Small scale yielding near a crack in plane strain: A finite element analysis

Abstract

This paper presents an incremental elastic-plastic finite element solution to the problem of small scale yieldmg near a crack in plane strain for a non-hardening material. Emphasis is placed on the design of finite elements which allow accurate reproduction, m a numerical solution, of the detailed structure of the near crack tip stress and strain fields, as understood from previous analytical studies of crack tip singularities. Numerical results are presented for: location of the elastic-plastic boundary, angular distribution of the strength of the strain singularity, crack tip opening displacemeat, stress distribution ahead of the crack, and angular variation of stresses at the tip. The latter results verify Rice's prediction of the Prandtl field in provldmg the limiting stress distribution as r ~ 0.

Continuing crack-tip deformation and fracture for plane-strain crack growth in elastic-plastic solids

“…The numerical investigations of SORENSEN (1977) provide crack surface displacements throughout the prescribed loading history. Figure 2 presents cracksurface profiles prior to crack advance and following the final step of crack growth.…”

“…These parameters are useful in quantifying the onset of fracture; however, the question of whether such fracture is initially stable or catastrophic remains unresolved and there is evidence for stable crack growth in many ductile metals, e.g. CLARKE et al (1976) GRIFFIS and YODER (1976), PARIS et al (1977) and CLARK et al (1978).…”

“…Numerical investigations of stable crack growth include the plane-strain studies of KFOURI and MILLER (1976) and SORENSEN (1977) and the plane stress studies of DE KONINC (1977) and ANDERSSON (1973). These latter two investigators conclude that a possible parameter for the characterization of continuing fracture is the crack-tip opening angle, the angle between the separating crack surfaces behind the extending crack tip.…”

“…The following discussion lends support to this kind of characterization but also suggests limitations to the universality of the stable growth representations thus obtained. (1977) presents finite element solutions for crack advance under wellcontained, small-scale yielding, plane-strain conditions. These solutions simulate crack advance through the finite element grid by the successive relaxation of nodal constraints; the external load is held constant during crack advance and is incremented at constant crack length between crack growth steps of one element each.…”

“…Typically, during the growth process, the maximum radius of the plastic zone was S-12 times the size of the near tip elements (although the plastic zone extends directly in front of the crack only over 2-3 elements). The material was modelled as an elastic-plastic Mises material satisfying the Prandtl-Reuss flow rule, and strain hardening was modelled by a power-law hardening formulation, such as that used by TRACEY (1976) (1977). Points marked "steady state" correspond to final advancing crack solution.…”