1. Reference problem

1.1. Geometry

Axisymmetric cylinder

1.2. Material properties

The material properties of the two sub-domains (blue and red) are those of 316L steel, described below. Work hardening restoration parameters are also defined but only on the red subdomain.

Thermal parameters:

Volume heat capacity \(\rho {C}_{p}=3.9\times {10}^{6}({\mathit{J.m}}^{-3.}°{C}^{-1})\)

Conductivity \(\lambda ({\mathit{W.m}}^{-1}°{C}^{-1})\):

T (°C)	\(\lambda\)
	15.2
	16.6
	17.9
	19.0
	20.6
	21.8
	23.1
	24.3
	27.3
	29.9

Thermo-mechanical parameters:

• Thermo-elastic parameters:

Young’s module \(E(\mathit{Pa})\)

Poisson’s ratio: \(\nu =0.3\)

Thermal expansion coefficient \(\alpha\)

Expansion coefficient definition temperature: \({T}_{\mathit{ref}}=20°C\)

Elasticity limit \({\sigma }_{y}(\mathit{Pa})\)

• Thermoplastic parameters (law with linear work hardening)

Tangent module \({E}_{T}(\mathit{Pa})\)

T (°C)	\({E}_{T}(\times {10}^{6})\)

• Work hardening restoration parameter: multiplicative function FONC_MULT

Restoration start temperature: Td = 600°C

Temperature at the end of restoration: Tf = 1000°C

1.3. Boundary conditions and loads

• Blockages:

uy = 0 in P1, P2, P3 and P4

• Charging:

The following thermal load is applied all over the mesh:

with T0 = 20°C and T1 = 1125°C