Numerical Analysis in Fracture Mechanics

Abstract

Recent developments in four numerical techniques in structural mechanics, which are used to extract fracture parameters for linear elastic, nonlinear and dynamic fracture mechanics, are reviewed. Primary emphasis is placed on the finite element methods for determining two- and three-dimensional (2-D and 3-D) stress intensity factors in linear elastic fracture mechanics. Crack opening displacements (COD) and J-integrals for 2-D, stable crack growth, ductile fracture, and use of elastic finite element method in its generation mode for obtaining dynamic elastic fracture parameters are discussed. The second topic is the finite difference method for analyzing the elasto-dynamic and elastic-plastic dynamic states in fracturing 2-D and 3-D problems. The third topic is the boundary element method which has evolved into a practical tool for numerical analysis in 3-D linear elastic fracture mechanics. The final topic is the updated alternating technique, which was merged with a 3-D finite element code and together with a break-through in its analytical formulation, has become a cost-effective numerical technique in solving part and complete elliptical crack problems in 3-D linear elastic fracture mechanics. Comparisons between the J-integral of a 3-point bend specimen, the stress intensity factor for a surface flaw specimen and the dynamic stress intensity factor of a fracturing dynamic tear test specimen obtained by various investigators are made.