A phase ordering viewpoint for fracture

A solid which is constrained to be strictly homogeneous at all times cannot fail: simply because regions of local failure (eg. cracks) explicitly violate this assumption of homogeneity. What is then the origin of elastic heterogeneities in a solid? We attempt to answer this question in the context of a Lennard Jones solid in two dimensions close to the triple point. Characterizing local regions using a parameter which measures the extent of inelasticity viz. the non-affine parameter($\chi$) we study the structure and dynamics of regions with relatively large values of $\chi$. We show that these regions occur spontaneously as droplet fluctuations with anomalous structural and dynamical properties. We argue that these fluctuations are droplets of the liquid within the solid close to the thermodynamic solid-liquid phase boundary.  An outcome of our study is a quantitative measure for the limit of metastability of the liquid phase at higher than freezing densities. We investigate the role of these droplet fluctuations in the mechanism of failure of the solid under tensile loading.