Efficient and accurate simulation of the Smith-Zener pinning mechanism during grain growth using a front-tracking numerical framework

TL;DR

The paper addresses predictive modeling of Smith-Zener pinning during grain growth by introducing a 2D front-tracking, full-field framework (TRM) that discretizes second-phase particles as circles and tracks their interactions with grain boundaries under curvature flow. It demonstrates high accuracy and improved computational efficiency compared with level-set approaches, and introduces Z-Nodes to extend the method to very small particles while enabling a hybrid discretization approach. Through extensive numerical tests, including domain-size convergence, particle dissolution, and bimodal particle populations, the work validates the method against LS-FE results and shows practical computation times for millimeter-scale domains. The framework offers a flexible, scalable tool for modeling grain-growth control via second-phase particles, with potential extensions to 3D, more complex particle shapes, and multimodal populations for industrial alloys.

Abstract

This study proposes a new full-field approach for modeling grain boundary pinning by second phase particles in two-dimensional polycrystals. These particles are of great importance during thermomechanical treatments, as they produce deviations from the microstructural evolution that the alloy produces in the absence of particles. This phenomenon, well-known as Smith-Zener pinning, is widely used by metallurgists to control the grain size during the metal forming process of many alloys. Predictive tools are then needed to accurately model this phenomenon. This article introduces a new methodology for the simulation of microstructural evolutions subjected to the presence of second phase particles. The methodology employs a Lagrangian 2D front-tracking methodology, while the particles are modeled using discretized circular shapes or pinning nodes. The evolution of the particles can be considered and modeled using a constant velocity of particle shrinking. This approach has the advantages of improving the limited description made of the phenomenon in vertex approaches, to be usable for a wide range of second-phase particle sizes and to improve calculation times compared to front-capturing type approaches.

Figures (17)

• Figure 1: Global loop for the TRM formulation Florez2020b: 1. and 2. Remeshing procedure steps enabling to treat topological changes and maintains the mesh quality potentially with parallel computation Florez2020c; 3. to 7. movement of interfaces using a Lagrangian scheme that updates the positions of the nodes of the mesh defining the GBs; and 8. output generation before the next time step.
• Figure 2: Example of the immersion of circular particles (cyan) in a meshed domain (orange). a. Initial mesh, b. mesh after the remeshing defining the boundaries of particles with an explicit mesh.
• Figure 3: Example of the cycle of the movement of a multiple junction in the boundary of a discretized particle (cyan). The initial position of the mutliple junction is displayed in red with an alpha component in all frames. a. Initial state and computation of the interfaces kinetics, b. displacement of the interfaces using the time-step and the velocity field, c. projection of the multiple junction of the meshed particle to the circle defining the particle domain, d. and e. new cycle, similar to b. and c.
• Figure 4: Rough illustration of pinning and unpinning events of a GB in a discretized particle.
• Figure 5: Example of the life cycle of the evolution of a discretized particle. a. Computation of the dynamics of the interfaces, b. displacement of the interfaces using the time-step and velocity, c. transformation of the circle defining the particle, d. projection of the interfaces of the meshed particle to the circle defining the particle domain.