1. Reference problem#
1.1. Geometry#
The crack is a circular crown in a plane orthogonal to the cylinder axis [Figure 1.1-a None None]. Parameters \(a\) and \(b\) determine the radius of the cylinder and the depth of the crack. The [Figure 1.1-b] is a section of the cylinder in the crack plane (plane \(\mathrm{Oyz}\)). For the medium to be considered infinite, the height of the cylinder is \(h=10b\).
Figure 1.1- a : Geometry of the cracked cylinder
Figure 1.1- b : Crack plan
1.2. Material properties#
Young’s module: \(E=205000\mathrm{MPa}\)
Poisson’s ratio: \(\nu =0.3\)
1.3. Boundary conditions and loads#
Three loads will be applied in order to calculate the stress intensity factors \(\mathrm{K1}\) and \(\mathrm{K3}\) in \(\mathrm{3D}\) using the POST_K1_K2_K3 operator.
Load 1 tests \(\mathrm{K1}\) and \(\mathrm{K3}\).
Charging 2 tests \(\mathrm{K2}\) without taking contact into account.
Charging 3 tests \(\mathrm{K2}\) with contact taken into account.
\(\mathrm{K1}\) and \(\mathrm{K3}\) are expected to be constant along the crack bottom and for \(\mathrm{K2}\) to vary.
Note: cases of traction and twisting can be treated equally with or without contact (here, without contact) because there is never a closure of the crack.
Case 1: traction and twist |
Case 2: non-contact bending |
Case 3: contact bending |
|
Top side |
\({N}_{x}=6\mathrm{MN}\) \({T}_{x}=3\mathrm{MN}\) |
|
|
Table 1.3-1: Load cases
The above efforts are applied to the structure through discrete \(\mathrm{3D}\) elements located at the center of the upper face. Note that the maximum opening point due to the imposed bending (next moment \(\mathrm{Oy}\)) will be the \(A\) node (see [Figure 1.1‑b].
Rigid body movements are blocked by the same method by embedding the center of the underside.