5. C modeling: validating DETECT_COHESIF

5.1. Characteristics of modeling

In this modeling, the initial crack is meshed. It is extended in its plane by a cohesive cracking zone, represented by level sets and whose discontinuity is described by method XFEM. Law CZM_LIN_MIX is introduced into model XFEM by command DEFI_CONTACT.

A monotone tensile load is applied: the cohesive zone opens, thus propagating the crack. At the end of the calculation, a detection of the new propagation front is carried out, which determines the upstream limit of the cohesive zone. It is performed by the operator PROPA_FISS, with the GEOMETRIQUE method, by specifying the operation DETECT_COHESIF (OPERATION = “DETECT_COHESIF”).

5.2. Characteristics of the mesh

The mesh is fairly coarse, but refined at the initial crack point. To make the detected front more regular, it is a mesh radiating around the tip.

Number of knots: 18167

Number of meshes and type: 15120 HEXA8 and 2440 PENTA6

Figure 5.2-1: sectional view of the cracked surface and radiating mesh

5.3. Tested sizes and results

Validation is carried out on the progress of the detected front after this first propagation step. In the absence of experimental data for a monotonic loading, this is a non-regression test. We have represented in figure the initial crack font and the front detected after the first propagation step. Although we do not have a quantitative reference, we note that the qualitative appearance of the forehead is similar to that of fatigue experiences.

Figure 5.3-1: initial edge and edge detected after the first propagation step

The position of the deepest crack bottom point is tested. This is equivalent to testing the maximum coordinate along the \(Y\) axis of the points at the bottom of the crack after a propagation step.

Identification	Reference Type	Reference Value	% Tolerance
\(\mathit{max}(Y)\)	“NON_REGRESSION”	1.61048 10-4	0.1%