Subcritical crack growth in elastic-plastic material with overshoot: Part I—analytical modelling

Abstract

Subcritical crack growth is associated with the situation where the driving force is sufficiently low such that the crack would arrest upon unloading. In metals, plastic deformation could further enhance the subcritical crack growth process. Analytical modelling of such behavior would necessitate discretizing the growth process into finite segments by assigning threshold levels to elements at the prospective site of failure. This gives rise to the so-called “overshoot” phenomenon because the elements nearest to the crack would be strained above and beyond the critical value due to the rapid elevation of the local stress and/or energy. The effect can be minimized by taking smaller crack growth segments but cannot be completely removed in analyses nor in experiments because increase in load occurs in finite steps. Modelled is subcritical crack growth in an elastic-plastic material with overshoot, the amount of which would depend on the fracture toughness, specimen size and loading step. Energy dissipated by plastic deformation is considered as part of the loss that is not available to drive the crack. Incremental theory of plasticity is employed where isotropic and kinematic hardening of the material are accounted for. Varied are the material type, specimen size and load steps such that their combined effects on crack growth would be reflected in the final results.