2. Benchmark solution

2.1. Calculation method

Stress intensity factors can be calculated using the following equations [bib1]:

\({K}_{I}\mathrm{=}\frac{1+\alpha }{16}\rho \omega \mathrm{²}\mathit{D²}\sqrt{\pi a}(F(a\mathrm{/}D)\mathrm{-}\frac{3\alpha \mathrm{-}1}{1+\alpha }G(a\mathrm{/}D))\)

with \(F(a\mathrm{/}D)\mathrm{=}\frac{\mathrm{1,122}+\mathrm{0,140}(a\mathrm{/}D)\mathrm{-}\mathrm{0,545}(a\mathrm{/}D)\mathrm{²}+\mathrm{0,405}(a\mathrm{/}D)\mathrm{³}}{{(1\mathrm{-}a\mathrm{/}D)}^{3\mathrm{/}2}}\)

\(G(a\mathrm{/}D)\mathrm{=}\frac{\mathrm{0,187}\mathrm{[}6\mathrm{-}9(a\mathrm{/}D)+5(a\mathrm{/}D)\mathrm{²}\mathrm{]}\mathrm{-}\mathrm{7,35}(a\mathrm{/}D)\mathrm{²}\mathrm{\cdot }(1\mathrm{-}A\mathrm{/}D)\mathrm{⁴}\mathrm{\cdot }(1\mathrm{-}\mathrm{0,5}(a\mathrm{/}D))}{{(1\mathrm{-}a\mathrm{/}D)}^{3\mathrm{/}2}}\)

and \(\alpha \mathrm{=}\frac{1}{2}(\frac{1}{1\mathrm{-}\nu })\) in plane constraints

2.2. Bibliographical references

[1] H. Tada, P.C. Paris, G.R. Irwin, « The Stress Analysis of Cracks Handbook -3rd Ed. », ASME Press 2000