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Functionally Graded Materials (FGMs) are those whose composition and hence the properties vary gradually as a function of position. The need to understand, quantify and improve the toughness of FGMs has brought interest in a fracture mechanics methodology for such materials. Due to the high cost and elaborate facilities required for experimental processing of FGMs, the numerical simulation of fracture behaviour of cracked FGMs has acquired special relevance. In this work, a complete scheme for numerical simulation of quasi-static mixed mode fracture in planar FGMs is developed. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. Finite element simulations were conducted in order to calculate the SIFs and the non singular T -stress at the precise instant of crack initiation. Computational results of fracture parameters and crack initiation angles are compared to available experimental results and good agreement is obtained. Once validated, the numerical model is developed in order to study unsolved problems of mixed-mode fracture in FGMs. A sensitivity analysis of fracture parameters under small variations in the numerical fit of the experimental data is performed. Both the SIFs and the T -stress show a high sensitivity, not only to small changes in local elastic properties at the crack tip, but also to little differences in the slopes of the numerical curve fit in the vicinity of the crack. Also, Poisson’s ratio effect on fracture parameters for a crack in FGMs under mixed-mode loading conditions is evaluated. The numerical results show that Poisson’s ratio has a significant influence on both SIFs and T stress for FGMs. This work emphasizes that more attention needs to be paid to Poisson’s ratio effect, specially when load direction becomes parallel to the direction of material gradation. Crack propagation path is then analyzed by means of the X-FEM, setting the maximum principal stress as the crack initiation criterion, based on the assumption that the graded material is locally homogeneous near the crack tip. Crack trajectories obtained by the present numercial simulation are compared with available experimental results and seem to agree reasonably well. Existing differences are discussed and, for some specific cases, a criterion that compares the stress field surrounding the crack to local failure properties is proposed. The goal of this work is to directly compare experiments and simulations so as to evaluate the applicability of the numerical scheme proposed in real cases, establishing a methodology for numerical simulation of fracture processes in FGMs under mixed-mode loading.

Análisis por el método de los elementos finitos de problemas de fractura en FGM