Revisiting Methodologies for Computing Fracture Mechanics Parameters


In this presentation, methodologies for computing fracture mechanics parameters such as the stress intensity factor and the energy release rate will be discussed. Although the use of the finite element method (FEM) to analyze fracture mechanics has a long history, it is still considered to be difficult. This is because it is necessary to create a good (optimized) mesh consisting of a regular arrangement of hexahedral finite elements in the vicinity of the crack front. However, fracture analysis becomes far easier if a bad (non-optimized) mesh is instead used. Here, methodologies for computing the stress intensity factor and the energy release rate in linear and elastic-plastic solids using such a bad mesh are discussed.

The reason that a good mesh is generally used is because it is considered necessary for accurate evaluation of the fracture parameters. The domain integral method and the virtual crack closure-integral method (VCCM, also known as the virtual crack closure technique, VCCT) are often used to compute fracture parameters, and they generally require a good mesh to obtain accurate results. This is most likely why fracture mechanics analysis is considered to be so troublesome. A popular approach to circumventing such difficulties is to avoid the need for remeshing when modeling a crack, by using techniques such as X-FEM and G-FEM.

It should also be pointed out that finite-element model generation for a three-dimensional crack problem becomes less difficult if tetrahedral finite elements are used even in the vicinity of the crack front. This is because automatic mesh generation methods can be customized for crack problems. However, it is still not easy to generate a good mesh. Thus, methodologies for computing fracture parameters even using bad meshes need to be developed.

In this presentation, the VCCM, J-integral method, and interaction integral method are considered for automatically generated meshes. Finally, a method for computing the energy release rate in the case of large-strain cyclic loading is discussed.