Statistical modelling of fracture using cellular atomata finite element

Abstract Fracture is an inherently statistical phenomenon as it is a function of micro-structural heterogeneities such as distributed defects and inclusions. This is evidenced by scatter in the toughness of seemingly identical specimens. Therefore, deterministic approaches do not give full picture of scatter in fracture behaviour. More suitable probabilistic methods have been devised to describe the scatter associated with fracture. While the probabilistic approaches provide a sound scientific basis for capturing the scatter in the fracture data through assuming a probability for the presence of fracture initiators, their microstructurally agnostic assumptions can limit their predictive capability. This is because there is no information on the microstructure such as grain size and morphology, texture, and other important features considered in them. An alternative class of models which take into account the distribution of toughness is cellular automata finite element models (CAFE). CAFE models are stronger in simulating the scatter in the fracture data through their ability to represent the microstructure although so far, they have been limited to fully brittle or quasi-brittle materials. In addition, the CAFE models they are computationally expensive, and their running time can be prohibitive for their application to large scale engineering components thus reducing their appeal. In this study, a CAFE model was developed to take advantage of the microstructural fidelity of CAFE but presented within the context of a probabilistic fracture approach. The CAFE based model calculates the macroscopic strain from the continuum FE model. The strain is then used to load a model which is defined in the cellular automata space. The CAFE model then simulates the initiation and propagation of fracture in the microstructure to fully capture the heterogeneity of the material at the lower length scale. The critical stress acting normal to the cleavage plane of each grain is calculated in the CAFE model and used to decide the onset of cracking in a probabilistic manner; the stress depends on the orientation of the grain in which microcrack initiates as well as depending on the orientation of the surrounding grains. To evaluate its performance, the model was calibrated using a set of experimental fracture toughness data and the results of its prediction were compared with an intendent and separate set of warm prestress experiments of the same material. Good agreement between the prediction and the experiment of the second set was observed giving confidence in the model.