Rigid-plastic torsion of a hollow tube in strain-gradient plasticity

Closed-form expressions for the Cauchy stress, microstress, moment-stress, and the torque-twist relationship in a twisted hollow circular tube are derived for a rigid-plastic strain-gradient plasticity. This is accomplished for any of the gradient-enhanced effective plastic strain measures from a considered broad class of these measures. Numerical results are given and discussed for the two most frequently utilized measures and for the three adopted stress-strain relationships modeling the uniaxial tension test. Solid circular rods and thin-walled tubes are both considered. The existence of the line forces is also discussed from the standpoint of the basic equilibrium considerations and the principle of virtual work.