2. Benchmark solution

2.1. Calculation method used for the 2D reference solution

We use the elastoplastic fracture energetic method based on the parameter \(\mathrm{Gp}\) [1], [2].

The notch bottom is formed by a semicircle with radius \(R\). The zone \(\mathrm{Ze}\) of length \(\Delta l\) corresponds to the virtual propagation of the notch and is cut into « chips ».

It determines at each moment the evolution of quantity \(\mathrm{Gp}(\Delta l)\) defined by:

\(\mathit{Gp}(\Delta l)=2[{W}_{\mathit{elas}}^{\mathit{traction}}(\Delta l)]/\Delta l\)

where \({W}_{\mathit{elas}}^{\mathit{traction}}(\Delta l)\) is the elastic tensile energy calculated on zone \(\mathrm{Ze}\). We must then calculate the maximum of this quantity in relation to \(\Delta l\), which we call « \(\mathrm{Gp}\) ».

\(\mathrm{Gp}=\underset{\Delta l}{\mathrm{Max}}\{\mathrm{Gp}(\Delta l)\}\)

The critical moment when the defect will begin to spread is then the moment when tenacity \(\mathrm{Kj}={\mathrm{Kj}}_{\mathrm{crit}}\). It is then said that \(\mathrm{Gp}\) reaches the critical value « \(\mathrm{Gpc}\) ».

2.2. Bibliographical references

1. WADIER Y.: « Brief presentation of the energetic approach to elastoplastic rupture applied to breakage by cleavage », Note EDF R&D HT-64/03/001/A, January 2003.

2. WADIER Y., LORENTZ E.: « Fracture mechanics in the presence of plasticity: modeling of the crack by a notch ». C.R.A.S. t. 332, series IIb, 2004.