Mixed Scheme of the Finite Element Method as a Basis for Computational Analysis of Model Crack Mechanics Problems

Abstract

The application and comparison of different fracture mechanics concepts are discussed to be used in computing stress intensity factors (SIF) from the numerical solutions of model crack theory problems with a mixed scheme of the finite element method. Approximation of displacements rests on piecewise-linear interpolation functions with triangular elements, and strain and stress distributions are approximated by the linear combination that includes the piecewise-linear interpolation and interior bell function. The latter ensures the stability and convergence of the approximate discrete problem solution. The solution results for linear elastic and elastoplastic model plane central mode I crack-strip tension problems under different loading and plane strain state conditions are presented. Elastoplastic calculations were made with an ideal elastoplastic material model. The application of the energy balance and G-integral concepts to the calculation of the specific work of fracture at the stationary crack tip is substantiated. It is shown that on condition of uniform plate partition in the vicinity of the crack tip, the application of those concepts to SIF calculation for one loading stage is consistent with the Irwin plastic zone correction, maintaining this approach in further mesh thickening. Elastoplastic calculations on repeated loading demonstrated that tensile stresses ahead of the crack tip were about the same as on the initial one, but the opening at the crack tip on the former was larger than on the latter, and this effect was most pronounced for the first half of active loading values. Several aspects of SIF calculations on repeated loading are presented.