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.

Random critical point separates brittle and ductile yielding transitions in amorphous materials

“…It has been recently argued that the finite-size effect of q is always a signature of a discontinuous yielding transition (60). At variance with this claim, we show here that a different finite-size behavior is observed at higher T ini where yielding is simply a smooth crossover.…”

Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain

“…(i) one must write the dynamical action in the co-shearing frame as in Eq. (14); the dynamical virial expansion can then be truncated to its first excess term;…”

Particle pinning suppresses spinodal criticality in the shear-banding instability

“…We report in this appendix the expression of the correlators we calculated in the main text. The details on how these expressions can be obtained can be found in [19,20]. The correlation function is the sum of two terms:…”

“…As for the nature of this transition, however, an established consensus is still missing. One point of view, advanced by some of us, advocates a transition in the form of a critical spinodal with disorder [18][19][20], wherein the growth in space of plastic events is controlled by a correlation length which diverges at the transition and can be measured from suitable multi-point correlators [19,20]; another one [21,22], inspired by previous work [23] on disordered spinodals in the context of the Random Field Ising Model [24][25][26] supports a picture in terms, again, of a spinodal transition, however not a critical one. In this view avalanches grow through nucleation around rare defects, rather than through a critical process involving a correlation length.…”

“…In this work, we apply the techniques formulated in [18][19][20] to the study of mechanical yield in such a model system, and use them to elucidate the mechanism leading to the suppression of shear bands: while a growing correlation length can still be measured, we show that it cannot diverge in a critical fashion, and is on the contrary bounded by the typical distance between pinned particles. Our picture of yield in terms of a critical spinodal is therefore able to capture and explain the qualitative changes in the yield and mechanics of glasses with pinned particles.…”