The finite element analysis of deformation and stress triaxiality of a mixed I + II mode elastic-plastic crack tip

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 in 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.