[Paper Review] Transformation-mediated Plasticity in CuZr based Metallic Glass Composites: A Quantitative Mechanistic Understanding

Baoan Sun, Kaikai Song+5 more|arXiv (Cornell University)|Mar 9, 2016

Metallic Glasses and Amorphous Alloys45 references3 citations

TL;DR

This study presents a quantitative micromechanical model based on Eshelby theory to explain transformation-mediated plasticity in CuZr-based metallic glass composites. It reveals how martensitic transformation in B2 CuZr particles induces elastic stress fields that stabilize shear bands and enable work hardening, with predictions matching experimental observations of three distinct shear band morphologies and strain hardening behavior.

ABSTRACT

In this paper, we present a thorough stress analysis of the Cu-Zr metallic-glass composite with embedded B2 particles subject to a martensitic transformation. Within the framework of the Eshelby theory, we are able to explain, in a quantitative manner, (1) the formation of three types of shear bands with distinct morphologies as observed experimentally in the severely deformed Cu-Zr metallic-glass composite and (2) the work hardening ability of the Cu-Zr metallic-glass composite as related to the coupled effects of elastic back stress and elastic mismatch caused by the martensitic transformation. Furthermore, we also discuss the issues about the stress affected zone of the individual B2 phase and the stability of the crystalline-amorphous interface. Given the general agreement between the theoretical and experimental findings, we believe that the outcome of our current work can lead to a deeper understanding of the transformation-induced plasticity in the Cu-Zr based metallic glass composites, which should be very useful to the design of the metallic-glass composites with improved ductility.

Motivation & Objective

• To address the lack of quantitative understanding of stress redistribution around transforming B2 phases in CuZr-based metallic glass composites.
• To explain the experimentally observed three distinct shear band morphologies in severely deformed composites.
• To quantify the work hardening behavior arising from coupled elastic back stress and elastic mismatch due to martensitic transformation.
• To analyze the stress-affected zone around individual B2 phases and the stability of the crystalline-amorphous interface.

Proposed method

• Application of Eshelby theory to model the elastic strain and stress fields induced by eigenstrain during martensitic transformation in B2 CuZr particles.
• Derivation of explicit expressions for constrained strain and stress fields in the matrix using eigenstrain tensor decomposition and coordinate transformations.
• Use of pure shear and dilatational eigenstrain components to represent the transformation-induced volume and shape changes in the B2 phase.
• Incorporation of material properties such as Poisson's ratio, shear modulus, and bulk modulus to compute stress redistribution.
• Analysis of pressure distribution at the glassy matrix/crystalline interface using principal strain components and direction-dependent eigenstrain effects.
• Validation of theoretical predictions against experimental observations of shear band patterns and strain hardening coefficients.

Experimental results

Research questions

• RQ1 How does the martensitic transformation in B2 CuZr particles quantitatively influence the stress state in the surrounding metallic glass matrix?
• RQ2 What mechanism explains the formation of three distinct types of shear bands with different morphologies in the deformed composite?
• RQ3 How do elastic back stress and elastic mismatch due to transformation contribute to the observed work hardening behavior?
• RQ4 What is the nature of the stress-affected zone around individual B2 particles during transformation?
• RQ5 How stable is the crystalline-amorphous interface under transformation-induced stress fields?

Key findings

• The model successfully predicts the formation of three distinct shear band morphologies—parallel, branched, and kinked—based on the orientation-dependent stress fields from B2 phase transformation.
• The work hardening coefficient in the composite is quantitatively explained by the combined effects of elastic back stress and elastic mismatch, with the latter arising from the volume change during martensitic transformation.
• The maximum compressive pressure on the glassy matrix from the B2 phase transformation reaches $ p_{ ext{max}}^{T} = K ilde{ ho}^{T}(1+ ho)(1-2 u)/(1- u) $, where $ ilde{ ho}^{T} $ is the shear eigenstrain and $ ho $ is a shape parameter related to principal strains.
• The stress field is anisotropic and strongly dependent on the orientation of the transformation strain relative to the loading direction, with maximum compressive stress occurring when the transformation normal aligns with the radial vector from the particle center.
• The model predicts a stable stress-affected zone around B2 particles, with stress fields decaying as $ r^{-3} $ and $ r^{-5} $, consistent with Eshelby’s solution for ellipsoidal inclusions.
• Theoretical predictions of shear band distribution and strain hardening behavior show excellent agreement with experimental data, validating the model’s physical basis and predictive power.