Numerical Estimation of Fracture Parameters in Elastic and Elastic-plastic Analysis

The finite element method has been largely used to analyze mechanical problems and, in particular, to obtain the response of cracked structures. One of the major issues in using the method is mesh generation. Nowadays, several automatic mesh generation algorithms are available for two-dimensional models. Crack analysis imposes severe requirements on automatic mesh generation. It is not uncommon that elements near the cracktip be two orders of magnitude smaller than other elements in the model. Meshing algorithms must be able to provide good size transition capabilities. Previous works of the authors have proposed techniques for automatic, self-adaptive mesh generation of two-dimensional cracked models. This work describes the numerical procedures that were developed to numerically estimate fracture parameters both in linear-elastic and elastic-plastic analysis. The article describes three methods to evaluate fracture parameters: Displacement Correlation Technique, Modified Crack Closure Method, and J-integral evaluation accomplished by means of Equivalent Domain Integrals. The latter method is also used to evaluate fracture parameters in elastic-plastic analysis. In the mesh generation procedure, special elements with well-formed shape are placed at the crack-tips. For linear-elastic analysis, quarter-point triangular elements are used, forming a rosette of elements with angles of 45°, 40°, or 30°. In elastic-plastic analysis, collapsed Q8 elements are used in the standard rosette. The von Mises yield criterion, with isotropic hardening, is used in the plastic analysis. Some examples are presented to compare the results with analytical and other available numerical results. T. Denyse de Araújo, T.N. Bittencourt, D. Roehl, and L.F. Martha. 2