PSI - Issue 13

Tomoki MIZOGUCHI et al. / Procedia Structural Integrity 13 (2018) 1071–1075 Tomoki Mizoguchi / Structural Integrity Procedia 00 (2018) 000 – 000

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To measure θ micro , the shape of the fatigue crack was digitally traced, and the positional data were extracted as XY coordinates. The digital positional data were used for the quantification of the crack roughness. Figure 3(b) shows an SE image of a fatigue crack. The yellow dashed line is the trace line along the crack surface. Although a zigzag morphology, which represents nano roughness, can be observed along the crack planes shown in Fig. 3(b), θ micro is defined as shown in Fig. 3(c). However, one shortcoming in the measurement of θ micro is that the value depends on the observation area. In particular, θ micro is dependent on how the “straight line” (the dashed line in Fig. 3(c)) is defined because the crack is always deflected or curved even in the nan o-scale. To solve this problem, we performed mesoscopic characterization of the crack roughness. Specifically, we used the relatively low spatial resolution image shown in Fig. 4(a). Because of the low spatial resolution, nano roughness could not be observed. The crack planes and the gap between them in the low spatial resolution SE images were then plotted to emphasize the contrast of the crack for the following digital binarization (Fig. 4(b)). The binarized images were used to trace the crack shape and plot the positional data using PC software: ImageJ and WebPlotDigitizer-3. The positional data of the crack surface were plotted as shown in Fig. 4(c). In this study, the positional data were plotted for each pixel, and the length of each pixel was 12 nm. Since the nano-roughness information could be eliminated, θ micro could be measured as the slope angle of two adjacent positional data points along the crack plane and was not dependent on artificial operations. This procedure has an advantage as a practical method in that it uses low-magnification images, which can reduce number of observations and analyses required to determine statistically reliable values of θ micro . In this context, the next problem to be solved is how to determine nano roughness using low spatial resolution images. In the next section, we will explain and define the method and parameters associated with nano-roughness.

Fig. 3. (a) Schematic for micro-roughness. (b) SE image showing an example of nano-roughness. Nano-roughness can be observed when the local region of the crack highlighted in (a) is magnified. (c) Schematic representation of micro-roughness and nano-roughness.

Fig. 4. (a) An example of SE image of fatigue crack. (b) Image of fatigue crack after painting, binarizing, and tracing. The inset shows the traced line. (c) Plotted line of crack surface. 3.2. Nano-roughness As shown in Fig. 3(b), nano-roughness can be observed in the present steel specimen. Parameters expressing nano-roughness are schematically shown in Fig. 3(c). Nano-roughness is expressed by three parameters: h , w , and θ nano . These parameters cannot be directly determined by the analyses of low spatial resolution images. Here, we note the microstructural characteristics that cause nano-roughness. In the present steel specimen, nano-roughness is generated by fatigue crack propagation across the lamellar structure. Figures 5(a) to (c) show a fatigue crack that propagates across the lamellae. These images indicate that nano-roughness in the steel specimen occurs when the crack meets the microstructural interface of the laminates, as schematically shown in Fig. 5(d). Therefore, for the steel specimen, some parameters can be approximated using the microstructural characteristics as follows. First, high-resolution images like Fig. 3(b) were exceptionally used to determine the nano-roughness height h . In this study, we obtained the nano-roughness heights for ten images and used the average h value. To reduce the required number of high-resolution