1. Reference problem

1.1. Geometry

C

D

B

A

Length	\(L=50\mathrm{mm}\)
Width	\(W=16\mathrm{mm}\)
Crack depth	\(a=6\mathrm{mm}\)

1.2. Material properties

The material is elastoplastic of the Von Mises type. For models A to D, there is no work hardening. For the E-modeling, various work-hardening laws are compared (linear or power hardening). The properties of the material are as follows:

Young’s module	\(E=\mathrm{2,0601}{10}^{5}\mathrm{MPa}\)
Poisson’s Ratio	\(\nu =0.3\)
Elastic limit	\({\sigma }_{y}=\mathrm{808,34}\mathrm{MPa}\)
Work hardening module	\(H=0\) (modeling A to D) or \(H=\mathrm{6,867}{10}^{4}\mathrm{MPa}\) (modeling E)

1.3. Boundary conditions and loading

For models A, B, and E, the model is limited to half of the structure, the plane of the vertical crack being a plane of symmetry. For the C and D models, the entire structure is represented.

Boundary conditions

Vertical displacement \(\mathrm{UX}=0\) at point \(B\)

Horizontal displacement \(\mathrm{UY}=0\) in ligament \(\mathrm{AB}\) (symmetry condition for models A, B and E)

Loading

Horizontal displacement imposed on segment \(\mathrm{CD}\): \(\mathrm{UY}=\delta\)