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[SCG62-P16] Phase field simulation of crack propagation: effects of material interfaces on crack paths
Keywords:Phase-field method, Energy release rate, Crack, Material boundary
Prediction of crack propagation paths is crucial for evaluating fault propagation near geologic boundaries and ensuring the safety of structures. For instance, accurate prediction of crack initiation and propagation paths is required for fault propagation during earthquakes and for fail-safe design of structures. Moreover, fracture propagation, which causes material degradation and destruction, is critical for long-term durability assessment and risk management. In this context, theoretical and computational methods have been developed to understand and numerically analyze the mechanisms of crack propagation.
Recently, variational approaches using energy functional theory for crack propagation have been attracting attention. Francfort & Marigo [1] formulates crack propagation as an energy minimization problem and proposes a framework for treating fracture mechanics in a unified and quantitative manner. Bourdin et al. [2] extended it and proposed a framework applicable to numerical analysis, and Miehe et al. [3] introduced the phase-field method to construct a thermodynamically consistent model. Furthermore, Ambati et al. [4] proposed an efficient computational method and systematized the review of this field. Thus, the phase-field method, which has been developed for this purpose, models the crack as a continuous field and can efficiently simulate crack initiation, propagation, and bifurcation. Phase-field methods are highly practical because they can handle complex geometries and propagation paths without the need to track the crack surface. From the perspective of numerical analysis, the problem reduces to solving initial and boundary value problems of coupled partial differential equations. Therefore, it is highly compatible with traditional discretization methods such as the finite element method and the finite difference method.
This study investigated the influence of material boundaries on crack propagation paths by simulating crack propagation using the phase-field method. The material boundary was assumed to be a strata boundary or a material junction surface, and numerical simulations were performed using a model under simple shear conditions. The model consists of a 1 mm square with a notch. A parametric study of 96 cases was performed, varying ratios of the critical energy release rate (R) and the angle between the crack growth direction and the boundary (θ). The series of simulations was implemented on the general-purpose engineering software COMSOL Multiphysics.
As a result, the effect of the material boundary was significant for θ < 30° and R > 1.8, and the cracks propagated along the boundary in many cases. A similar tendency of crack propagation along the boundary was also observed for extremely small R values. In contrast, the influence of the boundary surface decreases as θ increases, and in some cases the cracks diverge. As described above, this study provided a comprehensive understanding of the effect of the material interface characterized by the ratio of critical energy release rates on crack propagation. It should be noted that this study focused on homogeneous interface conditions. Future work should address more realistic problem settings by considering interface roughness and material composition heterogeneity.
References
[1] G. A. Francfort and J.-J. Marigo, “Revisiting brittle fracture as an energy minimization problem,” J. Mech. Phys. Solids, vol. 46, no. 8, pp. 1319–1342, 1998.
[2] B. Bourdin, G. A. Francfort, and J.-J. Marigo, “The variational approach to fracture,” J. Elasticity, vol. 91, no. 1-3, pp. 5–148, 2008.
[3] C. Miehe, F. Welschinger, and M. Hofacker, “Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations,” Int. J. Numer. Methods Eng., vol. 83, no. 10, pp. 1273–1311, 2010.
[4] M. Ambati, T. Gerasimov, and L. De Lorenzis, “A review on phase-field models of brittle fracture and a new fast hybrid formulation,” Comput. Mech., vol. 55, no. 2, pp. 383–405, 2015.
Recently, variational approaches using energy functional theory for crack propagation have been attracting attention. Francfort & Marigo [1] formulates crack propagation as an energy minimization problem and proposes a framework for treating fracture mechanics in a unified and quantitative manner. Bourdin et al. [2] extended it and proposed a framework applicable to numerical analysis, and Miehe et al. [3] introduced the phase-field method to construct a thermodynamically consistent model. Furthermore, Ambati et al. [4] proposed an efficient computational method and systematized the review of this field. Thus, the phase-field method, which has been developed for this purpose, models the crack as a continuous field and can efficiently simulate crack initiation, propagation, and bifurcation. Phase-field methods are highly practical because they can handle complex geometries and propagation paths without the need to track the crack surface. From the perspective of numerical analysis, the problem reduces to solving initial and boundary value problems of coupled partial differential equations. Therefore, it is highly compatible with traditional discretization methods such as the finite element method and the finite difference method.
This study investigated the influence of material boundaries on crack propagation paths by simulating crack propagation using the phase-field method. The material boundary was assumed to be a strata boundary or a material junction surface, and numerical simulations were performed using a model under simple shear conditions. The model consists of a 1 mm square with a notch. A parametric study of 96 cases was performed, varying ratios of the critical energy release rate (R) and the angle between the crack growth direction and the boundary (θ). The series of simulations was implemented on the general-purpose engineering software COMSOL Multiphysics.
As a result, the effect of the material boundary was significant for θ < 30° and R > 1.8, and the cracks propagated along the boundary in many cases. A similar tendency of crack propagation along the boundary was also observed for extremely small R values. In contrast, the influence of the boundary surface decreases as θ increases, and in some cases the cracks diverge. As described above, this study provided a comprehensive understanding of the effect of the material interface characterized by the ratio of critical energy release rates on crack propagation. It should be noted that this study focused on homogeneous interface conditions. Future work should address more realistic problem settings by considering interface roughness and material composition heterogeneity.
References
[1] G. A. Francfort and J.-J. Marigo, “Revisiting brittle fracture as an energy minimization problem,” J. Mech. Phys. Solids, vol. 46, no. 8, pp. 1319–1342, 1998.
[2] B. Bourdin, G. A. Francfort, and J.-J. Marigo, “The variational approach to fracture,” J. Elasticity, vol. 91, no. 1-3, pp. 5–148, 2008.
[3] C. Miehe, F. Welschinger, and M. Hofacker, “Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations,” Int. J. Numer. Methods Eng., vol. 83, no. 10, pp. 1273–1311, 2010.
[4] M. Ambati, T. Gerasimov, and L. De Lorenzis, “A review on phase-field models of brittle fracture and a new fast hybrid formulation,” Comput. Mech., vol. 55, no. 2, pp. 383–405, 2015.