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Stress Intensity Factors

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Encyclopedia of Tribology


K I ; K II ; K III ; SIF


The stress intensity factor is the magnitude of the stress singularity at the tip of a mathematically sharp crack in a linear elastic material. Each mode of fracture has an associated stress intensity factor. The Mode-I, Mode-II, and Mode-III stress intensity factors, labeled K I , K II , and K III are defined with respect to Fig. 1 by

$$\eqalign{{K_I}= \mathop{{\lim}}\limits_{{r \to 0}} \sqrt {{2\pi r}} {\sigma_{{22}}}(r,\,\,\theta = 0) \cr{K_{{II}}}=\mathop{{\lim}}\limits_{{r \to 0}} \sqrt {{2\pi r}} {\sigma_{{12}}}(r,\,\,\theta = 0) \cr {K_{{III}}} = \mathop{{\lim }}\limits_{{r \to 0}} \sqrt {{2\pi r}} {\sigma_{{32}}}(r,\,\,\theta = 0) \cr }$$
Stress Intensity Factors, Fig. 1
figure 19302

Crack tip coordinate system

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Correspondence to Alan T. Zehnder .

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Zehnder, A.T. (2013). Stress Intensity Factors. In: Wang, Q.J., Chung, YW. (eds) Encyclopedia of Tribology. Springer, Boston, MA.

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