Simulation of Stochastic Discrete Dislocation Dynamics in Ductile Vs Brittle Materials

TL;DR

This work analyzes dislocation dynamics in ductile vs brittle materials by combining 2D-DDD simulations of Aluminium and Tungsten with a data-driven nonlocal continuum model. It converts dislocation trajectories into time-varying PDFs via Adaptive Kernel Density Estimation and then learns a nonlocal parabolic transport operator, characterized by a horizon $\delta$ and kernel power $\alpha$, that reproduces PDF evolution from the microscale data. The study finds Aluminium exhibits mixed anomalous-diffusive motion ($\alpha\approx 2.15$, $\delta$ of a few lattice units) while Tungsten shows predominantly super-diffusive behavior ($\alpha\approx 1.96$, larger $\delta$), and reports low relative errors in PDF predictions, underscoring the value of data-driven nonlocal models to bridge microscale dislocation dynamics and mesoscopic transport descriptions. Overall, the paper provides a principled pipeline to extract nonlocal transport parameters from high-fidelity dislocation data and to quantify material-specific diffusion regimes that underpin ductility and brittleness.

Abstract

Defects are inevitable during the manufacturing processes of materials. Presence of these defects and their dynamics significantly influence the responses of materials. A thorough understanding of dislocation dynamics of different types of materials under various conditions is essential for analyzing the performance of the materials. Ductility of a material is directly related with the movement and rearrangement of dislocations under applied load. In this work, we look into the dynamics of dislocations in ductile and brittle materials using simplified two dimensional discrete dislocation dynamics (2D-DDD) simulation. We consider Aluminium (Al) and Tungsten (W) as representative examples of ductile and brittle materials respectively. We study the velocity distribution, strain field, dislocation count, and junction formation during interactions of the dislocations within the domain. Furthermore, we study the probability densities of dislocation motion for both materials. In mesoscale, moving dislocations can be considered as particle diffusionm, which are often stochastic and super-diffusive. Classical diffusion models fail to account for these phenomena and the long-range interactions of dislocations. Therefore, we propose the nonlocal transport model for the probability density and obtained the parameters of nonlocal operators using a machine learning framework.

Figures (13)

• Figure 1: Illustrative diagram for (a) annihilation and (b) multiplication
• Figure 2: Illustrative figure for junction formation and immobile dislocations
• Figure 3: Dislocation density (a) before relaxation (b) after relaxation.
• Figure 4: Time-series plots of dislocation count, average velocity, and plastic strain over the duration of relaxation.
• Figure 5: Collective velocity of dislocation