2. Benchmark solution#

2.1. Calculation method used for the reference solution#

BROWN & STRAWLEY [bib1] reference solution:

\(J\mathrm{=}{F}^{2}\pi a{\sigma }^{2}\mathrm{/}E\) with \(F=1.98\)

\(a\) in \(\mathit{mm}\)

\(\sigma\) and \(E\) in \(N/{\mathrm{mm}}^{2}\)

2.2. Reference results for \(G\)#

Benchmark results \(G={1.98}^{2}\times \pi \times 37.5\times 0.5{10}^{-5}=2.3093{10}^{-3}\mathrm{Mpa.mm}\)

The formula

_images/Object_3.svg

(IRWIN) = \(\frac{1}{E}({K}_{1}^{2}+{K}_{2}^{2})\) conduit, like

_images/Object_5.svg

, at \({K}_{1}=21.491{\mathrm{MPa.mm}}^{1/2}\)

2.3. Reference results for derivatives of \(G\)#

By varying the Young’s modulus and the load \(\mathrm{Fy}\), we see that:

\(G\mathrm{=}\alpha {F}_{Y}^{2}\) with \(\alpha \mathrm{=}2.3{10}^{\mathrm{-}3}\) being \(\frac{\mathrm{\partial }G}{\mathrm{\partial }{F}_{Y}}\mathrm{=}2\alpha {F}_{Y}\) ————————————— —- —-

\(G\mathrm{=}\frac{\beta }{E}\) with \(\beta \mathrm{=}460.\) being \(\frac{\mathrm{\partial }G}{\mathrm{\partial }E}\mathrm{=}\mathrm{-}\frac{G}{E}\)

2.4. Bibliographical reference#

  1. BROWN - STAWLEY ASTM Special Technical Publication No. 410 (1966)