5. C modeling#

5.1. Simulation 1#

This is a thermomechanical test with zero imposed deformation along axis \(x\). The test is performed on a hardware point with the SIMU_POINT_MAT command. The temperature varies from \({T}_{0}=20°C\) to \({T}_{\mathrm{max}}=500°C\). The transition consists of NCAL steps. The reference temperature is \({T}_{\mathrm{Ref}}=20°C\).

5.2. Simulation 2#

It is a question of looping on mechanical NCALcalculs. For each calculation \(i\), the imposed load consists of the thermal deformation \({\varepsilon }_{\mathrm{xx}}=-{\varepsilon }_{\mathrm{th}}=-\alpha (T)({T}_{i}-{T}_{\mathrm{Ref}})\). The initial load consists of the deformations, stresses and internal variables from the previous mechanical calculation.

5.3. Behavioral law and material parameters#

The law of behavior tested is” ELAS_VMIS_PUIS “, is documented in documentation R5.03.02.

It is a « nonlinear » law of elastic behavior (law of HENCKY) from VON MISES with nonlinear isotropic work hardening defined by a power function.

The elastic parameters are as follows:

\(E(T)\), \(\nu (T)\), \(\alpha (T)\), \({\sigma }_{y}(T)\),, \(a(T)\), and \(n(T)\)

Values of the parameters used:

Parameter

\(T=20°C\)

\(T=500°C\)

\(E(T)\)

\(200000.\) MPa

\(100000.\) MPa

\(\nu (T)\)

\(0.\)

\(0.\)

\(\alpha (T)\)

\(1.\times {10}^{-4}\) \({K}^{-1}\)

\(2.\times {10}^{-4}\) \({K}^{-1}\)

\({\sigma }_{y}(T)\)

\(1000.\) MPa

\(800.\) MPa

\(a(T)\)

\(1.\)

\(0.8\)

\(n(T)\)

\(7.\)

\(6.\)

5.4. Tested sizes and results#

Validation is carried out by comparing the fields calculated at each step of the transient on the one hand and the result of a mechanical calculation on the other hand.

The command used is TEST_TABLE which tests the reference value against the calculated value.

The reference value being the field component extracted at a given time \(i\) from the first thermomechanical simulation performed over NCAL times. The calculated value is the one obtained at the end of the mechanical calculation \(i+1\) of the loop on the NCAL.

Result at serial number i

Name of the tested parameter

Reference type

Reference value

tolerance

RESU_i

NOM_PARA

VALE_REF

TOLE

RESU_19

VMIS

NON_REGRESSION

2008.142

0.1%

RESU_19

TRACE

NON_REGRESSION

-2008.142

0.1%

RESU_19

V1

NON_REGRESSION

0.0759186

0.1%