Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Mesocale Modeling of Damage Nucleation in Titanium Aluminum Grain Boundaries

Darren E. Mason

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.

This work is funded by the