1. Reference problem#

1.1. Geometry#

images/Groupe5.gif _images/10000200000002FF0000041AB4B6F1BB61585083.png

Length

\(L=400\mathit{mm}\)

Width

\(W=100\mathit{mm}\)

Crack depth

\(a=50\mathit{mm}\)

1.2. Material properties#

The material obeys a « non-linear » law of elastic behavior (Hencky’s law) from von Mises with linear isotropic work hardening (EMAS_VMIS_LINE).

The properties of the material are as follows:

Young’s module

\(E=\mathrm{2,1}\times {10}^{5}\mathit{MPa}\)

Poisson’s Ratio

\(\mathrm{\nu }=0.3\)

Linear elastic limit

\({\mathrm{\sigma }}_{y}=150\mathit{MPa}\)

Traction curve slope

\(\text{D\_SIGM\_EPSI}=\mathrm{5,25}\times {10}^{4}\mathit{MPa}\)

Expansion coefficient

\(\mathrm{\alpha }={1.10}^{-5}\)

Reference temperature

\(\text{VALE\_REF}=20°C\) (AFFE_MATERIAU keyword)

1.3. Boundary conditions and loading#

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

Boundary conditions

A and C models:

Horizontal displacement \(\mathrm{UX}=0\) at point \(F\)

Vertical displacement \(\mathrm{UY}=0\) in ligament \(\mathit{EF}\) (symmetry condition)

B and D modeling:

Horizontal displacement \(\mathrm{UX}=0\) on segment \(\mathit{AB}\)

Vertical displacement \(\mathit{UY}=0\) on segment \(\mathit{AB}\)

Loading mechanical

A and C models:

Normal surface force applied to segment \(\mathit{CD}\)

B and D modeling:

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

Vertical displacement imposed on segment \(\mathrm{CD}\): \(\mathit{UX}=\mathrm{\delta }\)

Thermal load

A to C modeling:

No thermal loading.

D modeling:

Stationary temperature dependent on the \(x\) axis and increasing linearly between 0°C in \(x={x}_{A}=0\) and 200°C in \(x={x}_{B}=w\). The reference temperature is fixed at 100° C.