Efficient physical and data-driven simulation techniques for temperature-dependent plasticity in magnesium

Abstract

Magnesium (Mg) has immense potential to replace aluminum and steel in certain lightweight structural applications in numerous industries. However, the material suffers from significant drawbacks, notably a low ductility at ambient temperatures and poor thermal hardening. The main goal of this thesis is to understand and model thermal effects on the microstructure of the material and the corresponding response of Mg in an efficient manner in a push toward an integrated, computational framework in a bid to accelerate the material design process for Mg. We further divide this broad goal into two aspects; first, to investigate the material’s plastic behavior at elevated temperatures and find potential solutions to existing drawbacks, and second, to accelerate the process of designing novel Mg-based materials with enhanced properties by numerical means, within the framework of an integrated computational material-by-design approach. Improving the understanding of Mg’s microstructure development at elevated temperatures is imperative to alleviate the material’s key draw- backs. We develop a novel, efficient crystal plasticity model seamlessly integrating the behavior on the temperature range from 25-250◦C. Modeling Mg across this range is challenging and must account for the experimentally reported competition between compressive twins and pyramidal slip and the thermally introduced changes to the microstructure. Only a few temperature-aware models for pure Mg and Mg alloys currently exist and most either disregard compressive twins entirely or suffer from efficiency or calibration issues. Additionally, experimental evidence on the activity of the deformation modes has remained inconclusive. The presented model is thus meticulously calibrated with single-crystal experimental data to predict single- and polycrystal stress–strain responses accurately. By comparing two implementations of the model – with and without the compressive twins – we showcase their impact on the microstructure and texture evolution. Results highlight a transition in deformation modes from compressive twins at low temperatures to pyramidal II slip at elevated temperatures, confirming that the temperature dependence of pure Mg is primarily governed by non-basal slip. The second part of the thesis is concerned with addressing the computational bottleneck of existing high-fidelity material models. We thus develop a neural network-based surrogate for the temperature-dependent material model to reduce the overall computation time of simulations. The surrogate seamlessly maps the deformation and temperature history undergone by the material to its stress response, thus providing relief from explicitly computing plastic updates. This direct approach to mapping the temperature-dependent constitutive response of a highly anisotropic mate- rial poses a formidable challenge to data-driven methods in general and cannot be fulfilled in a satisfactory manner by existing recurrent network architectures. We, therefore, apply a novel architecture, based on recurrent neural operators, and learn the constitutive response of the material with great accuracy. The presented architecture outperforms state-of-the-art re- current network architectures in terms of accuracy and training time and provides a self-consistent formulation that provides a time-step independent implementation of the surrogate model. The recurrent neural operator further shows the capability to generalize its predictions for varying temperature and strain paths with short stints of transfer learning. In addition, it was possible to identify a minimal number of state variables for the recurrent neural operator of the same order of magnitude as the underly- ing model, indicating the physical interpretability of the neural network’s state space. Ultimately, the surrogate model was applied at the mesoscale for multiscale simulations of Mg with commercial FE software, leading to unprecedentedly quick computations of truly multiscale simulations. Finally, as an outlook on ongoing and future work, we present an ap- proach following the material-by-design paradigm to improve Mg’s strength via thermomechanical hardening. Experimental work on binary Mg-Aluminium alloys suggests that this type of processing leads to the formation of nano- precipitates in a process called deformation-induced precipitation. This leads to a high number-density of small precipitates that effectively oppose basal dislocation motion whilst also promoting pyramidal ⟨c + a⟩ dislocation climb, thus resulting in increased mobility on the pyramidal planes and reduced anisotropy and improved hardening on the basal planes. We perform full-field simulations of textured, polycrystalline Mg and investigate the distribution of key drivers of deformation-induced precipitation in the sample, and suggest a formulation of a fully-coupled thermomechanical hardening and precipitation framework.