2. Benchmark solution

2.1. Method used for the reference solution

For a circular crack of radius \(a\) in an infinite medium, subjected to a uniform traction \(\sigma\) following the normal to the plane of the lips, the local energy release rate \(G(s)\) is independent of the curvilinear abscissa along the crack front \(s\) and is expressed as follows [1]:

\(G(s)\mathrm{=}\frac{(1\mathrm{-}{\nu }^{2})}{\pi E}4{\sigma }^{2}a\)

Stress intensity factor \({K}_{I}(s)\) is given by Irwin’s formula:

\(G(s)\mathrm{=}\frac{(1\mathrm{-}{\nu }^{2})}{E}{K}_{I}^{2}\), which is \({K}_{I}(s)\mathrm{=}\frac{2\sigma \sqrt{a}}{\sqrt{\pi }}\)

2.2. Benchmark results

With the numerical values of the statement, we find: \({K}_{I}=\mathrm{1,5957}\mathit{MPa}\mathrm{.}\sqrt{m}\) and \(G\mathrm{=}\mathrm{11,59}{\mathit{J.m}}^{\mathrm{-}2}\).

2.3. Bibliographical references

• 8. Tada, P. Paris, G. Irwin, G. Irwin, The Stress Analysis of Cracks Handbook, 3rd edition, 2000