Crack tip fields in ductile crystals

Abstract

Abstract.Results on the asymptotic analysis of crack tip fields in elastic-plastic single crystals are presented and some preliminary results of finite element solutions for cracked solids of this type are summarized. In the cases studied, involving plane strain tensile and anti-plane shear cracks in ideally plastic fc c and b c c crystals, analyzed within conventional small displacement gradient assumptions, the asymptotic analyses reveal striking discontinuous fields at the crack tip.For the stationary crack the stress state is found to be locally uniform in each of a family of angular sectors at the crack tip, but to jump discontinuously at sector boundaries, which are also the surfaces of shear discontinuities in the displacement field. For the quasi-statically growing crack the stress state is fully continuous from one near-tip angular sector to the next, but now some of the sectors involve elastic unloading from, and reloading to, a yielded state, and shear discontinuities of the velocity field develop at sector boundaries. In an anti-plane case studied, inclusion of inertial terms for (dynamically) growing cracks restores a discontinuous stress field at the tip which moves through the material as an elastic-plastic shock wave. For high symmetry crack orientations relative to the crystal, the discontinuity surfaces are sometimes coincident with the active crystal slip planes, but as often lie perpendicular to the family of active slip planes so that the discontinuities correspond to a kinking mode of shear.The finite element studies so far attempted, simulating the ideally plastic material model in a small displacement gradient type program, appear to be consistent with the asymptotic analyses. Small scale yielding solutions confirm the expected discontinuities, within limits of mesh resolution, of displacement for a stationary crack and of velocity for quasi-static growth. Further, the discontinuities apparently extend well into the near-tip plastic zone. A finite element formulation suitable for arbitrary deformation has been used to solve for the plane strain tension of a Taylor-hardening crystal panel containing, a center crack with an initially rounded tip. This shows effects due to lattice rotation, which distinguishes the regular versus kinking shear modes of crack tip relaxation, and holds promise for exploring the mechanics of crack opening at the tip.

Asymptotic tensile crack-tip stress fields in elastic-perfectly plastic crystals

“…Rice also established several features for equilibrium stress distribution around a crack tip that are important to the present analysis; these will be summarized in the next section. Rice et al's [2] finite element analysis confirmed the crystal slip pattern obtained in the asymptotic analysis [1].…”

“…Rice [1] found an asymptotic stress field around the crack tip, which gives the stresses ahead of the crack as ~rlll0___o --2x/~r = 4.90% az210=0 = 3v/6r = 7.35% O"1210=0 : 0, (1) where 7-is the critical resolved shear stress for the primary slip systems {1 1 1}(1 1 0) in fcc crystals. This field occurs around the tip of an external crack in a perfectly plastic crystal and was verified by Rice et al's [2] finite element analysis. Based on the limit analysis, Rice [1] found another asymptotic field that may occur around the tip of an internal crack in a crystal and gave the stresses ahead of the crack tip as Crlllo=o : 0, crz2lo=o = x/67-= 2.457-, ~lzlo=o : 0.…”

Fatigue-induced grain coarsening in nanocrystalline platinum films

“…As the crack tip stress field becomes more intense, additional transverse planes allow for through-thickness slip of dislocations. This evolution is similar to the plane strain to plane stress transitions that occur in single crystals [33]. While this trend appears in both nano-and micrograined textured films, there is an important grain-coarsening phenomenon that is enabled by cyclic plastic deformation.…”

Recent advances in fatigue crack growth modeling

“…The macroscopic slip is calculated by averaging the microscopic slip at every Gauss point in the mesh. This model has been successfully used to model the tensile deformation of both BCC and FCC crystals [75], and later to study stationary cracks [76]. A more detailed description of the constitutive relation used to model the double slip phenomenon has been discussed [42][43][44].…”