Metal microstructures modeling

Multiscale phenomena: a bottleneck in decoding process-structure-property relations

New sustainable metals are on the horizon – from greener steel alloys to alternative lightweight metals such as magnesium. However, determining how these materials behave and the best methods for processing them can take many years before they can be widely used. This is largely due to the difficulty in decoding the intricate interactions between the materials’ processing conditions (e.g., temperature, deformation) which control the microstructural evolution (i.e., texture, grain shape and size, precipitate distribution) and in turn, determine the mechanical properties (e.g., stress-strain response, strength, ductility). The challenge arises due to the multiscale nature of metal thermomechanical processing with relevant physical phenomena spanning several orders of lengthscales – from the microstructures to the macroscale thermomechanical deformations.

Bridging across scales for metal processing modeling

Schematic illustration of the vertical scale-bridging approach which is based on a meshless solver for the macroscale boundary value problem, a polycrystal and recrystallization model on the mesoscale, and a crystal plasticity model on the subgranular microscale (Kumar et al., 2020).

To this end, we introduced a multiscale framework that aims at efficiently modeling thermomechanical processes while effectively capturing the underlying physics across all relevant scales. At the level of the macroscale boundary value problem, an enhanced maximum-entropy meshless method is employed. Compared to finite elements and other meshless techniques (see detailed assessment), this method offers a stabilized finite-strain updated-Lagrangian setting for improved robustness with respect to mesh distortion arising from large plastic strains. At each material point on the macroscale, we described the polycrystalline material response via a Taylor model at the mesoscale, which captures discontinuous dynamic recrystallization through the nucleation and growth/shrinkage of grains. Each grain, in turn, is modeled by a finite-strain crystal plasticity model at the microscale. Our framework describes not only the evolution of strain and stress distributions during the process but also grain refinement and texture evolution, while offering a computationally feasible treatment of the macroscale mechanical boundary value problem.

Machine learning to enable high-throughput and on-demand optimization

Despite the recent advances in speeding up these multiscale models (including ours — as discussed above), the computational runtimes for a single simulation can be in the order of days to months. This is prohibitive to achieving high-throughput and on-demand optimization of the process parameters, microstructures, and mechanical properties. For example, a big bottleneck in the adoption of recycled steel is the regularly varying scrap metal composition, which necessitates dynamically adapting the process-structure-property maps. We are tackling the above challenge by accelerating the process-structure-property maps of metallic systems with a combination of physics-based modeling and machine learning. Specifically, we are focussing on a two pronged solution: (i) a multiscale learning approach to address the issue of disparity in lengthscales when modeling metallic systems, and (ii) a multi-fidelity learning approach to synergistically maximize the utilization of both inexpensive but abundant low fidelity training data as well as expensive but scarce high-fidelity data from simulations and experiments.

Publications

S. Kumar*, A. D. Tutcuoglu*, Y. Hollenweger, D. M. Kochmann, A meshless multiscale approach to modeling severe plastic deformation of metals: Application to ECAE of pure copper, Computational Material Science, 173 (2020), 109329.
S. Kumar, K. Danas, D. M. Kochmann, Enhanced local maximum-entropy approximation for stable meshfree simulations, Computer Methods in Applied Mechanics and Engineering, 344 (2019), 858-886.
S. Kumar, A. Vidyasagar, D. M. Kochmann, An assessment of numerical techniques to find energy‐minimizing microstructures associated with nonconvex potentials, International Journal for Numerical Methods in Engineering, 121 (2020), 1595-1628.
J. Voss, R. J. Martin, O. Sander, S. Kumar, D. M. Kochmann, P. Neff, Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture, Journal of Nonlinear Science, 32, 77 (2022).
J. Tang, S. Kumar, L. De Lorenzis, E. Hosseini, Neural cellular automata for solidification microstructure modelling, Computer Methods in Applied Mechanics and Engineering, 414 (2023), 116197. [code]

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