Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

Analytical calculation by Hankel transform.


Benchmark results
----------------------

For the reference solution, the rays should check the condition a/b < 0.5.

:math:`\eta =\frac{a}{b}<\mathrm{0,5}`

:math:`{K}_{I}=\frac{E\alpha {T}_{f}}{1-\nu }\cdot \sqrt{(\frac{a}{\pi })}\cdot {F}_{I}`

:math:`{F}_{I}=1-0.6366\eta -0.4053{\eta }^{2}+2.0163{\eta }^{3}-0.6773{\eta }^{4}-3.8523{\eta }^{5}+4.1687{\eta }^{6}+3.2741{\eta }^{7}`


Uncertainty about the solution
----------------------------

Poorly-defined. For low values of the a/b ratio, the solution should asymptotically approximate the reference solution calculated for = 0, i.e. FI = 1, which is then accurate (see MURAKAMI 11.23, page 1069).


Bibliographical references
----------------------------


1. Y. MURAKAMI: Stress Intensity Factors Handbook, box 11.39, pages 1089-1090. The Society of Materials Science, Japan, Pergamon Press, 1987.