Thermal-mechanical crack propagation in orthotropic composite materials by the extended four-node consecutive-interpolation element (XCQ4)

Abstract

A numerical study of thermal-mechanical crack growth in orthotropic composite materials by the recently developed extended nodal gradient finite element method is presented. The extended four-node consecutive-interpolation quadrilateral element (XCQ4) used in this work is the conventional four-node quadrilateral element, but it is enhanced by additional terms of averaged nodal gradients to smoothen the derivative fields and increase the accuracy of solution, while keeping the same total number of degrees of freedom (DOFs) as that of the traditional element. Inspired by enrichment partition-of-unity method, the singularity and discontinuity of temperature, heat flux, and displacements due to the presence of crack are mathematically described through known enrichment functions. Once the stress fields are obtained, stress intensity factors (SIFs) can thus be evaluated by interaction integral technique. The SIFs are then used to predict crack growth direction. Unlike isotropic media, material orientation plays a critical role and that has to be considered when modeling the evolution of crack in orthotropic composite materials under thermo-mechanical loading condition. In addition, we introduce for the first time an improved way for the enriched approximation of discontinuous temperature field in cracked orthotropic media by taking into account the effect of material orientation. Several numerical examples for thermo-mechanical fracture problems in orthotropic composites with both isothermal and adiabatic loading conditions are analyzed to show the accuracy and performance of the present XCQ4. The computed results of the SIFs are compared with reference solutions derived from experiments, the standard extended four-node quadrilateral element (XQ4), and other numerical methods available in literatures.