An experimental-analytical hybrid model for the elasto-plastic stresses at a crack

The primary obstacle preventing the analytical determination of physically sensible stresses at a crack tip is the presence of a mathematical singularity there. This singularity is best known in its elastic form; however it persists even in elasto-plastic crack-tip stresses. To overcome the difficulty we adopt the following strategy: we attempt to capture initial elastic stresses experimentally, than track subsequent elasto-plastic stress distributions analytically.We infer a finite stress at a crack tip from the experimental behaviour of cracked specimens at fracture when the specimens are made of a truly brittle material. Given a size-independent result, we argue that the crack-tip stress at fracture must equal the ultimate stress for such a material; thus dividing by the applied stress at the same point gives a measure of the stress concentration factor, K_T. The approach is checked for size independence and against hole configurations with known theoretical, yet physically reasonable, K_T. Then the effective experimental KT are taken as inputs for the second phase of the study in which we model the crack as being a smooth notch having the same stress concentration factor as found experimentally. In this way our configuration initially shares the same stresses at the crack tip as we inferred physically. Next we track effects of incremental plastic flow on a set of finite element grids. Satisfactory resolution in return for modest computational effort is obtained by employing a substructuring method. The accuracy in both the elastic and the elasto-plastic regime is checked against trial problems with exact solutions. Thereafter, physically interpretable stress distributions ahead of the crack are determined for a range of materials and for varying load levels.