The Finite Analysis of Deformation and Stress Triaxiality of a Mixed I + II Mode Elastic-Plastic Crack Tip

Abstract

The deformation and distribution of stress triaxiality σ_{_m}/σ of mixed I + II mode elastic-plastic cracks under plane strain and plane stress conditions were analysed by the large strain finite element method and were compared with the HRR field. The results show that, (1) the model of crack-tip deformation under mixed I + II mode loading is sharpening-blunting, the sharpening and blunting deformation is acted on by compressive stress (σ_{_m}/σ > 0) and tensile stress (σ_{_m}/σ > 0), respectively; (2) in the plane strain case, the (σ_{_m}/σ)_{_max} of the real crack tip decreases with an increase of mode II component, but increases with an increasing strain hardening n for every mixed ratio. For the loading of K_{_I}/K_{_II} > 0.5, the (σ_{_m}/σ)_{_max} value of the real crack tip is less than that of the (σ_{_m}/σ)_{_max} given by the HRR field, but the opposite holds true cases where K_{_I}/K_{_II} > 0.5; (3) in the plane stress case, the (σ_{_m}/σ)_{_max} decreases a few values with an increasing mode II component, the values of (σ_{_m}/σ)_{_max} of every mixed ratio are far less than these of the corresponding loading condition in the plane strain case. In the plane stress case, the (σ_{_m}/σ)_{_max} values of every mixed ratio for any strain hardening exponent n are almost constant.