2. Benchmark solution#
2.1. Calculation method#
The calculation of stress intensity factors is obtained in [1] by a semi-analytical procedure which consists in superimposing displacement profiles verifying free stress conditions on the crack lips.
2.2. Reference quantities and results#
The values of \({K}_{1}\) and \({K}_{2}\) given in [1] are compared to crack bottoms.
Points |
\({K}_{1}\) |
\({K}_{2}\) |
Points |
\({K}_{1}\) |
\({K}_{2}\) |
|
\(A\) |
1,7943 |
2.8522 |
\(A\text{'}\) |
3,7215 |
2.3379 |
|
\(B\) |
1,9932 |
2.4042 |
\(B\text{'}\) |
2.6700 |
1.0248 |
|
\(C\) |
-1.6920 |
-0.1337 |
\(C\text{'}\) |
5.3966 |
-0.1143 |
|
\(F\) |
0.0510 |
0.2894 |
\(F\text{'}\) |
4.3255 |
-0.1661 |
|
\(G\) |
-0.5317 |
0.1885 |
\(G\text{'}\) |
3.6812 |
0.9279 |
|
\(H\) |
-0.0517 |
-0.1979 |
\(H\text{'}\) |
0.4157 |
-0.3947 |
|
\(I\) |
-0.1933 |
0.0213 |
\(I\text{'}\) |
1.0043 |
0.0648 |
Table 2: stress intensity factors at the bottom of cracks obtained in [1].
2.3. Uncertainty about the solution#
The number of significant figures given in Table 2 reflects the quality of the semi-analytical solution. In fact, convergence towards these figures can be verified in the case of an increasingly fine mesh.
2.4. Bibliographical references#
YAVUZ, S. L. PHOENIX, « Multiple Crack Analysis in Finite Plates », AIAA Journal, Vol. 44, No. 11, November 2006.
SIAVELIS, M. GUITON, P. MASSIN, N. MOËS « Large sliding contact along branched discontinuities with X- FEM », under review, 2012.