 20.25 12.7 12.62 8.15

149.18 19.72 3.39 19.17 19.2 19.65 20.23 12.8 12.65 8.01

Average 149.42 19.28 3.4 19.23 19.28 19.69 20.24 12.7 12.67 8.08

2 149.5 19.84 3.18 19.08 19.1 20 20.13 12.67 12.5 8.2

149.47 19.76 3.2 19.11 19.14 20.01 20.15 12.65 12.54 8.25

149.51 19.69 3.21 19.08 19.16 20 20.18 12.56 12.61 8.24

Average 149.49 19.76 3.2 19.09 19.13 20 20.15 12.63 12.55 8.23

Length Width Thickness

Material Load Block

Table 2 sample dimension for Mode I test Sample 1 and 2

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Figure 5 The testing equipment and the CCTV equipment used and the ELS test setup

Procedure for pre-cracking (both for DCB and ELS)

1. Sample loaded to the machine marked with white fluid and a scale

2. Rate of loading set to 5mm/min for pre crack

3. Load applied

4. Crack prorogation watched on the monitor

5. Pre- cracking stopped after crack length reaches 50mm

6. Unload the sample and return to previous position

Procedure for test (both for DCB and ELS)

1. Sample loaded to the machine marked with white fluid and a scale

2. Rate of loading set to 5mm/min until it reaches the pre-crack length

3. Rate of loading set to 1mm/min for the rest of the test

4. Load applied

5. Crack propagation watched on the monitor

6. Data collected manually of the crack length from the monitor and machine

displacement rerecorded for that crack length

7. Crack length allowed to reach 100m

8. Unload the sample and return to previous position

9. Repeat for other samples

Result analysis

This section summarises the different formulae’s used to deduce the results the correction

factors .The method used for analysis is via corrected beam theory and modified compliance

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calibration method (MCC).Simple beam theory cannot be applied here as assumption of built

in beam is not strictly correct ( low shear modulus of polymeric fibre composites leads to

deflections and rotations occurring at the crack tip).Large displacement so the beam cause

shortening of the moment arm and because of the use of end blocks the stiffness is a false

stiffness and hence correction factors are derived. Crack length is apparently longer due to

deflections and rotation occurring at crack tip this is corrected by introducing a correction

factor χ. Shortening of the moment arm is corrected by introducing a factor F derived using

small displacement beam theory. Correction factor N is used to correct the increased stiffness

obtained by using the end blocks. These factors and there derivation is outside the scope of

this report and these have been used by referring to work done by S. Hashemi; A. J. Kinloch;

J. G. Williams(The Analysis of Interlaminar Fracture in Uniaxial Fibre-Polymer Composites;

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,

Vol. 427, No. 1872. (Jan. 8, 1990), pp. 173-199.

Equations ( from the report above )

(a) The mode I DCB test

Θ1=3/10

Θ2=3/2

(b) The mode II test

2342

1 ])/(31/[))/(63)/(5015(20

3LaLaLa

For h1=h2=h, and

])/(31/[)/(31)(/(3 32

2 LaLaaL

(c) The mode 1 DCB test

Θ3=1, Θ4=9/8[1-(l2/a)2], Θ3=9/35

(d) The mode II ELS test

],)/(31/[4 3

3 La

23

22

2

23

4])/(31[

]})/(31][)/(1[)/(4])/(31)[/(1{(

4

9

La

LaalLaLaLa

33

423

5])/(31[

]})/(63])/(7035[)/(8

31{[(

35

36

La

LaLaLa

Equation 9 is the basic equation in which correction factors are then applied to obtain

the equation (10,11)

a

C

b

PG

.

2

2

Other correction factors are

F= 1- Θ1(δ/L)2- Θ2(δl1/L

2)

(1)

(2)

(7)

(4)

(3)

(5)

(6)

(8)

(9)

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N= 1- Θ3(l2/L)3- Θ4(δl1/L

2)- Θ5(δ/L)

For mode one testing the formulae can be summarsied as below

Mode II

For ELS specimens as shown in Figure 3

Notations

l1,l2,h,a,B,L are shown in figure 2 and are dimensions of the sample and the block

Θ1, Θ2 ,Θ3, Θ4, Θ5, Θ6 are geometric correction factors as stated by S. Hashemi

C is the compliance and can be defined as C =δ/P, where δ is the displacement and P is the

load.

F is the correction factor for effective shortening of the beams due to the large displacements

and the tilting of end blocks.

N is the correction factor for the increased stiffness obtained by using the end blocks.

χ is for rotation occurring at crack tip. This was found from the plot of (C/N)^(1/3) vs a as

shown in results section

GI is the fracture energy for mode I .

GII is the fracture energy for mode II.

Equation (1) to (9) was used for calculations of the results and is presented in the next

section.

(10)

(11)

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4. Result

Figure 6 Load –displacement graph for DCB testing Mode I

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Figure 7 (C/N)^(1/3) vs crack length graph which is used to deduce χ

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Figure 8 R curved behaviour of DCB sample from mode I testing (fracture Energy vs crack length )

Mode II results

Figure 9 Load –displacement graph for ELS testing Mode II

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Figure 10 R curved behaviour of ELS sample from mode II testing (fracture Energy vs crack length )

Summary table

GIC sample one intiation value Mode I DCB 300Jm-2

GIC sample Two intiation value Mode I DCB 315Jm-2

GIIC sample one intiation value Mode II ELS 815J m-2

GIIC sample one intiation value Mode II ELS 435J m-2

GIIC Propogation value

E11 for mode I Average value 117GPa

GIC sample one intiation value Mode I DCB 5% offset value

305J m-2

GIC sample two intiation value Mode I DCB 5% offset value

375Jm-2

Table 3 Summary table showing the different values deduced from the experiment conducted

The two failure mechanism observed during the mode I and II interlaminar facture test were :

(a) Interlaminar crack growth involving fibre bridging and pullout at crack tip.

(b) Interlaminar crack growth involving crack tip splitting.

All the specimens tested exhibited this mechanism , the degree of fibre bridging and

splitting was not the same for all material.

Sample calculation

(a) For mode I calculation the

3/1

N

Cvs ‘a’ was plotted to find the value of the

correction factor χ .Load and displacement was measured in the machine and markers

were manually made using the CCTV for every cracklength this displacement was

matched and data processed. The mode I DCB test

Θ1=3/10

Θ2=3/2

(b) The mode 1 DCB test

Θ3=1, Θ4=9/8[1-(l2/a) 2], Θ3=9/35

Θ4=9/8[1-(l2/a) 2] , Θ4=9/8[1-(9.6/63)

2]= Θ4= 1.09

Θ5=9/35

Other correction factors are

F= 1- Θ1(δ/L)2- Θ2(δl1/L

2) = (1-((3/10)*(7.77/139.8)

2)((3/2)*(7.77*8.04/(139.8

2)) = 0.99

N= 1- Θ3(l2/L)3- Θ4(δl1/L

2)- Θ5(δ/L)

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N=1-(1*(9.6/139.8)3-(1.098*((7.77*8.04)/139.8

2)-(9/35*(7.7/139.8

2) = 0.995

E11 = =(37.2/7.77)*(8)*(1)*(633)/(19.28)*(1.693) = 90.46GPa

C= displacement /load = 7.77/37.2= 0.24

χ was deduced from the

3/1

N

Cvs ‘a’ graph and χ for sample one was deduced as 5.5

GIC= (0.99/0.995)*(3*32.7*7.77)/(2*19.28)*(63+(6)) = 275 Jm-2

Calculation similar were performed to obtain the results presented in this section and this was

to demonstrate a sample calculation.

5. Discussion The interlaminar crack energy of ACG MTM 44-1 were measured using DCB and ELS

method. For mode I fracture testing. The facture mechanism observed for both testing was

involved fibre bridging, pull-out and crack tip splitting which lead to more fibre bridging.

The evidence of the above mentioned mechanism can been seen in load vs displacement

graph in figure 6 and figure 9.The interlaminar crack grew in stable ,continuous manner

thought he DCB specimen and the load displacement curves shown in figure 6 and 9.Load

displacement curves indicated linear elastic, nonlinear elastic and nonlinear inelastic

behaviour. Linear response was observed in the beginning of the test at lower load (~35N).

The second response was non-linear elastic response, which occurred in the middle of the

trace as the nearby material gets stiffer as the load increases. The third type was the nonlinear

inelastic response, which occurred at high loads and can be associated with onset of crack

growth and the decrease in slope of the load- displacement trace. The nonlinear inelastic

response in these materials can be associate with large displacement being present in the test

specimen this has been taken into account by using an correction factor, but other mechanism

which has affected the experiment are fibre birding and crack tip splitting. Fibres resist crack

opening by stretching and absorb energy and hence increasing the toughness. Toughness

increase with crack length for mode one sample this is evident with the resistance curve

behaviour as shown in figure 8.The value obtained for fracture energy for Initial crack was

found to be around 300Jm-2

, the quality of this has been compared with other published

literature and for an epoxy system like MTM 44-1this is an comparable value .The effect of

crack length on GIC( fracture Energy ) is clear from figure 8, GIC value associated with the

onset of the crack is different to the values obtained for crack propagation and this is reflected

on the R curve as shown in Figure 8. Beam theory correction required to analyse the data and

the correction factors were applied a shown in the procedure section.

For mode II testing there is no recognised standard for testing of material in mode II. There

are four methods currently used but no agreement on which method to standardise. The

method used for this experiment was End Load Splitting (ELS) some of the problem

associate with ELS testing are role of friction during the test, how much energy is absorbed

by friction can this be calculated and accounted for in the analysis and is it possible to reduce

friction experimentally. Micro cracking has also been reported by several researchers and to

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model this and calculate this will be very complex. The fracture energy against crack length

is plotted as seen in Figure 10 and unlike mode I there is a difference in the nature , the

fracture energy is going up with crack length and this is due to the friction, fibre bridging,

crack tip splitting and this is reflected in the figure . There is a very big difference in the

crack Initiation values and propagation value and they can be quoted as450 and 950 Jm-2

.

Mode II values obtained are comparable with the literature but has to be treated with caution

as there are no standard methods available and hence the details of the experimentation needs

to be checked before comparing like to like data. The load- displacement graph has a linear

and non-linear area similar to the mode I. The Fracture energy values obtained from Mode I

and Mode II cannot be compared ad they are very different and involved different

mechanism.

The quality of the fracture energy values have been compared with the published data and

they are comparable and as the test was carried out according to standard test methods the

results obtained are good quality . There were a few problems during the experiment like the

white ink used to mark the specimen was applied thick and during testing some of the cracks

were propagation under the crack and were difficult to detect. Despite the difficulties the data

analysed produced meaningful results and was comparable with published data.

6. Conclusion Inter-laminar fracture behaviour of ACG MTM 44-1 was studied using Mode I DCB and

Mode II ELS.

The load- displacement graph shows non-linear behaviour, mainly due to the large

displacements in the specimen and the fracture mechanism like fibre-bridging, crack

splitting and friction.

Modified beam theory with correction factors were used to deduce the fracture energy

following S Hashemi et al (Hashemi, 1990b)

The Fracture energy values obtained from Mode I and Mode II cannot be compared

and they are very different and involved different mechanism. Correction factors were

used to ensure the value obtained is more in sync with the actual testing.

Mode I testing was done according to ISO 15024 but mode II testing has no agreed

international standard.

The fracture energy obtained for two DCB sample tested are GIC initiation energy was

~300Jm-2

and this was comparable with the literature for epoxy matrix and there was

an increase in the fracture energy with crack length which is associated with fibre

bridging, crack end splitting and friction.

For mode II ELS testing the GIIC initiation energy was found to be ~450Jm-2

and

there was an increase in the fracture energy with crack length which is associated with

fibre bridging, crack end splitting and friction.

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Mode II fracture energy VS crack length graph was a bigger scatter and the ‘R’

curved behaviour was not very obvious. Initiation and propagation values were

compared with previous work done by S Hameshi and the values obtained are

comparable taking into the experimental error.

There were few problem associated with the testing in terms of data collection, the

marking fluid being thick and crack propagation not visible due to this. Overall the

experiment was success in measuring the fracture energy for this ACG MTM 44-1

material and obtained comparable data with published results.

7. References

Advanced Composite Group. (04/11/2011) ACG MTM 44-1 product information. [Online]

Available from: http://www.advanced-

composites.co.uk/data_catalogue/catalogue%20files/pds/PDS1189_MTM44-1_Issue7b.pdf .

Department of Aeronautics, Laboratories booklet 2011/2012 . (2011/2012) MSc in

composites Laboratory Handout. Tensile Testing. In: Anonymous pp. 32-46.

Hashemi, S. (1990a) The Analysis of Interlaminar Fracture in Uniaxial Fibre-Polymer

Composites. Proceedings of the Royal Society of London.Series A, Mathematical and

Physical Sciences. 427 (1872), 173-199.

Hodgkinson J M. (2000) Mechanical Testing of Advanced Fibre Composites. , Woodhead

Publishing Limited.

Naghipour, P. B. (2010) Effect of fiber angle orientation and stacking sequence on mixed

mode fracture toughness of carbon fiber reinforced plastics: Numerical and experimental

investigations. Materials Science Engineering.A, Structural Materials: Properties,

Microstructure and Processing. 527 (3), 509-517.

Taylor Ambrose Dr. (2011) Fracture. Lecture Notes Imperial College Course. 2, .

Williams, J. (1988) On the calculation of energy release rates for cracked laminates.

International Journal of Fracture. 36 (2), 101-119.

http://www.advanced-composites.co.uk/data_catalogue/catalogue%20files/pds/PDS1189_MTM44-1_Issue7b.pdf

http://www.advanced-composites.co.uk/data_catalogue/catalogue%20files/pds/PDS1189_MTM44-1_Issue7b.pdf

fracture short report - j gopal

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