Relationship of Flaw Crack Size, Stress, and Notch Toughness

Fracture mechanics uses stress analysis techniques to define a stress intensity factor (KI) which is proportional to the product of stress and the square root of flaw size. Fracture occurs when the stress intensity factor exceeds a critical value. For a given material, the critical value is a function of temperature, loading rate, and thickness.

For slow loading rates, the critical value is applicable to static loads and is designated KIc. For dynamic loading (as in impact tests), the critical value is designated KId. We are usually interested in the KIc values for essentially static loading conditions. However, we must also consider the possibility of more rapid loading rates, which can cause much lower KId values (see Figure 500-12).

Schematic of the Shift in Transition Temperature Due to Loading Rate

KIc (or KId) is a material’s fracture toughness at a given temperature and loading rate. It is a material property, as yield and tensile strength are. Steels with a guaranteed KIc are not commercially available, so we have to use other methods to specify and purchase, such as Charpy V-Notch testing.

Figure 500-13 illustrates limits of allowable stress and crack size combinations for different KIc values. Above the curve for a given fracture toughness, fracture occurs. Figure 500-13 shows that at a given stress level, a larger flaw is tolerable as tougher materials are used.

Relationship of Toughness, Stress, and Crack Size

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