PSI - Issue 13

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

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images, the average h was assumed to be constant in the same grain and under identical experimental conditions, because h was almost constant as an experimental fact. The nano-roughness wavelength w could be determined using high-resolution images by dividing the crack length by the number of crack deflections. For instance, in the case of Fig. 3(c), the crack length corresponded to the length of the dashed line and the number of crack deflections was six. Alternatively, using low-resolution images, w in the laminated TRIP-maraging steel could be calculated using θ micro , h , and the size of the austenite/martensite pair along the horizontal line (//loading direction), l x . The average l x could be calculated by dividing the length of the horizontal line by the number of lamellae. This was because the lamellar structure dominated the nanometer-scale crack deflection. Thus, w is calculated by the following equation:

2

2

l

w



x

tan





micro

w

(1)

l

w  

x

2

tan

1





micro

The remaining parameter θ nano is difficult to be measured directly even from Fig. 3(b). A direct and accurate measurement of θ nano requires further high-resolution observation. Instead, θ nano can be indirectly determined using w and h as follows:

w

/ 2

(2)

1



tan





nano

h

Fig. 5. SE images of nano-roughness introduced by crack propagation across lamellar structures. Fatigue crack (a) under unloading condition and (b) at 800 MPa. (c) Identical region was chemically etched after unloading. (d) Schematic representations of four kinds of nano-roughness: ( ⅰ ) crack propagation from soft phase interior to microstructural boundary of laminates, ( ⅱ ) inclination of crack propagation path at microstructural boundary, and ( ⅲ ) crack propagation from hard phase interior to microstructural boundary. 3.3. Roughness-induced stress shielding by friction Based on the definitions of nano- and micro-roughness, we interpret the effect of RISS by friction as follows. Figures 6(a 1 ) to (b 2 ) show the schematics of the effect of friction. When θ micro was larger than θ nano , the crack opened without frictional force (Figs. 6(a 1 ) and (a 2 )). When θ micro was smaller than θ nano , the crack surfaces contacted with each other during opening, resulting in RISS (Figs. 6(b 1 ) and (b 2 )). To estimate the fraction of the effective crack surface area where friction stress acted significantly, the projected length of the region where θ micro < θ nano in the x direction was calculated. Specifically, the length of the θ micro < θ nano region was divided by the propagation length of each crack. Fraction of the effective crack surface area for friction is a new parameter proposed in this study. In the next section, we will show the microstructural dependence of the fraction of the effective crack surface area for friction.

Fig. 6. Schematic representation of effect of RISS due to friction between fatigue crack surfaces. (a 1 ) θ micro > θ nano (unloading), (a 2 ) θ micro > θ nano (loading), (b 1 ) θ micro < θ nano (unloading), and (b 2 ) θ micro < θ nano (loading).