[Paper Review] Perfect plasticity of metals under simple shear as the result of percolation transition on grain boundaries

Yan Beygelzimer, Н. М. Лавріненко|arXiv (Cornell University)|Jun 22, 2012

Microstructure and mechanical properties7 references4 citations

TL;DR

This paper proposes that perfect plasticity in metals under simple shear at low homologous temperatures arises from a percolation transition at grain boundaries, driven by nonlocal interactions. The mechanism, supported by geometric reasoning, simulations, and experimental data, explains the critical, scale-invariant behavior observed in plastic deformation as a result of interconnected grain boundary networks reaching a percolation threshold.

ABSTRACT

A mechanism of perfect plasticity under low homological temperatures has been suggested. According to this mechanism, the phenomenon under study is of critical nature. It connects with percolation transition in the net of grain boundaries and with nonlocal interaction of fragments uniquely under simple shear mode. The mechanism is justified by general reasoning, mainly of geometrical character, and also by employing computational modeling and well-known experimental results.

Motivation & Objective

• To explain the origin of perfect plasticity in metals at low homologous temperatures.
• To identify the role of grain boundary networks in enabling large-scale plastic deformation.
• To establish a connection between percolation transitions and critical plastic behavior.
• To unify geometric reasoning, computational modeling, and experimental observations in a single mechanism.
• To demonstrate that nonlocal interactions on grain boundaries drive the transition to perfect plasticity.

Proposed method

• The mechanism is derived from geometric reasoning focusing on the connectivity of grain boundaries under simple shear.
• A percolation transition model is applied to the network of grain boundaries to describe the onset of plasticity.
• Computational modeling simulates the evolution of grain boundary networks under shear stress.
• The model incorporates nonlocal interactions between grain boundary fragments, essential for macroscopic plasticity.
• Theoretical predictions are validated against known experimental results on metal plasticity.
• The approach treats the system as a critical phenomenon, analogous to percolation in statistical physics.

Experimental results

Research questions

• RQ1 What physical mechanism enables perfect plasticity in metals under simple shear at low homologous temperatures?
• RQ2 How do grain boundaries collectively contribute to large-scale plastic deformation?
• RQ3 What role does percolation transition play in the onset of plasticity?
• RQ4 How do nonlocal interactions between grain boundary segments influence macroscopic plastic behavior?
• RQ5 To what extent can geometric and percolation models explain experimental observations of plasticity?

Key findings

• Perfect plasticity emerges as a critical phenomenon linked to a percolation transition in the grain boundary network.
• The transition is driven by nonlocal interactions between grain boundary fragments under simple shear.
• Geometric reasoning alone explains the emergence of scale-invariant plastic behavior.
• Computational modeling confirms the existence of a critical threshold for plastic deformation.
• The model is consistent with experimental observations of plasticity in metals at low temperatures.
• The mechanism provides a unified explanation for the sudden onset of large plastic strains without hardening.