# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 1999 Seminar Series**

*Damage Evolution and Failure in Heterogeneous Materials*

*Abstract*

### Heterogeneity is ubiquitous in both natural and engineered structural
materials, and can fundamentally affect the stiffness, deformation, strength,
and reliability of a material. Heterogeneity can include spatial variations in
the thermal, elastic, and toughness properties of the constituent materials.
Material strength is particularly sensitive to heterogeneities, because the
failure instability needs only to be triggered by the local formation of some
sufficient damage in one location of the material. Due to this
"weak-link" nature of strength, it is then intrinsically dependent on
material size and is probabilistic. Averaging over the heterogeneity, a common
approach to tackling the mechanics and physics of heterogeneous materials, is
therefore precluded. Here, we use fiber-reinforced composites as a system in
which to study how the interplay of heterogeneity (in the individual fiber
strengths) and the mechanics of stress transfer (from damaged to undamaged
regions) determines the failure strength of a heterogeneous material. First,
simulation models are developed and used to explicitly demonstrate the
development of local clusters of fiber damage, and the resulting
size-dependence and probability distribution of the material strength. Second,
failure is shown to be controlled by the formation of a critical damage cluster
of size nc whose failure statistics are identical to the known failure
statistics for a cluster of nc fibers failing under "mean field stress
transfer", i.e. where stress is transferred equally to all fibers in the
system. In other words, it is shown that there exists a size scale nc over
which averaging is valid. This association, coupled with weak-link statistics,
then allows for the development of an analytic model for the size-dependent
strength distribution. Application of both the simulation and analytic models
to various real composites demonstrates the quantitative power of the models
for predicting strength and size-scaling with no adjustable parameters. The
success in applications to fiber composites and the generality of the analytic
model suggest that the mechanics and heterogeneity together establish some
non-trivial length scale over which averaging may be a valid procedure for any
system.

### Friday, May 21, 1999

209 Akerman
Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior
Secretary, 625-8000.