Viscoplastic constitutive relation for relaxation of prestressing steel at varying strain and temperature

The stress relaxation of prestressing steel tendons is normally measured at constant strain and constant temperature. The measurement results, embodied in empirical formulas, are then directly used to predict the prestress losses. This classical approach is contingent upon assuming the strain changes during structural lifetime to be negligible compared to the initial strain in steel, and the temperature changes to be unimportant. Recently, however, it transpired that, in creep-sensitive structures (such as large-span, segmentally erected, box girders) dominated by their self-weight, the strain changes in concrete are not negligible and the temperature rise in concrete slabs exposed to sun may be important. To take this into account, the existing empirical formulas used in the European (CEB-fib) Model Code and the American practice, which are valid only for constant strain and constant temperature, are now generalized to arbitrary time-variable strain and variable temperature, heeding obvious asymptotic restrictions and the fact that steel is a viscoplastic material whose constitutive principles are well known. The resulting formula is a memory-less, nonlinear equation for the viscoplastic strain rate of steel as a function of the current stress, strain and temperature. Close fits of all the main test data from the literature, including the available data on the effect of strain changes and temperature changes, are achieved. The effect of temperature is found to be important and is formulated on the basis of the activation energy of viscoplastic flow of metals.