Operands ========= Generic operands -------------------- Operand TABLE ~~~~~~~~~~~~~~~ .. code-block:: text ♦ TABLE = tab, [table] This operand allows you to choose the table on which the operations are performed. This table comes from either command CALC_G or command POST_K1_K2_K3. Operand OPERATION ~~~~~~~~~~~~~~~~~~~ .. code-block:: text ♦ operation =/'ABSC_CURV_NORM', /'ANGLE_BIFURCATION', /'LOI_PROPA' This operand allows you to choose the operation to be performed. For an explanation of the various operations, see the corresponding paragraphs below. Operands for the 'ABSC_CURV_NORM' operation -------------------------------------------- .. code-block:: text The 'ABSC_CURV_NORM' operation creates a new column in the output table, corresponding to the standard curvilinear abscissa along the crack bottom. To do this, it is necessary that the input table contains a column 'ABSC_CURV'. The entrance table may have several crack bottoms. It may contain one or more moments for each of the crack bottoms. Operand NOM_PARA ~~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ NOM_PARA =/'ABSC_CURV_NORM' [DEFAUT] /para_name, [TXT] This operand allows you to choose the name of the new column created. Operands for the 'ANGLE_BIFURCATION' operation ---------------------------------------------- .. code-block:: text The operation 'ANGLE_BIFURCATION' creates a new column in the output table, corresponding to the angle of bifurcation of the crack, which is given in degrees. The entrance table may have several crack bottoms. It may contain one or more moments for each of the crack bottoms. Operand NOM_PARA ~~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ NOM_PARA =/'BETA' [DEFAUT] /angle_name, [TXT] This operand allows you to choose the name of the new column created. Operand CRITERE ~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ criterion =/'SITT_MAX' [DEFAUT] /'SITT_MAX_DEVER' /'K1_ MAX ', /'K2_ NUL ', /'PLAN', This operand makes it possible to choose the criterion for calculating the angle of bifurcation: * 'SITT_MAX': maximum circumferential stress criterion (Maximal Hoop Stress criterion, [:external:ref:`R7.02.05 §2.5.2 `]) this is the criterion by default. It is calculated using the values of :math:`\mathit{K1}` and :math:`\mathit{K2}`. It is available in 2D and 3D. * 'SITT_MAX_DEVER': criterion of the maximum circumferential stress (Maximal Hoop Stress criterion, [:external:ref:`R7.02.13 §2.1 `]) with the mode III taken into account and calculation of the angle of discharge. * 'K1_ MAX ', 'K2_ NUL ':criteria of Amestoy, Bui and Dang-Van [:external:ref:`R7.02.05 §2.5.1 `]. These 2 criteria are only available in 2D. The angle is given to within 10 degrees. .. code-block:: text Attention, we note that the criterion 'K2_ NUL 'does not work for an angle greater than :math:`60°`. * 'PLAN': Define a zero angle. Operands for the 'K_EQ' operation --------------------------------- .. code-block:: text The operation 'K_EQ' creates a new column in the output table, corresponding to the accumulation of modes. It may contain one or more moments, but the Young's modulus and the Poisson's ratio in the case of accumulation of the type 'CUMUL_G' or 'QUADRATIQUE' must be defined as constant in time. Operand NOM_PARA ~~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ NOM_PARA =/'K_EQ' [DEFAUT] /cumulative_name, [TXT] This operand allows you to choose the name of the new column created. Operand CUMUL ~~~~~~~~~~~~~~~ .. code-block:: text ◊ CUMUL =/'CUMUL_G' [DEFAUT] /'QUADRATIQUE', /'LINEAIRE', /'MODE_I', This operand allows you to choose the rule for combining modes: * 'CUMUL_G': this is the accumulation by default. It is calculated using the energy return ratio :math:`G`, the values of the Young's modulus :math:`E` and the Poisson's ratio :math:`\nu`. It is available in 2D and 3D. :math:`\sqrt{\frac{GE}{1\mathrm{-}{\nu }^{2}}}` * 'QUADRATIQUE': This sum is calculated using the :math:`\nu` Poisson Ratio values. It is available in 2D and 3D. In 2D, this accumulation is written as: :math:`\sqrt{{\mathit{K1}}^{2}+{\mathit{K2}}^{2}}` In 3D, this accumulation is written: :math:`\sqrt{{\mathit{K1}}^{2}+{\mathit{K2}}^{2}+\frac{{\mathit{K3}}^{2}}{1\mathrm{-}\nu }}` * 'LINEAIRE': In 2D, this accumulation is written as: :math:`\mathit{max}(\mathit{K1}\mathrm{,0})+∣\mathit{K2}∣` In 3D, this accumulation is written: :math:`\mathit{max}(\mathit{K1}\mathrm{,0})+∣\mathit{K2}∣+\mathrm{0,74}∣\mathit{K3}∣` .. code-block:: text * 'MODE_I': This accumulation is available in 2D and 3D and is written as: :math:`\mathit{K1}` Operands for operation 'DELTA_K_EQ' ------------------------ .. code-block:: text The 'DELTA_K_EQ' operation creates a new column in the output table, corresponding to the accumulation of modes. It may contain one or more moments, but the Young's modulus and the Poisson's ratio in the case of accumulation of the type 'CUMUL_G' or 'QUADRATIQUE' must be defined as constant in time. Operand NOM_PARA ~~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ NOM_PARA =/'DELTA_K_EQ' [DEFAUT] /cumulative_name, [TXT] This operand allows you to choose the name of the new column created. Operand CUMUL ~~~~~~~~~~~~~~~ .. code-block:: text ◊ CUMUL =/'CUMUL_G' [DEFAUT] /'QUADRATIQUE', /'MODE_I', This operand allows you to choose the rule for combining modes: * 'CUMUL_G': this is the accumulation by default. It is calculated using the energy return ratio :math:`G`, the values of the Young's modulus :math:`E` and the Poisson's ratio :math:`\nu`. It is available in 2D and 3D. :math:`\sqrt{\frac{GE}{1-{\nu }^{2}}}` * 'QUADRATIQUE': This sum is calculated using the :math:`\nu` Poisson Ratio values. It is available in 2D and 3D. In 2D, this accumulation is written as: :math:`\sqrt{\Delta {\mathit{K1}}^{2}+\Delta {\mathit{K2}}^{2}}` In 3D, this accumulation is written: :math:`\sqrt{\Delta {\mathit{K1}}^{2}+\Delta {\mathit{K2}}^{2}+\frac{{\Delta \mathit{K3}}^{2}}{1\mathrm{-}\nu }}` * 'MODE_I': This accumulation is available in 2D and 3D and is written as: :math:`\Delta \mathit{K1}` Operands for operation 'COMPTAGE_CYCLES' -------------------------------------------- .. code-block:: text The operation 'COMPTAGE_CYCLES' makes it possible to calculate the cycles linked to the evolution of one (or more) quantity (s). This operation creates a new table, with a column CYCLES and a column corresponding to the change in quantity counted per cycle. The entrance table may have several crack bottoms. Operand NOM_PARA ~~~~~~~~~~~~~~~~~~ .. code-block:: text ♦ NOM_PARA =/para_name, [TXT] This operand allows you to choose the name of the quantity on which the cycles are counted. It is possible to count on several quantities (for example :math:`\mathit{K1}`, :math:`\mathit{K2}` and :math:`\mathit{K3}`), provided that the same number of cycles is found for each quantity. Operand COMPTAGE ~~~~~~~~~~~~~~~~~~ .. code-block:: text ♦ COMPTAGE =/'RAINFLOW', /'RCCM', /'NATUREL', /'UNITAIRE' This operand makes it possible to choose the cycle counting method. Except for counting UNITAIRE, we use the POST_FATIGUE command. For more information on counting methods, see the documentation [:ref:`R7.04.01 `]. The input table may contain one or more moments, but corresponding to the same crack background. Counting UNITAIRE is a special case for linear elastic calculations. In this case, the input table should only contain a single moment and the variation in quantity will then be determined by the operands COEF_MULT_MINI and COEF_MULT_MAXI. Operand DELTA_OSCI ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ DELTA_OSCI =/0. [DEFAUT] /delta, [R] see documentation [:external:ref:`U4.83.01 `] Operands COEF_MULT_MINI and COEF_MULT_MAXI ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text ♦ COEF_MULT_MINI = cmini [R] ♦ COEF_MULT_MAXI = cmax [R] For unit counting, the variation in the quantity to be counted is as follows: :math:`\Delta q\mathrm{=}{q}_{u}(\mathit{cmaxi}\mathrm{-}\mathit{cmini})` where :math:`q` is the quantity to be counted, and :math:`{q}_{u}` the unit value of this quantity (the only value in the input table). Operands for operation 'LOI_PROPA' -------------------------------------- .. code-block:: text The operation 'LOI_PROPA' creates a new column in the output table, corresponding to the unit progress (i.e. for one cycle) of a crack taking into account a fatigue propagation law. The entrance table may have several crack bottoms. It may contain one or more moments for each of the crack bottoms. Operand NOM_PARA ~~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ NOM_PARA =/'DELTA_A' [DEFAUT] /name_da, [TXT] This operand allows you to choose the name of the new column created. Operands LOI, C, M, NOM_DELTA_K_EQ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text ♦/LOI =/'PARIS' [DEFAUT] /C = c, [R] /m = m, [R] ◊ DELTA_K_SEUIL =/0. [DEFAUT] /val_threshold, [R] ◊ NOM_DELTA_K_EQ =/'DELTA_K_EQ' [DEFAUT] /dkeq_name [TXT] The LOI operand makes it possible to specify the chosen fatigue propagation law. For the moment, only the Paris law is available. This law is written as: :math:`\frac{\mathit{da}}{\mathit{dN}}=\mathit{C.}{(\Delta {K}_{\mathit{eq}}-\Delta {K}_{\mathit{seuil}})}^{m}` where :math:`C` and :math:`m` are material coefficients, supplied by the operands C and M. :math:`\Delta {K}_{\mathit{seuil}}` is the propagation threshold, adjustable by the optional parameter DELTA_K_SEUIL, whose value by default is 0. If :math:`\Delta {K}_{\mathit{eq}}\le \Delta {K}_{\mathit{seuil}}`, then the progress is zero. The column in the input table corresponding to :math:`\Delta {K}_{\mathit{eq}}` is specified by the NOM_DELTA_K_EQ operand. We then calculate the unit advance (:math:`\Delta N\mathrm{=}1` implicitly): :math:`\Delta a=\mathit{C.}{(\Delta {K}_{\mathit{eq}}-\Delta {K}_{\mathit{seuil}})}^{m}` Note: In pure :math:`I` mode: :math:`\Delta {K}_{\mathit{eq}}` equals :math:`\Delta {K}_{I}`. In mixed mode, :math:`\Delta {K}_{\mathit{eq}}` can be written :math:`{(\Delta K)}_{\mathit{eq}}` or :math:`\Delta ({K}_{\mathit{eq}})`, depending on the conventions. These two quantities are generally different. However, there are cases where these two quantities are identical: * in pure mode 1 if :math:`\mathit{K1}` is always positive, * in mixed linear mode for a :math:`(0\mathrm{-}\mathit{max})` cycle. .. code-block:: text Operands for operation 'CUMUL_CYCLES' ----------------------------------------- .. code-block:: text The operation 'CUMUL_CYCLES' makes it possible to accumulate a quantity previously counted for each cycle by calculating the average over all the cycles. The created table contains all columns from the original table except column CYCLE. Attention, at the bottom, the other columns of the table must not vary during the cycles. The name of the column corresponding to the cumulative quantity does not change. The entrance table may have several crack bottoms. Operand NOM_PARA ~~~~~~~~~~~~~~~~~~ .. code-block:: text ◊ NOM_PARA =/'DELTA_A' [DEFAUT] /name_da, [TXT] This operand allows you to specify the name of the parameter on which the accumulation is performed. By default, the accumulation is performed on 'DELTA_A'. Operand CUMUL ~~~~~~~~~~~~~~~ .. code-block:: text ◊ CUMUL = 'linear' [DEFAUT] This operand is not used for the moment, because the only accumulation authorized is the linear accumulation (arithmetic mean over the cycles): :math:`{q}_{\mathit{cumul}}\mathrm{=}\frac{1}{N}\mathrm{\sum }_{i\mathrm{=}1}^{N}{q}_{i}` where :math:`{q}_{i}` corresponds to the value for cycle :math:`i` of the quantity to be accumulated. Operands for operation 'PILO_PROPA' ------------------------ .. code-block:: text The 'PILO_PROPA' operation makes it possible to control the propagation of several crack bottoms (for the moment, limited to a single crack). Piloting is done: * or by imposing the increment of the number of cycles (cycle control); * or by imposing the maximum advance increment of the crack bottom (forward control). .. code-block:: text This management takes into account all the points of all the bottoms and all the cracks. The input table should contain the DELTA_A parameter. Delta_a_max operands and DELTA_N ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text ♦/Delta_a_max = da, [R] /delta_n = dn, [R] To control the propagation in cycles, delta_n is used. This has the effect of multiplying the value of the advance (unit) by a factor :math:`\mathit{dn}` for all the points of all the bottoms of all the cracks. The other control mode consists in setting the maximum advance increment :math:`\mathit{da}` via the Delta_a_max operand. First, we determine the point on all the bottoms of all the cracks that has the highest advance. Let's note this advance :math:`\mathit{damax}`. The number of cycles applied will then be :math:`\frac{\mathit{da}}{\mathit{damax}}`. Operands for the 'K1_ NEGATIF 'operation ------------------------ .. code-block:: text The purpose of the 'K1_ NEGATIF 'operation is to treat background points where the stress intensity factor :math:`\mathit{K1}` is negative. For these points where the values of :math:`\mathit{K1}` are negative, :math:`\mathit{K1}` is set to zero and the return rates :math:`G` and/or :math:`{G}_{\mathit{IRWIN}}` are recalculated by the Irwin formula. If at least one of the two reproduction rates is present in the input table, the latter must also contain the parameter :math:`\mathit{K2}` (and :math:`\mathit{K3}` in 3D). The input table may include several calculation moments and several crack bottoms. Operand m ODELISATION ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text ♦ MODELISATION =/'3D' /'C_ PLAN ' /'D_ PLAN ' /'AXIS' This operand makes it possible to choose the Irwin formula adapted to the type of modeling used. When :math:`\mathit{K1}` is zero, Irwin's formula is: In 3D: :math:`G\mathrm{=}\frac{1\mathrm{-}\nu \mathrm{²}}{E}\mathit{K2²}+\frac{1+\nu }{E}\mathit{K3}\mathrm{²}` In plane deformations and for axisymmetry along the :math:`Y` axis: :math:`G\mathrm{=}\frac{1\mathrm{-}\nu \mathrm{²}}{E}\mathit{K2²}` In plane constraints: :math:`G\mathrm{=}\frac{\mathit{K2²}}{E}` where :math:`E` is Young's modulus and :math:`\nu` is the Poisson's ratio. Operand m ATER ~~~~~~~~~~~~~~~ .. code-block:: text ♦ MATER = mat, [material] This operand gets the name of the material used for the calculations. The material parameters are then used in the Irwin formula to recalculate the restoration rate (s). The Young's modulus and the Poisson's ratio must be defined to be constant in time.