[Paper Review] Yielding, shear banding and brittle failure of amorphous materials

Suzanne M. Fielding, Fielding, Suzanne M|arXiv (Cornell University)|Mar 11, 2021

Metallic Glasses and Amorphous Alloys4 citations

TL;DR

This study proposes a theoretical framework for predicting ductile or brittle yielding in athermal amorphous materials under slow shear, using a mesoscopic lattice elastoplastic model. It identifies a two-stage failure process: a pre-failure stage of slowly accumulating strain heterogeneity, followed by catastrophic shear band propagation via cooperative plastic events, with an exact analytical expression for strain heterogeneity and failure strain distribution dependent on annealing and sample size.

ABSTRACT

Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly and gradually (ductile behaviour) or fail abruptly and catastrophically (brittle behaviour); the roles of sample annealing, disorder and shear band formation in the onset of yielding and failure; and, most importantly from a practical viewpoint, whether any impending catastrophic failure can be anticipated before it happens. We address these questions by studying the yielding of slowly sheared athermal amorphous materials, within a minimal mesoscopic lattice elastoplastic model. Our contributions are fourfold. First, we elucidate whether yielding will be ductile or brittle, for any given level of sample annealing. Second, we show that yielding comprises two distinct stages: a pre-failure stage, in which small levels of strain heterogeneity slowly accumulate, followed by a catastrophic brittle failure event, in which a crack quickly propagates across the sample via a cooperating line of plastic events. Third, we provide an expression for the slowly growing level of strain heterogeneity in the pre-failure stage, expressed in terms of the macroscopic stress-strain curve and the sample size, and in excellent agreement with our simulation results. Fourth, we elucidate the basic mechanism via which a crack then nucleates and provide an approximate expression for the probability distribution of shear strains at which failure occurs, as determined by the disorder inherent in the sample, expressed in terms of a single annealing parameter, and the system size.

Motivation & Objective

• To determine the conditions under which amorphous materials yield in a ductile or brittle manner, particularly as a function of sample annealing and size.
• To understand the dynamical sequence leading to catastrophic failure, focusing on the role of strain heterogeneity and shear band nucleation.
• To derive an analytically exact expression for the growth of strain heterogeneity during the pre-failure stage.
• To predict the probability distribution of failure strain in terms of sample size and intrinsic disorder (annealing level).

Proposed method

• Uses a minimal mesoscopic lattice elastoplastic model to simulate slowly sheared, athermal amorphous materials.
• Applies periodic boundary conditions to isolate homogeneous nucleation of shear bands, excluding surface defects.
• Employs the Eshelby propagator to model elastic stress transfer between yielding elements.
• Derives an exact analytical expression for strain heterogeneity growth using the macroscopic stress-strain curve and system size.
• Performs extensive simulations to validate the analytical predictions across varying annealing levels and system sizes.
• Analyzes the cooperative dynamics of plastic events to explain shear band nucleation and propagation.

Experimental results

Research questions

• RQ1 Under what conditions does a given amorphous material exhibit ductile versus brittle yielding?
• RQ2 How does the size of the sample influence the transition from ductile to brittle behavior, particularly in poorly annealed materials?
• RQ3 What is the nature of the pre-failure stage, and how does strain heterogeneity evolve before catastrophic failure?
• RQ4 What is the mechanism by which a shear band nucleates and propagates across the sample?
• RQ5 Can the distribution of failure strains be predicted from measurable macroscopic properties and material disorder?

Key findings

• Highly annealed samples exhibit brittle yielding for all system sizes, while poorly annealed samples show a size-dependent transition from ductile to brittle yielding as sample size increases.
• Yielding proceeds in two stages: a pre-failure phase with slowly growing strain heterogeneity, followed by a rapid, catastrophic failure via a propagating shear band.
• An exact analytical expression for strain heterogeneity growth is derived, depending only on the macroscopic stress-strain curve and sample size, with excellent agreement to simulation data.
• Shear band nucleation results from the onset of cooperativity among localized plastic events, forming a percolating chain along a line via elastic stress transfer.
• The probability distribution of failure strain is predicted in terms of sample size and annealing level (disorder), offering a potential route to early failure prediction.
• The model predicts that more strongly annealed samples should exhibit brittle yielding at smaller system sizes, a testable hypothesis confirmed by recent molecular simulations.