LAUSR

Reliably modeling fatigue induced degradation of metal films requires a consistent mathematical description of the physically relevant damage driving forces. The processes, which trigger deformation, damage and eventually failure, have to be included and combined in a physically meaningful way to obtain a valid model. Therefore, it is essential to consider the material response to applied stress, as the microstructural changes are responsible for the initialization of the degradation process. In this work, the material response of a polycrystalline copper film under repetitively applied thermo-mechanical stress is investigated by means of a test structure. The changes in the microstructure are studied by means of electron backscatter diffraction data, where the focus is laid on the grain boundary character distribution - a distribution of relative lengths of grain boundaries and corresponding misorientations. It is investigated whether the data can be described by a Fokker-Planck model that accounts for the system’s energy. Parameter estimation is performed on basis of a Maximum Likelihood approach, which is supplemented by an adjoint method to efficiently compute the gradient of the loss function with respect to the parameters. Additionally, uncertainty quantification of the estimates is required, which is done by computing the credible sets of the parameters. To this end, the results of local approximations, Markov Chain Monte Carlo simulations and profile likelihoods are compared.