4. B modeling#

4.1. Characteristics of modeling#

The objective of B modeling is to validate the entire process of calculating the priming factor, from solving the mechanical problem to post-processing with POST_RCCM.

The calculation is carried out on a 2D modeling of plane deformations, with a material with linear elastic behavior.

4.2. Characteristics of the mesh#

Number of knots: 30000

Number of cells: 10000 quadratic cells (SEG3, TRIA6 and QUAD8)

_images/Object_26.png

  1. Overview

 _images/Object_27.png

  1. Zoom on the bottom of the crack

Figure 4.2-a : Mesh - test case rccm09b

4.3. Tested values and results#

The various values tested are grouped together in the table below.

The good precision on the stress intensity factor shows that the mesh used is fine enough to capture the singularity of the movements at the bottom of the crack.

The comparison of the constraints \({\sigma }_{\theta \theta }\) as a function of the angle \(\theta\) is also satisfactory: the difference in the maximum value of \({\sigma }_{\theta \theta }\), obtained for \(\theta \mathrm{=}0\), is 2%. The difference between analytical solution and numerical solution can be explained by the effects of the edge of the structure on the stress field: in fact, an analytical solution obtained in an infinite medium is compared to a calculation on a finite structure (crack \(15\mathrm{mm}\) deep, plate \(72\mathit{mm}\) wide).

The maximum priming factor, calculated for \(\theta \mathrm{=}0\), is close to the analytical solution for the two cases studied. For \(\theta \mathrm{=}90°\), the gap is significant, as a consequence of the gap already noted in the constraints.

Value tested

Reference

Aster

Variance

\({K}_{I}\) (\(\mathit{MPa.}\sqrt{\mathit{mm}}\)) (method 3)

2.874

2.855

-0.6%

\({\sigma }_{\theta \theta }\) (\(\theta \mathrm{=}0°\)) (\(\mathit{MPa}\))

53.5

54.5

2%

\({\sigma }_{\theta \theta }\) (\(\theta \mathrm{=}90°\)) (\(\mathit{MPa}\))

18.9

17.5

-7%

\({\mathit{FA}}_{1}\) (\(\theta \mathrm{=}0°\))

0.607

0.673

11%

\({\mathrm{FA}}_{1}\) (\(\theta \mathrm{=}90°\))

2.01.10-3

1.32.10-3

-34%

\({\mathrm{FA}}_{2}\) (\(\theta \mathrm{=}0°\))

0.819

0.909

11%

\({\mathrm{FA}}_{2}\) (\(\theta \mathrm{=}90°\))

2,72.10-3

1,786.10-3

-34%

Note:

The constraint \({\sigma }_{\theta \theta }\) corresponds, in the array produced by MACR_LIGN_COUPE , to the component \(\mathit{SIZZ}\) .