Analytical model of the in-plane torsion test

Abstract In research and industry, the in-plane torsion test is applied to investigate material behaviour at large plastic strains: a sheet clamped in two concentric circles, boundaries are twisted against each other applying torque, simple shear of arises. This deformation analysed within scope finite elasto-plasticity. An additive decomposition Almansi strain tensor derived, valid as an approximation for arbitrary strains sufficiently small elastic rotations. Constitutive assumptions von Mises yield criterion, associative flow rule, isotropic hardening, physically linear elasticity relation. The incremental formulation relation applies covariant Oldroyd derivatives stress tensors. combined with equilibrium conditions lead evolution equations distribution stresses accumulated strain. nonzero circumferential must be determined from condition because no present tangential direction. As result, differential-algebraic-equation (DAE) system consisting three ordinary differential one algebraic side condition. example material, properties dual phase steel DP600 numerically 3.0. Radial normal 3.1% 1.0% determined. influence additional on determination curve 0.024%, which negligibly comparison experimental influences measurement accuracies affecting determination.