Reference problem ===================== Tank geometry -------------------- The geometry studied is that of the core zone of a generic tank of the 900 MWe level, of which an azimuthal portion of 45° is shown schematically in FIG. 1.1-a. .. _RefWarning_schema_Cadre2: Warning: **odt2sphinx failed to: schema Frame2** Figure 1.1-a: View of a 45° section of the core zone of a generic 900 Mwe level tank Characteristics of the defect under consideration ------------------------------------ In method :math:`K\beta`, the defect is not modeled in the mesh. The mesh makes it possible to calculate the stresses at the nodes. A first post-treatment is first applied to calculate the strength factor of the elastic stresses at the points of the defect from the stresses at the nodes (the method is detailed in [:ref:`R7.02.10 `]). A second post-treatment is then applied to calculate the intensity factor of the elasto-plastic stresses using the so-called "correction b" method (see documentation R7.02.10]). For this test, the under-coating defect in question is elliptical in shape, has a longitudinal orientation and is offset in the base metal. Its dimensions are as follows (see figure below): * Depth: :math:`{\mathit{prof}}_{\text{def}}\mathrm{=}\mathrm{6mm}` * Width: :math:`\mathrm{2b}\mathrm{=}\mathrm{60mm}` * Several offsets in the base metal are considered: :math:`\text{-}\mathit{decalage}\mathrm{=}0.0\mathit{mm}` :math:`\text{-}\mathit{decalage}\mathrm{=}2.5\mathit{mm}` :math:`\text{-}\mathit{decalage}\mathrm{=}5.0\mathit{mm}` :math:`\text{-}\mathit{decalage}\mathrm{=}7.5\mathit{mm}` :math:`\text{-}\mathit{decalage}\mathrm{=}10.0\mathit{mm}` .. image:: images/Shape2.gif .. _RefSchema_Shape2.gif: Figure 1.1-b: Defect position Material properties ----------------------- **For thermal calculation:** Two properties are specified, they are: * LAMBDA: isotropic thermal conductivity as a function of temperature, expressed in :math:`{\mathit{W.m}}^{\mathrm{-}1}\mathrm{.}{K}^{\mathrm{-}1}`, * BETA: volume enthalpy as a function of temperature, expressed in :math:`{\mathit{J.m}}^{\mathrm{-}3}`. For the coating: .. csv-table:: "**Temperature (** :math:`°C` **)**", "**LAMBDA**" "0", "14.7" "20", "14.7" "50", "15.2" "100", "15.8" "150", "16.7" "200", "17.2" "250", "18" "300", "18.6" "350", "19.3" .. csv-table:: "**Temperature (** :math:`°C` **)**", "**BETA**" "0", "0.000000.E+00" "50", "1.102100.E+08" "100", "3.013300.E+08" "150", "5.014300.E+08" "200", "7.081300.E+08" "250", "9.188800.E+08" "300", "1.132910.E+09" "350", "1.348980.E+09" For the base metal: .. csv-table:: "**Temperature (** :math:`°C` **)**", "**LAMBDA**" "0", "37.7" "20", "37.7" "50", "38.6" "100", "39.9" "150", "40.5" "200", "40.5" "250", "40.2" "300", "39.5" "350", "38.7" .. csv-table:: "**Temperature (** :math:`°C` **)**", "**BETA**" "0", "0.000000.E+00" "50", "1.061900.E+08" "100", "2.903300.E+08" "150", "4.829100.E+08" "200", "6.832800.E+08" "250", "8.921600.E+08" "300", "1.109440.E+09" "350", "1.335060.E+09" **For mechanical calculation:** Four parameters are filled in, they are: .. csv-table:: "* :math:`E`:", "Young's modulus, expressed in :math:`\mathit{Pa}`," "* :math:`\mathit{nu}\mathrm{=}0.3` ", "Poisson's ratio," "* ALPHA:", "isotropic thermal expansion coefficient, expressed in :math:`°C`," "* TEMP_DEF_ALPHA = 20", "value of the temperature at which the values of the thermal expansion coefficient ALPHAont were determined, expressed in :math:`°C`." "* VALE_REF = 287°", "Reference temperature :math:`{T}_{\mathit{Réf}}`, for which the thermal deformation is zero, expressed in :math:`°C`." For the coating: .. csv-table:: "**Temperature (** :math:`°C` **)**", ":math:`E`" "0", "1.985E+11" "20", "1.97E+11" "50", "1.95E+11" "100", "1.915E+11" "150", "1.875E+11" "200", "1.84E+11" "250", "1.8E+11" "300", "1.765E+11" "350", "1.72E+11" .. csv-table:: "**Temperature (** :math:`°C` **)**", "**ALPHA**" "0", "1.64E-05" "20", "1.64E-05" "50", "1.654E-05" "100", "1.68E-05" "150", "1.704E-05" "200", "1.72E-05" "250", "1.75E-05" "300", "1.777E-05" "350", "" For the base metal: .. csv-table:: "**Temperature (** :math:`°C` **)**", ":math:`E`" "0", "2.05E+11" "20", "2.04E+11" "50", "2.03E+11" "100", "2E+11" "150", "1.97E+11" "200", "1.93E+11" "250", "1.89E+11" "300", "1.85E+11" "350", "1.8E+11" .. csv-table:: "**Temperature (** :math:`°C` **)**", "**ALPHA**" "0", "1.122E-05" "20", "1.122E-05" "50", "1.145E-05" "100", "1.179E-05" "150", "1.214E-05" "200", "1.247-05" "250", "1.278E-05" "300", "1.308E-05" Boundary conditions and loads ------------------------------------- Step 1: non-linear thermal calculation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The limit conditions applied to the thermal calculation are summarized in Figure 1.3-a and are broken down as follows: * fluid temperature and exchange coefficient imposed on the inner wall, * thermal insulation on the external wall. .. image:: images/10000000000002B9000001243A3DF5F1118F9B84.png :width: 6.889in :height: 2.8854in .. _RefImage_10000000000002B9000001243A3DF5F1118F9B84.png: Figure 1.3-a: Thermal problem considered Step 2: mechanical calculation in linear elasticity ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The boundary conditions of the mechanical problem are summarized in Figure 1.3-b below and are broken down as follows: * fluid pressure on the inner wall, * symmetry along the Oz axis on the lower segment, * shape effect as well as uniform movement along the Oz axis on the upper segment. .. image:: images/1000000000000286000001ABD35DAA628CF557F9.png :width: 6.7291in :height: 4.448in .. _RefImage_1000000000000286000001ABD35DAA628CF557F9.png: Figure 1.3-b: Mechanical problem considered