Phase field benchmark problems for dendritic growth and linear elasticity

Abstract

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem for solidification and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. These numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

“…As discussed in the introduction, open-source frameworks for phase-field modeling are increasing in popularity. To compare the performance of PRISMS-PF to other such frameworks, we reference results that have been uploaded to the PFHub phasefield benchmarking website for 2D dendritic solidification in a pure material [27][28][29] . Note that this benchmark problem can be solved to reasonable accuracy using less than 20,000 DOF, a small enough problem size that the advantage of the explicit time stepping scheme in PRISMS-PF over implicit/semi-implicit Table 1.…”

Numerical Benchmark of Phase-Field Simulations with Elastic Strains: Precipitation in the Presence of Chemo-Mechanical Coupling

“…The first set of these benchmarks was published in 2017 by Jokisaari et al [45], consisting of an Ostwald ripening model and a spinodal decomposition model with different geometries of simulation domain and two different adaptive time stepping techniques. The second set of benchmarks [46] comprises a study of dendritic growth model and a multiphysics model for an elastically constrained precipitate, where the bifurcation of precipitate shape versus the L parameter (characteristic ratio between elastic and interfacial energies [47]) is stressed. On the dendritic growth, similar benchmark studies was conducted by Karma and Rappel [48] in developing quantitative phase-field schemes for solidification studies.…”

“…On the dendritic growth, similar benchmark studies was conducted by Karma and Rappel [48] in developing quantitative phase-field schemes for solidification studies. In this work we present and apply benchmarks on solid-state precipitation, similar to the latter benchmarks of Jokisaari et al [46], but with a focus on a chemo-mechanical coupling effect that features cross-coupled numerical solutions for diffusion and mechanical problems.…”

PFHub: The Phase-Field Community Hub

“…The current PFHub deployment [12] focuses on improving cross-collaboration between phase-field code developers and practitioners by providing a standardized set of benchmark problems [13,14] and a workflow for uploading and comparing benchmark results from different phase-field codes.…”