An increasing number of engineering applications depend on the use of material systems such as fiber-reinforced composites. For the most part, the manner in which these systems are “designed” is presently heuristic. Although much analysis and understanding of “how such materials are made” is available, there is comparatively less systematic rigor that addresses “how such materials should be made”. This is a serious inhibition to the exploitation of these materials and material systems.
During the last few years, a variety of approaches has been developed for the analysis of composite materials, especially fiber-reinforced systems. The body of literature is especially replete in the technical area of “effective stiffness” models, many of which are sophisticated and well founded—and reasonably well validated. A comparable body of work which addresses “effective strength” is not available. However, the author and his colleagues have developed a mechanistic approach of this type, that is generally referred to as the “critical element concept,” whereby careful laboratory work is used to define representative volumes of material that enclose a “typical” failure mode. This representative volume is divided into a “critical element” that controls the final failure event, and “subcritical elements” that alter the local stress state around the critical element.
The present paper extends this concept to the fiber/matrix level by introducing micromechanical strength models to be used in the critical elements. The result of this advance is that mechanistic models that include explicit representations of the parameters that describe the manner in which the material systems are made can be used to estimate remaining strength when those parameters change during the lifetime of the material. Moreover, the model can then be used to “design” or tailor a material system for specific long-term performance. This last topic is the focus of the present paper. The approach will be demonstrated, and the influence of several parameters will be discussed. This discussion will then be used to advance several concepts for the rigorous design of material systems for damage tolerance.