Issue34

M. Goto et alii, Frattura ed Integrità Strutturale, 34 (2015) 427-436; DOI: 10.3221/IGF-ESIS.34.48 432 0.266 and 0.189 for the zx -plane crack, and 0.389 and 0.550 for the xy -plane crack, respectively. Fig. 6b shows the crack face profile at  a = 90 MPa. There was no significant difference in the crack face shape between the zx - and xy -plane cracks. The value of t / l (= T / L ) at the deepest point was 0.41 for both planes. D ISCUSSION FG materials processed by SPD techniques have non-equilibrium microstructures [24, 25] with limited thermal and mechanical stability. Such non-equilibrium microstructures can easily change properties under applied cyclic stressing at a certain temperature. Remarkable levels of grain coarsening as the result of dynamic recrystallization have generally occurred in post-fatigued high-purity UFG copper [26, 27], whereas it has been shown that no grain coarsening occurred in cyclically deformed UFG copper [23, 28]. To study the grain growth as a result of cyclic stressing, EBSD analysis of the post-fatigued specimens was conducted. In order to conduct EBSD analysis of the post-fatigued microstructure just under the specimen surfaces, 0.15 mm surface layers of the post-fatigued round bar specimens were polished off to make a flat surface for EBSD analysis. The procedure for making the flat surface and the area analysed by EBSD are shown in a previous work [20]. Fig. 8a shows inverse pole figure (IPF) maps and grain boundary (GB) map of a post-ECAP sample (pre-fatigue) in the zx -plane. Figs. 8b and 8c show the microstructure after a constant stressing of  a = 240 and 90 MPa, respectively. The GBs in the GB maps are denoted either by red lines corresponding to low angle GBs (LAGBs) where the misorientation,  , is between 2˚ and 15˚ or by black lines corresponding to high angle GBs (HAGBs) with  > 15˚. The IPF maps for the post-fatigued sample indicates the development of subgrains within elongated grains, isolated with LAGBs. Image quality maps [27] showed that the microstructure in post-ECAP copper has enhanced strain energy due to the redundant defect structure, and the microstructure was therefore in the process of evolving to equiaxed grains isolated with HAGBs. The post-fatigue microstructure subjected to the constant stressing experienced grain coarsening, but the coarse grain sizes depended on the applied stress amplitudes. At high stress amplitude of  a = 240 MPa, coarse grains evolved from 1 to a few  m (Figs. 8b). No significant difference in coarse grain sizes between the zx - and xy -planes was observed. At  a = 90 MPa, long-term repetitions produced large coarse grains in excess of several tens of micrometres (Fig. 8c). Like the zx- -plane, large coarse grains were observed in the xy -plane fatigued at  a = 90 MPa. Accordingly, it should be concluded that the damaged traces greater than a few tens of micrometers initiated at a low stress (Fig. 3b) were slip-bands formed in the coarse grains generated as a result of dynamic recrystallization. Regarding SB formation in the LCF regime, many investigators have observed morphological features and microstructure of SBs, discussing the formation mechanism of SBs in conjunction with the grain coarsening. However, clear evidence for an SB formation in UFG copper is still lacking, there are opposite views; for example, i) in ref.[26], the mechanism responsible for the SB formation was found to be the interaction of cyclically induced cell/grain coarsening, which led to strain localization, and ii) no grain coarsening occurred in cyclically deformed UFG copper (99.9% Cu [23]), and the coordinating GB sliding along the shear plane of the last ECAP pass could be the decisive mechanism in SB formation. The role of grain coarsening on the formation of SBs have been under discussion for a long time and are still awaiting final answers. Regarding the crack paths, at low stress amplitudes (HCF regime), the growth direction of fatigue cracks in UFG copper was perpendicular to both the surface and loading direction regardless of the initiation site of cracks. There was no effect of microstructural inhomogeneity resulted from ECAP processing on the crack growth direction. This was because of the grain coarsening. As a result of generation of dynamically recrystallized coarse grains, the inhomogeneity of matrix caused by the ECAP processing is likely to disappear, giving rise to the macroscale growth-path perpendicular to both the specimen surface and loading direction. Accordingly, like conventional grain-sized materials, the crack at low stresses propagates via the striation formation mechanism [27], which is associated with crack tip retardation and blunting. However, the crack growth direction in the LCF regime (high stress amplitudes) was different from that in the HCF regime. In order to investigate the physical background of the unique crack growth directions at high stress amplitudes from the viewpoints of the deformation mode at the crack tip, the SIF values were evaluated, by assuming a semi-infinite body with inclined semi-elliptical surface cracks, subjected to tension stress in the x -direction at infinity. The applied tension stress is resolved into two stress components perpendicular and tangential to the crack face. Accordingly, a 45° inclined surface crack is subjected to both normal,  (= 1), and shear stress,  (= 1), as illustrated in Figs. 9a and 9b. Noda et al. [29] analysed the SIFs of a semi-elliptical surface-crack subjected to modes I, II and III loading. The values of dimensionless SIF (DL-SIF), F I , F II , F III , for the current surface-crack were taken from Noda’s solution calculated for Poisson’s ratio:  = 0.3. The DL-SIF, F I (  ), F II (  ), F III (  ), were defined as; U