Frequency-dependent stress response under thermal cycle: A thermal-crystal plasticity and dynamic mode decomposition study

Abstract

Thermal cycle environments involving repeated temperature changes are common conditions observed in modern engineering processes. Under such conditions, materials undergo repeated thermal expansion and contraction, forming complex thermal stress fields. Thermal-crystal plasticity simulations that account for stress fields and thermal conduction at the polycrystalline microstructure scale are an effective method for numerically reproducing thermal cycle environments. However, the influence of thermal cycle frequency on the temporal behavior of the stress field and plastic response has not yet been fully understood, partly because a systematic analysis method capable of simultaneously capturing spatial heterogeneity and temporal evolution remains limited. In this study, we predicted the thermal stress field generated under different thermal cycle frequencies using thermal-crystal plasticity simulations and investigated the effect of frequency on the spatiotemporal structure of the stress response. The present framework illustrates that the resulting thermal-mechanical response can be represented as a superposition of multiple effective temporal components, reflecting the increased complexity of the system behavior. By employing dynamic mode decomposition (DMD) as a diagnostic and post-processing technique, we demonstrate that the spatiotemporal structure of the stress field under thermal cycle conditions can be systematically extracted and compactly represented. This approach enables a quantitative characterization of frequency-dependent changes in the thermal stress response beyond conventional averaging or snapshot-based analyses. The results highlight the utility of DMD as a framework for organizing complex simulation data and for interpreting the temporal structure of plastic response under cyclic thermal loading.