| Crack tip fields are analyzed in order to explain fracture processes in ductile crystals. The focus is to understand the stress and deformation fields, and cracking mechanisms. Both asymptotic and finite element models based on continuum plasticity for single crystals are used.; The ductility of interfacial fracture in {dollar}Sigma{dollar}9 copper bicrystals has been observed experimentally to depend on the cracking direction, with the {dollar}lbrack 1overline{lcub}14{rcub}rbrack{dollar} being the brittle cracking direction and the (114) the ductile one. Although the continuum plasticity solutions given here show that the tensile stresses ahead of the crack is essentially identical for the two cracking directions, the overall plastic zone size is much larger in the ductile case. Also, the orientations of the zones of concentrated shearing ahead of the crack, observed in the ideally plastic model, suggest two different dislocation shearing mechanisms.; Analysis of the crack tip field for an ideally plastic NiAl single crystal which has only 3 independent slip systems at room temperature (the {dollar}{lcub}110{rcub}{dollar} {dollar}langle 100rangle{dollar} systems), shows that the stress field has a lnr type singularity, with a shearing discontinuity at 90{dollar}spcirc{dollar}. The largest zone over which the stresses on either {dollar}{lcub}110{rcub}{dollar} {dollar}langle 111rangle{dollar} or {dollar}{lcub}112{rcub}{dollar} {dollar}langle 111rangle{dollar} systems exceeds the critical resolved shear stress on the {dollar}{lcub}110{rcub}{dollar} {dollar}langle 100rangle{dollar} system is of the same order as the plastic zone size, although very close to the crack tip the stresses on some of these systems become significant due to the stress singularity, and thus they may become activated.; A finite element model based on single crystal plasticity was adopted to examine the domain of validity of HRR fields. The results show that domain of validity of HRR stress fields increases from 0.4% to 5% of the overall plastic zone size as the hardening exponent n increases from 3 to 20. Both the finite element and the HRR asymptotic results converge to the discontinuous stress field of Rice's (1987) solution for ideally plastic material as n gets larger. Even though clear the displacements remain continuous in the ideally plastic limit, zones of very high slopes located across the sector boundaries can be observed in the finite element results. |
