Crack Initiation Analysis in Residual Stress Zones with Finite Element Methods

This research explores the nearly untapped research area of the analysis of fracture mechanics in residual stress zones. This type of research has become more prevalent in the field in recent years due to the increase in prominence of residual stress producing processes. Such processes include additive manufacturing of metals and installation procedures that lead to loads outside the anticipated standard operating load envelope.

Abaqus was used to generate models that iteratively advanced toward solving this problem using the compact tensile specimen geometry. The first model developed in this study is a two-dimensional fracture model which then led to the development of an improved three-dimensional fracture model. Both models used linear elastic fracture mechanics to determine the stress intensity factor (K) value. These two models were verified using closed-form equations from linear elastic fracture mechanics. The results of these two models validate the modeling techniques used for future model iterations. The final objective of this research is to develop an elastic-plastic fracture mechanics model. The first step in the development of an elastic-plastic fracture model is a three-dimensional quasi-static model that creates the global macroscale displacement field for the entire specimen geometry. The global model was then used to create a fracture submodel. The submodel utilized the displacement field to reduce the model volume, which allowed a higher mesh density to be applied to the part. The higher mesh density allowed more elements to be allocated to accurately represent the model behavior in the area local to the singularity. The techniques used to create this model were validated either by the linear elastic models or by supplementary dog bone prototype models. The prototype models were run to test model results, such as plastic stress-strain behavior, that were unable to be tested by just the linear elastic models. The elastic-plastic fracture mechanics global quasi-static model was verified using the plastic zone estimate and the fracture submodel resulted in a J-integral value.

The two-dimensional linear elastic model was validated within 6% and the three-dimensional linear elastic model was validated within 0.57% of the closed-form solution for linear elastic fracture mechanics. These results validated the modeling techniques. The elastic-plastic fracture mechanics quasi-static global model formed a residual stress zone using a Load-Unload-Reload load sequence. The quasi-static global model had a plastic zone with only a 0.02-inch variation from the analytical estimate of the plastic zone diameter. The quasi-static global model was also verified to exceed the limits of linear elastic fracture mechanics due to the size of the plastic zone in relation to the size of the compact specimen geometry. The difference between the three-dimensional linear elastic fracture model J-integral and the elastic-plastic fracture submodel initial loading J-integral was 3.75%. The J-integral for the reload step was 18% larger than the J-integral for the initial loading step in the elastic-plastic fracture submodel.