Computation of Effective Fracture Toughness of Porous Materials using a Fracture Phase-Field Model
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This work investigates the simulation-based determination of the effective fracture resistance of porous materials. Following the approach proposed by Hossain et al., numerical experiments are conducted to identify effective crack resistance as a macroscopic material parameter. Displacement boundary conditions corresponding to a steadily propagating macroscopic crack are applied to representative microstructures. At the microscale, crack growth is simulated without prescribing crack paths, continuity of propagation, or other kinematic assumptions. The maximum value of the macroscopically acting J-integral defines the driving force required to advance the crack by a macroscopic length increment without arrest. This value is interpreted as the effective crack resistance of the porous material. Crack evolution at the microscale is modeled using a phase-field approach, which provides a regularized representation of cracks and introduces an intrinsic internal length scale, making it particularly suitable for complex fracture processes in heterogeneous materials. The results show that crack re-nucleation constitutes a toughness-governing failure mechanism in porous media. The influence of several parameters on the characteristic length associated with crack re-nucleation is investigated, revealing a strong correlation with the internal length scale of the phase-field formulation. Furthermore, the effective crack resistance is analyzed for simplified porous microstructures, with a focus on the effects of pore shape and pore spacing. These parameters are shown to significantly affect the fracture resistance and overall failure behavior. In the second part of the study, microstructures derived from CT scans of real metallic foams are employed, enabling realistic simulations and improved prediction of the fracture properties of heterogeneous porous materials.
