Special Issue on New Aspects of Martensitic Transformations II
Development of Digital Holographic Microscope for In-Situ Surface Relief Measurement of Low-Carbon Steel
2020 Volume 61 Issue 1 Pages 42-48
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2020 Volume 61 Issue 1 Pages 42-48
Digital holographic microscope (DHM) system was designed to extend an existing reflected light microscope. The developed DHM system was applied for the observations of plastic deformation of an upper bainite and martensitic transformation of a low-carbon steel to clarify its potential for analyzing surface reliefs observed during these processes. It was demonstrated that the height measurement accuracy is almost equivalent to that of AFM. The exceptional temporal and spatial resolutions provided by the developed DHM system was shown to have a potential to clarify the mechanism behind the formation of surface reliefs by plastic deformation and phase transformation.
Fig. 3 Reconstruction process of real image from holographic pattern. (a) Intensity obtained by CMOS camera, (b) Fourier transformed pattern, (c) filtered object beam, (d) object amplitude, (e) object phase shift, (f) unwrapped phase shift.
During the development of multilayered steel composite,1) it was clarified that an extreme strength and ductility combination can be realized through the exceptionally large uniform plastic deformation induced in hard and highly brittle layers.2–4) In order to achieve further improvement in the mechanical properties of multilayered steel, the mechanism behind the deformation behavior of hard martensitic layers under tensile deformation was investigated using various techniques, such as in-situ tensile-testing in SEM,5) digital image correlation (DIC),6) electron backscatter diffraction (EBSD) analysis conjunction with crystal plasticity analysis,7) and the combination of them.8,9) From these investigations, it was clarified that the slip bands accompanying sharp surface reliefs parallel to martensite laths quickly develop during the early stage of deformation, and the slip band formations are mostly observed in martensite blocks with a high Schmid factor for the in-lath plane slip systems.5,6) In addition, it was demonstrated that anisotropic activation of slip systems in martensite is responsible for the microscopically non-uniform deformation of martensite.7–9) A number of experimental investigations using micro-tensile specimen also support our observations of the slip band formation and the anisotropic activation of slip system in martensite.10–12) Furthermore, recent FIB-TEM observation confirmed that the formation of slip bands are actually along the intergranular boundaries, such as lath and block boundaries.13) However, even with the application of those recent experimental approaches, there still exists a debate concerning the mechanism which induces formation of such a sharp surface relief in lath martensite; one claims that the existence of thin retained austenite film at lath boundary is the primary cause of the formation,14,15) and the other proposes that it is a kind of plastic instability resulting from the non-Schmid effect of bcc screw dislocation.13,16)
In addition to the deformation mechanism, the formation mechanism of martensite is also important to control the microstructure of high strength steels to have an optimum strength and deformability combination. As such, the formation mechanism of martensite has also been investigated. Especially, the physical origin of variant selection remains a subject of recent investigations. For instance, Stormvinter et al.17) clarified from the detailed EBSD analysis of various Fe–C alloys that the dominant variant pair changes from sub-block type boundaries (V1/V4) to twin-related boundaries (V1/V2) with lowered transformation temperature. Same tendency was also found in the in-situ observation of a low-carbon steel using a laser confocal microscope and a high-speed camera.18) It is not clearly mentioned in the text, since the primary objective of the paper was to clarify the effect of free surface. It is, however, clear from the figure showing selected variants clarified by the in-situ observation (Fig. 14 in Ref. 18)) that at the beginning of transformation the sub-block type boundaries (V1/V4) were dominantly selected and that the twin-related boundaries (V1/V2) were selected in the blocks that fill the remaining austenite. Mishiro et al.19) also demonstrated using EBSD analysis that the applied stress during transformation induces the formation of variants with greater external work only in the earlier stage, while no clear effects are identified for those formed later. Even though these observations clarified a temperature dependency of variant selection of lath martensite, the underlying mechanism has not been clarified yet.
One of the reasons for the difficulty in identifying the underlying mechanisms of the slip band formation and the temperature dependency of variant selection is partly due to the lack of experimental technique which enables a direct measurement of surface relief effect with high temporal and spatial resolutions. Accordingly, the present study aims to develop a new experimental apparatus, so-called Digital Holographic Microscopy (DHM), which provides a nondestructive, contact-free optical measurement, and to apply the tool for in-situ measurement of surface relief induced by plastic deformation as well as phase transformation.
The concept of digital holography was first demonstrated by Goodman and Lawrence.20) Since then the basic idea has not been changed much. In digital holography, the coherent light reflected from an object, $U_{r}(x,y) = a_{r}(x,y)e^{i\phi _{r}(x,y)}$, interferes with reference light, $U_{0}(x,y) = a_{0}(x,y)e^{i\phi _{0}(x,y)}$, and forms an image on CCD or CMOS sensors with the intensity given as follows:
| \begin{align} I(x,y) & = | U_{0} + U_{r} |^{2}\\ & = | U_{0} |^{2} + | U_{r} |^{2} + U_{0}^{*}U_{r} + U_{0}U_{r}^{*}\\ & = a_{0}^{2} + a_{r}^{2} + a_{0}a_{r}e^{i(\phi_{r} - \phi_{0})} + a_{0}a_{r}e^{i(\phi_{r} + \phi_{0})}. \end{align} | (1) |
To reconstruct the shape of object from the extracted holographic image $u(x,y) = a_{0}a_{r}e^{i(\phi _{r} + \phi _{0})}$, Fresnel-Kirchhoff diffraction theory is applied. The Fresnel-Kirchhoff integral results in the complex amplitude of the real image u(xd, yd; z) in the plane located at a distance z from the holographic image:
| \begin{equation} u(x_{d},y_{d};z) = \frac{z}{i\lambda} \iint u(x,y)\frac{\exp ikr}{r^{2}}dxdy, \end{equation} | (2) |
| \begin{align} u(x_{d},y_{d};z) & = \frac{\exp ikz}{i\lambda z} \iint u(x,y)\\ &\quad \times\exp \left\{\frac{ik}{2z}[(x_{d} - x)^{2} + (y_{d} - y)^{2}] \right\}dxdy\\ & = \frac{\exp ikz}{i\lambda z}\left\{u(x_{d},y_{d}) \otimes \exp \left[i\frac{\pi}{\lambda z}(x_{d}^{2} + y_{d}^{2}) \right] \right\} \end{align} | (3) |
In the present study, DHM was constructed on top of a conventional reflected light microscope (Olympus BX53M). The setup of the developed DHM system as schematically shown in Fig. 1 consists of an optically pumped semiconductor laser operating at 640 nm of 100 mW (LF, Coherent OBIS LX), a variable beam splitter (VBS), two beam splitters (BS), a condenser lens (CL), a collimator (C), a λ/4 retardation waveplate (WP), an objective lens with infinite correction (OL), a tube lens (TL), and the CMOS camera with maximum frame rate of 180 fps at 2048 × 2048 px (AMS CMV4000). The photos of the actual setup are shown in Fig. 2. The polarized beam emitted by LF is first split into illuminating and reference beams by VBS. Then, the illuminating beam is focused by CL on the back focal plane of OL after reflected by BS, so that a parallel laser beam will illuminate a sample after refracted by OL. The waveplate is inserted in the light path of the illuminating and the reflected object beam to maximize the intensity of the object image on the CMOS camera. The tilt angle of BS for the illuminating beam is controlled to have an optimum off-axis configuration. In general, for an off-axis configuration, the angle between the reference and the object beams should not exceed a maximum value given by
| \begin{equation} \theta_{\textit{max}} = \sin^{-1}\left(\frac{\lambda}{2\Delta} \right), \end{equation} | (4) |
Schematic diagram of digital holographic microscope designed to extend an existing conventional reflected light microscope.
Photos of entire digital holographic microscope developed in the present study.
Three kinds of experiments are conducted; one is to demonstrate the reconstruction procedure as well as the accuracy of the height measurement by DHM, another is to capture shapes of surface reliefs induced by a sharp slip bands formation along substructure boundaries, and the other is to capture those induced by a martensitic transformation.
4.1 Height measurement by DHMThe steel alloy specimen with the chemical composition of Fe–0.15C–1.44Mn (mass%) was austenitized in an ambient mixture gas of argon–3% hydrogen at 1473 K for 10 s to obtain average grain size of approximately 250 µm, and then cooled continuously at 10 K/s to have a mixture of Widmanstatten and Bainitic ferrites. The accuracy of the measurement by DHM was verified from the comparison with the measurement by AFM after cooling to room temperature.24)
Typical intensity captured in the present study is shown Fig. 3(a). The angle between the reference and the object beams are controlled so that a sharp diffraction fringe can be captured by a CMOS camera as shown in the magnified view in the figure. With the off-axis configuration, the object pattern can be easily be separated from the conjugate twin pattern as well as the zero-order pattern after taking Fourier transform as shown in Figs. 3(b) and (c). Then, by applying reconstruction based on the Fresnel approximation to the object pattern, one can obtain the amplitude and phase shift as shown in Figs. 3(d) and (e). The reconstructed phase is ranging from −π to π, because of the inverse tangent operation. As a result, the phase distribution is wrapped into this range and jumps occur for variations of more than 2π. In the case of a perfectly smooth surface without spike, the phase can be unwrapped by scanning a fringe edge, and adding or subtracting 2π at the edge. However, in practice it is not possible to avoid spike noise in the real experimental setup. Thus, in the present study, minimum spanning tree method25) is applied, and the result is shown in Fig. 3(f).
Reconstruction process of real image from holographic pattern. (a) Intensity obtained by CMOS camera, (b) Fourier transformed pattern, (c) filtered object beam, (d) object amplitude, (e) object phase shift, (f) unwrapped phase shift.
One of the examples of plan-view height images taken by DHM and AFM from the same area of observation after continuous cooling are compared in Figs. 4(a) and (b), respectively. Figure 4(c) show the cross-sectional profiles along the line indicated by AB in the figure. Even though there is a limitation in the precision in the lateral direction owing to the diffraction-limit, the height measurements of DHM are almost equivalent to that of AFM.24)
Surface relief induced by phase transformation measured by (a) DHM and (b) AFM. (c) Cross-sectional profiles along the line AB indicated in (a) and (b).
The steel alloy specimen with the chemical composition of Fe–0.35C–0.83Mn–0.23Si–1.0Cr–0.17Mo (mass%) was austenitized at 1373 K for 600 s, subsequently held at 673 K in salt bath for 900 s. This heat-treatment leads the formation of upper bainite in the alloy. After the heat-treatment, a small tensile specimen with a gauge length of 10 mm, a width of 4 mm, and a thickness of 1.0 mm was cut out from the sample, and in-situ tensile test was performed using the DHM system.26) Although the DHM system provides a precise height measurement even for an as-cut or a sand-polished surfaces, the sample surface was mirror polished with colloidal silica for ease of identifying slip bands by human eyes through optical microscopy.
Figure 5(a) shows the slip bands found after the 2% elongation. Even in upper bainite, it is clear that sharp slip bands are quickly formed with small strain as observed previously in lath martensite.5) Figures 5(b) and (c) show series of the cross-sectional profiles of the slip bands indicated as SB1 and SB2, respectively, in Fig. 5(a). It is clearly demonstrated that, right after the initiation of plastic deformation, block-wise uniform deformations were first induced throughout the specimen. Subsequently, it was followed by a sudden formation of sharp steps, i.e. slip bands, at around 1.5% strain. In Fig. 5, only profiles of every 0.1% strain intervals are shown, but actually the changes in surface relief were captured continuously by the DHM system. Accordingly, it is possible to identify the onset of bifurcation from the uniform strain distribution to the localized one by the DHM system at smaller strain intervals. In addition, the application of the DHM system enables the precise height measurements without unloading or load-holding, which is the must in the conventional height measurement techniques.
(a) Optical micrograph of slip bands observed after elongation of 2% strain. Cross-sectional profiles of slip bands, (b) SB1 and (c) SB2 as indicated in (a).
Since this is the first attempt to measure the slip band formation process, the experiment was conducted using OL of 20x, which will provide a wider area of observation at the expense of a lower value of numerical aperture, that is, a lower lateral resolution. By applying OL with a higher magnification or a better numerical aperture, one might be able to capture much clearer perspective of the slip band formation with the DHM system.
4.3 Martensitic transformationTo conduct in-situ measurement of surface relief induced by martensitic transformation, the steel alloy with the chemical composition of Fe–0.18C–0.89Mn–0.21Si–1.51Cr–2.88Ni–0.40Mo (mass%) was selected. The sample was austenitized in an ambient mixture gas of argon–3% hydrogen at 1373 K for 10 s to obtain average grain size of approximately 200 µm, and then cooled continuously at 10 K/s while the change in the surface roughness was continuously measured by DHM.27) Even for this case, a perfect surface treatment is not necessary for the DHM height measurement. The sample surface was, however, mirror polished with colloidal silica in order to minimize the effect of surface roughness on phase transformation as well as on EBSD analysis after the in-situ measurement.
Figures 6(a) and (b) show the martensitic block captured by DHM just at the Ms temperature of the alloy and the IPF map obtained from the same area of observation obtained at room temperature. It should be noted that the martensitic block was formed instantly within one single frame even with the frame rate of 50 fps. Figure 6(c) compares the cross-sectional profiles along the red line in Fig. 5(a) between the two consecutive frames with and without the formation of the martensitic block. It is clear from the frame just before the formation, there exists a small roughness presumably due to thermal grooving during the austenitizing process. Therefore, the profile without the martensitic block was subtracted from that with the martensitic block, and the result is shown in the Fig. 6(d). From the figure, the plastic deformation induced in the surrounding austenite is clearly captured.
(a) Surface relief by martensitic block M1 captured by DHM. (b) IPF map obtained from the same area of observation. (c) Cross-sectional profile before and after the formation of M1. (d) Effect of transformation revealed from the difference in the profiles before and after the formation of M1.
Figure 7(a) and (b) show, respectively, the height contrast and the IPF map of the bump that was formed in the remaining austenite at the temperature around 15 K below Ms. From the IPF map, the bump is found to be composed of a pair of twin-related variants. As is the case with the block shown in Fig. 6, the bump appeared within one frame, and the height difference between frames with and without the bump are shown in Fig. 7(c). It is clear from the figure that there is no clear indication of plastic deformation in the remaining austenite.
(a) Surface relief by martensitic block M2 captured by DHM. (b) IPF map obtained from the same area of observation. (c) Difference in cross-sectional profile before and after the formation of M2.
The observations indicate that the temperature dependency of variant selection in lath martensite is affected by the difference in the strain accommodation process, plastic accommodation in austenite or self-accommodation accompanying plastic accommodation in martensite. From these measurements, one might be able to directly compare the slope induced by the transformation with the phenomenological theory of martensite crystallography without the effect of artifact, such as thermal grooving, as shown in our previous study concerning the formation of Widmanstatten ferrite and bainite.24) Such kind of analyses to clarify the unresolved mechanism of temperature dependency of variant selection will be presented in the future study.27)
DHM system was developed by modifying the existing reflection light microscopy, and applied to clarify its potential for analyzing mechanism behind the formation of surface relief by plastic deformation and phase transformation. The results obtained are summarized as follows:
The present study demonstrates only a part of the potential applications of DHM. However, with the enhanced temporal and spatial resolutions achieved by further improvement of the present DHM system, one might be able to capture physics which has never been revealed by the conventional height measurement techniques, such as AFM and confocal laser microscopy.
The authors gratefully acknowledge the financial support by JSPS KAKENHI Grant Number 15H04151.
