The role of strain ratcheting and mesh refinement in finite element analyses of plasticity induced crack closure

Numerical investigations of plasticity induced crack closure using the finite element method typically assume: (1) the opening behavior remains independent of the simulated rate of crack growth, and (2) a threshold element size exists below which crack opening loads become mesh independent. Nevertheless, examples in the recent literature and also in the present work indicate these assumptions do not always hold. The current work demonstrates the field results (displacements, stress-strain) for cyclic loading of stationary cracks converge with mesh refinement. However, when the cyclic load regime includes systematic crack extension, certain conditions lead to highly mesh dependent fields and opening loads. The cyclic accumulation of permanent deformation (strain ratcheting) necessarily produces mesh dependence when the finite element size dictates the rate of crack growth. Moreover, extensive ratcheting leads to physically unrealistic shapes of the crack opening profiles. This work explores the link between strain ratcheting, mesh dependence and load-cycle effects within a small-scale yielding framework, including the influence of plane strain vs. plane stress constraints, constitutive definition (non-hardening, linear kinematic hardening and nonlinear kinematic hardening) and the monotonic flow properties. Key conclusions from this work include: (1) near-tip strain ratcheting generally increases with decreased hardening and can be much more pronounced in plane strain than in plane stress; (2) for models with significant ratcheting, slower rates of simulated growth due to smaller element size and/or more load cycles between crack advancements generally reduce the opening loads; and (3) the computed opening loads depend intrinsically on the amount of ratcheting, and the rate of crack growth as determined by the element size and number of load cycles between crack advancements.