Reference problem ===================== Geometry --------- .. image:: images/10000000000000BC000000BEAC47153FF6FB5862.png :width: 1.9472in :height: 1.972in .. _RefImage_10000000000000BC000000BEAC47153FF6FB5862.png: **Figure** 1.1-a **: Geometry of the problem, cube with a side of 1mm.** Material properties ----------------------- The material parameters used in this test case **should not be used for studies**. They do not correspond to real characteristics. The various material properties are given below, with: • :math:`T`: temperature in :math:`°C` • :math:`\mathrm{IRRA}`: irradiation in :math:`\mathrm{dpa}` [:ref:`R5.03.23 `] Young's module: :math:`E=210000.0–30.0T` in :math:`\mathrm{MPa}` Poisson's ratio: :math:`\nu =0.30+5.0E-05T` Coefficient of thermal expansion: :math:`\alpha =\left(15.0+0.002\right)1.0E-06` *Plastic part* :math:`\kappa =0.8` Elastic limit at 0.2% in :math:`\mathrm{MPa}`: :math:`{R}_{02}={R}_{02}^{0}\mathrm{.}{C}_{w}\text{\_}{R}_{e}\mathrm{.}{I}_{r}\text{\_}{R}_{e}` with :math:`{R}_{02}^{0}=270.0-0.65T+0.0010{T}^{2}` :math:`{C}_{w}\text{\_}{R}_{e}=1.0` :math:`{I}_{r}\text{\_}{R}_{e}=\left(4.0–3.0{e}^{\frac{-\mathit{IRRA}}{3}}\right)` Ultimate compulsion in :math:`\mathrm{MPa}`: :math:`{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 :math:`{R}_{m}^{0}=600.0-1.5T+0.010{T}^{2}` :math:`{C}_{w}\text{\_}{R}_{m}=0.50` :math:`{I}_{r}\text{\_}{R}_{m}=0.005-0.0020\left(1.0-{e}^{\frac{-\mathit{IRRA}}{8.0}}\right)+{e}^{\frac{-\mathit{IRRA}}{3.0}}` Distributed elongation: :math:`{ϵ}_{u}=\mathrm{ln}(1.0+{ϵ}_{u}^{0}.{C}_{w}\text{\_}{ϵ}_{u}.{I}_{r}\text{\_}{ϵ}_{u}1.0E-02)` with :math:`{ϵ}_{u}^{0}=50.0-0.15T+0.007{T}^{2}` :math:`{C}_{w}\text{\_}{ϵ}_{u}=1.0` :math:`{I}_{r}\text{\_}{ϵ}_{u}={e}^{-\mathit{IRRA}}` .. csv-table:: "*Irradiation part*", "*Swelling part*" ":math:`{A}_{\mathit{i0}}=3.0E-06{\text{MPa}}^{-1}{\text{dpa}}^{-1}` :math:`{\eta }_{\mathit{is}}=1000\text{MPa.dpa}` "," :math:`R=0.0020{\text{dpa}}^{-1}` :math:`\alpha =1.0` :math:`{\varphi }_{0}=45.0\text{dpa}` or :math:`{\varphi }_{0}=1.0\text{dpa}`" Boundary conditions and loads ------------------------------------- **Modeling A** For nodes 1, 2, 3, 4: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=0` For nodes 5, 6, 7, 8: :math:`\mathrm{DX}=\mathrm{DY}=0` In addition, a linear temperature ramp with a maximum of :math:`400°C` as well as a linear irradiation ramp with a maximum of :math:`140\mathrm{dpa}` (figure) is applied. The material characteristics for swelling are those of the lower bound. +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------+ |**B Modeling** | | + + .. image:: images/10000000000000BC000000BEAC47153FF6FB5862.png + | Travel conditions :math:`\mathrm{DX}=0`, nodes: 1, 4, 5, 5, 8 :math:`\mathrm{DY}=0`, nodes: 1, 2, 5, 6 :math:`\mathrm{DZ}=0`, knots: 1, 4, 2, 3 | :width: 1.9472in | + Nodes: 2, 3, 6, 6, 7 Nodes: 2, 3, 6, 6, 7 :math:`\mathrm{DX}=0.0` :math:`t=\mathrm{0.0}\mathrm{sec}` :math:`\mathrm{DX}=3.0E-03` :math:`t=\mathrm{10.0}\mathrm{sec}` :math:`\mathrm{DX}=3.0E-03` :math:`t=\mathrm{90.0}\mathrm{sec}` + :height: 1.972in + | | | + + + | | | +-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------+ .. image:: images/100002000000032A000001738C7989DA95C0A168.png :width: 6.3272in :height: 2.898in .. _RefImage_100002000000032A000001738C7989DA95C0A168.png: **Figure** 1.3-a **: Temperature and irradiation conditions at all nodes as a function of time.** The modeling is done a first time with the swelling characteristics that correspond to the upper bound and then a second time with the swelling characteristics that correspond to the lower bound.