Strain Measurement of Micrometre-Sized Structures under Tensile Loading by Using Scanning White-Light Interferometry*1

Takashi Ito1,*2, Yoji Mine1,*3, Masaaki Otsu2 and Kazuki Takashima1

1Department of Materials Science and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto 860–8555, Japan2Department of Mechanical Engineering, Graduate School of Engineering, University of Fukui, Fukui 910–8057, Japan

A scanning white-light interferometry (SWLI) technique was used to image the surface topography and measure the in-plane strain in micrometre-sized structures subjected to uniaxial tensile deformation. This technique was applied to observing the macro and local deformation behaviours in micrometre-sized Au specimens. Reproducible stress–strain curves were successfully obtained using SWLI during the intermittent tensile tests. The local strain distribution was also calculated from the movement of natural gauge marks that are characteristic of triangular el-ements. Combining this micro-tensile test with orientation imaging microscopy enables crystal plasticity of mesoscale structures to be revealed. [doi:10.2320/matertrans.MG201616]

(Received February 29, 2016; Accepted April 5, 2016; Published May 13, 2016)

Keywords:　 scanning white-light interferometry, micro-tensile test, crystallographic orientation, slip deformation, crystal plasticity

1.　 Introduction

For advances in micro/nanoelectromechanical system (MEMS/NEMS) technology, mechanical characterisations of micro- and nano-scale components are necessary, and the mi-cro- and nanomechanical testing methods also need to be standardised. In particular, studies using nanopillars have shed light on the dimensional size effects on the mechanical properties and the deformation behaviour of metallic materi-als1–6). Meanwhile, in micro-tensile testing using a mesoscale specimen with a length on the order of a few tens of microme-tres, the dimensional size effects were reduced7,8). The length scales of these structures are equivalent to those of their mi-croconstituents such as grains and secondary phases in con-ventional metallic alloys. Thus, this testing method reveals the mechanical response of each microconstituent.

In general, yielding occurs at a local region in the gauge section, and then this plastically deformed region is expanded through tensile loading. Unlike in the case of bulk specimens, a fraction of the gauge section of the micrometre-sized speci-men undergoes plastic deformation immediately after the on-set of yielding. Thus, the microstructural effects are expected to be emphasised in the stress–strain response obtained in the micro-tensile test9,10). In addition, studying a small specimen allows the observation of the local and entire deformation be-haviours simultaneously. Therefore, the contributions of the individual microconstituents to the deformation process can be revealed. The strain in the mesoscale specimen has been principally measured by image analyses11–15), whereas a strain gauge attached to the specimen surface has been em-ployed for the bulk specimens. In the case of the micro-ten-sile test, gauge marks have been occasionally made on the specimen surface, e.g., by using vapour deposition and preci-

sion fabrication techniques; these gauge marks may affect the deformation and fracture behaviours of the micrometre-sized structures. This study used scanning white-light interferome-try (SWLI) that enables the optional location on the surface of the micrometre-sized specimen to be recognised by precision surface sensing without fabricating gauge marks. Moreover, tracing multiple points can calculate the distribution of the local strain. These techniques are suitable for analyses of de-formation and fracture behaviours of steels, titanium alloys, and magnesium alloys with a hierarchical structure. In this study, a pure Au foil that exhibits conventional mechanical properties was employed to evaluate the suitability and repro-ducibility of the developed strain measurement technique for micro-tensile testing to characterise the local and entire de-formation behaviours of micrometre-sized structures.

2.　 Experimental Details

2.1　 Material and micro tensile testThe material used in this study was supplied in the form of

a cold-rolled pure Au (99.99%) tape with a thickness of 10 μm. A thin rectangle was cut from the Au tape and was heated to a temperature of 673 K, which was held for 1.8 ks, followed by furnace cooling. A strong texture having sub-grains of approximately 20 μm was developed after anneal-ing, as shown in Fig. 1. Figure 2 shows a plain specimen with a gauge section of 50 μm (L) ×  20 μm (W) ×  10 μm (B) fabri-cated in the thin rectangle using focused ion beam machining (FIB), where L, W, and B are the length, width, and thickness of the specimens, respectively. A single-edge-notched (SEN) specimen with dimensions of 10 mm (L)  ×  1 mm (W)  ×  0.01 mm (B) was also prepared for measuring the local strain distribution, where a notch 150 μm deep was introduced us-ing FIB machining. Figure 3 shows the scanning ion micros-copy image at the notch tip. A Hitachi SU6600 �eld emission gun scanning electron microscope with an electron back scat-tered diffraction (EBSD) analyser was used for observing the notch tip area before micro-tensile testing. The crystal orien-tation was determined using automatic beam scanning, with a

*1 This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 80 (2016) 22–26.

*2 Graduate Student, Kumamoto University. Present address: Magnesium Research Centre, Kumamoto University

*3 Corresponding author, E-mail: mine@msre.kumamoto-u.ac.jp

Materials Transactions, Vol. 57, No. 8 (2016) pp. 1252 to 1256 Special Issue on Frontier Researches Related to Nano/Microstructure, Microstructure Control and Mechanical Properties of Materials ©2016 The Japan Institute of Metals and Materials

step size of 2 μm at an accelerating voltage of 20 kV. EBSD analysis was carried out using the TexSEM Laboratories ori-entation imaging microscopy (OIM) software (v.6.1.3). A clean-up procedure was applied to all EBSD images to adjust single points with misorientations of more than 5° to the neighbours.

A tensile test with a micro-gluing grip14) was performed at a crosshead speed of 0.1 μm s−1, at room temperature and in atmospheric air. The thin rectangular sample was held by glu-ing both ends, more than 1 mm away from the gauge section or the notch, as shown in Fig. 4. A piezoelectric actuator with a position accuracy of 10 nm was used for displacement con-trol. The load was measured by means of a load cell with a 2 N capacity. The test was interrupted at predetermined dis-

placements to monitor the length of the elongated gauge part and measure the surface undulation by SWLI with a high res-olution of 0.1 nm.

2.2　 Calculation of strain distributionA metal’s surface has many concave and convex features at

the nanometre scale, even if it has been carefully polished. These features move when applying a load and therefore can be used as ‘natural’ gauge marks. In this study SWLI was used to recognise surface patterns in the stretched specimen. The pattern recognition was conducted by template matching us-ing a cross-correlation coef�cient technique. The macro-strain was determined from the normal strain in the loading direc-tion calculated from a change in the distance between two selected gauge marks. The local strain was calculated from the movement of three selected gauge marks in a triangular con�guration. The longitudinal, εx, transverse, εy, and shear,

Fig. 2　Scanning electron micrograph of micrometre-sized plain specimen (Thickness: 10 μm). LD and TD represent the loading and transverse di-rections of the tensile specimen, respectively.

Fig. 3　Scanning ion micrograph showing subgrains at the notch tip in a single-edge-notched specimen. LD and ND represent the loading and notch directions, respectively.

Fig. 4　Schematic illustration of the process for sample mounting.

Fig. 1　An example of (100) pole �gure of annealed Au tape exhibiting strong texture determined from the 180 μm ×  540 μm area by EBSD anal-ysis.

1253Strain Measurement of Micrometre-Sized Structures under Tensile Loading by Using Scanning White-Light Interferometry

γxy, components of the in-plain strain with respect to the load-ing direction were expressed by

εx

εy

γxy

=

12A

y2 − y3 0 y3 − y1

0 x3 − x2 0x3 − x2 y2 − y3 x1 − x3

0 y1 − y2 0x1 − x3 0 x2 − x1

y3 − y1 x2 − x1 y1 − y2

u1

v1

u2

v2

u3

v3

,

(1)

where (x, y) and (u, v) are the position and the displacement of each node, respectively, and the subscript represents the ordinal number of the node. The area of the triangular ele-ment, A, is given by

A =12

(x1y2 + x2y3 + x3y1 − x1y3 − x2y1 − x3y2). (2)

In this study, we dealt with the maximum shear strain, γmax, to evaluate the shear deformation as follows:

γmax = (εx − εy)2 + γ2xy. (3)

The distribution of local strain can be determined using mul-tiple target points. In this study, the observed area, with a di-mension of 71 μm ×  95 μm, was divided by 32 triangular ele-ments.

3.　 Results and Discussion

3.1　 Stress–strain behaviour of micrometre-sized Au structures

Figure 5 shows a typical load–displacement (P–δ) curve obtained for the plain specimen while interrupting the tensile test. Load drops corresponding to the respective interruptions of the tensile test are visible in the P–δ curve. These are at-tributed to stress relaxation in the adhesive connecting be-tween the sample and the tools (Fig. 4). Figure 6 shows the SWLI contour maps obtained by interrupting a micro-tensile

Fig. 5　Load–displacement plot obtained for the micrometre-sized plain specimen of annealed Au. The indexes correspond to those in Fig. 6.

Fig. 6　A series of contour maps of the stretched gauge part during uniaxial tensile loading measured by SWLI.

Fig. 7　Stress–strain curves for micrometre-sized plain specimens of an-nealed Au obtained by coupling the intermittent micro-tensile test with SWLI.

1254 T. Ito, Y. Mine, M. Otsu and K. Takashima

test of the plain specimen, where the indexes correspond to those in Fig. 5. The initial portion of the P–δ curve, between individual load drop points, exhibited a roughly liner relation-ship (Fig. 5), while a uniformly deformed gauge section was observed in the SWLI maps (compare Figs. 6(a) and (b)). The uniform deformation was retained until the stress reached the maximum value (Fig. 6(c)). Surface inhomogeneity appeared

at a displacement of 22.5 μm (Fig. 6(d)), and �nally led to necking (Fig. 6(e)). Thus, SWLI could observe the details of localized deformation process in a micrometre-sized struc-ture.

To obtain the actual stress–strain behaviour, the two natural gauge marks were selected in the SWLI images and traced through the tensile test. Figure 7 contains the stress–strain curves for three micro-tensile specimens. The tensile test re-sults showed good reproducibility with a yield stress of 40–68 MPa, which is an expected value for coarse-grained Au16).

3.2　 Local strain distribution at the notch tipFigure 8 shows the P–δ curve (a), the surface topographies

(b, c), and the local strain distribution (d) for the SEN speci-men. After the linear behaviour in the P–δ curve (Fig. 8(a)), the notch tip was open and the left-side leading �ank of the notch was extended (Fig. 8(b)). At a displacement of 70 μm, surface undulations arose at the right-side leading �ank of the notch as well (Fig. 8(c)). The distribution map of the maxi-mum shear strain constructed from the SWLI images at dis-placements of 20 and 70 μm shows that the intensi�ed strain occurred at angles of 46.5°, 52° and −36.5° with respect to the notch direction (Fig. 8(d)). Figure 9 shows the colour-coded map and the corresponding stereographic projection of the

Fig. 8　(a) Load–displacement plot, (b, c) SWLI images and (d) local strain distribution map at the notch tip.

Fig. 9　(a) Colour-coded map showing grains at the notch tip and (b) stereo-graphic projection of the notch tip grain in the SEN specimen. LD and ND denote the loading and notch directions, respectively. White lines are drawn on the grain boundaries with misorientation angles between 2° and 15°, and black lines with misorientation angles larger than 15°.

1255Strain Measurement of Micrometre-Sized Structures under Tensile Loading by Using Scanning White-Light Interferometry

grain at the notch tip obtained before tensile loading.As shown in Fig. 3, the notch depth was 150 μm and the

notch tip was located in a single crystal with a grain size of ~20 µm. In this case, the stress and strain distributions are predicted to differ from those in an isotropic homogenous medium because of the anisotropic elastic characteristics of Au crystals. It was reported that the in�uence of the anisotro-py on the stress and strain distributions was reduced when the depth of the notch was suf�ciently larger than the size of the grain at the notch tip, and this grain was surrounded by grains with different crystallographic orientations17). In addition, calculation with zero T-stress conditions revealed that the mode I stress �eld in a ductile FCC single crystal with a (010) [101] notch was similar to that in an isotropic medium18). As-suming an elastic isotropic medium with a crack in mode I loading, we calculated the resolved shear stress in the slip system on the basis of the crack-tip stress �eld expressed by the following equations:

σx =KI√2πr

cosθ

21 − sin

θ

2sin

3θ2

(4)

σy =KI√2πr

cosθ

21 + sin

θ

2sin

3θ2

(5)

τxy =KI√2πr

cosθ

2sinθ

2cos

3θ2

(6)

σz = 0 (7)

where σ and τ are the normal and shear stress, respectively, and the subscripts x, y, and z represent the notch direction, the loading direction, and the direction perpendicular to the face plane, respectively, r is the distance from the crack tip, θ is the angle from the notch direction on the xz-plane, and KI is the mode I stress intensity factor. Table 1 lists the relative shear stresses, τ   =  τ

√2πr  /KI, on predicted slip planes. The angles

and the gradient directions of the surface undulations at a dis-placement of 20 μm corresponded to those of the two slip systems that exhibited the �rst and second highest resolved shear stresses, i.e., (1̄1̄1) [101] and (111) [1̄01] (Figs. 8(b), 8(d), and 9(b), and Table 1). At a displacement of 70 μm, the

(1̄11) [101] slip was additionally activated (Figs. 8(c), 8(d) and 9(b)). Coupling the micro-tensile testing technique using SWLI with OIM enabled crystal plasticity of mesoscale structures to be revealed.

4.　 Conclusions

A non-contact strain measurement system for micro-ten-sile testing of micrometre-sized specimens was developed using scanning white-light interferometry (SWLI). This sys-tem provides tracing natural gauge marks on the surface of micrometre-sized specimens during tensile testing. Tensile tests of micrometre-sized Au specimens were performed to measure the macro and local strains. A reliable stress–strain curve could be obtained by means of the intermittent tensile test with SWLI. Local strain distributions at the notch tip de-picted the crystal plasticity well. SWLI is a powerful tool for imaging surface topography and measuring macro and local strains in micrometre-sized specimens.

Acknowledgments

This work was supported by a Grant-in-Aid for Scienti�c Research (B) 24360293 from the Japan Society for the Pro-motion of Science (JSPS).

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Table 1　Relative shear stress, τ’, imposed on predicted slip systems.

Slip plane Slip direction

(1̄1̄1) [1̄10] [011] [101]

0.383 0.275 0.646

(111) [1̄10] [1̄01] [01̄1]

0.321 0.620 0.335

(11̄1) [1̄01] [011] [110]

0.611 0.348 0.282

(1̄11) [01̄1] [101] [110]

0.403 0.607 0.211

1256 T. Ito, Y. Mine, M. Otsu and K. Takashima