Stress singularity of symmetric free-edge joints with elasto-plastic behaviour

The stress singularity for symmetric free-edge joint is presented for isotropic elastic and elasto-plastic materials. Complex functions were used to describe the elastic stress and displacement fields and an eigenvalue problem was solved. The singularity orders for the elastic materials were plotted versus joint angles for different material combinations investigating the influence of Poisson’s ratio.For Ramberg–Osgood power-law hardening materials the shooting method was implemented to obtain the unknown boundary conditions at free-edge, necessary for solving numerically the eigenvalue problem, using a fourth-order Runge–Kutta method. The obtained numerical results are compared with those of a highly focused finite element (FE) analysis.The authors proposed a new formula to estimate the singularity order for the elasto-plastic stress singularity based on the hardening parameter and the computed elastic singularity for incompressible material.

Research highlightsThe stress singularity for symmetric free-edge joint is determined. The Runge–Kutta algorithm in conjunction with the shooting method was applied. The stress singularity increases with increasing joint angle. The stress singularity decreases with increasing hardening exponent. A new formula of stress singularity for elasto-plastic joints was proposed.