The Mechanics of Composite Strength Evolution: Concepts and Applications
Authors: Reifsnider Ken 
Published: January 2022

Abstract
There does not seem to be a universal answer to the question of how mechanics is related to material strength. It is clear that the results of mechanics estimates of point-wise stress and strain values and distributions are inputs to the question of “how strong is this material.” But these quantities have no direct interpretation in terms of strength. Small stress or strain values may be “critical” in local regions or directions of very small material strength, for example, and “infinitely” large values may be artifacts of analysis and may not cause actual material failure. Interpretations of the results of mechanics analyses are essential to a “philosophy of strength.” One of the most popular interpretations is based on concepts collectively known as “fracture mechanics.” The object of this approach is the representation of the field stress and strain near the tip of a single crack. An amplitude of the singularity of that field, called the field stress intensity, is typically associated with a material strength parameter, generally referred to as fracture toughness. The assumption is that global fracture is induced by the conditions at the tip of a single crack (or dominant single crack) in the medium, and that strength is determined by those local conditions.
Modern engineering composites typically use fiber reinforcements that are made from light, strong, and very brittle materials. Matrix materials are used to create the continuity necessary to transfer loads to the fibers, and to defeat the propagation of defects so that the global response is damage tolerant. Such materials are designed to avoid single crack growth; composite materials that fail by single crack growth are not widely used. Most modern composites fail by the accumulation of “degradation.” This degradation may include matrix cracking and other micro-defects, oxidation or chemical degradation, thermodynamic effects (especially microstructure changes), kinetic events (such as diffusion), and time-dependent deformation. Remarkably, changes in stiffness and strength during service of such materials may be quite large, of the order of 30 to 40 percent before “fracture” occurs.
These large changes in properties create a special challenge in the effort to interpret mechanics analysis in terms of strength and remaining strength. Strength definitions and interpretations must involve careful analyses not only of stress states but also of material states. And those states are generally functions of time, sequence, statistical variations, and history over the life of a component. The present paper discusses an approach to this problem, and postulates a philosophy that uses careful definitions of strength, precise laboratory analysis of failure modes, micromechanical models of damage and failure modes, and kinetic theory to construct a mechanics analysis that predicts the remaining strength and life of composite materials and systems under combined conditions of mechanical, thermal, and chemical applied environments. Strengths, weaknesses, and applications of the approach will be described. Future opportunities and needs in this general field will also be discussed.