Engineering materials are subjected to thermal, mechanical, and chemical loads during service. The design of sturdy materials that do not loose their beneficial properties in harsh environments, hence, requires an interdisciplinary, holistic approach that considers that degradation of properties is the result of combined thermo-chemo-mechanical loads. An example for the complex interplay between thermal and mechanical loads, which is further influenced by the local chemical composition, is the degradation of metallization layers in semiconductor devices. Here, we present a crystal plasticity-based continuum model to study the copper metallization layers during cyclic thermo-mechanical loads. The physics-based formulations used in the model make it possible to parametrize it with the help of simulations at smaller length scales and experiments. Hence, it can be used for scale-bridging simulations in the context of integrated computational materials engineering (ICME). The proposed model is implemented into DAMASK, the Düsseldorf Advanced Material Simulation Kit and its capabilities are demonstrated on selected examples.