Numerical phase-field modeling of damage in heterogeneous materials

Material failure is still one of the central issues in modern engineering. Its prediction and prevention are being tackled early in the product design stage. Materials used in modern engineering often exhibit significant microstructural heterogeneity. The size, shape, distribution and properties of microconstituents considerably influence the heterogeneous material properties. Nowadays, numerical simulations play an essential role in component design and material development, gradually supplanting and replacing expensive and time-consuming experiments. However, it is worth noting that many complex fracture processes occur at microstructural scale making the fracture analysis an especially challenging and interesting problem. One of the methods for the numerical modelling of fracture capable of efficiently recovering these complex fracture processes is the recently emerged phase-field method. It approximates the sharp crack discontinuity with a diffusive band regulated by a length-scale parameter, thus separating the broken and intact material states. Although extensive research has been carried out on the development of phase-field fracture theory over the past decade, certain challenges still exist in the computational implementation of the method. Within the finite element framework, a fine spatial discretization is often required to resolve the smooth phase-field distribution regulated by a small length scale parameter. Thus, coupling phase-field method with an inefficient solution scheme can be computationally rather expensive. In this work, a novel generalized phase-field framework capable of simultaneously recovering brittle, ductile, and fatigue fracture in three-dimensional settings is developed. The robustness and accuracy of the results is ensured by the development of an efficient residual control algorithm and its implementation in the commercial finite element software ABAQUS. Major advantage of such implementation is the high usability of different underlying solvers, convergence criteria and other additional options including automatic incrementation, element deletion, coupled contact analysis, thread parallelization or restart analyses, used and thoroughly discussed in this work. The full source code together with the presented examples and explanations is made publicly available, thus promoting the phase-field fracture methodology. The proposed implementation is exhaustively tested on a large number of different benchmark examples, verified and validated in comparison with numerical and experimental data from available literature. The importance of a stopping criterion within a staggered scheme is emphasised in the illustrative examples. The detailed discussions regarding the proposed implementation’s accuracy and CPU time usage are provided. Special attention is given to the verification of fatigue fracture examples through the parametric study. Main features of fatigue, including Wohler and Paris law curves in low- and high-cycle regimes, are easily recovered without any additional criteria. The cycle skipping technique is implemented to allow for the calculation of a very high number of cycles on moderate size examples. Finally, the potential of the implementation is demonstrated on the different-sized samples of nodular cast iron with their actual heterogeneous microstructure obtained from microtomography. Specimens are tested in both monotonic and cyclic loading regimes. The results clearly show the size-effect behaviour as well as the influence of microstructural topology on fracture patterns.