Residual stress effects on crack-tip stress singularity in XFEM fracture analysis

Crack domain may be affected by a thermodynamic process such as forming, welding on structural steel, during which significant residual stresses of the same order of the yield strength of the structural steel are remained. In these cases, the post-yield stiffness characteristics of the material, similar to a stress state dependent functionally graded material (FGM), characterizes the order of stress singularity reproduced at the heterogeneous crack-tip area. In this paper, the order of stress singularity and the singular mode shapes of free cracks within arbitrary FGMs, in two-dimensional are calculated using a finite element asymptotic analysis. Subsequently, the local distribution of tangent modulus in structural steel due to thermodynamic process, in the presence of a crack, is determined and the singular crack-tip fields based on the real state of the non-constant tangent modulus in the vicinity of the crack-tip are proposed and assessed as per von Mises plasticity model. It is shown that, thermal conductance of the crack edges and heat flux and stiffness of the connecting parts on either side of the crack, affects the intensity of the high gradient fields reproduced at the crack-tip in post-weld condition. Finally, the proposed singularity modal analysis results are implemented in a direct extended finite element (Direct-XFEM) algorithm and the accuracy and the rate of convergence of different XFEM formulations are examined. •The effect of residual stress and plastic strain due to high thermal interactions on the crack-tip area has been discussed.•A finite element asymptotic expansion for singularity modal analysis (SMA) is proposed.•Singularity modal analysis results for free cracks surrounded by heterogeneous elastoplastic materials are proposed.•Direct-XFEM for efficient implementation of singularity modal analysis results has been proposed.