Abstract

Aimed at the low accuracy problem of shear strain measurement in Moiré methods, a two-dimensional (2D) Moiré phase analysis method is proposed for full-field deformation measurement with high accuracy. A grid image is first processed by the spatial phase-shifting sampling Moiré technique to get the Moiré phases in two directions, which are then conjointly analyzed for measuring 2D displacement and strain distributions. The strain especially the shear strain measurement accuracy is remarkably improved, and dynamic deformation is measurable from automatic batch processing of single-shot grid images. As an application, the 2D microscale strain distributions of a titanium alloy were measured, and the crack occurrence location was successfully predicted from strain concentration.

© 2017 Optical Society of America

1. Introduction

High strength metallic materials with a high ductility has been developed by designing multi-phase microstructures [1, 2]. However, local damage formation occurs due to heterogeneous deformation associated with complexity of the multi-phase microstructures [1]. This fact has been concerned for a further improvement of the ductility. For instance, a Titanium 6-Aluminium 4-Vanadium (Ti-6Al-4V) alloy with an hcp/bcc laminated microstructure shows intensive strain localization along a microstructure interface, which causes failure probably due to local accumulation of dislocations [3]. Therefore, it is vitally necessary to measure the micro and nano-scale strain distributions coupled with an analysis on strain components such as shear strain related to slip deformation.

In recent decades, optical techniques for deformation measurement are gaining more and more attention due to their non-contact, non-destructive and high-sensitivity features. Among various optical techniques, the grid-based techniques including geometric phase analysis (GPA) and the moiré technique also get rapid development and have been widely used in deformation measurement of various materials and structures. GPA usually uses fast Fourier transform (FFT) to get the grating phase for shortening the computation time, and then obtain the deformation from the grating phase difference [4, 5]. However, when the grating has strong local distortion or the deformation is highly nonuniform, a non-negligible error will occur in the phase calculation, because it is difficult for FFT to accurately acquire the fundamental frequency component in the case of a wide frequency band.

For the moiré technique, one of the greatest strengths is deformation visualization as a moiré pattern can be considered as an amplification phenomenon of a specimen grating. Moiré fringes are caused by the interference of two gratings or grids. Since the moiré technique was first reported in 1948 [6], various moiré methods have been successively developed for in-plane and out-of-plane deformation measurement. The geometric moiré [7] and the overlapping moiré [8] method visually show moiré fringes generated from superposition of two gratings, and are suitable for measuring large deformation. The charge coupled device (CCD) or complementary metal oxide semiconductor (CMOS) moiré method treats the pixel array of an imaging sensor as the reference grating. As the CCD or CMOS moiré fringes are unclear when the light intensity is weak or when there is a glass cover or when the grating pitch is not suitable, this method is constrained in applications for deformation measurement. Moiré interferometry [9] uses a coherence laser beam to serve as the reference grating in a large field of view with one side of dozens of millimeters. This method has high deformation measurement sensitive, i.e., the displacement sensitivity is usually 0.417 μm/fringe, and the strain sensitivity can reach several micro strains. However, the complicated operation and the weakness in noise resistance limit its pervasive application.

In the microscope scanning moiré method such as the scanning electron microscope (SEM) moiré [10–12], the transmission electron microscope (TEM) moiré [13], the atomic force microscope (AFM) moiré [14], the laser scanning microscope (LSM) [8] or laser scanning confocal microscope (LSCM) moiré [15, 16] method, the scanning lines or scanning dots are considered as the reference grating. As commercial microscopes are easy to operate and have high resolutions, the scanning moiré method has been extensively used for micro- and nano-scale deformation measurement of various materials. A three-dimensional deformation method has been reported based on SEM moiré fringes [17]. The digital moiré method [18] employs a computer to generate moiré fringes, and has great flexibility in the specimen grating pitch.

The aforementioned moiré methods mainly use the fringe-centering technique to process moiré fringes. Only the information of centerlines of moiré fringes is used, and thus the deformation measurement accuracy is low. Besides, it is difficult to automatically batch deformation analysis, because the centerlines of moiré fringes often need to be manually repaired. Although the temporal phase-shifting moiré technique [19] can improve the deformation measurement accuracy, a phase-shifting device is necessary, and it takes time to record several images making this technique not suitable for dynamic analysis.

In the recent years, a sampling moiré method [20] has been proposed and developed for deformation measurement. The displacement can be accurately measured from a single-shot grid image using the spatial phase-shifting technique. At present, the sampling moiré method is mainly applied in structural health monitoring by measuring the displacement of infrastructures such as long crane [21], thermal power plant [22] and bridges, etc. Furthermore, by use of multiple frequencies information of the sampling moiré fringe, arbitrary repeated pattern can be used to measure the displacement and strain measurement [23]. In addition, to develop this method from large scale monitoring to small scale inspection, a reconstructed multiplication moiré method using two-pixel sampling moiré fringes [24] and a strain distribution measurement method using multi-pixel sampling moiré fringes [25] have been developed. The 2D full-field normal strains at the micro and nano- scales can be accurately measured, when the principal directions (perpendicular to the grating or grid lines) of the 2D grid are exactly parallel and perpendicular to the measuring direction.

However, there are usually angles between the principal directions of the 2D grid and the measuring direction in the practical experiments, because it is difficult to precisely control the grid direction in many grid fabrication techniques. In this case, the accuracy of the shear strain measurement in the present sampling moiré method is low, because the displacement measurement in either direction only considers a one-dimensional (1D) grating with the principal direction of close to this direction. Actually, both the two 1D gratings are necessary to be considered for displacement measurement in either direction [26].

For high-accuracy shear strain measurement, in this study, a 2D moiré phase analysis method is proposed by combining the sampling moiré (spatial phase-shifting) method and the conjoint analysis of 2D phases. The spatial phase shifting technique adopts a local discrete Fourier transform (DFT) algorithm to get the moiré phase by extracting the fundamental frequency component directly. Simulations are performed to verify the measurement accuracy of this method. The normal and shear strain distributions of a titanium (Ti) alloy in a tensile test are measured and successfully used for predicting the crack occurrence location.

2. Deformation measurement principle

To accurately measure the strain distributions from a single-shot periodic pattern nondestructively, a moiré technique is proposed by combining the spatial phase-shifting (sampling moiré) method and a 2D phase analysis. The spatial phase-shifting (sampling moiré) method can determine the accurate phase distributions in the x and y directions, and the 2D phase analysis provides accurate displacement and strain distributions from phase differences.

2.1 Measurement principle for Moiré phase

A 2D periodic pattern (grid for short) can be considered as a combination of two 1D gratings, i.e., grating X and grating Y, as seen in Fig. 1. At beginning, when the specimen grating is fabricated, suppose the pitches of grating X in the x (horizontal rightwards) and y (vertical upwards) directions are pXx and pXy, and the pitches of grating Y in the x (horizontal rightwards) and y (vertical upwards) directions are pYx and pYy, respectively. The intensity of the 2D grid before deformation can be expressed as

I=AXcos[2π(xpXx+ypYy)]+AYcos[2π(xpYx+ypYy)]+B
where AX and AY are the modulated amplitudes of grating X and grating Y, respectively, and B includes the background and high-order intensities.

 

Fig. 1 (a) Diagram of a 2D grid including 2 parallel gratings on specimen, (b) Geometric relationship of gratings before and after deformation.

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After using a low pass filter or Fourier transform, the 2D grid can be separated to grating X and grating Y. The intensities of grating X and grating Y can be repetitively indicated by

IX=AXcos[2π(xpXx+ypXy)]+BX=AXcosφX+BX
IY=AYcos[2π(xpYx+ypYy)]+BY=AYcosφY+BY
where BX means the background and high-order intensities of grating X, BY gives the background and high-order intensities of grating Y, and φX and φY stand for the phases of grating X and grating Y, respectively.

After the specimen deformed, grating X and grating Y will change to grating X’ and grating Y’, as shown in Fig. 1. Suppose the pitches of grating X’ in the x and y directions are p’Xx and p’Xy, and the pitches of grating Y in the x and y directions are p’Yx and p’Yy, respectively. The intensities of the 2D grid, grating X’ and grating Y’ after deformation can be respectively represented by

I=AXcos[2π(xpXx+ypYy)]+AYcos[2π(xpYx+ypYy)]+B
IX=AXcos[2π(xpXx+ypXy)]+BX=AXcosφX+BX
IY=AYcos[2π(xpYx+ypYy)]+BY=AYcosφY+BY
where A’X and A’Y are the modulated amplitudes of grating X’ and grating Y’, respectively, and B’, BX and BY show the background and high-order intensities of the 2D grid, grating X’ and grating Y’, respectively, and φ’X and φ’Y indicate the phases of grating X’ and grating Y’, respectively.

From Eqs. (2), (3), (5) and (6), the phase differences of grating X and grating Y due to temperature change are respectively obtainable from

ΔφX=φXφX=2π[(xpXx+ypXy)(xpXx+ypXy)]
ΔφY=φYφY=2π[(xpYx+ypYy)(xpYx+ypYy)]

For grating X and grating X’, spatial phase-shifting moiré fringes in the x direction can be generated from Nx-pixels down-sampling and intensity interpolation shown in Fig. 2. The intensities of Nx–step phase-shifting moiré fringes before and after deformation can be respectively expressed by:

IX,mx(kx)=AXcos[2π(xpXx+ypXyxNx+kxNx)]+BX=AXcos[φX,mx+2πkxNx)]+BX
IX,mx(kx)=AXcos[2π(xpXx+ypXyxNx+kxNx)]+BX=AXcos[φX,mx+2πkxNx)]+BX(kx=0,1,,Nx1)
where φX,mx and φ’X,mx mean the phases of moiré fringes when kx = 0 generated from grating X and grating X’ in the x direction, respectively.

 

Fig. 2 Principle of the sampling moiré method for calculating phase distribution from an oblique grating.

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For grating Y and grating Y’, spatial phase-shifting moiré fringes in the y direction can be formed from Ny-pixel down-sampling and intensity interpolation shown in Fig. 2. The intensities of Ny–step phase-shifting moiré fringes before and after deformation can be respectively represented by:

IY,my(ky)=AYcos[2π(xp2x+ypYyyNy+kyNy)]+BY=AYcos[φY,my+2πkyNy)]+BY
IY,my(ky)=AYcos[2π(xp2x+ypYyyNy+kyNy)]+BY=AYcos[φY,my+2πkyNy)]+BY(ky=0,1,...,Ny1)
where φY,my and φ’Y,my signify the phases of moiré fringes when ky = 0 generated from grating Y and grating Y’ in the y direction, respectively.

The phases φX,mx, φ’X,mx, φY,my and φ’Y,my of moiré fringes in Eqs. (9)-(12) can be calculated from the phase-shifting method using a discrete Fourier transform algorithm, as shown in

φJ,mj=-arctankj=0Tj1IJ,mj(kj)sin(2πkj/Nj)kj=0Tj1IJ,mj(kj)cos(2πkj/Nj)φJ,mj=-arctankj=0Tj1IJ,mj(kj)sin(2πkj/Nj)kj=0Tj1IJ,mj(kj)cos(2πkj/Nj){j=xwhenJ=Xj=ywhenJ=Y

2.2 Measurement principle for displacement and strain distributions

From Eqs. (9), (10) and (7), the phase difference of moiré fringes in the x direction is equal to the phase difference of grating X, which is determinable from

ΔφX,mx=φX,mxφX,mx=2π(xpXx+ypXyxNx)2π(xpXx+ypXyxNx)=2π[(xpXx+ypXy)(xpXx+ypXy)]=ΔφX

From Eqs. (11), (12) and (8), the phase difference of moiré fringes in the y direction is equivalent to the phase difference of grating Y, which is determinable from

ΔφY,my=φY,myφY,my=2π(xpYx+ypYyyNy)2π(xpYx+ypYyyNy)=2π[(xpYx+ypYy)(xpYx+ypYy)]=ΔφY

Suppose the displacements of the specimen in the x and y directions are ux and uy, respectively, the phases of grating X and grating Y after deformation can also be expressed as

φX=2π(xuxpXx+yuypXy)
φY=2π(xuxpYx+yuypYy)

From Eqs. (2), (3), (16) and (17), the phase differences of grating X and grating Y due to loading change can also be determined by

ΔφX=2π(xuxpXx+yuypXy)2π(xpXx+ypXy)=2π(uxpXx+uypXy)
ΔφY=2π(xuxpYx+yuypYy)2π(xpYx+ypYy)=2π(uxpYx+uypYy)

As known from Eqs. (14) and (15), the phase differences of moiré fringes in the x and y directions are equal to the phase differences of grating X and grating Y, respectively. Consequently, based on Eqs. (18) and (19), the relationship among the phase differences of moiré fringes and the displacements of the specimen can be obtained from

(ΔφX,mxΔφY,my)=2π(1/pXx1/pXy1/pYx1/pYy)(uxuy)

Therefore, the displacements of the specimen in the x and y directions are measurable from

(uxuy)=12π(1/pXx1/pXy1/pYx1/pYy)1(ΔφX,mxΔφY,my)=M2π(ΔφX,mxΔφY,my)
where M stands for the matrix comprised of four pitch components of grating X and grating Y in the x and y directions.

Since the strains in different directions are the partial differentials of the displacements, the x-direction strain, the y-direction strain and the shear strain can be measured by the following equation

(εxxεxyεyxεyy)=M2π(ΔφX,mxxΔφX,mxyΔφY,myxΔφY,myy)γxy=εxy+εyx

The relationship between the deformation and the phase difference shown in Eqs. (16)-(22) is essentially same to that in GPA. The difference between the proposed method and GPA lies in the phase extraction method represented in Eqs. (1)-(15). Instead of calculating the grating phase by FFT, the proposed method computes the moiré phase by local DFT which is fast and effective even when the grating pitch is highly nonuniform. Besides, as the moiré spacing is greater than the grating spacing, the moiré phase is easier to be smoothed compared with the grating phase using a sine/cosine filter [27] to reduce the influence of noise.

2.3 Deformation measurement from an orthogonal grid

Suppose the pitch and the angle of grating X are pX and θX, respectively, and the pitch and the angle of grating Y are pY and θY, respectively, as seen in Fig. 1. The angles θX and θY are defined as positive when anticlockwise rotation from the x direction. The matrix M in Eqs. (21) and (22) can also be expressed as

M=(sinθX/pXcosθX/pXsinθY/pYcosθY/pY)1

If the fabricated grating at room temperature is a standard cross grating with a uniform pitch, i.e., pX = pY = p and θX-π/2 = θY = θ, the matrix M in Eqs. (21) and (22) can be transformed into

M=(sin(θ+π2)/pcos(θ+π2)/psinθ/pcosθ/p)1=p(cosθsinθsinθcosθ)1

As the fabricated grating is a standard cross grating in most cases, the most common calculation equations for displacement and strain measurement are as follows

(uxuy)=p2π(cosθsinθsinθcosθ)1(ΔφX,mxΔφY,my)
(εxxεxyεyxεyy)=p2π(cosθsinθsinθcosθ)1(ΔφX,mxxΔφX,mxyΔφY,myxΔφY,myy)γxy=εxy+εyx

2.4 Deformation measurement procedure

The flow chart and measurement process of the 2D phase analysis moiré technique for deformation measurement is presented in Fig. 3. A grating was first fabricated on a specimen if there is no periodic structure on its surface. Then, the grating image was recorded by an image recorder (such as a microscope, a CCD/CMOS image sensor, etc.). Next, the grating images was processed by down-sampling with the pitch of close to (or integral multiple or fractional multiple) the specimen grating pitch, and intensity interpolation to generate sampling moiré fringes. After that, the phase of the moiré fringes before deformation is calculated by the spatial phase-shifting using a Fourier transform algorism.

 

Fig. 3 Flow chart and measurement process of the proposed technique for accurate strain distribution measurement.

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According to the same procedure, the phase of the moiré fringes after deformation can also be obtained, after the specimen is deformed under an external load (such as mechanical, electrical, magnetic, mechanical-heating, electrical-heating, magnetic-heating, mechanical-electrical, etc.). After the phase differences of the moiré fringes before and after deformation are determined, the displacement and strain distributions can be measured using a 2D phase analysis.

3. Simulation verification of strain measurement accuracy

3.1 Comparison of measurement accuracy with conventional methods

This section is used to compare the proposed technique with the traditional sampling moiré technique, and verify the 2D deformation measurement accuracy of the proposed technique from simulation. In the traditional sampling moiré method using 1D phase analysis [25], the displacement in one direction is only calculated using the moiré phase difference in that direction, i.e., ux=pXxΔφX,mx/2π, uy=pYyΔφY,my/2π. The strain components are obtained from the partial differentials of the displacements, i.e., εxx=ux/x, εyy=uy/y and γxy=ux/y+uy/x. However, in the proposed 2D moiré phase analysis method, the displacement in one direction is obtained from the joint analysis of the moiré phase differences in two directions as shown in Eq. (21) or (25). The strain components are also obtained from the partial differentials of the displacements as shown in Eq. (22) or (26).

A cross grating with the pitches of 10 pixels in both the x and y directions was first rotated by different angles to become a series of inclined gratings. The size of the grating image was 480 × 400 pixels. These inclined gratings were then deformed by exerting theoretical x-direction, y-direction, and shear strains. Next, these deformations were measured using the proposed technique.

Figure 4(a) shows an example of deformation measurement when the grating oblique angle is 10 degrees. For the 2D grid before deformation in Fig. 4(b), the grating image was first processed to two 1D gratings in Fig. 4(c) by two low pass filters in the x and y directions, respectively. Spatial phase-shifted sampling moiré fringes in Fig. 4(d) were then generated, and two phase maps in Fig. 4(e) of moiré fringes before deformation in the x and y directions were calculated. Similarly, two phase maps of moiré fringes after deformation in the two directions were also obtained. Next, phase differences of moiré fringes due to deformation were determined in the x and y directions, as shown in Fig. 4(f).

 

Fig. 4 (a) Diagram of a regular grid under an applied 2D strain status when the oblique angle θ is variable, and (b)-(g) Measurement process of 2D strain distributions.

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Based on 2D phase analysis, the 2D displacement and strain distributions were measured as represented in Fig. 4(g). The average x-direction, y-direction and shear strains were 0.01138, −0.00354 and 0.00543, respectively, almost equal to the preset theoretical x-direction, y-direction and shear strains which were 0.01152, −0.00352 and 0.00547, respectively. However, if using the traditional 1D phase analysis, the average x-direction, y-direction and shear strains were 0.01186, −0.00402 and 0.00280, respectively, deviating from the theoretical strains especially for the shear strain.

When the oblique angles of the 2D grid in Fig. 4(a) were 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 16, 19, 22, 25 degrees, the average strains measured from the proposed 2D phase analysis and the traditional 1D phase analysis moiré techniques were compared with the theoretical strains. Figure 5(a) gives the comparison of the x-direction and y-direction strains, and Fig. 5(b) presents the comparison results of the strain under different oblique angles of the 2D grid. It can be seen that, the measurement results from the proposed technique are much closer to the theoretical values than those from the traditional technique.

 

Fig. 5 Comparison of the proposed 2D phase analysis technique and the traditional 1D phase analysis method in measurements of the x-direction strain, the y-direction strain and the shear strains.

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Figure 6 gives the relative errors of the measured strains relative to the theoretical strains. It is obvious that, the measurement accuracies for all the x-direction, y-direction and shear strains of the proposed technique are much higher than those of the traditional technique.

 

Fig. 6 Relative errors of the measured x-direction, y-direction and shear strains from the proposed 2D phase analysis technique and the traditional 1D phase analysis method relative to the theoretical strains along with the grid oblique angle.

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3.2 Measurement accuracy from an oblique grating with random noise

This section illustrates the strain measurement from an inclined grating with random noise. The inclined grating can be separated to grating X and grating Y, which are perpendicular to each other. The oblique angles of grating Y from the x direction and grating X from the y direction are 10 degrees shown in Fig. 7(a). The grating pitches of grating X in the x and y directions were 10.1543 and 57.5877 pixels, respectively, and the grating pitches of grating Y in the x and y directions were 57.5877 and 10.1543 pixels, respectively. The size of the grating image was 480 × 400 pixels. A random noise with the amplitude of σ = 2% of the grating amplitude was added to the oblique grating. The grating at load N1 was deformed to the grating at load N2 by exerting x-direction, y-direction and shear strains.

 

Fig. 7 (a) Diagram of a regular grid with a random noise of σ = 2% under a 2D strain status when the oblique angle is 10° (b)Absolute errors, (c) relative errors and (d) standard deviations of the measured 2D strains from the proposed technique along with the theoretical strains.

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The strains of this grating were measured using the proposed technique. The absolute errors, the relative errors and the standard deviations of the measured strain along with the theoretical strains were listed in Fig. 7(b). All the absolute errors were within −0.00014 to 0, the relative errors range from −1.2% to 0.6%, and the standard deviations were less than 0.0015, suggesting the high accuracy of the proposed technique for strain measurement when the oblique grating has a random noise.

4. Strain distribution measurement of Ti alloy

4.1 Grid fabrication and tensile experiment

The specimen was a Ti-6.29Al-4.35V-0.155O-0.225Fe alloy [28]. Figure 8 presents the specimen geometry and the used mechanical loading device. The thickness and the minimum width of the specimen were 1 mm and 1.8 mm, respectively. A grid with the pitches of 3 μm in two perpendicular directions was produced by UV nanoimprint lithography (EUN-4200 device) in an area of 1.8 × 15 mm2. Since it is difficult to control the exact direction of the fabricated grid in nanoimprint lithography [29, 30], the grid oblique angle relative to the axial direction of the specimen (x direction) were necessary to be measured. In this experiment, the included angle between one grating line and the x direction was measured to be 2 degrees by MB-ruler. The tensile test was performed under a laser scanning microscope (Lasertec OPTELICS HYBRID). In the tensile test, an area of 219 × 204 μm2 containing a prior β grain boundary at one edge of the specimen was chosen as the region of interest, as indicated in Fig. 9.

 

Fig. 8 (a) Specimen geometry of the Ti alloy and (b) the used tensile device under a laser scanning microscope.

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Fig. 9 Region of interest on the Ti alloy and the fabricated 3-μm-pitch grid image.

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4.2 Strain distributions under different loads

The grating images in this region of interest under different tensile loads were recorded, and the corresponding strain distributions were measured using the proposed technique. The sampling pitch was 4 pixels to generate 4-step phase-shifting moiré fringes. A sine/cosine filter [27] with size of 5 × 5 pixels was used to smooth the moiré phases, and an average filter with size of 13 × 13 pixels was used to smooth the strain data. Examples of the 4-pixel sampling moiré fringes and moiré phases in the x and y directions are shown in Fig. 10 when the tensile load is 604 MPa. Some typical grating images, and the 4-pixel down-sampling moiré fringes in the x and y directions were illustrated in Fig. 11 when the nominal stresses are 0, 225, 604 and 660 MPa, respectively. The corresponding phases of these moiré fringes in the x and y directions were then calculated. From the phase differences relative to the phase under 0 MPa, the distributions of x-direction, y-direction and shear strains were measured as seen in Fig. 11 under 225, 604 and 660 MPa, respectively.

 

Fig. 10 Process of moiré phase analysis on the Ti alloy when the tensile load is 604 MPa. (a) Grid image, (b) and (c) spatial phase-shifting moiré fringes in the x and y direction, respectively, and (d) and (e) moiré phases in the x and y direction, respectively.

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Fig. 11 Distributions of x-direction, y-direction and shear strains of the Ti alloy under tensile loads of (a)-(d) 225 MPa, (e)-(h) 312 MPa, (i)-(l) 478 MPa, (m)-(p) 604 MPa, and (q)-(t) 660 MPa before damage occurrence.

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From the grating images, no obvious deformation could be observed under 604 MPa. However, from the distributions of the x-direction and shear strains in Fig. 11, obvious microscale strain concentration could be observed under 604 MPa. Finally, microscale initial crack was found at the strain concentration region from the grating image under 710 MPa in Fig. 12. It indicates that the proposed technique can provide accurate strain distributions which enable precise prediction of crack occurrence location.

 

Fig. 12 (a) Grid image and (b) enlarge image around prior β boundary on the Ti alloy after unloading from 710 MPa.

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Besides, oblique slip lines with different orientations were observed in different grains under greater tensile loads, as shown in Fig. 13. The slip lines were able to be visualized from the distribution of a part of shear strain εyx = ∂uy/∂x, as seen in Fig. 13. Since nature of dislocation slip is plastic shear deformation, the appearance of shear strain corresponding to the slip lines is reasonable. The slip-resolved strain mapping will be helpful information to clarify an underlying mechanism of damage initiation associated with local dislocation accumulation.

 

Fig. 13 Grid images and distributions of a part of shear strain of the specimen under 655, 682, 669 and 683 MPa along with time.

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5. Summary

A two-dimensional moiré phase analysis method was proposed to accurately measure the in-plane strain distributions even if the specimen grid is inclined at a large angle. The relative error of the shear strain measurement relative to the theoretical value was significantly reduced from 50% to 0.8% when there was an angle between the grating principal direction and the measuring direction. The measured normal and shear strain distributions of a Ti alloy was successfully used to predict the crack occurrence location from the strain concentration. Dynamic test and automatic batch processing are realizable for accurate strain distribution measurement in the proposed method. This method is useful for failure analysis, residual stress measurement, strengthening and toughening of materials ranging from nanoscale to meter scale, optimal design of interfaces, production quality control, structural health monitoring, etc.

Funding

Cross-ministerial Strategic Innovation Promotion Program - Innovative Measurement and Analysis for Structural Materials (SIP-IMASM) (Unit D66); Japan Society for the Promotion of Science (JSPS) KAKENHI (JP16K17988, JP16K05996).

Acknowledgments

The authors are grateful to Dr. Masataka OHKUBO in AIST, and Drs. Yoshihisa TANAKA and Kimiyoshi NAITO in NIMS for discussion on experimental design.

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11. Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012). [CrossRef]  

12. S. Kishimoto, Q. Wang, H. Xie, and Y. Zhao, “Study of the surface structure of butterfly wings using the scanning electron microscopic moiré method,” Appl. Opt. 46(28), 7026–7034 (2007). [CrossRef]   [PubMed]  

13. E. Okunishi, N. Endo, and Y. Kondo, “Atomic column elemental mapping by STEM-Moire Method,” Microsc. Microanal. 20(S3), 586–587 (2014). [CrossRef]   [PubMed]  

14. H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000). [CrossRef]  

15. H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007). [CrossRef]  

16. M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010). [CrossRef]  

17. C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013). [CrossRef]   [PubMed]  

18. Q. Wang, S. Kishimoto, and Y. Yamauchi, “Three-directional structural characterization of hexagonal packed nanoparticles by hexagonal digital moiré method,” Opt. Lett. 37(4), 548–550 (2012). [CrossRef]   [PubMed]  

19. A. Asundi and K. H. Yung, “Phase-shifting and logical moiré,” J. Opt. Soc. Am. A 8(10), 1591–1600 (1991). [CrossRef]  

20. S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010). [CrossRef]  

21. S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012). [CrossRef]  

22. S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013). [CrossRef]  

23. S. Ri, S. Hayashi, S. Ogihara, and H. Tsuda, “Accurate full-field optical displacement measurement technique using a digital camera and repeated patterns,” Opt. Express 22(8), 9693–9706 (2014). [CrossRef]   [PubMed]  

24. Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016). [CrossRef]   [PubMed]  

25. Q. Wang, S. Ri, and H. Tsuda, “Micro/nano-scale strain distribution measurement from sampling Moiré fringes,” J. Vis. Exp.in press.

26. Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013). [CrossRef]  

27. H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999). [CrossRef]  

28. M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017). [CrossRef]  

29. S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995). [CrossRef]  

30. M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012). [CrossRef]   [PubMed]  

References

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  1. C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
    [Crossref]
  2. M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
    [PubMed]
  3. G. Lütjering and J. C. Williams, Titanium, 2nd ed. (Springer-Verlag Berlin Heidelberg, Berlin, 2007).
  4. X. Huang, Z. Liu, and H. Xie, “Recent progress in residual stress measurement techniques,” Guti Lixue Xuebao 26, 570–583 (2013).
  5. Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
    [Crossref]
  6. R. Weller and B. Shepard, “Displacement measurement by mechanical interferometry,” Proc. Soc. Exp. Stress Anal. 6, 35–38 (1948).
  7. S. Yokozeki, Y. Kusaka, and K. Patorski, “Geometric parameters of moiré fringes,” Appl. Opt. 15(9), 2223–2227 (1976).
    [Crossref] [PubMed]
  8. Q. Wang, H. Tsuda, and S. Kishimoto, “Moire techniques based on memory function of laser scanning microscope for deformation measurement at micron/submicron scales,” Int. J. Automot. Technol. 9(5), 494–501 (2015).
    [Crossref]
  9. P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
    [Crossref]
  10. S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
    [Crossref]
  11. Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
    [Crossref]
  12. S. Kishimoto, Q. Wang, H. Xie, and Y. Zhao, “Study of the surface structure of butterfly wings using the scanning electron microscopic moiré method,” Appl. Opt. 46(28), 7026–7034 (2007).
    [Crossref] [PubMed]
  13. E. Okunishi, N. Endo, and Y. Kondo, “Atomic column elemental mapping by STEM-Moire Method,” Microsc. Microanal. 20(S3), 586–587 (2014).
    [Crossref] [PubMed]
  14. H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
    [Crossref]
  15. H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007).
    [Crossref]
  16. M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
    [Crossref]
  17. C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
    [Crossref] [PubMed]
  18. Q. Wang, S. Kishimoto, and Y. Yamauchi, “Three-directional structural characterization of hexagonal packed nanoparticles by hexagonal digital moiré method,” Opt. Lett. 37(4), 548–550 (2012).
    [Crossref] [PubMed]
  19. A. Asundi and K. H. Yung, “Phase-shifting and logical moiré,” J. Opt. Soc. Am. A 8(10), 1591–1600 (1991).
    [Crossref]
  20. S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
    [Crossref]
  21. S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
    [Crossref]
  22. S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013).
    [Crossref]
  23. S. Ri, S. Hayashi, S. Ogihara, and H. Tsuda, “Accurate full-field optical displacement measurement technique using a digital camera and repeated patterns,” Opt. Express 22(8), 9693–9706 (2014).
    [Crossref] [PubMed]
  24. Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
    [Crossref] [PubMed]
  25. Q. Wang, S. Ri, and H. Tsuda, “Micro/nano-scale strain distribution measurement from sampling Moiré fringes,” J. Vis. Exp.in press.
  26. Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
    [Crossref]
  27. H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
    [Crossref]
  28. M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
    [Crossref]
  29. S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
    [Crossref]
  30. M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012).
    [Crossref] [PubMed]

2017 (2)

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

2016 (1)

2015 (2)

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Q. Wang, H. Tsuda, and S. Kishimoto, “Moire techniques based on memory function of laser scanning microscope for deformation measurement at micron/submicron scales,” Int. J. Automot. Technol. 9(5), 494–501 (2015).
[Crossref]

2014 (2)

2013 (4)

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013).
[Crossref]

Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
[Crossref]

C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
[Crossref] [PubMed]

X. Huang, Z. Liu, and H. Xie, “Recent progress in residual stress measurement techniques,” Guti Lixue Xuebao 26, 570–583 (2013).

2012 (4)

Q. Wang, S. Kishimoto, and Y. Yamauchi, “Three-directional structural characterization of hexagonal packed nanoparticles by hexagonal digital moiré method,” Opt. Lett. 37(4), 548–550 (2012).
[Crossref] [PubMed]

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012).
[Crossref] [PubMed]

2011 (1)

Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
[Crossref]

2010 (3)

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

2007 (2)

H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007).
[Crossref]

S. Kishimoto, Q. Wang, H. Xie, and Y. Zhao, “Study of the surface structure of butterfly wings using the scanning electron microscopic moiré method,” Appl. Opt. 46(28), 7026–7034 (2007).
[Crossref] [PubMed]

2000 (1)

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

1999 (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

1995 (1)

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[Crossref]

1993 (1)

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

1991 (1)

1976 (1)

1948 (1)

R. Weller and B. Shepard, “Displacement measurement by mechanical interferometry,” Proc. Soc. Exp. Stress Anal. 6, 35–38 (1948).

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

Asundi, A.

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

A. Asundi and K. H. Yung, “Phase-shifting and logical moiré,” J. Opt. Soc. Am. A 8(10), 1591–1600 (1991).
[Crossref]

Bechtold, M.

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Boay, C. G.

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

Chou, S. Y.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[Crossref]

Dai, F.

H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007).
[Crossref]

Diehl, M.

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Du, H.

Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
[Crossref]

Egashira, M.

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

Endo, N.

E. Okunishi, N. Endo, and Y. Kondo, “Atomic column elemental mapping by STEM-Moire Method,” Microsc. Microanal. 20(S3), 586–587 (2014).
[Crossref] [PubMed]

Fujigaki, M.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Hamano, Y.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Han, B.

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

Hayashi, S.

Huang, X.

X. Huang, Z. Liu, and H. Xie, “Recent progress in residual stress measurement techniques,” Guti Lixue Xuebao 26, 570–583 (2013).

Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
[Crossref]

Ifju, P.

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

Kishimoto, S.

Q. Wang, H. Tsuda, and S. Kishimoto, “Moire techniques based on memory function of laser scanning microscope for deformation measurement at micron/submicron scales,” Int. J. Automot. Technol. 9(5), 494–501 (2015).
[Crossref]

Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
[Crossref]

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

Q. Wang, S. Kishimoto, and Y. Yamauchi, “Three-directional structural characterization of hexagonal packed nanoparticles by hexagonal digital moiré method,” Opt. Lett. 37(4), 548–550 (2012).
[Crossref] [PubMed]

H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007).
[Crossref]

S. Kishimoto, Q. Wang, H. Xie, and Y. Zhao, “Study of the surface structure of butterfly wings using the scanning electron microscopic moiré method,” Appl. Opt. 46(28), 7026–7034 (2007).
[Crossref] [PubMed]

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

Kobayashi, D.

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

Kondo, Y.

E. Okunishi, N. Endo, and Y. Kondo, “Atomic column elemental mapping by STEM-Moire Method,” Microsc. Microanal. 20(S3), 586–587 (2014).
[Crossref] [PubMed]

Koyama, M.

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Krauss, P. R.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[Crossref]

Kusaka, Y.

Li, C.

Li, X.

Li, Y.

Liu, Z.

Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
[Crossref]

C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
[Crossref] [PubMed]

X. Huang, Z. Liu, and H. Xie, “Recent progress in residual stress measurement techniques,” Guti Lixue Xuebao 26, 570–583 (2013).

Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
[Crossref]

Lou, X.

Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
[Crossref]

Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
[Crossref]

Mitsuhara, M.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Morimoto, Y.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Muramatsu, T.

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

Nanbara, K.

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

Ngoi, B. K.

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

Noguchi, H.

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Ogihara, S.

Ohkubo, M.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Okunishi, E.

E. Okunishi, N. Endo, and Y. Kondo, “Atomic column elemental mapping by STEM-Moire Method,” Microsc. Microanal. 20(S3), 586–587 (2014).
[Crossref] [PubMed]

Patorski, K.

Peranio, N.

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Ponge, D.

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Raabe, D.

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Renstrom, P. J.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[Crossref]

Ri, S.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
[Crossref] [PubMed]

S. Ri, S. Hayashi, S. Ogihara, and H. Tsuda, “Accurate full-field optical displacement measurement technique using a digital camera and repeated patterns,” Opt. Express 22(8), 9693–9706 (2014).
[Crossref] [PubMed]

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Micro/nano-scale strain distribution measurement from sampling Moiré fringes,” J. Vis. Exp.in press.

Roters, F.

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Saka, M.

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

Schemmann, L.

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Shepard, B.

R. Weller and B. Shepard, “Displacement measurement by mechanical interferometry,” Proc. Soc. Exp. Stress Anal. 6, 35–38 (1948).

Shinya, N.

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

Tanaka, Y.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Tang, M.

M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012).
[Crossref] [PubMed]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

Tasan, C. C.

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Tsuda, H.

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
[Crossref] [PubMed]

Q. Wang, H. Tsuda, and S. Kishimoto, “Moire techniques based on memory function of laser scanning microscope for deformation measurement at micron/submicron scales,” Int. J. Automot. Technol. 9(5), 494–501 (2015).
[Crossref]

S. Ri, S. Hayashi, S. Ogihara, and H. Tsuda, “Accurate full-field optical displacement measurement technique using a digital camera and repeated patterns,” Opt. Express 22(8), 9693–9706 (2014).
[Crossref] [PubMed]

Q. Wang, S. Ri, and H. Tsuda, “Micro/nano-scale strain distribution measurement from sampling Moiré fringes,” J. Vis. Exp.in press.

Tsuzaki, K.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

Wang, M.

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

Wang, Q.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
[Crossref] [PubMed]

Q. Wang, H. Tsuda, and S. Kishimoto, “Moire techniques based on memory function of laser scanning microscope for deformation measurement at micron/submicron scales,” Int. J. Automot. Technol. 9(5), 494–501 (2015).
[Crossref]

Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
[Crossref]

Q. Wang, S. Kishimoto, and Y. Yamauchi, “Three-directional structural characterization of hexagonal packed nanoparticles by hexagonal digital moiré method,” Opt. Lett. 37(4), 548–550 (2012).
[Crossref] [PubMed]

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007).
[Crossref]

S. Kishimoto, Q. Wang, H. Xie, and Y. Zhao, “Study of the surface structure of butterfly wings using the scanning electron microscopic moiré method,” Appl. Opt. 46(28), 7026–7034 (2007).
[Crossref] [PubMed]

Q. Wang, S. Ri, and H. Tsuda, “Micro/nano-scale strain distribution measurement from sampling Moiré fringes,” J. Vis. Exp.in press.

Weller, R.

R. Weller and B. Shepard, “Displacement measurement by mechanical interferometry,” Proc. Soc. Exp. Stress Anal. 6, 35–38 (1948).

Wu, D.

Xie, H.

C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
[Crossref] [PubMed]

X. Huang, Z. Liu, and H. Xie, “Recent progress in residual stress measurement techniques,” Guti Lixue Xuebao 26, 570–583 (2013).

Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
[Crossref]

M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012).
[Crossref] [PubMed]

Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
[Crossref]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007).
[Crossref]

S. Kishimoto, Q. Wang, H. Xie, and Y. Zhao, “Study of the surface structure of butterfly wings using the scanning electron microscopic moiré method,” Appl. Opt. 46(28), 7026–7034 (2007).
[Crossref] [PubMed]

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

Yamanouchi, K.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Yamasaki, S.

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Yamauchi, Y.

Yan, D.

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Yokozeki, S.

Yu, J.

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

Yung, K. H.

Zhang, Z.

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

Zhao, Y.

Zheng, C.

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Zhu, J.

M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012).
[Crossref] [PubMed]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

Annu. Rev. Mater. Res. (1)

C. C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama, K. Tsuzaki, and D. Raabe, “An overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design,” Annu. Rev. Mater. Res. 45(1), 391–431 (2015).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[Crossref]

Exp. Mech. (4)

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52(4), 331–340 (2012).
[Crossref]

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamic thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling moiré method and grating magnets,” Exp. Mech. 53(9), 1635–1646 (2013).
[Crossref]

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

Guti Lixue Xuebao (1)

X. Huang, Z. Liu, and H. Xie, “Recent progress in residual stress measurement techniques,” Guti Lixue Xuebao 26, 570–583 (2013).

Int. J. Automot. Technol. (1)

Q. Wang, H. Tsuda, and S. Kishimoto, “Moire techniques based on memory function of laser scanning microscope for deformation measurement at micron/submicron scales,” Int. J. Automot. Technol. 9(5), 494–501 (2015).
[Crossref]

J. Appl. Phys. (1)

H. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007).
[Crossref]

J. Micromech. Microeng. (1)

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

J. Opt. Soc. Am. A (1)

Mater. Charact. (1)

M. Koyama, K. Yamanouchi, Q. Wang, S. Ri, Y. Tanaka, Y. Hamano, S. Yamasaki, M. Mitsuhara, M. Ohkubo, H. Noguchi, and K. Tsuzaki, “Multiscale in situ deformation experiments: A sequential process from strain localization to failure in a laminated Ti-6Al-4V alloy,” Mater. Charact. 128, 217–225 (2017).
[Crossref]

Meas. Sci. Technol. (2)

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

Z. Liu, X. Huang, H. Xie, X. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011).
[Crossref]

Microelectron. Reliab. (1)

Q. Wang, S. Kishimoto, H. Xie, Z. Liu, and X. Lou, “In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis,” Microelectron. Reliab. 53(4), 652–657 (2013).
[Crossref]

Microsc. Microanal. (1)

E. Okunishi, N. Endo, and Y. Kondo, “Atomic column elemental mapping by STEM-Moire Method,” Microsc. Microanal. 20(S3), 586–587 (2014).
[Crossref] [PubMed]

Nanotechnology (1)

H. Xie, S. Kishimoto, A. Asundi, C. G. Boay, N. Shinya, J. Yu, and B. K. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[Crossref]

Opt. Commun. (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4-6), 205–210 (1999).
[Crossref]

Opt. Eng. (1)

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Proc. Soc. Exp. Stress Anal. (1)

R. Weller and B. Shepard, “Displacement measurement by mechanical interferometry,” Proc. Soc. Exp. Stress Anal. 6, 35–38 (1948).

Science (1)

M. Koyama, Z. Zhang, M. Wang, D. Ponge, D. Raabe, K. Tsuzaki, H. Noguchi, and C. C. Tasan, “Bone-like crack resistance in hierarchical metastable nanolaminate steels,” Science 355(6329), 1055–1057 (2017).
[PubMed]

Other (2)

G. Lütjering and J. C. Williams, Titanium, 2nd ed. (Springer-Verlag Berlin Heidelberg, Berlin, 2007).

Q. Wang, S. Ri, and H. Tsuda, “Micro/nano-scale strain distribution measurement from sampling Moiré fringes,” J. Vis. Exp.in press.

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Figures (13)

Fig. 1
Fig. 1 (a) Diagram of a 2D grid including 2 parallel gratings on specimen, (b) Geometric relationship of gratings before and after deformation.
Fig. 2
Fig. 2 Principle of the sampling moiré method for calculating phase distribution from an oblique grating.
Fig. 3
Fig. 3 Flow chart and measurement process of the proposed technique for accurate strain distribution measurement.
Fig. 4
Fig. 4 (a) Diagram of a regular grid under an applied 2D strain status when the oblique angle θ is variable, and (b)-(g) Measurement process of 2D strain distributions.
Fig. 5
Fig. 5 Comparison of the proposed 2D phase analysis technique and the traditional 1D phase analysis method in measurements of the x-direction strain, the y-direction strain and the shear strains.
Fig. 6
Fig. 6 Relative errors of the measured x-direction, y-direction and shear strains from the proposed 2D phase analysis technique and the traditional 1D phase analysis method relative to the theoretical strains along with the grid oblique angle.
Fig. 7
Fig. 7 (a) Diagram of a regular grid with a random noise of σ = 2% under a 2D strain status when the oblique angle is 10° (b)Absolute errors, (c) relative errors and (d) standard deviations of the measured 2D strains from the proposed technique along with the theoretical strains.
Fig. 8
Fig. 8 (a) Specimen geometry of the Ti alloy and (b) the used tensile device under a laser scanning microscope.
Fig. 9
Fig. 9 Region of interest on the Ti alloy and the fabricated 3-μm-pitch grid image.
Fig. 10
Fig. 10 Process of moiré phase analysis on the Ti alloy when the tensile load is 604 MPa. (a) Grid image, (b) and (c) spatial phase-shifting moiré fringes in the x and y direction, respectively, and (d) and (e) moiré phases in the x and y direction, respectively.
Fig. 11
Fig. 11 Distributions of x-direction, y-direction and shear strains of the Ti alloy under tensile loads of (a)-(d) 225 MPa, (e)-(h) 312 MPa, (i)-(l) 478 MPa, (m)-(p) 604 MPa, and (q)-(t) 660 MPa before damage occurrence.
Fig. 12
Fig. 12 (a) Grid image and (b) enlarge image around prior β boundary on the Ti alloy after unloading from 710 MPa.
Fig. 13
Fig. 13 Grid images and distributions of a part of shear strain of the specimen under 655, 682, 669 and 683 MPa along with time.

Equations (26)

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I= A X cos[2π( x p Xx + y p Yy )]+ A Y cos[2π( x p Yx + y p Yy )]+B
I X = A X cos[2π( x p Xx + y p Xy )]+ B X = A X cos φ X + B X
I Y = A Y cos[2π( x p Yx + y p Yy )]+ B Y = A Y cos φ Y + B Y
I = A X cos[2π( x p Xx + y p Yy )]+ A Y cos[2π( x p Yx + y p Yy )]+ B
I X = A X cos[2π( x p Xx + y p Xy )]+ B X = A X cos φ X + B X
I Y = A Y cos[2π( x p Yx + y p Yy )]+ B Y = A Y cos φ Y + B Y
Δ φ X = φ X φ X =2π[( x p Xx + y p Xy )( x p Xx + y p Xy )]
Δ φ Y = φ Y φ Y =2π[( x p Yx + y p Yy )( x p Yx + y p Yy )]
I X,mx ( k x )= A X cos[2π( x p Xx + y p Xy x N x + k x N x )]+ B X = A X cos[ φ X,mx +2π k x N x )]+ B X
I X,mx ( k x )= A X cos[2π( x p Xx + y p Xy x N x + k x N x )]+ B X = A X cos[ φ X,mx +2π k x N x )]+ B X ( k x =0, 1,, N x 1 )
I Y,my ( k y )= A Y cos[2π( x p 2x + y p Yy y N y + k y N y )]+ B Y = A Y cos[ φ Y,my +2π k y N y )]+ B Y
I Y,my ( k y )= A Y cos[2π( x p 2x + y p Yy y N y + k y N y )]+ B Y = A Y cos[ φ Y,my +2π k y N y )]+ B Y ( k y =0, 1,..., N y 1 )
φ J,mj =-arctan k j =0 T j 1 I J,mj ( k j )sin(2π k j / N j ) k j =0 T j 1 I J,mj ( k j )cos(2π k j / N j ) φ J,mj =-arctan k j =0 T j 1 I J,mj ( k j )sin(2π k j / N j ) k j =0 T j 1 I J,mj ( k j )cos(2π k j / N j ) { j=x when J=X j=y when J=Y
Δ φ X,mx = φ X,mx φ X,mx =2π( x p Xx + y p Xy x N x )2π( x p Xx + y p Xy x N x ) =2π[( x p Xx + y p Xy )( x p Xx + y p Xy )]=Δ φ X
Δ φ Y,my = φ Y,my φ Y,my =2π( x p Yx + y p Yy y N y )2π( x p Yx + y p Yy y N y ) =2π[( x p Yx + y p Yy )( x p Yx + y p Yy )]=Δ φ Y
φ X =2π( x u x p Xx + y u y p Xy )
φ Y =2π( x u x p Yx + y u y p Yy )
Δ φ X =2π( x u x p Xx + y u y p Xy )2π( x p Xx + y p Xy ) =2π( u x p Xx + u y p Xy )
Δ φ Y =2π( x u x p Yx + y u y p Yy )2π( x p Yx + y p Yy ) =2π( u x p Yx + u y p Yy )
( Δ φ X,mx Δ φ Y,my )=2π( 1/ p Xx 1/ p Xy 1/ p Yx 1/ p Yy )( u x u y )
( u x u y )= 1 2π ( 1/ p Xx 1/ p Xy 1/ p Yx 1/ p Yy ) 1 ( Δ φ X,mx Δ φ Y,my )= M 2π ( Δ φ X,mx Δ φ Y,my )
( ε xx ε xy ε yx ε yy )= M 2π ( Δ φ X,mx x Δ φ X,mx y Δ φ Y,my x Δ φ Y,my y ) γ xy = ε xy + ε yx
M= ( sin θ X / p X cos θ X / p X sin θ Y / p Y cos θ Y / p Y ) 1
M= ( sin(θ+ π 2 )/p cos(θ+ π 2 )/p sinθ/p cosθ/p ) 1 =p ( cosθ sinθ sinθ cosθ ) 1
( u x u y )= p 2π ( cosθ sinθ sinθ cosθ ) 1 ( Δ φ X,mx Δ φ Y,my )
( ε xx ε xy ε yx ε yy )= p 2π ( cosθ sinθ sinθ cosθ ) 1 ( Δ φ X,mx x Δ φ X,mx y Δ φ Y,my x Δ φ Y,my y ) γ xy = ε xy + ε yx

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