Numerical modeling issues in finite element simulation of plasticity induced crack closure with an emphasis on material model effects

Plasticity induced crack closure (PICC) has a potentially strong effect on the growth rate of fatigue cracks in metal structures. As a crack grows through previously yielded material, the permanent deformation in the crack wake Shields the crack tip from the full impact of the remote load. This work sought to add to the large body of PICC finite element studies by introducing two nonlinear plasticity models---nonlinear kinematic hardening (Armstrong and Frederick's model) and nonlinear plastic strain evolution (Lubliner's generalized plasticity)---into a 3D small scale yielding boundary layer approximation of a mode I crack. With the traditional method of growing the crack by one element per load cycle, the results display strong sensitivity to the element size. This work and the PICC literature demonstrate that linear plasticity models may also produced mesh dependent results in certain conditions. The manifestation of mesh sensitivity depends on not only the material model, but also the material parameters, whether the model is 3D, 2D plane strain, or 2D plane stress, and if the T-stress is compressive or tensile. This work reveals that cyclic accumulation of permanent deformation (strain ratcheting) is responsible for mesh dependence when the rate of growth depends on the element size. Mesh refinement may commute with the use of multiple load cycles between crack growth increments to provide the same effective growth rate. Sufficient cycles between crack growth increments can reduce mesh dependence while approaching real crack growth rates. For conditions that create severe ratcheting, the number of cycles needed to obtain fully mesh independent results may be impractical. Spontaneous crack growth shows some promise for reducing mesh dependence; a critical COD criterion for crack extension produced similar crack growth rate and opening loads for different mesh sites. Nevertheless, strong gradients in crack closure near the crack tip imply that there will always be an element size effect with respect to measuring 3D variations in near-tip behavior.