Albion College
Mathematics and Computer Science
Mesocale Modeling of Damage Nucleation in Titanium Aluminum Grain Boundaries
Darren E. Mason

Associate Professor

Mathematics and Computer Science

Albion College

Is there a way to predict when and where such failure occurs? In this talk I will discuss some recent research directed at providing answers to these critical real-world problems. After a brief tutorial on the basic math, physics, and metallurgy required to attempt to answer such questions, I will review prior work that used a well characterized patch of Titanium Aluminum (TiAl) to evaluate the utility of a scalar fracture initiation parameter (fip) to predict the relative resistance of grain boundaries to microcracking when subjected to stress. I will then discuss new research that has generalized the idea of a scalar fip to a physically motivated damage tensor D that measures the amount of physical damage that accumulates at stressed grain boundaries as they evolve through space and time. Local lattice curvature near the grain boundary, local elastic and plastic stress evolution, and accumulated dislocation content at the grain boundary are among the quantities considered. Then, using data generated from a three dimensional, nonlinear, crystal plasticity finite element simulation of the same experimental TiAl region, the ability of this the tensor D to predict the location of "weak" grain boundary locations where micro-cracking is likely to occur.

This work is funded by the NSF Materials World Network Grant DMR-0710570, the Deutsche Forschungsgemeinschaft (DFG) Grant EI 681/2-1, and the Department of Mathematics and Computer Science at Albion College.
All are welcome!
Palenske 227
September 23, 2010