1. Introduction

The moiré method [1–3 ] is a high-sensitivity, full-field, noncontact, and flexible approach to determining the in-plane and off-plane deformation fields of a specimen over a broad range of scales. To implement the moiré method, a grating is pre-fabricated on a specimen surface, which is referred to as the specimen grating or deformed grating. Then, a standard grating (or virtual grating) is superimposed on the specimen grating to form light and dark lines, referred to as fringes. Each fringe represents a contour line of displacement in the measured direction and, thus, the full-field deformation can be determined. The available literature reflects the extremely wide application of the moiré method, and includes measurements of constitutive parameters [4], residual stress [5, 6 ], thermal mismatch [7, 8 ], crack tip displacement fields [9, 10 ], grain boundary sliding [11], creep deformation [3, 12 ], and periodic structure characterization [13, 14 ].

There are three main moiré methods: geometrical moiré [1], moiré interferometry [2], and scanning moiré [3]. The displacement sensitivity of the moiré method is proportional to the grating frequency and, thus, a high-frequency grating is crucial to ensure precise measurement. Geometrical moiré is the traditional technique, in which fringes are created by superimposing low-frequency gratings (only a few tens of lines per millimeter). However, the resultant displacement sensitivity is inadequate for the majority of modern measurements. Moiré interferometry combines the concepts and techniques of geometrical moiré and laser interference, and can be used to measure displacement over a large area with both high sensitivity and excellent clarity. Therefore, moiré interferometry is widely employed in analyses of the mechanics and micromechanics of materials and structures [2]. Finally, scanning moiré is an advanced geometrical moiré technique in which the standard reference grating is replaced by the scanning lines of a scanning imaging microscope (referred to as a virtual grating). The frequency of the specimen grating can be very high in this case. Therefore, the displacement sensitivity of scanning moiré can be extremely high, although the measurement area is reduced because of the limited number of scanning lines.

Moiré interferometry and scanning moiré have potential applications in engineering; however, difficulties regarding specimen-grating fabrication significantly hamper industrialization of these techniques [4]. When a grating is employed in a moiré test, several technical parameters must be considered, including the frequency uniformity, thickness, working area, micromorphology, and diffraction efficiency. The frequency uniformity is a key parameter affecting the null field, in which no fringe is desired, and a grating with poor frequency uniformity yields a number of severe distortion fringes that can cause the experiment to fail. The grating thickness is related to the shear lag, which is due to attenuation of the shear stress in the grating as it propagates through the grating material. Therefore, a thick grating may cause a concealed error. In addition, an overly thick grating will also delaminate easily. The working area determines the test region, and a large test region can offer more information and increased test efficiency. The micromorphology is important as regards the clarity of the fringe pattern, particularly for scanning moiré, and high clarity is necessary for fluent data processing. In moiré interferometry, a grating with high diffraction efficiency can allow lower-power lasers to be used. In addition, such a grating can reduce the exposure time, which is desirable in the case of a dynamic measurement. In summary, a specimen grating should possess excellent uniformity, small thickness, a large working area, fine micromorphology, and high diffraction efficiency in order to guarantee a successful test.

To date, several techniques for producing high-frequency specimen gratings have been developed, including holographic photolithography (or laser interferometry photolithography) [15], electron beam lithography (EBL) [3, 16 ], focused ion beam (FIB) lithography [17], nanoimprint lithography (NIL) [18], and solvent-assisted microcontact molding (SAMIM) [19]. Unfortunately, these methods can only satisfy a few of the above technical requirements and exhibit various disadvantages, which limit their application significantly. For example, although holographic photolithography is generally used to create gratings with a frequency of several thousand lines per millimeter, it is difficult to fabricate a grating on a specimen directly using this method, because of the resist spin-coating step; thus, an additional replication process is required [2]. In addition, holographic photolithography has strict requirements for a coherent light source and a vibration isolation platform. Both EBL and FIB exhibit fine precision and flexibility, being capable of yielding ultra-high-frequency gratings (up to tens of thousands of lines per millimeter); however, as a result of their low-efficiency serial manufacturing, these methods are not suitable for large-area patterning. Although NIL is a large-area manufacturing method with high precision, a fragile stamp is employed and target surface flatness is strictly required. As a result, this technique is restricted to direct imprinting of a grating on a specimen surface. SAMIM is similar to NIL but, in this case, a soft elastomeric stamp is employed to mold the microstructure. Thus, the requirement for target surface flatness is relaxed. However, it is difficult to fabricate a grating on a specimen directly using SAMIM, owing to the resist spin-coating step involved in this technique. Instead, the grating is first molded on a medium polymer substrate and then transferred onto the specimen using an additional replication process. Based on the disadvantages of the various techniques described above, it is apparent that a low-cost grating fabrication technique that yields gratings with high frequency, high efficiency, and large area is required.

Solute-solvent separation soft lithography (3S soft lithography) [20] is an emerging technique for the molding of microstructures using a soft elastomeric stamp, the operational principles of which are similar to SAMIM. However, 3S soft lithography is more versatile and flexible. In this process, a specific stamp is used to mold a solution pool that is prepared on a substrate by mixing a resist and solvent. The solvent is absorbed by the stamp, but the resist solidifies on the substrate and copies the relief pattern on the stamp. Thus, the basic mechanism behind 3S soft lithography is that the stamp absorbs the solvent and filters the resist. 3S soft lithography offers the following advantages: First, this technique has a proven capability to fabricate large-area microstructures. Second, its molding process, stamp fabrication, and solution preparation are all simple and can be realized in an ordinary laboratory, rendering it an affordable technique for use in experimental mechanics testing. Third, patterns can be fabricated without resist residues, which is an attractive advantage as regards the preparation of a zero-thickness grating [2].

In this study, 3S soft lithography is employed to fabricate both a transfer grating and a zero-thickness grating, and the technical parameters of these gratings, i.e., the frequency uniformity, micromorphology, thickness, and shear lag, are studied. As two typical applications, use of the fabricated gratings in moiré interferometry and scanning moiré is demonstrated experimentally.

2. Grating fabrication based on 3S soft lithography

2.1. Principles of 3S soft lithography

In 3S soft lithography, a solution is first prepared by mixing the resist and solvent. In this study, polymethyl methacrylate (PMMA) and acetone were employed as the resist and solvent, respectively. Then, the solution is dropped onto a polished substrate (specimen or glass) and covered by a polydimethylsiloxane (PDMS) stamp. Conformal contact is maintained through application of additional pressure for several minutes. Hence, a negative resist pattern is obtained on the substrate after demolding. If a diluted solution is employed, a residual-layer-free pattern can be obtained; otherwise, a residual resist emerges, as shown in Fig. 1 .

 

Fig. 1 Principles of 3S soft lithography.

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2.2. Fabrication and characterization of hybrid PDMS stamp

For effective application of the moiré method, the grating must have high frequency uniformity, as an initial distortion could disturb the measurement and lead to unreliable results [19]. The conventionally used PDMS stamp is too soft to resist deformation (PDMS shear modulus: ~1 MPa) and thus, the in-plane/lateral distortion of the PDMS stamp must be constrained. However, the off-plane flexibility should be retained, because abundant off-plane flexibility is necessary to obtain intimate contact between the stamp and the substrate surface. Considerable research effort has been employed in order to solve this problem and, in our experience, the hybrid PDMS stamp [21, 22 ] seems to be very effective. Therefore, a two-layer hybrid PDMS stamp was employed in this study, so as to increase the PDMS in-plane stiffness without degrading the off-plane flexibility. The hybrid PDMS stamp was composed of quartz and PDMS (Sylgard 184, Dow Corning; mixing mass ratio: 10:1). Thus, the quartz could support and restrain the PDMS layer (which was affected by curing shrinkage, solvent-induced swelling, and compressive deformation).

Figure 2 shows the hybrid PDMS stamp fabrication process. A thin primer (92-023 primer, Dow Corning) layer was placed on a clean quartz slice via spin coating, with rotate speed of 3000 r/min for 60 s. The geometric dimensions of the quartz slice were 64 mm × 64 mm × 1 mm. Then, the PDMS prepolymer was degassed using a centrifugal machine and poured on a master mold. The master gratings were holographic gratings (including crossing type and parallel type gratings), the frequencies were 600 line/mm and 1200 line/mm, and the groove depths were about 300 nm and 100 nm, respectively. The quartz slice was immersed in the PDMS prepolymer, and the lower part of the PDMS layer was squeezed through application of pressure on the quartz slice. The PDMS prepolymer was then cured at 65°C for 2 h under 10-Pa vacuum pressure (in a vacuum drying oven). Finally, the hybrid PDMS stamp was obtained following demolding and peeling of the supernatant PDMS. The grating area was 55 mm × 55 mm and the PDMS layer had 150 ± 10-μm thickness. Hybrid PDMS stamps with PDMS layer thicknesses of 1 and 2 mm were also fabricated using the above method, to facilitate comparison between different stamps.

 

Fig. 2 Schematic diagram of two-layer hybrid PDMS stamp-fabrication process.

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During the stamp fabrication process, curing shrinkage of the PDMS prepolymer can induce undesired in-plane distortion, which degrades the frequency uniformity. Therefore, moiré interferometry was employed in order to measure this distortion. Note that the height of the grating line or dot (grating microstructure) on the PDMS was approximately 100 nm, and a line or dot of that size can only minimally influence the in-plane deformation of a PDMS layer with a thickness of more than 150 μm. Therefore, the grating microstructure was ignored during the characterization of the in-plane distortion. In this study, a moiré interferometer was designed for a grating with 1200-line/mm frequency; thus, a hybrid PDMS stamp with a grating frequency of 1200 line/mm was examined as a sample case. For a grating frequency of 1200 line/mm, the displacement increment between two adjacent fringes is 417 nm (see Eq. (2), section 4.1), and any region with an in-plane displacement of more than 417 nm is defined as a failure zone. (For more details on this characterization method, please refer to our previous work [23].) The characterization results are shown in Fig. 3 . Note that the fringes become too dense to be distinguished near the border, which indicates a severe in-place distortion. Obviously, the distortion is severe near the stamp border and weak in the central region, and the failure zone expands as the PDMS-layer thickness increases. This result suggests that the quartz slice can constrain the PDMS layer with 150-μm thickness effectively; thus, this stamp design was used in the subsequent grating fabrication.

 

Fig. 3 In-plane distortion characterization results for hybrid PDMS stamps with different PDMS layer thicknesses. (a) Location of characterization region A. Fringe patterns of stamps with (b) 153-μm, (c) 1-mm, and (d) 2-mm PDMS layer thicknesses. The numbers in Figs. 3(b)-3(d) indicate the widths of distortion regions, and the unit of scale is millimeter.

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2.3. Grating fabrication

The grating fabrication process is shown in Fig. 4 . First, a grating was fabricated on the surface of a polished specimen or glass using 3S soft lithography. If the solution concentration was less than 0.22 g/100 ml [20], a residual-layer-free grating could be obtained (zero-thickness grating; Fig. 4(a)). Otherwise, a grating with a residual resist was obtained (transfer grating; Fig. 4(b)). In this study, solutions with concentrations of 0.15 and 0.30 g/100 ml were used for the zero-thickness grating and the transfer grating, respectively.

 

Fig. 4 Schematic diagram of grating fabricated via 3S soft lithography procedure. (a) Grating fabrication process on specimen/glass surface (zero-thickness grating). (b) Transfer of grating onto specimen surface (transfer grating).

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As shown in previous tests, zero-thickness gratings are versatile [2]. For example, the fringes obtained using such gratings in scanning electron microscopy (SEM) moiré have high clarity, owing to the contrast between the atomic structures of the resist and specimen material. In moiré interferometry, following evaporation of a refractory metal film on the grating, zero-thickness gratings can be employed in high-temperature tests. In addition, zero-thickness gratings can be processed using reactive ion etching (RIE) to yield a more durable grating. In the RIE process, a specimen with a zero-thickness grating is ion etched in a gas atmosphere that reacts chemically with the specimen material. The rate of attack on the specimen material is significantly higher than that on the resist; thus, the grating can be etched deeply into the specimen surface. Further, zero-thickness gratings are free from shear lag and delamination disturbances. If a grating is to be fabricated on the specimen directly, the specimen surface should be polished to a smooth mirror-like finish. However, if the specimen material cannot be polished (for example, ceramics and composites), a transfer type grating can be used instead, as the adhesive can compensate for the rugged surface of the specimen.

A grating with a residual resist can serve as a master mold for a transfer grating [4]. Note that transfer gratings are generally fabricated on glass slices, because of this material’s high stiffness and ease of cutting. The residual resist can fully separate the coated metal film and glass and prevent the formation of strong adhesion, so that the metal film can be stripped off using a common epoxy adhesive. Further, Al film can be evaporated on a grating with a residual resist fabricated on a specimen surface; this is beneficial as the resultant grating has low thickness as well as high diffraction efficiency.

The transfer grating process is shown in Fig. 4(b). First, a thin metal film is coated on the resist using a vacuum thermal evaporation technique, following the 3S soft lithography process shown in Fig. 4(a). Then, the metal film is transferred to the specimen using an adhesive, which must be stronger than the interfacial strength between the metal film and PMMA. Before this adhesive is coated on the film, the air bubbles should be removed from the adhesive using a centrifuge machine. In addition, an appropriate pressure is required in order to fix the grating and to thin the adhesive layer. After curing, the specimen and glass can be separated carefully, and the acetone can be used to eliminate the PMMA transferred to the specimen surface along with the metal film. The metal film can be Al or Cr; Al film yields superior diffraction efficiency as a result of its high reflectivity, whereas Cr film can withstand higher temperatures during testing [4].

3. Quality characterization

3.1. Frequency uniformity

In a moiré test, a grating with poor frequency uniformity or distortion will yield an extremely irregular initial fringe pattern. Thus, the test will fail, as the specimen deformation will be occluded by the irregular fringes. Although the shrinkage distortion of the 150-μm hybrid PDMS stamp was constrained in this study, the PDMS swelled when absorbing the solution and deformed under compression during the 3S soft lithography process. Further, certain random factors, such as uneven pressure and trapped dust particles and bubbles, can deform the hybrid PDMS stamp. Of course, any lateral deformation of the elastomeric stamp is inherited by the fabricated grating, and this can degrade the grating frequency uniformity. Therefore, it is of considerable importance that the grating distortion is characterized before use.

Here, in order to examine the grating distortion, gratings with 1200-line/mm frequency were fabricated (concentrate solution: 0.30 g/100 ml). Three regions were examined, on the middle M, border B, and corner C of each grating (Fig. 5 ), and the corresponding results on the master mold were also obtained for comparison. The characterization results for one grating are shown in Fig. 6 . Obviously, the frequency uniformity of the master mold is acceptable (Figs. 6(a)−6(c)) as there is only one fringe, which may have been caused by a moiré interferometer system error. However, the dense fringe patterns exhibit severe distortion at the border and corner of the fabricated grating (Figs. 6(e) and 6(f)). Here, the fringe density is proportional to the frequency error, and 1 fringe/mm corresponds to a frequency error of 0.5 line/mm. Based on the characterization of other transfer gratings, a conservative conclusion that the effective zones of these gratings are approximately 70% of the working area can be drawn (the width of the failure zone around the border is less than 10 mm).

 

Fig. 5 Schematic diagram of three characterization regions M, B, and C on fabricated grating. The unit of scale is millimeter.

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Fig. 6 Fringe-pattern characterization results. (a), (b), and (c) are the fringe patterns of the master mold corresponding to the M, B, and C regions in Fig. 5.(d), (e), and (f) are the fringe patterns of the fabricated grating corresponding to the M, B, and C regions in Fig. 5. The numbers in Figs. 6(e) and 6(f) indicate the widths of distortion regions, and the unit of scale is millimeter.

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3.2. Grating micromorphology and thickness

The micromorphologies and thicknesses of the fabricated gratings were then examined. A zero-thickness grating was fabricated on a polished nickel base alloy (GH4169), and a transfer grating was also transferred to another nickel base alloy (unpolished). Both gratings were parallel type with 1200-line/mm frequency. Their micromorphologies were observed via SEM (Quanta 450, FEI), as shown in Fig. 7 . The zero-thickness grating exhibited high contrast because of its sharp edge and variations in chemical composition, whereas the contrast of the transfer grating was slightly weak, owing to its smooth geometric shape and single-chemical composition.

 

Fig. 7 SEM images of gratings with 1200-line/mm frequency. (a) Zero-thickness grating and (b) transfer grating.

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The grating thicknesses were determined from their cross sections. Note that Au particles were sputtered on the gratings to enhance the electric conduction of the epoxy. The cross section of the transfer grating could then be easily viewed via SEM. As shown in Fig. 8 , the transfer grating thickness was approximately 25 μm. However, for the zero-thickness grating, it was difficult to obtain a clear image by observing the cross section directly via SEM, because of the degradation of the grating near the specimen border. Therefore, FIB (LYRA3, Tescan) was used to etch a wedge on the grating for viewing of the cross section. The grating was first fabricated on an Si wafer (which is easily etchable), and a thin layer of Au was then sputtered on the grating surface to enhance the electric conduction of the PMMA. An SiO₂ protective layer was then deposited on the etching region and a deep wedge was etched, so as to facilitate the viewing of the cross section (Fig. 9 ). In Fig. 9, it is apparent that there is no residual resist and that the grating line height is approximately 72 nm. Note that atomic force microscopy (AFM) can also be used to measure the height of the grating line; however, this technique cannot indicate whether or not any residual resist is present.

 

Fig. 8 Transfer-grating cross section.

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Fig. 9 Zero-thickness-grating cross section.

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The transfer grating fabricated using the method presented in this study has a smooth shape and can be transferred to various macroscopic specimen surfaces (for example, metals, ceramics, and composites); thus, it is suitable for moiré interferometry testing. Further, its 25-μm thickness causes almost no deformation of the macroscopic specimen. The zero-thickness grating produced using the proposed method exhibits high contrast under SEM; thus, it is suitable for SEM moiré. In addition, the zero-thickness grating can also serve as a mask for subsequent etching or deposition (following the grating preparation) to fabricate a high-temperature-resistant grating.

3.3. Shear lag

Although we wished to measure the deformation of the specimen surface, only the grating deformation could be recorded. The difference in deformation between the grating and subjacent specimen can be non-negligible, under conditions of large gradient deformation and for a grating layer that is overly thick. The reason for this is the shear lag, whereby the shear stress in the grating attenuates as it propagates through the grating material (recall that the magnitude of the shear lag is influenced by the grating thickness) [2]. In this part of the study, the impacted indentation method was used to induce severe deformation around indentations on the nickel base alloy, as shown in Fig. 10 , and the grating morphologies and deformations around the indentations were then detected using SEM and SEM moiré (Quanta 450, FEI).

 

Fig. 10 Schematic diagram showing indentation locations (U and S) on nickel base alloy.

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As shown in Fig. 11 , the fringe yielded by the zero-thickness grating is sharp, and the edge of the indentation is clear and well-defined. In contrast, the fringe yielded by the transfer grating is obscure, the edge of the indentation is indistinct, and some delimitation between the Al film and epoxy has occurred. Because the nickel base alloy is a crystalline material, the deformation of the crystal grains is unevenly distributed in terms of both intensity and direction. In addition, slip lines are apparent where the deformation was within the plasticity range. Therefore, the strain on the transfer grating was discontinuous, i.e., there was a large strain gradient, which could lead to severe shear lag in this grating. This conclusion is confirmed by the smooth fringes. Obviously, the zero-thickness grating more accurately reflected the severe deformation caused by the indentation, as a result of its ultra-low thickness.

 

Fig. 11 SEM moiré analysis of the region to the right of indentation U (test region, Fig. 10). Specimens with (a) zero-thickness grating and (b) transfer grating.

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In addition, we also noted a feature of the transfer grating that should be considered during application. As shown in Fig. 12 , a microcrack occurs on the nickel base alloy, but not in the epoxy, which obstructs the microcrack at the interface. The grating is required to indicate the specimen surface deformation faithfully; however, it may yield inaccurate information for damaged regions. In other words, the transfer grating is not suitable for application under conditions involving large strain gradients and fracturing.

 

Fig. 12 SEM image of region above indentation S (test region, Fig. 10) on specimen with transfer grating. (a) Overview of S, (b) micrograph of epoxy and nickel base alloy interface.

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4. Application in moiré interferometry

4.1. Principles of moiré interferometry

The principles of moiré interferometry are shown schematically in Fig. 13 . Diffraction occurs when two coherent laser beams symmetrically illuminate a specimen grating. If the laser wavelength λ, incident angle α, and specimen grating frequency f_s satisfy

 

Fig. 13 Schematic of moiré interferometry setup and principles.

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Before a test, the null field (the case in which there are almost no fringes in the view field) is required in order to confirm the acceptability of the moiré interferometer and specimen grating conditions. Following specimen deformation, additional fringes occur, which represent the displacement contours in the measured direction. The displacement fields (u, v) and the strain fields (${\epsilon }_x,{\epsilon }_y,{\gamma }_{xy}$) can be extracted from the fringe pattern using

4.2. Residual stress measurement

Residual stresses influence the service performance of practical engineering components significantly, having a notable effect on their strengths, fatigue lifetimes, and dimensional stability [24]. Therefore, determining the magnitudes of these stresses is of considerable importance, and many such methods have been developed. Among the relaxation methods for measuring residual stress, the hole-drilling method is probably the most widely used [24]. In this technique, a small hole is drilled in the surface of the specimen and the in-plane deformation around the hole is measured. Traditionally, strain gauges were used for this measurement [25], however, full-field optical techniques such as moiré interferometry have been employed more recently [26].

In this study, the feasibility of the transfer grating was demonstrated by using it to determine the residual stress (design value: 105 ± 23 MPa) of a specially designed interference fit structure. A crossing grating with a frequency of 1200 line/mm was employed, and the diameter and depth of the hole were 2.0 and 1.9 mm, respectively. The hole was drilled using a flat-end drilling cutter. Figure 14 shows the results of our residual stress test. By comparing the experimental data with the results of a finite element calculation [27], the residual stress was determined to be 97 MPa, which is within the acceptable range of deviation from the designed residual stress.

 

Fig. 14 Residual stress test results. (a) Surface of specimen with grating and small hole, (b) SEM image of crossing grating with 1200-line/mm frequency, (c) fringe pattern around hole, (d) displacement field around hole.

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4.3. Principles of SEM moiré

The principles of SEM moiré are shown schematically in Fig. 15 . The SEM records an image by scanning the specimen surface line-by-line; the scanning lines can therefore be regarded as a reference/virtual grating. When a grating is scanned by an SEM with a matching scanning-line spatial frequency, a fringe pattern can be created. In essence, SEM moiré is achieved via superposition of the scanning electron beams and the specimen grating.

 

Fig. 15 Schematic diagram of SEM moiré method.

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When a spatial length L is scanned using a certain number of scanning lines n, the spatial frequency f of the reference grating can be determined from

Based on the geometric moiré theory, the u, v and ${\epsilon }_x,{\epsilon }_y,{\gamma }_{xy}$ values can be extracted from

Note that Eqs. (5) and (6) are similar to Eqs. (2) and (3) , and the only difference is the frequency coefficient. This difference results from the difference in the fringe generation mechanism.

4.4. Crack opening displacement measurement

The crack opening displacement (COD) is a critical parameter in fracture mechanics and can be easily determined from the moiré fringe [10]. The determination process is shown in Fig. 16 . First, the intersection points (M and N) of the two sides of the crack are located. Then, the change in the fringe numbers in the surrounding area before and after loading is obtained. Finally, the COD is determined using Eq. (5). In other words, if the fringe numbers before and after loading are m and n, respectively, the COD is (m − n)/f.

 

Fig. 16 Schematic diagram of COD calculation method using moiré fringes.

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In this part of the study, the COD of a microcrack was determined using a zero-thickness grating and SEM moiré, and the feasibility of the zero-thickness grating was also demonstrated. First, a steel tensile sample with a semicircular notch (diameter: ~200 μm) was fabricated via wire cutting. Then, a microcrack was prepared via fatigue precracking, which was then polished to a smooth, mirror-like finish. Next, a crossing grating with 600-line/mm frequency was fabricated on the specimen. The specimen was examined under an SEM with a loading machine (Shimadzu SS-550, f = 664.7 line/mm at 200 × ). SEM images of the microcrack and grating are shown in Fig. 17 . Note that a carrier fringe formed as a result of the frequency mismatch between the specimen and reference gratings; this is inevitable, as the SEM magnification cannot be adjusted continuously. Fortunately, the carrier fringe disturbance can be eliminated by calculating the value of m − n.

 

Fig. 17 SEM image of microcrack and grating on steel tensile specimen.

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As shown in Fig. 18 , the value of m for the area surrounding the microcrack is significantly less than 1; however, n = 3 is obtained after loading with 1050 N (orders: −1, 0, 1). Thus, the COD was determined to be approximately 4.5 μm (1.50 μm/fringe, see Eq. (5)). Note that the fringe patterns in Fig. 18 exhibit more noise than those in Fig. 11, because the SEM employed in this study was old and slightly outdated. However, the fringes are distinguishable.

 

Fig. 18 Fringe patterns in area surrounding crack tip before and after loading.

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5. Conclusion

In this paper, a multipurpose specimen-grating fabrication technique for moiré methods based on 3S soft lithography was presented, which can be used to manufacture both transfer and zero-thickness gratings. The proposed grating fabrication method has the advantages of a simple process, low cost, and high throughput, and yields gratings with sufficient flexibility and high frequency. A hybrid PDMS stamp was used to minimize the lateral distortion, and its fabrication process and effectiveness were demonstrated. The frequency uniformity, micromorphologies, thicknesses, and shear lags of the fabricated gratings were then characterized.

The characterization results indicate the following: The frequency uniformity is acceptable in the middle of the grating, and the effective area is more than 70% of the total. The micromorphology of the zero-thickness grating is sharp, whereas that of the transfer grating is smooth. The transfer grating has a severe shear lag if the deformation gradient is high, whereas that of the zero-thickness grating is negligible. Further, it was verified for the first time that the transfer grating can block microcracks. The transfer and zero-thickness grating thicknesses were approximately 25 μm and less than 100 nm, respectively.

As regards moiré interferometry, the transfer grating can compensate for the roughness of the specimen surface and it is suitable for use under mild deformation conditions. The zero-thickness grating is preferable for cases of severe deformation, however. On the other hand, the zero-thickness grating can also serve as a mask for subsequent etching or deposition techniques employed to fabricate a high-temperature-resistant grating. As regards SEM moiré, the zero-thickness grating yields higher-contrast results than the transfer grating and, thus, the former is more appropriate for SEM moiré measurements.

In summary, a versatile grating fabrication method was presented in this study, and a comprehensive characterization of the features of gratings fabricated using the proposed technique was conducted. Based on the characterization results, we believe that the presented grating fabrication technique has considerable potential for wide application, not only with regard to the moiré method, but also in association with other grating-based deformation-measurement methods.