Simulation of Fatigue Crack Growth in Gold-Based MEMS Notched Specimen and Numerical Validation
In recent years, micro-electro-mechanical systems (MEMS) devices have become a well-established technology, given the growing need for integrated and miniaturized systems with advanced functionality. MEMS can suffer mechanical fatigue as they integrate electronic and mechanical components, usually leading to the complete failure of the device. This works aims to characterize the fatigue fracture behavior of MEMS gold-based notched specimen subjected to cyclic loading. A test microstructure with a central notched specimen is specifically designed and built to perform on-chip fatigue test, with the central specimen undergoing cyclic loading due to the application of alternating voltage.
A coupled field electromechanical fracture finite element model is built in COMSOL Multiphysics® to simulate crack propagation in the notched specimen caused by the application of the actuation voltage during the fatigue test. A particular procedure is adopted to improve the numerical efficiency of the model, avoiding repeating the high-demanding multiphysics simulations at each incremental crack step. Specifically, the entire test microstructure is simulated using the solid mechanics interface and the electromechanics multiphysics interface to solve the coupled mechanical and electrostatics physics and obtain the displacement field in the central specimen as a result of the applied actuation voltage.
Then, simulation of fatigue crack growth is performed just modeling the central notched specimen. For each crack growth step, the displacement field previously computed with the multiphysics simulation is applied as boundary conditions. Then, fracture parameters, i.e. J integral and stress intensity factors, are determined using the structural mechanics module interface. The crack tip position is determined according to linear elastic fracture mechanics (LEFM) theory and the criterion of the maximum circumferential stress, based on the computed stress intensity factors values. Then, the geometry and the mesh are updated according to the new crack tip position and the procedure is repeated until the crack reaches one of the edge of the specimen.
Finally, scanning electrode microscope (SEM) analyses of notched specimen after failure are also performed, confirming that crack starts at the notch root, which acts as local stress and strain raiser fostering crack propagation. Furthermore, the comparison between the crack propagation path resulting from SEM images and obtained from the fracture model shows a good agreement, demonstrating the validity of the linear elastic fracture mechanics theory in characterizing the fatigue fracture behavior of microstructures, as well as the effectiveness of the developed multiphysics fracture model in predicting crack growth in micro-size samples.