Families of asymptotic tensile crack tip stress fields in elastic-perfectly plastic single crystals

Abstract

In this work, two families of asymptotic near-tip stress fields are constructed in an elastic-ideally plastic FCC single crystal under mode I plane strain conditions. A crack is taken to lie on the (010) plane and its front is aligned along the [101] direction. Finite element analysis is first used to systematically examine the stress distributions corresponding to different constraint levels. The general framework developed by Rice (Mech Mater 6:317-335, 1987) and Drugan (J Mech Phys Solids 49:2155-2176, 2001) is then adopted to generate low triaxiality solutions by introducing an elastic sector near the crack tip. The two families of stress fields are parameterized by the normalized opening stress (τ A 22 /τ o ) prevailing in the plastic sector in front of the tip and by the coordinates of a point where elastic unloading commences in stress space. It is found that the angular stress variations obtained from the analytical solutions show good agreement with finite element analysis.

Effect of loading rate on crack tip fields in three point bend fracture specimen of FCC single crystal

“…(4)). The stress trajectory pertaining to _ J ¼ 2:5 Â 10 4 N=ðmm-sÞ corroborates well with quasi-static solution corresponding to moderate levels of constraint loss as reported by Patil et al (2009a). The elastic unloading commences from point E 00 on the stress trajectory for dynamic loading with _ J ¼ 3:7 Â 10 4 N=ðmm-sÞ (see Fig.…”

“…The near-tip angular stress distributions shown in Figs. 8 and 9 corroborate well with the quasi-static analytical solutions pertaining to different constraint levels presented by Patil et al (2009a). For example, the variations corresponding to _ J ¼ 3:7 Â 10 4 N=ðmm-sÞ at J/ (s o c o ) = 0.0075 in Fig.…”

“…The loci in stress plane determined from these analytical solutions corroborate well with those obtained from quasi-static boundary layer simulations. Further, Patil et al (2009a) showed that the near-tip angular stress variation corresponding to each member of the two families agrees well with the results of finite element simulations for a certain value of T-stress. Patil et al (2008bPatil et al ( , 2011 also found that the slip and kink shear band patterns near the notch tip are strongly influenced by the constraint level.…”

“…However, the trajectories in stress plane as the crack tip is traversed in the anti-clockwise sense did not agree with those assumed by Crone and Drugan (2001) and Drugan (2001). This prompted Patil et al (2009a) to propose two families of solutions having high and low stress triaxiality. The loci in stress plane determined from these analytical solutions corroborate well with those obtained from quasi-static boundary layer simulations.…”

“…7(a)). However, this elastic sector joins with a plastic sector having a stress state represented by point F 00 (see also quasi-static solution given in Patil et al (2009a) pertaining to case with acute constraint loss).…”