Mechanical Failure in Amorphous Solids: Scale Free Spinodal Criticality

Abstract: The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free", indicating some type of criticality. In spite of attempts to invoke "Self-Organized Criticality", the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Recently we proposed that the precise nature of this critical behavior is manifested by a spinodal point of a thermodynamic phase transition. Moreover, at the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. Demonstrating this requires the introduction of an "order parameter" that is suitable for distinguishing between disordered amorphous systems, and an associated correlation function, suitable for picking up the growing correlation length. The theory, the order parameter, and the correlation functions used are universal in nature and can be applied to any amorphous solid that undergoes mechanical yield. Critical exponents for the correlation length divergence and the system size dependence are estimated. The phenomenon is seen at its sharpest in athermal systems, as is explained below; in this paper we extend the discussion also to thermal systems, showing that at sufficiently high temperatures the spinodal phenomenon is destroyed by thermal fluctuations.