Coupled numerical analysis for in-plane elastic T-stress evaluation in isotropic FG solids

Abstract

This contribution establishes a coupled numerical method to show its effectiveness in the simulation of LEFM problems. The semi-meshless method uses the MLPG1 meshfree theory to discrete governing equations while geometry is modeled by simple CPS3 triangular cells. The cells help to propose an efficient neighboring method for meshfree interpolations. Three benchmark homogeneous cases are considered whose analytical solutions are available to carefully examine the accuracy of this method and validate the numerical implementation by comparing relative errors in terms of error norms, crack onset angle and also fracture parameters, i.e. KI, KII and T-stress that characterize the crack tip condition. Good computational accuracy is observed in this article. Three FG structures by simple linear, exponential and complex hyperbolic-tangent gradations are taken from the literature and investigated under thermo-mechanical conditions. A thermal barrier coating with an FG structure is also modeled. Then, fracture parameters and crack growth angles with and without considering T-stress are compared with FE solutions. Generalized maximum tangential stress (GMTS) criterion and interaction integral method are used to respectively compute crack growth angle and capture T.