Stress intensity factor information

In fracture mechanics, the stress intensity factor ( $K$ ) is used to predict the stress state ("stress intensity") near the tip of a crack or notch caused by a remote load or residual stresses.^[1] It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of damage tolerance. The concept can also be applied to materials that exhibit small-scale yielding at a crack tip.

The magnitude of $K$ depends on specimen geometry, the size and location of the crack or notch, and the magnitude and the distribution of loads on the material. It can be written as:^[2]^[3]

K=\sigma {\sqrt {\pi a}}\,f(a/W)

where $f(a/W)$ is a specimen geometry dependent function of the crack length, $a$ , and the specimen width, $W$ , and $σ$ is the applied stress.

Linear elastic theory predicts that the stress distribution ( $\sigma _{ij}$ ) near the crack tip, in polar coordinates ( $r,\theta$ ) with origin at the crack tip, has the form ^[4]

\sigma _{ij}(r,\theta )={\frac {K}{\sqrt {2\pi r}}}\,f_{ij}(\theta )+\,\,{\rm {higher\,order\,terms}}

where $K$ is the stress intensity factor (with units of stress × length^1/2) and $f_{ij}$ is a dimensionless quantity that varies with the load and geometry. Theoretically, as $r$ goes to 0, the stress $\sigma _{ij}$ goes to $\infty$ resulting in a stress singularity.^[5] Practically however, this relation breaks down very close to the tip (small $r$ ) because plasticity typically occurs at stresses exceeding the material's yield strength and the linear elastic solution is no longer applicable. Nonetheless, if the crack-tip plastic zone is small in comparison to the crack length, the asymptotic stress distribution near the crack tip is still applicable.

^ Anderson, T. L. (2005). Fracture mechanics: fundamentals and applications. CRC Press.
^ Soboyejo, W. O. (2003). "11.6.2 Crack Driving Force and Concept of Similitude". Mechanical properties of engineered materials. Marcel Dekker. ISBN 0-8247-8900-8. OCLC 300921090.
^ Janssen, M. (Michael) (2004). Fracture mechanics. Zuidema, J. (Jan), Wanhill, R. J. H. (2nd ed.). London: Spon Press. p. 41. ISBN 0-203-59686-2. OCLC 57491375.
^ Hiroshi Tada; P. C. Paris; George R. Irwin (February 2000). The Stress Analysis of Cracks Handbook (3rd ed.). American Society of Mechanical Engineers.
^ Liu, M.; et al. (2015). "An improved semi-analytical solution for stress at round-tip notches" (PDF). Engineering Fracture Mechanics. 149: 134–143. doi:10.1016/j.engfracmech.2015.10.004. S2CID 51902898.

[ander-1] Anderson, T. L. (2005). Fracture mechanics: fundamentals and applications. CRC Press.

[2] Soboyejo, W. O. (2003). "11.6.2 Crack Driving Force and Concept of Similitude". Mechanical properties of engineered materials. Marcel Dekker. ISBN 0-8247-8900-8. OCLC 300921090.

[3] Janssen, M. (Michael) (2004). Fracture mechanics. Zuidema, J. (Jan), Wanhill, R. J. H. (2nd ed.). London: Spon Press. p. 41. ISBN 0-203-59686-2. OCLC 57491375.

[4] Hiroshi Tada; P. C. Paris; George R. Irwin (February 2000). The Stress Analysis of Cracks Handbook (3rd ed.). American Society of Mechanical Engineers.

[notch-5] Liu, M.; et al. (2015). "An improved semi-analytical solution for stress at round-tip notches" (PDF). Engineering Fracture Mechanics. 149: 134–143. doi:10.1016/j.engfracmech.2015.10.004. S2CID 51902898.

Stress intensity factor information

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