The rigid bodies—spring models and their applications to three-dimensional crack problems

Abstract

The rigid bodies—spring models (RBSM) were applied to the phenomenon of crack growth in three-dimensional problems and demonstrated the effectiveness of the models. The characteristic of RBSM is to give practical answers withing a relatively small number of degrees of freedom in the limit analyses such as strongly non-linear and fracture analyses; the models have already proved useful for the analysis of two-dimensional problems. In this paper, the practical application of the three-dimensional RBSM is presented, and the conventional constitutive law of steels is discussed. Compared with the experimental data, the potential fracture criteria are determined. The stable crack growth in an arbitrarily shaped intitial crack is simulated. The plastic zone of the crack tip demonstrate that Mohr—Coulomb's law may be more suitable than von Mises'. The effectiveness of the cutting criterion for the springs of the RBSM is verified in the application to an arbitrarily shaped crack. In an application to dynamic crack propagation of brittle material, the simulated crack propagation is in resonable agreement with the actual crack propagated in the residual stress field of the welded plate.