Overview
A microscopic constitutive theory has been developed to describe the nonlinear deformation of amorphous materials, specifically metallic and polymer glasses. This theory encompasses the full stress-strain response, from linear elasticity through stress overshoot and yielding, leading to steady plastic flow. It integrates nonaffine elasticity with irreversible many-body relaxation to account for the observed mechanical phenomena.
Research Context
Understanding the mechanical behavior of amorphous materials, particularly their response to stress and strain, involves several complex phenomena. These include stress overshoot, a peak in stress before reaching a steady state of plastic flow, and strain hardening, where material resistance to deformation increases with strain. The current research aims to provide a unified microscopic framework that connects these behaviors to the underlying relaxation dynamics of the materials.
Approach
The constitutive theory developed in this work is based on two primary mechanisms: nonaffine elasticity and irreversible many-body relaxation. Nonaffine elasticity is characterized by an instability induced by strain, leading to a loss of mechanical connectivity at the atomic/molecular level. Irreversible many-body relaxation contributes viscous dissipation, which is associated with structural changes within the material. The theory posits that the competition between this nonaffine elastic instability and viscous dissipation is the origin of stress overshoot.
For polymer glasses, the theory incorporates finite chain extensibility as the mechanism responsible for strain hardening at large deformation. The primary dynamical input for the theory is a stretched-exponential relaxation exponent, which can be independently obtained from stress or modulus relaxation measurements. The model utilizes a small set of 'physically meaningful parameters' to describe the material behavior.
Findings
The theory predicts the complete stress-strain response of amorphous materials, including linear elasticity, stress overshoot, yielding, and steady plastic flow. A key finding is that stress overshoot results from the interplay between a nonaffine elastic instability, driven by strain-induced mechanical disconnection at the microscopic level, and viscous dissipation arising from structural relaxation.
For polymer glasses, the theory identifies finite chain extensibility as the mechanism that naturally explains strain hardening under large deformation. The model has been shown to quantitatively reproduce experimental stress-strain curves across a broad range of strain rates. This quantitative agreement was observed for various materials, including metallic glasses, polycarbonate, PMMA, and epoxy resins. The stretched-exponential relaxation exponent, derived from stress or modulus relaxation, serves as a crucial dynamical input to the theory.
Why This Matters
These results establish a unified microscopic framework that links several critical aspects of amorphous solid behavior: relaxation dynamics, yielding, plastic flow, and strain hardening. This framework could provide a deeper understanding of how these materials deform under stress and strain.