Issue34

M. Goto et alii, Frattura ed Integrità Strutturale, 34 (2015) 427-436; DOI: 10.3221/IGF-ESIS.34.48 434 Tabs. 1 and 2 show the DL-SIF values of cracks with the aspect ratio, b / a = 0.38 ( T / L = 0.189) for the zx -plane crack, and 1.1 ( T / L = 0.550) for the xy -plane crack, which are given from Fig. 6a. The value of F I for the zx -plane crack is larger at the crack bottom (  = 90°), than at the surface (  = 1°). Therefore, it is natural to consider that the crack growth rate toward the inner direction should be larger than that toward the crack length direction in the surface, giving rise to an aspect ratio larger than 1. However, the actual aspect ratio was much smaller than 1. Regarding the value of F II , it was 0.77 at the surface, but it was 0 at the bottom. The large F II value at the surface promotes in-plane shear-mode crack growth. At the bottom, F III takes a value of 0.83, but it seems reasonable to assume that anti-plane shear-mode deformation at the deepest point is negligible for the inward crack growth. Consequently, the zx -plane crack predominantly propagated at the surface due to in-plane shear-mode deformation, which brings the generation of new SBs and extension of pre-existent SBs around the crack tip areas, producing the aspect ratio much smaller than 1. The tensile-mode deformation reflected by large F I values should play the role of crack growth. However, by considering a shallow semi-elliptical shape of crack face, it can be expected that the tensile-mode crack growth has negligible effect on the formation of shallow crack face shape. Rather, the tensile-mode deformation might assist shear-mode growth, through the de-bonding of SBs around the crack tip. It was shown that in stress-controlled fatigue tests of UFG Cu corresponding to an LCF regime [20], the crack grows along the direction at an incline of 45° to the loading axis, because of the shear banding induced by the maximum shear stress and SB decohesion process. Under frictionless condition, the growth resistance to shear-mode crack is likely to be smaller than that to tensile-mode crack. It was shown that in conventional grain sized Cu alloys [31], the growth rate of the shear-mode crack is larger than that of the tensile-mode crack, with the same crack length and same stress amplitude. Type of crack  (deg) F Ⅰ F Ⅱ F Ⅲ zx -plane crack b / a = 0.38 1 0.68 0.77 0.31 90 0.93 0 0.83 Table 1 : Dimensionless stress intensity factors for the zx -plane crack ( b / a = 0.38, a = L /2). Type of crack  (deg) F Ⅰ F Ⅱ F Ⅲ xy -plane crack b / a = 1.1 1 0.74 -0.08 0.09 90 0.60 0.53 0 Table 2 : Dimensionless stress intensity factors for the xy -plane crack ( b / a = 1.10, a = L /2). For the xy -plane crack (Tab. 2), the F I value at the surface was 0.74, which is larger than 0.60 at the bottom. This should lead to a superior extension of crack length, compared to the crack depth ( b / a < 1), if the crack growth was dominantly controlled by the tensile-mode. However, the actual crack extension was accelerated at the bottom, rather than the surface. On the other hand, the F II value was higher at the bottom (0.53) than the surface (-0.08), suggesting that the deep semi-elliptical shape of the xy -plane crack was attributable to the crack extension due to in-plane shear-mode deformation at the bottom. At the surface, mode I crack growth appeared to be predominant, because of negligible values of F II and F III . In addition, the de-bonding of pre-existent SBs in the heavily deformed zone around crack tips occurred due to the tensile-mode deformation, forming a zigzag crack path, as the result of joining the crack and de-bonded SBs. Such a growth path may be convenient for roughness-induced crack closure, which contributes to a decrease in CGR at the surface. It can be concluded, therefore, that mode II crack growth plays an important role in determining the crack face shape of ECAPed UFG copper in LCF regime. It has been shown that the SBs appear on the zx -plane at 45° to the loading direction, mainly because it is the plane of maximum resolved shear stress. However, as innumerable planes of maximum shear stress exist, why does only one set of SBs form? To answer this question regarding the formation of only one “family” (one plane and shear direction), Agnew et al. [22] suggested the action of a small sample misalignment. During the full tension-compression of such small samples (2 × 2 mm cross section), alignment is critical and any deviation would increase the likelihood of the nucleation one type of SBs. Goto et al. [32] monitored the surface of ECAPed copper fatigued by a rotating-bending fatigue machine that has no structural misalignment relating to the nucleation of one type of SBs, showing that SBs were oriented along one set of