14. Material data associated with post-treatments#
14.1. Keyword factor FATIGUE#
We can refer to [R7.04.01] and [R7.04.03].
14.1.1. Operand WOHLER#
This operand makes it possible to introduce the Wöhler curve of the material in a discretized form point by point. This function gives the number of cycles at break \({N}_{\mathit{rupt}}\) as a function of the stress half-amplitude \(\frac{\mathrm{\Delta }\sigma }{2}.\).
The Wöhler curve is a function for which the user chooses the interpolation mode:
LOG LOG: logarithmic interpolation on the number of cycles at break and on the half-magnitude of the stress (piecewise Basquin formula),
LIN LIN: linear interpolation on the number of cycles at break and on the half-amplitude of the stress (this interpolation is not recommended because the Wöhler curve is absolutely not linear in this coordinate system),
LIN LOG: linear interpolation on the half-amplitude of stress, and logarithmic on the number of cycles at break, which corresponds to the expression given by Wöhler.
The user must also choose the type of extension of the function to the right and to the left.
14.1.2. Operands A_BASQUIN/BETA_BASQUIN#
A_BASQUIN = A
BETA_BASQUIN = beta
These operands make it possible to introduce the Wöhler curve of the material in the analytical form of BASQUIN [R7.04.01].
\(D=A{S}_{\mathit{alt}}^{\beta }\) where \(A\) and \(\beta\) are two material constants,
\({S}_{\mathit{alt}}\) = alternating cycle stress = \(\frac{\Delta \sigma }{2}\) and \(D\) the elementary damage.
14.1.3. Operands A0/ A1/ A2/ A3/ SL#
A0 = a0, A1 = a1, A2 = a1, A2 = a2, A3 = a3, SL = SL
These operands make it possible to define the Wöhler curve in analytical form as a « current zone » [R7.04.01].
\({S}_{\mathit{alt}}\) = alternating stress = \(\frac{1}{2}\frac{{E}_{C}}{E}\Delta \sigma\)
\(\begin{array}{c}X={\mathit{log}}_{10}\left({S}_{\mathit{alt}}\right)\hfill \\ {N}_{\mathit{rupt}}={10}^{\mathrm{a}0+\mathrm{a}1\mathrm{x}+\mathrm{a}2{\mathrm{x}}^{2}+\mathrm{a}3{\mathrm{x}}^{3}}\\ D=\{\begin{array}{c}1/N\text{si}{S}_{\mathit{alt}}\ge {S}_{l}\\ 0.\text{sinon}\end{array}\hfill \end{array}\)
This list of operands makes it possible to introduce the various parameters of this analytical form.
\(\mathit{a0}\), \(\mathit{a1}\), \(\mathit{a2}\), and \(\mathit{a3}\) material constants,
\({S}_{l}\) material endurance limit.
Young’s modulus \(E\) is introduced in DEFI_MATERIAU (keyword factor ELAS operand E).
The value of \(\mathrm{Ec}\), Young’s modulus associated with the fatigue curve of the material, is also introduced in DEFI_MATERIAU under the keyword factor FATIGUE, operand E_REFE.
14.1.4. Operand MANSON_COFFIN#
MANSON_COFFIN = f_mans
This operand makes it possible to introduce the Manson-Coffin curve of the material in a discretized form point by point. This function gives the number of cycles at break as a function of the half-amplitude of deformations \(\frac{\Delta \varepsilon }{2}\).
14.1.5. Operand E_REFE#
E_REFE = Ec
This operand makes it possible to specify the value of the Young’s modulus associated with the fatigue curve of the material. Among other things, this value makes it possible to define the Wöhler curve as a « current zone » [R7.04.01].
14.1.6. Operands D0/ TAU0#
D0 = d0
Allows you to specify the value of the endurance limit in pure alternating traction-compression. This value is used in calculating the Crossland and Dang Van Papadopoulos criteria [R7.04.01] by ordering POST_FATIGUE [U4.83.01].
TAU0 = tau0
Allows you to specify the value of the endurance limit in pure alternating shear. This value is used in calculating the Crossland and Dang Van Papadopoulos criteria [R7.04.01] by ordering POST_FATIGUE [U4.83.01].
14.2. Keyword factor DOMMA_LEMAITRE#
Under this keyword factor are grouped all the material characteristics necessary for the calculation of Lemaitre damage and the Lemaitre-Sermage law (option ENDO_ELGA from CALC_CHAMP, [U4.81.04]).
14.2.1. S operand#
S = s
\(S\) is a material parameter required to calculate Lemaitre damage. \(S\) should be a function of the \(\mathrm{TEMP}\) parameter.
14.2.2. Operand EPSP_SEUIL#
EPSP_SEUIL = Pseuil
Allows you to specify the value of the damage threshold \(\mathit{pd}\), necessary to calculate the Lemaitre damage.
14.2.3. Operand EXP_S#
EXP_S = pdf
Allows you to define the Lemaitre-Sermage law, the default value \((1.0)\) corresponds to the Lemaitre damage calculation.
14.3. Keyword factor CISA_PLAN_CRIT#
Under this keyword factor are grouped all the material characteristics necessary for the implementation of criteria with critical plans [R7.04.04].
14.3.1. Operand MATAKE_A#
MATAKE_A = a,
Allows you to specify the value of the dimensionless coefficient :math:`a`, present in the criteria MATAKE_MODI_ACet MATAKE_MODI_AV, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`].
14.3.2. Operand MATAKE_B#
MATAKE_B = b,
Allows you to specify the value of the coefficient b, present in criteria MATAKE_MODI_ACet MATAKE_MODI_AV, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`].
14.3.3. Operand COEF_FLEX_TORS#
COEF_FLEX_TORS = c_flex_tors,
Allows you to specify the value of the ratio of the endurance limits in alternating bending and twisting, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`]. This value must be greater than or equal to one and less than or equal to :math:`\sqrt{3}`. This operand is to be used in the criteria: MATAKE_MODI_ACet MATAKE_MODI_AV.
14.3.4. Operand D_VAN_A#
D_VAN_A = a,
Allows you to specify the value of the dimensionless coefficient :math:`a`, present in the criteria DANG_VAN_MODI_ACet DANG_VAN_MODI_AV, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`].
14.3.5. Operand D_VAN_B#
D_VAN_B = b,
Allows you to specify the value of the coefficient :math:`b`, found in the criteria DANG_VAN_MODI_ACet DANG_VAN_MODI_AV, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`].
14.3.6. Operand COEF_CISA_TRAC#
COEF_CISA_TRAC = c_cisa_trac,
Allows you to specify the value of the ratio of the endurance limits in alternating bending and twisting, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`]. This value must be greater than or equal to one and less than or equal to :math:`\sqrt{3}`. This operand is to be used in the criteria: DANG_VAN_MODI_AC, DANG_VAN_MODI_AVet FATESOCI_MODI_AV, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`].
14.3.7. Operand FATSOC_A#
FATSOC_A = a,
Allows you to specify the value of the coefficient :math:`a`, present in criterion FATESOCI_MODI_AV, confer [R7.04.01] and [:external:ref:`U4.83.02 <U4.83.02>`].
14.4. Keyword factor HHO#
We can refer to [R3.06.14].
14.4.1. Operand COEF_STAB#
This operand makes it possible to give the stabilization coefficient for method HHO. If it is not given, an automatic coefficient is determined based on the physics of the problem.
14.5. Tag factor WEIBULL, WEIBULL_FO#
Definition of the coefficients of the Weibull model [R7.02.06].
Briefly, the cumulative failure probability of break \({P}_{r}\) of a structure is written, in the case of a monotonic load:
\({P}_{r}\mathrm{=}1\mathrm{-}\mathrm{exp}\left[\mathrm{-}\mathrm{\sum }_{{V}_{p}}({(\frac{{\sigma }_{I}}{{\sigma }_{u}})}^{m}\frac{{V}_{p}}{{V}_{0}})\right]\)
where the summation relates to plasticized \({V}_{p}\) cells (i.e. cumulative plastic deformation greater than an arbitrarily chosen value \({p}_{s}\)) and \(m,{s}_{u},{V}_{0}\) are the parameters of the Weibull model.
In the case of any loading path:
\({P}_{r}(t)=1-\mathrm{exp}\left[-{(\frac{{\sigma }_{w}}{{\sigma }_{u}})}^{m}\right]\)
with:
\({\sigma }_{{\omega }^{m}}=\sum _{V}{\left[\underset{\left\{u<t,\dot{p}(u)>0\right\}}{\mathrm{max}}\left\{\tilde{{\sigma }_{I}}(u)\right\}\right]}^{m}\frac{V}{{V}_{0}}\),
\(\dot{p}\) designating the cumulative plastic deformation rate, \(\tilde{{\sigma }_{I}}\) the greatest principal stress at time \(t\) [R7.02.06].
Finally, if the cleavage stress depends on the temperature (WEIBULL_FO):
\({P}_{r}(t)=1-\mathrm{exp}\left[-{(\frac{{\sigma }_{\omega }^{0}}{{\sigma }_{u}^{0}})}^{m}\right]\),
\({\sigma }_{\omega }^{0}\) designating the Weibull constraint defined conventionally for \({\sigma }_{u}^{0}\) given:
\({\sigma }_{\omega }^{{0}^{m}}\mathrm{=}\mathrm{\sum }_{V}\underset{\left\{u<t,\dot{p}(u)>0\right\}}{\mathit{max}}{\left[\frac{{\sigma }_{u}^{0}\mathrm{.}{\sigma }_{I}(u)}{{\sigma }_{u}(\theta (u))}\right]}^{m}\frac{V}{{V}_{0}}{A}^{{p}^{m}}\)
\(\theta (u)\) designating the temperature in the element \(\delta V\).
14.5.1. Operands#
M = m, SIGM_REFE = sigmu, SIGM_CNV = sigm0u, VOLU_REFE = V0
Parameters associated with the Weibull model.
SEUIL_EPSP_CUMU = not
Cumulative plastic deformation threshold.
14.7. Keyword factor CRIT_RUPT#
Definition of the quantities required for the critical stress failure criterion implemented by the keyword POST_ITER/CRIT_RUPT under COMPORTEMENT. If the greatest mean principal stress in an element exceeds a given threshold sigc, the Young’s modulus is divided by the coef coefficient.
This criterion is available for behavior laws VISCOCHAB, VMIS_ISOT_TRAC (_ LINE), and VISC_ISOT_TRAC (_ LINE), and validated by the SSNV226A, B, C tests.
14.7.1. Operands SIGM_C, COEF#
Value of the sigc threshold stress (in stress units) and of the coef coefficient (without units).
14.8. Keyword factor REST_ECRO#
Definition of the data necessary to take into account the phenomenon of work-hardening restoration implemented by the keyword POST_INCR = » REST_ECRO « under COMPORTEMENT. At the end of each calculation time step, the internal variable corresponding to the cumulative plastic deformation (isotropic work hardening) is modified.
This criterion is available for behavior laws VMIS_ISOT_TRAC (_ LINE), (_), VMIS_ECMI_LINE,),, VMIS_CIN1_CHAB, and VMIS_CIN2_CHAB, and for 3D models, AXIS, D_PLANet C_PLAN.
14.8.1. Operands TEMP_MINI, TEMP_MAXI, and TAU_INF#
TEMP_MINI is the temperature value for the start of work hardening restoration and TEMP_MAXI is the temperature for the total work hardening restoration (total but limited by the parameter TAU_INF).
We do not restore all work hardening, residual work hardening is a function of temperature \(T\) and of the initial work hardening (before restoration) \({r}_{0}\). We proceed with the separation of the variables
The user enters the function \({\tau }_{\mathrm{\infty }}(T)\) (parameter TAU_INF).
TEMP_MINI and TEMP_MAXI have the dimension of a temperature (in °C in code_aster), TAU_INFest a unitless function.
14.8.2. Operands COEF_ECRO and EPSQ_MINI#
The COEF_ECRO function quantifies the restoration speed and EPSQ_MINI makes it possible to delay the triggering of the process by giving a minimum value to the cumulative plastic deformation from which the restoration takes place. These two parameters have no unity.
14.9. Keyword factor VERI_BORNE#
This keyword allows a verification of the field of validity of the parameters of a law of behavior. In fact, the identification of the parameters of these laws is always done within a certain range of deformation and temperature. The objective is to warn the user if in his study he leaves this field where the parameters have been identified. These terminals are defined under the keyword VERI_BORNE. Exceeding the limits during the calculation results in the emission of an alarm.
14.9.1. Operands#
Value of the limits in terms of maximum total deformation, deformation rate, and extreme temperatures.
14.10. Keywords factors POST_ROCHE and POST_ROCHE_FO#
Material dedicated only to macro control POST_ROCHE. It integrates material parameters related to the Ramberg-Osgood law of plasticity, as well as parameters from RCCM -Rx.
Function parameters may depend on temperature only. The temperature field is provided via AFFE_MATERIAU/AFFE_VARC/CHAM_GD or EVOL. It is preferable to use the keyword CHAM_GD, but if one is forced to use the keyword EVOL, it is then necessary to specify the moment to be taken into account in POST_ROCHE by giving the keyword INST_TEMP.
14.10.1. Operands linked to the Ramberg-Osgood law#
The Ramberg-Osgood law of plasticity is defined by the deformation curve as a function of stress according to the following expression:
\(\epsilon =\frac{\sigma }{E}+{\epsilon }_{M,p}(\sigma )\) with \({\epsilon }_{M,p}(\sigma )=K{(\frac{\sigma }{E})}^{1/n}\)
\(E\) corresponds to Young’s modulus, \(K\) and \(n\) are the parameters for the keyword POST_ROCHE.
14.10.2. Operands linked to the codification of RCCM -Rx#
RP02_MIN: minimum conventional elastic limit at 0.2% deformation
This parameter is mandatory:
on the parts defined as « elbows » in operator POST_ROCHE
on the entire pipe line if RCCM_RX =” OUI “in POST_ROCHE
It is not used in other cases.
RM_MIN: minimum tensile strength
This parameter is mandatory on the entire pipe line if RCCM_RX =” OUI “in POST_ROCHE. It is not used in other cases.
RP02_MOY: conventional average elastic limit at 0.2% deformation
This parameter is required on the entire pipe line if RCCM_RX =” OUI “in POST_ROCHE, if it is not provided in this case, it is considered equal to 1.25*rp02min. It is not used in other cases.
COEF: Dimensional coefficient
This setting is only used if RCCM_RX =” OUI “in POST_ROCHE.