A Geometric Approach to Modeling Microstructurally Small Fatigue Crack Formation

The objective of this paper is to develop further a framework for computationally modeling microstructurally small fatigue crack growth in AA 7075-T651 [1]. The focus is on the nucleation event, when a crack extends from within a second-phase particle into a surrounding grain, since this has been observed to be an initiating mechanism for fatigue crack growth in this alloy. It is hypothesized that nucleation can be predicted by computing a non-local nucleation metric near the crack front. The hypothesis is tested by employing a combination of experimentation and nite element modeling in which various slip-based and energy-based nucleation metrics are tested for validity, where each metric is derived from a continuum crystal plasticity formulation. To investigate each metric, a non-local procedure is developed for the calculation of nucleation metrics in the neighborhood of a crack front. Initially, an idealized baseline model consisting of a single grain containing a semi-ellipsoidal surface particle is studied to investigate the dependence of each nucleation metric on lattice orientation, number of load cycles, and non-local regularization method. This is followed by a comparison of experimental observations and computational results for microstructural models constructed by replicating the observed microstructural geometry near second-phase particles in fatigue specimens. It is found that orientation strongly influences the direction of slip localization and, as a result, in uences the nucleation mechanism. Also, the baseline models, replication models, and past experimental observation consistently suggest that a set of particular grain orientations is most likely to nucleate fatigue cracks. It is found that a continuum crystal plasticity model and a non-local nucleation metric can be used to predict the nucleation event in AA 7075-T651. However, nucleation metric threshold values that correspond to various nucleation governing mechanisms must be calibrated

Modeling shear waves through a viscoelastic medium induced by acoustic radiation force

In this study, a finite element model of a tissue-mimicking, viscoelastic phantom with a stiffer cylindrical inclusion subjected to an acoustic radiation force (ARF) is presented, and the resulting shear waves through the heterogeneous media are simulated, analyzed, and compared with experimental data. Six different models for the ARF were considered and compared. Each study used the same finite element model, but applied the following: (1) full radiation push; (2) focal region push; (3) single element focal point source; or (4) various thresholds of the full radiation push. For each case, displacements at discrete locations were determined and compared. The finite element simulation results for the full radiation push matched well with the experimental data with respect to replicating the shear wave speed and attenuation in the peak displacements through the background medium and inclusion, but did not illustrate comparable recovery after the peak displacements. As a result of this study, it has been shown that a focal region or point source push is not adequate to accurately model the effects of the full radiation push, but thresholding the full push can produce comparable results and reduce computation time