K
5.1 The KR curve characterizes the resistance to fracture of materials during slow, stable crack extension and results from the growth of the plastic zone ahead of the crack as it extends from a fatigue precrack or sharp notch. It provides a record of the toughness development as a crack is driven stably under increasing applied stress intensity factor K. For a given material, KR curves are dependent upon specimen thickness, temperature, and strain rate. The amount of valid KR data generated in the test depends on the specimen type, size, method of loading, and, to a lesser extent, testing machine characteristics.
5.2 For an untested geometry, the KR curve can be matched with the crack driving (applied K) curves to estimate the degree of stable crack extension and the conditions necessary to cause unstable crack propagation (1).4 In making this estimate, KR curves are regarded as being independent of original crack size ao and the specimen configuration in which they are developed. For a given material, material thickness, and test temperature, KRcurves appear to be a function of only the effective crack extension Δae (2).
5.2.1 To predict crack behavior and instability in a component, a family of crack driving curves is generated by calculating K as a function of crack size for the component using a series of force, displacement, or combined loading conditions. The KR curve may be superimposed on the family of crack driving curves as shown in Fig. 1, with the origin of the KR curve coinciding with the assumed original crack size ao. The intersection of the crack driving curves with the KR curve shows the expected effective stable crack extension for each loading condition. The crack driving curve that develops tangency with the KR curve defines the critical loading condition that will cause the onset of unstable fracture under the loading conditions used to develop the crack driving curves.
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