Small Cracks and the Transition to Long Cracks
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oundary, slowed momentarily, or hardly influenced by the boundary. The strength of thèse effects dépends on the state of surface microplastic déformation and hence on cyclic stress. Tanaka et al.10 hâve formula ted a theory of crack growth threshold for such a grain boundary blockage of the slip process, and there hâve been several elaborations of this since.1112 This review emphasizes the implications of small cracks and the attendant approaches to the study of small crack phenomena. The substantial influence of environmental effects are not included. Small Cracks and Structural Design Small cracks are a hidden yet important factor in the validity of lifetime analysis of structural components subject to fatigue loading. Consider several common philosophies of lifetime analysis. Fracture mechanics has been used for 30 years to design critical structures that must not fail in service. Cyclic loadings, such as with each takeoff and landing of an aircraft, fatigue components at highly stressed sites. Small cracks in fillets or fastener holes grow progressively larger and, if not found by inspection, will ultimately reach a critical size that précipitâtes catastrophic failure. For sufficiently long cracks, fracture mechanics provides the relationships among crack size and shape, the detailed local load spectra (loading and unloading times and levels), laboratory growth rate data, and predicted growth rates in service. Good design strategy ensures that the intended service lifetime is a "suitably" small fraction of the time to probable component failure. How small dépends on various tradeoffs between performance, inspection frequency, and life cycle costs. Often, four service lifetimes
are allowed for a crack to propagate from some small length a0 to failure (see Figure 1). A décade ago design tactics began to change. This paralleled the growing realization that while many 0.050 in. cracks could be found by inspection, occasionally one 0.5 in. long would be missed. The "damage tolérant" philosophy that ensued resolved the safety issue by requiring that critical load bearing structures be able to contain large cracks for long periods, as seen in Figure 1. Another approach to design which predates fracture mechanics is still employed when large sections of structure are highly stressed. This crack initiation analysis requires that several service lifetimes be necessary to form an observable crack (a0). Frequently this analysis is done for cyclic strains 2050% larger than will be experienced in service, providing an additional safety margin. Initiation-based design is usually applied to components (e.g., aircraft landing gear) that cannot readily be made to tolerate large cracks. How do small cracks fit into ail this? A major complication of small cracks comes from their propensity to grow faster than predicted by fracture mechanics based on data from long cracks (Figure 2). If a0 is in the "small" régime, then the fracture-mechanicsbased estimâtes of Figure 1 are in error, nonconservatively. Large scatter in growth rates a
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