Failure of heterogeneous materials: A dynamic phase transition?

Abstract While there exists a unified theoretical framework–Linear Elastic Fracture Mechanics–to describe the failure of homogeneous materials, understanding and modeling the mechanical properties of heterogeneous media continue to raise significant fundamental challenges. Stress enhancement in the vicinity of cracks indeed makes classical homogenization methods irrelevant to predict the toughness and lifetime of heterogeneous materials. “Mean field” approaches have been proposed to estimate these quantities, but they remain limited to dilute damage. Numerical simulations do not suffer from such limitations, and disorder can be tuned continuously. Molecular Dynamics simulations allow one to characterize damage and fracture in amorphous materials at the nanoscale, i.e. at the scale of their inhomogeneities. However, these simulations are up to now limited to dynamic fracture, which confers further complexity to the observed mechanisms. A “minimalist” approach consists in exploiting the analogy between scalar mode III elasticity and electricity through the study of random fuse networks breakdown. In two dimensions, powerful algorithms can compute the exact stress field in an elastic medium containing cracks of arbitrary shapes. However, although these tools have been useful in solving some classical problems (e.g. size dependence of materials strength), a clear predictive unified theoretical framework is still missing. An efficient theory should be able to predict, a minima , the morphology of fracture surfaces, which encodes the interaction between the propagating crack front and the surrounding microstructure. We provide a review of recent quantitative fractography experiments. The most striking observations in this field is the existence of universal morphological features, independent of both the material and the loading conditions, reminiscent of interface growth problems. In this context, we analyze models which describe the crack front as an elastic line that propagates in a random potential. In these models, the onset of crack propagation is interpreted as a dynamic phase transition, while sub-critical crack growth is assimilated to thermally assisted depinning.