Extending the Local Approach to Fracture: Methods for Direct Incorporation of Microstructural Effects Into Finite Element Models of Fracture

The Local Approach to fracture phenomena has been very successful in helping to transfer information derived from testing one geometry on a material (laboratory specimens) to the prediction of the crack growth performance of another (the structure). At least in its most pervasive manifestations, it depends upon constructing finite element models with a ruling element size that is appropriate for the physical scale of the dominant failure mechanism. Since these are primarily of the order of the material microstructure, there is a consequential very strong mesh gradient towards the region of Local Approach interest. When applied to structures of engineering interest, which can be large, the resultant finite element models become very big, sufficiently so that they cannot be run on many computers, if at all. When there is more than one material scale involved, the situation becomes impossible to resolve with conventional finite elements, except through the use of compromise local finite element sizes that blend the requirements from each micro-scale into a smeared cell at the finite element level. Such models have shown considerable success in predicting the performance of a range of components and structures by a number of research groups. Even so, the method is constrained by the excessive computational costs associated with modeling realistic structures, and by other concerns derived from its smearing of possibly incompatible underlying physical effects. CAFE modeling, the coupling of Cellular Automata at the microstructural scale(s) with finite elements that are scaled only for the strain gradients expected at the macro-scale in the structure, offers a way out of these potential problems. The structural level field quantities, held at the element Gauss points, are modified according to information coming from the Cellular Automata with which each Gauss point is associated. Suitable code representing fracture initiation and propagation at the micro-level generates changes incrementally to the Gauss point field variables, which are then brought to equilibrium by the FE modeler (whenever it is an implicit FE system). The method allows a natural representation of the multiple scale interactions typical of the fracture of low alloy steels in the transition region.