Title: 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.