Investigating amorphization as a deformation mechanism using a novel phase field model at the mesoscale

TL;DR

The paper tackles the problem of understanding deformation-induced amorphization in crystalline materials under severe plastic deformation by proposing a mesoscale phase-field model that couples elastoplasticity with a deviatoric-stress–driven transformation strain. The approach integrates a phase-field variable $\eta$ and an energy functional including local phase separation $\psi^{ch}$, gradient $\psi^{\nabla}$, and elastic energies $\psi_e^c$, $\psi_e^g$, ensuring thermodynamic consistency via the Clausius-Duhem framework and TDGL-type kinetics. Key findings include the emergence of amorphous shear bands driven by elastic instabilities, grain-size dependent amorphization with avalanche-like dynamics, and surface-assisted nucleation in 3D compression, together reproducing Hall-Petch-like behavior even without dislocations. The framework provides a thermodynamically sound continuum tool for predicting stress-induced amorphization and offers design insights for materials resisting extreme mechanical loading.

Abstract

Amorphization during severe plastic deformation has been observed in various crystalline materials, yet its underlying mechanisms remain poorly understood. This study introduces a novel phase-field model at the mesoscale, integrating elastoplastic theory with a deviatoric stress-dependent transformation strain tensor to capture stress-induced amorphization. The model enables quantitative predictions of amorphous phase nucleation and propagation under high stress, resolving distinctive microstructural patterns such as amorphous shear bands. Simulations reveal key phenomena, including avalanche-like amorphization, grain size effects, the Hall-Petch effect, and surface amorphization, consistent with experimental observations. By bridging phase-field methods with elastoplastic theory, this work provides a robust framework for studying amorphization as a deformation mechanism and offers valuable insights for designing materials resistant to extreme mechanical conditions.

Figures (11)

• Figure 1: The decomposition of the deformation gradient for each phase. For the crystalline phase, the deformation gradient is expressed as $\bm{F}_c = \bm{F}_e^c \bm{F}_p^c$, where $\bm{F}_e^c$ and $\bm{F}_p^c$ denote the elastic and plastic components, respectively. In contrast, the deformation gradient for the amorphous phase is given by $\bm{F}_g = \bm{F}_e^g \bm{F}_t \bm{F}_p^g$, where $\bm{F}_t$ accounts for the transformation strain during amorphization. $\bm{F}_e^g$ and $\bm{F}_p^g$ represent the elastic and plastic components of the amorphous phase, respectively.
• Figure 2: Schematic of the additive decomposition of the total strain for materials under deformation.
• Figure 3: Numerical setup of shear in two dimensions. $\dot{\varepsilon}$ is the loading rate. $L$ is the size of the simulation square cell. The purple box gives the initial amorphous defects.
• Figure 4: Results of shear deformation in two dimensions. The first row shows the evolution of the amorphous phase, while the second row presents the corresponding shear stress $\sigma_{xy}$. The orange box highlights the formation the amorphous shear band. The change of elastic strain energy in the crystalline and amorphous phases of the small green box is compared in the Figure \ref{['energycomparison']}.
• Figure 5: Comparison of the elastic strain energy stored in the crystalline and amorphous phases. (a) The small green box in Figure \ref{['shearresults1']} is chosen for the energy comparison. (b) The elastic energy stored in the crystalline (blue) and amorphous (red) phases, respectively.