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

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. Test data for proportionate loading were in excellent agreement with either the total-strain theory or the incremental-strain theory. Data for nonproportionate loading, in which one deformation was kept constant as the other was increased, fell between the two theories and were in closer agreement with the predictions of the incremental theory.