Incremental versus total-strain theories for proportionate and nonproportionate loading of torsion-tension members

Abstract

Incremental and total-strain theories have been presented in the literature for hollow and solid circular torsion-tension members. The differential equations obtained for the incremental theory have been solved only for the conditions that the torsion-tension member is made of a nonstrain-hardening material and is subjected to restricted deformation histories. Computer programs were written to obtain numerical incremental solutions for hollow and solid circular torsion-tension members made of strain-hardening materials and subjected to any deformation or loading path. Test data were obtained for three different materials: (a) a nonstrain-hardening steel, annealed SAE 1035 steel, with identical properties in tension and compression; (b) a strain-hardening steel, annealed rail steel, with identical properties in tension and compression; (c) a strainhardening alumimum alloy, 2024-T4, with different properties in tension and compression. In all cases, the average of the tension and compression stress-strain diagram was approximated by two straight lines to obtain material properties.