On Predicting Nucleation of Microcracks Due to Slip-Twin Interactions at Grain Boundaries in Duplex Near $γ-TiAl$

Simkin et al. (2003, “A Factor to Predict Microcrack Nucleation at Gamma-Gamma Grain Boundaries in TiAl,” Scr. Mater., 49(2), 149–154) proposed a relationship for predicting crack initiation in $γ-TiAl$ in a scenario where a mechanical twin interacts with a grain boundary. This correlation (quantified using a fracture initiation parameter or fip) was based only on 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 paper 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 versus secondary slip systems is assessed. When compared to fips that can be constructed through a variety of other combinations of nine geometrical parameters that could affect grain boundary damage nucleation, the fip obtained by multiplying Simkin’s original parameter by $Emin∕Emax$⁠, the ratio of Young’s modulus in the stress direction in the two grains, is best able to distinguish between cracked and intact grain boundary populations. Cracked and intact boundaries are also characterized to assess tilt and twist character and whether they are low $Σ$ (or coincident site lattice) boundaries (using a cubic criterion). It is also shown that fips based on $Σ$ values or the tilt and twist character of the boundary lead to an unacceptably high probability of incorrectly distinguishing between cracked and intact grain boundaries, implying that these are not critical parameters affecting crack nucleation at the grain boundary in duplex near-$γ$ TiAl. The paper closes with a 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 multigrain ensembles.