A Micro-mechanical Model for Multiaxial High Cycle Fatigue at Small Scales

The grain microstructure and damage mechanisms at the grain level are the key factors that influence fatigue of metals in small dimensions. This is addressed by establishing a micro-mechanical model for the prediction of multiaxial high cycle fatigue (HCF) at a length scale of about 100 μm, which is typical for micro-electro- mechanical systems (MEMS). The HCF model considers elasto-plastic behavior of metals at grain level and microstructural parameters, i.e. grain size and grain orientation. While for individual grains a deterministic failure prediction is obtained, the model serves as a failure criterion in probabilistic studies on aggregates of grains. For this, it is assumed that a fatigue crack initiates in a grain, if the accumulated plastic shear strain in the grain exceeds a critical limit. For model validation, the grain size and grain orientation on the surface of nickel micro-samples were measured with Electron Backscatter Diffraction (EBSD) analysis after fatigue testing. The overall predictive power of the HCF model - which grains will be damaged by fatigue- is validated. Nevertheless, some misclassifications occur as some grains are damaged, which were predicted to be safe. For some cases, post-fatigue investigations on individual grains reveal reasons for those misclassifications.