1. Reference problem#
1.1. Geometry#
It is a square plate with side \(1\mathrm{mm}\)
Figure 1.1-a : Problem geometry.
1.2. Material properties#
The various material properties are given below.
The material parameters used in this test case should not be used for studies. They do not correspond to real characteristics.
Young’s module: \(E=210000.0–30.0T\) in \(\mathrm{MPa}\)
Poisson’s ratio: \(\nu =0.30+5.0E-05T\)
Coefficient of thermal expansion: \(\alpha =\left(15.0+0.002T\right)1.0E-06\)
Plastic part
\(\kappa =0.8\)
Elastic limit at \(\text{0.2\%}\) in \(\mathrm{MPa}\): \({R}_{02}={R}_{02}^{0}\mathrm{.}{C}_{w}\text{\_}{R}_{e}\mathrm{.}{I}_{r}\text{\_}{R}_{e}\)
with
\({R}_{02}^{0}=270.0-0.65T+0.001{T}^{2}\)
\({C}_{w}\text{\_}{R}_{e}=1.0\)
\({I}_{r}\text{\_}{R}_{e}=\left(4.0–3.0{e}^{\frac{-\mathit{IRRA}}{3}}\right)\)
Ultimate compulsion in \(\mathit{MPa}\): \({R}_{m}={R}_{02}(T,\mathrm{IRRA})+({R}_{m}^{0}–{R}_{02}^{0})\mathrm{.}{C}_{w}\text{\_}{R}_{m}\mathrm{.}{I}_{r}\text{\_}{R}_{m}\)
with
\({R}_{m}^{0}=600.0-1.5T+0.010{T}^{2}\)
\({C}_{w}\text{\_}{R}_{m}=0.50\)
\({I}_{r}\text{\_}{R}_{m}=0.005-0.002\left(1.0-{e}^{\frac{-\mathit{IRRA}}{4.0}}\right)+{e}^{\frac{-\mathit{IRRA}}{1.8}}\)
Distributed elongation: \({ϵ}_{u}=\mathrm{ln}(1.0+{ϵ}_{u}^{0}.{C}_{w}\text{\_}{ϵ}_{u}.{I}_{r}\text{\_}{ϵ}_{u}.1.0E-02)\)
with
\({\epsilon }_{u}^{0}\mathrm{=}5.0\mathrm{-}0.15T+0.0007{T}^{2}\)
\({C}_{w}\text{\_}{ϵ}_{u}=1.0\)
\({I}_{r}\text{\_}{\epsilon }_{u}\mathrm{=}{e}^{\mathrm{-}\mathit{IRRA}}\)
Irradiation part |
Swelling part |
\({A}_{\mathit{i0}}=3.0E-06{\mathit{MPa}}^{-1}.{\mathit{dpa}}^{-1}\) \({\eta }_{\mathit{is}}=1000\mathit{MPa.dpa}\) |
\(\alpha =1.0\) \({\phi }_{\mathrm{0 }}=40.0\mathrm{dpa}\) |
1.3. Boundary conditions and loads#
For edges \(\mathrm{AB}\) and \(\mathrm{DC}\), \(\mathrm{DY}=0\)
For edge \(\mathrm{AD}\), \(\mathrm{DX}=0\)
In addition, a linear temperature ramp having a maximum \(400°C\) as well as a linear irradiation ramp having a maximum of \(140\mathrm{dpa}\) are applied.