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Table 1 Thermally triggered necking of an anisotropic circular bar—material parameters

From: A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions

Shear modulus

G

\(80.2\;\mathrm {GPa}\)

Bulk modulus

\(\kappa \)

\(164.2\;\mathrm {GPa}\)

Initial yield stress

\(y_0(T)\)

\((1-\omega _0(T-T_0))\; 450\;\mathrm {MPa} \)

Anisotropy parameters

\(y_{11}\)

\(y_{11} = \{0.825 y_0,y_0\}\)

\(y_{22},y_{33},y_{12},y_{13},y_{23}\)

\(y_{22}=y_{33}=y_{12}=y_{13}=y_{23}=y_0\)

Linear hardening modulus

\(H^i(T)\)

\((1-\omega _h(T-T_0))\;129.24\;\mathrm {MPa} \)

Saturation yield stress

\(y_\infty (T)\)

\((1-\omega _h(T-T_0))\;715\;\mathrm {MPa} \)

Hardening exponent

\( \delta \)

16.93

Density

\(\rho _0\)

\(7.8\cdot 10^{-9}\;\frac{\mathrm {N}\,\mathrm {s}^2}{\mathrm {mm}^4}\)

Heat capacity

\(C_v\)

\(3.588\;\frac{\mathrm {N}}{\mathrm {mm}^2\,\mathrm {s}^2\,\mathrm {K}} \)

Heat conductivity

\(k_0\)

\(45\;\frac{\mathrm {N}}{\mathrm {s}\,\mathrm {K}}\)

Expansion coefficient

\(\alpha _T\)

\(10^{-5}\;\frac{1}{\mathrm {K}}\)

Yield stress softening

\(\omega _0\)

\(0.002\;\frac{1}{\mathrm {K}}\)

Hardening softening

\(\omega _h\)

\(0.002\;\frac{1}{\mathrm {K}}\)

Dissipation factor

\(\beta \)

0.9

Initial temperature

\(T_0\)

\(293\;\mathrm {K}\)

surrounding temperature

\(T_\infty \)

\(293\;\mathrm {K}\)

Convection coefficient

\(h_c\)

\(17.5\;\frac{\mathrm {N}}{\mathrm {mm}\,\mathrm {s}\,\mathrm {K}}\)