3. Modeling A#

3.1. Characteristics of modeling#

There are 4 crowns defined by command CALC_G:

Crown 1:

\(\mathrm{Rinf}=10.\)

\(\text{Rsup}=40.\)

Crown 2:

\(\mathrm{Rinf}=15.\)

\(\text{Rsup}=45.\)

Crown 3:

\(\mathrm{Rinf}=5.\)

\(\text{Rsup}=47.\)

Crown 4:

\(\mathrm{Rinf}=3.\)

\(\text{Rsup}=48.\)

The crack bottom is defined by DEFI_FOND_FISS, and for each crown we perform:

  • a classic \(G\) calculation (option G_ EPSI from CALC_G),

  • a calculation of \(G\) using the IRWIN formula using the stress intensity coefficients

    _images/Object_5.svg

and

_images/Object_6.svg

(option K from CALC_G).

  • a calculation of

    _images/Object_10.svg

starting with \(G\) and the IRWIN formula (option KJ_EPSI from CALC_G)

3.2. Characteristics of the mesh#

Number of knots: 853

Number of meshes and types: 359 TRIA6 meshes and 27 QUAD8 meshes

3.3. Test values and modeling results A#

The values tested are those of \(G\) obtained by the classical method and those of \({G}_{\mathrm{IRWIN}}\) obtained by the formula d’IRWIN from the stress intensity coefficients:

Identification

Reference

Tolerance

Crown 1 \(G\)

3.8535 10 —1

8.00%

Crown 1 \({G}_{\mathrm{IRWIN}}\)

3.8535 10 —1

8.00%

Crown 1 \(\mathit{KJ}\)

9.2029 10 1

8.00%

Crown 2 \(G\)

3.8535 10 —1

8.00%

Crown 2 \({G}_{\mathit{IRWIN}}\)

3.8535 10 —1

8.00%

Crown 2 \(\mathit{KJ}\)

9.2029 10 1

8.00%

Crown 3 \(G\)

3.8535 10 —1

8.00%

Crown 3 \({G}_{\mathit{IRWIN}}\)

3.8535 10 —1

8.00%

Crown 3 \(\mathit{KJ}\)

9.2029 10 1

8.00%

Crown 4 \(G\)

3.8535 10 —1

8.00%

Crown 4 \({G}_{\mathit{IRWIN}}\)

3.8535 10 —1

8.00%

Crown 4 \(\mathit{KJ}\)

9.2029 10 1

8.00%

3.4. notes#

The numerical values are stable with respect to the various integration crowns and almost identical for the two calculation methods. However, the difference with the reference values is of the order of 6 to \(\text{7\%}\), which seems high.