Numerical and Analytical Multiscale Modeling of High Cycle Fatigue in Advanced Materials

Abstract

Integrated Computational Materials Engineering (ICME) approaches are gaining popularity in various industries, such as electronics, automobile, and aerospace, due to their focus on multiscale simulation-based design and analysis. The multiscale approach is especially useful for fatigue modeling of advanced materials that have different local structure-property relationships at different length scales. Broadly, fatigue crack growth is classified into the following categories: crack initiation (atomic-scale), microstructurally short crack growth (micro-scale), physically short crack growth (meso-scale), and long crack growth (macro-scale).

In this dissertation, we develop numerical and analytical models to primarily predict microstructural effects on fatigue crack growth and subsequent long crack growth behavior. In the macro-scale, the new contribution is a variational multiscale cohesive method (VMCM) to determine the fatigue crack growth rates in the long crack growth regime. The calibration of the macro-scale VMCM cohesive parameters, which represent the crack tip mechanics, is addressed with the development of a linear elastic fracture mechanics (LEFM)-based irreversible cohesive model. The LEFM-based irreversible cohesive model is validated with macro-scale experiments. The model also provides a way to link the cohesive parameters with micro-scale experiments. In the micro-scale, we develop a VMCM approach that incorporates local microstuctural information, such as grain orientations and slip systems, and predicts the microstructurally short crack growth paths through slip planes that are in multiple grains and across grain boundaries. We employ dislocation theories to calibrate the microstructural cohesive parameters. This dislocation theory-based cohesive model efficiently predicts the microstructurally short fatigue crack growth rates through multiple grains. The calibration of this model is done with micro-scale experiments on a single crystal and on a polycrystalline modification of a Ni-based CMSX-4 alloy.

For a microstructurally short crack, the local microstructure plays an important role in the fatigue behavior of the material. Thus, for accurate representation of the mechanisms happening at the crack front, microstructural barriers such as grain boundaries have to be taken into consideration. This mechanism of crack plane-grain boundary interaction is addressed next with the development of a phenomenological grain boundary interaction model. This model takes into account the coupling between the tilt and twist misorientations (located between the crack plane and a favorable plane in the next grain and calculated at a grain boundary), the Schmid factor, and the critical crack transmission stress, which is a form of a microscopic stress intensity factor. However, these two-dimensional models can only give information about the surface crack growth rates. The last chapter extends a three-dimensional microstructurally short fatigue crack growth model in order to better understand the sub-surface crack interactions with multiple grain boundaries. This method is utilized to model two cases of microstructurally short fatigue crack-grain boundary interactions in a magnesium WE43 alloy: the interaction of a crack front growing towards a grain boundary with the grain boundary and the interaction of a crack front spanning across multiple grains with the grain boundary it crosses. Thus, the tools developed in this dissertation aid in improving our understanding of the interaction between the microstructurally short fatigue crack growth and the local microstructure.