Przypadek Jednoczesnego Rozciągania i Skręcania Pręta o Przekroju Kołowym w Zakresie Sprężysto-Plastycznym - Życzkowski, Michał (Engineering Transactions, 1955)
The problem is solved on the basis of Hencky's theory of plastic deformations. General equations are derived and boundary conditions stated. The general equations are integrated in an exact manner in the case of an incompressible material having Poisson's ratio equal to 1/2. In the case of a compressible material an approximate integration is carried out together with the evaluation of error.The problem of simultaneous tension and torsion of a bar can be characterized by means of five parameters: torque Ms, longitudinal force N, radius c of the boundary separating the plastic region from the elastic region, unit elongation ε and unit angle of twist p. The relations between these parameters are considered in detail. The stresses can be expressed in terms of strains by means of elementary functions. The inverse relations however have not this property. They are expressed graphically and numerically.The results permit to determine any three parameters in the elasto-plastic and plastic range, when two other parameters have a known value.