2. Benchmark solution

2.1. Calculation method

Three propagations of the crack are calculated. The two cracks always advance by the same distance and their stress intensity factors are always equal to each other.

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

\({K}_{I}\mathrm{=}Y\mathrm{\cdot }P\mathrm{\cdot }\sqrt{a}\)

\(Y\mathrm{=}1.99+0.76\mathrm{\cdot }\frac{a}{L}\mathrm{-}8.48\mathrm{\cdot }{(\frac{a}{L})}^{2}+27.36\mathrm{\cdot }{(\frac{a}{L})}^{3}\)

\({K}_{\mathit{II}}\mathrm{=}0\)

2.2. Reference quantities and results

For the three propagations calculated in the tests, the half-length of the crack is as follows:

Propagation	\(a\) [\(\mathrm{mm}\)]
1	330.0
2	360.0
3	390.0

Table 2.1

The expected value of \({K}_{I}\) is therefore as follows for each propagated background:

Propagation	\({K}_{I}\) [\(\mathit{Pa}\sqrt{\mathit{mm}}\)]
1	3.7992E+07
2	4.1791E+07
3	4.6316E+07

Table 2.2

The expected value of \({K}_{\mathit{II}}\) is always zero.

2.3. Bibliographical references

[1] D.Broek, « Elementary Engineering Fracture Mechanics », Martinus Nijhoff Publishers, The Hague, The Netherlands, 1982