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D.E. Mason
Department of Mathematics and Computer Science
Albion College, Albion, MI, USA
Recently, geometrical relationships have been proposed for predicting crack initiation in γ-TiAl when a twin interacts with a grain boundary. This correlation (quantified using a fracture initiation parameter or fip) was based only upon the geometry of the Burgers vectors as they are related to slip transfer across the grain boundary and the mode I type opening force experienced by the grain boundary. Generally, a fip is a mathematical combination of factors that allow weak boundaries to be probabilistically identified in the context of a state of stress. This talk further develops this approach by considering the inclusion of the mismatch between the slip planes in the grain boundary and a parameter that accounts for the different elastic properties in adjoining grains. Also, the significance of primary twin (slip) systems vs. secondary slip systems is assessed. Further, cracked and intact boundaries are characterized to assess tilt and twist character and whether they are low Σ (or coincident site lattice) boundaries (using a cubic criterion) to determine whether such properties are statistically significant factors affecting crack nucleation at grain boundaries in duplex near-γ-TiAl. Finally, a brief discussion on how combined microscopic and crystal plasticity finite element analyses provide insights on local stress-strain relationships that can be used to evaluate a fip in the context of heterogeneous deformation in multi-grain ensembles will be discussed.
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