Numerical Analysis of Stable Crack Growth in Elastic-Plastic Materials in Small Scale and General Yielding
Lam, Poh-Sang
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https://hdl.handle.net/2142/71672
Description
Title
Numerical Analysis of Stable Crack Growth in Elastic-Plastic Materials in Small Scale and General Yielding
Author(s)
Lam, Poh-Sang
Issue Date
1983
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Abstract
Stable crack growth problems in elastic-plastic materials are investigated with the aid of the finite element method. The formulation used for steady state crack growth under small scale yielding conditions has the feature that the finite element mesh convects along with the moving crack tip. Various models for plastic flow were used. In Mode III, calculations were carried out for J(,2) incremental theory and a modified J(,2) deformation theory meant to introduce effects related to flow at a yield surface vertex.
In plane strain Mode I calculations, the elastic-perfectly plastic solution shows that elastic unloading wedges subtended by the crack tip in the plastic wake region do exist and that the stress state around the crack tip is similar to the modified Prandtl fan solution. To demonstrate the effects of a vertex on the yield surface, a small strain version of a phenomenological J(,2) corner theory of plasticity with a power law stress strain relation is used to govern the strain hardening of the material. To take account of Bauschinger like effects caused by the stress history near the crack tip, a simple kinematic hardening rule with a bilinear stress strain relation is also studied. There appears to be more potential for steady state crack growth in the conventional J(,2) incremental plasticity material than in the other two plasticity laws considered here if a crack opening displacement fracture criterion is used. However, a fracture criterion dependent on both stress and strain could lead to a contrary prediction.
Another set of analyses deals with stable crack growth under large scale yielding conditions in an elastic-perfectly plastic compact tension specimen. In this case a Lagrangian formulation is used. The crack tip nodal reactions are first computed and then gradually released to simulate an increment of stable crack growth. We also derive an approximate formula for the J-integral for the compact tension specimen. The numerical values of the J-integral from the finite element calculations are compared with estimates based on a pure bending approximations of the experimental results for an AISI-4140 steel specimen. These values are similar to each other in our specimen but differences would be expected in less-deeply cracked configurations.
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