1. Reference problem#
1.1. Geometry#
Consider a notched cylindrical test piece:
diameter of the test piece: \(18\mathrm{mm}\),
notch radius: \(5\mathrm{mm}\).
1.2. Material properties#
We adopt a Von Mises elasto-plastic behavior law with isotropic work hardening TRACTION whose traction curve is given point by point:
\(\varepsilon\) |
0.0027 |
0.005 |
0.005 |
0.01 |
0.01 |
0.015 |
0.02 |
0.03 |
0.04 |
0.05 |
0.05 |
0.05 |
0.075 |
0.075 |
0.1 |
\(\sigma\) (\(\mathit{MPa}\)) |
555 |
589 |
589 |
589 |
631 |
631 |
657 |
704 |
725 |
741 |
741 |
772 |
794 |
0.125 |
0.15 |
0.2 |
0.2 |
0.3 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.8 |
0.9 |
812 |
827 |
851 |
887 |
887 |
97 |
912 |
933 |
950 |
965 |
978 |
990 |
The deformations used in the behavior relationship are linearized deformations. Young’s modulus \(E\) is \(200\mathit{GPa}\) while the Poisson’s ratio \(\nu\) is equal to \(\mathrm{0,3}\).
The coefficients of the Weibull and Bordet models used are as follows:
\(m=8\),
\({V}_{0}\mathrm{=}100\mu m\),
\({\sigma }_{u}\mathrm{=}2630\mathit{MPa}\),
\({\sigma }_{\mathit{ys}\mathrm{,0}}\mathrm{=}{\sigma }_{\mathit{ys}}\mathrm{555MPa}\),
\({\sigma }_{\mathit{th}}\text{=}\mathrm{600MPa}\).
1.3. Boundary conditions and loads#
With reference to the figure in [§3.1] the boundary conditions are as follows:
\(\mathrm{BC}\): displacement imposed according to \((Y)\),
\(\mathrm{OA}\): movements blocked according to \((Y)\),
\(\mathrm{OB}\): movements blocked following \((X)\).
1.4. Initial conditions#
Zero stresses and deformations.