are frequently encountered. For example, many successfully designed composites and brittle materials such as concrete fracture under rising load with an extensive damage zone at the crack tip. Typically, the macrocrack surfaces remain bridged by incompletely pulled out fibers, or by frictionally restrained aggregate particles, and this provides a significant contribution to material toughness.

At present, empirical relations are used in life prediction studies to describe the rates of growth of cracks or accumulation of damage in terms of load history, temperature, and environment. The complexity of these problems dictates that such empirical procedures will remain prominently in use, but an achievable goal for research is the provision of a more enlightened basis for them. For example, research in macroscopic fracture mechanics in the nonlinear range has identified parameters that, in certain defined circumstances, characterize the severity of deformation near the crack tip and hence serve as the loading variable in terms of which crack growth rate should be characterized in empirical studies. Current approaches to ductile tearingmode cracking and elevated-temperature creep crack growth provide examples. Also, simple theoretical models of creep deformation and cavity growth, over a broad range of stresses and temperatures, lead to maps of deformation and fracture mechanisms. These maps subdivide the stress and temperature plane into regimes in which one mechanism or another (e.g., diffusive creep versus dislocation creep, diffusive cavity growth versus plastically assisted cavity growth) is dominant. The map concept provides a caution that empirically based relations will, likewise, have limited domains in which they accurately describe deformation, and the maps themselves suggest where to look for those limits.

Nondestructive Evaluation

The aim of fracture mechanics is to predict the growth to failure of cracks or other damage in materials. To be effective for predicting lifetimes, such work should go hand in hand with nondestructive evaluation of materials and structures for defects. Here, research challenges occur in sensor technology for making the necessary measurements, sometimes under hostile conditions and with limited access. Also, research is needed on the quantification of nondestructive evaluation signals so that the information about the state of the material provided by such techniques can be used with confidence in estimating lifetimes.

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