University of Minnesota
Aerospace Engineering and Mechanics
Spring 1999 Seminar Series

Damage Evolution and Failure in Heterogeneous Materials

Professor William A. Curtin

Division of Engineering, Brown University


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.