On the construction of constitutive equations for orthotropic materials with different properties under tension and compression in creep

Constitutive steady-state creep equations are proposed for orthotropic materials with different tensile and compressive resistance properties. Power functions with different exponents for tension and compression are used to describe the resistance. The equations of the problems of tension and shear and the equations of the plane stress problem are given. The model is used to solve the problem of torsion of annular cross-section rods cut from a plate of AK4-1 transversally isotropic alloy in the normal and longitudinal directions by a constant moment at a temperature $T=200^\circ$C. Constitutive equations for torsion are obtained. Values of model parameters were obtained in experiments on uniaxial tension and compression of solid round samples cut in various directions. An analytical solution for the rate of torsion angle of an annular cross section rod cut in the normal direction of the plate was obtained for the same exponent index under tension and compression. For a rod cut in the longitudinal direction of the plate, an upper bound of the rate of torsion angle was obtained. The calculation results are in satisfactory agreement with the experimental data.