Stress Intensity Factor - Stress Intensity Factors For Various Modes

Stress Intensity Factors For Various Modes

Three linearly independent cracking modes are used in fracture mechanics. These load types are categorized as Mode I, II, or III as shown in the figure. Mode I, shown to the left, is an opening (tensile) mode where the crack surfaces move directly apart. Mode II is a sliding (in-plane shear) mode where the crack surfaces slide over one another in a direction perpendicular to the leading edge of the crack. Mode III is a tearing (antiplane shear) mode where the crack surfaces move relative to one another and parallel to the leading edge of the crack. Mode I is the most common load type encountered in engineering design.

Different subscripts are used to designate the stress intensity factor for the three different modes. The stress intensity factor for mode I is designated and applied to the crack opening mode. The mode II stress intensity factor, applies to the crack sliding mode and the mode III stress intensity factor, applies to the tearing mode. These factors are formally defined as

$\begin{align} K_{\rm I} & = \lim_{r\rightarrow 0} \sqrt{2\pi r}\,\sigma_{yy}(r,0) \\ K_{\rm II} & = \lim_{r\rightarrow 0} \sqrt{2\pi r}\,\sigma_{yx}(r,0) \\ K_{\rm III} & = \lim_{r\rightarrow 0} \sqrt{2\pi r}\,\sigma_{yz}(r,0) \,. \end{align}$

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