1. Reference problem#

1.1. Geometry and loading#

We consider a Compact Tension specimen (\(\mathit{CT}\)) with a thickness of \(25\mathit{mm}\). The geometry includes a rigid pin to which the load is applied.

_images/10000200000002110000014980051032472A5BCD.png

Figure 1: Geometry

1.2. Material properties#

To describe the behavior of the axisymmetric specimen material (bulk material), an elastoplastic behavior law with isotropic work hardening is used (law VMIS_ISOT_TRAC).

We take: \(E\mathrm{=}207\mathit{GPa}\) and \(\nu \mathrm{=}0.3\) and the work hardening curve used is given below:

_images/10000200000001C100000134E1017A238A1EAC7A.png

Figure 2: Isotropic work hardening curve of solid material.

For interface elements the following parameters are used in law CZM_TRA_MIX:

\({\sigma }_{c}\mathrm{=}1800\mathit{MPa}\), \({G}_{c}\mathrm{=}150\mathit{MPa}\mathrm{\cdot }\mathit{mm}\), \({\delta }_{e}\mathrm{=}0.01\mathit{mm}\), \({\delta }_{p}\mathrm{=}0.06\mathit{mm}\), \({\delta }_{c}\mathrm{=}0.117\mathit{mm}\)

The resulting law is shown schematically below.

_images/100002000000016900000108F387E7EDCA4FFB9E.png

Figure 3: Law of behavior of interface elements.

NB: Only half of the crack is modelled thanks to the symmetry of the problem, the toughness of the material is \(2{G}_{c}\).

Finally, the rigid pin has elastic behavior (law ELAS) with: \(E\mathrm{=}1\mathrm{\times }{10}^{9}\mathit{MPa}\), \(\nu \mathrm{=}0.3\)

1.3. Boundary conditions and loading#

The limit conditions imposed on the pin are as follows:

  • move to \(X\) blocked,

  • imposed displacement \(l\) in the \(Y\) direction.

The evolution of displacement \(l\) over time is given in the following table:

Time \(\mathrm{[}s\mathrm{]}\)

0

0.4

Displacement \(l\) \(\mathrm{[}\mathit{mm}\mathrm{]}\)

0

1.6

The cohesive zone is represented by the interface elements on the test piece ligament. The boundary conditions on the interface elements are:

  • displacement in \(X\) imposed identical on both lips of the cohesive zone,

  • \(Y\) movement stuck on the lower lip.