On the superposition of flow stress contributions at finite temperatures and in the athermal limit

The functional form of the equation describing the superposition of contributions to the flow stress due to various strengthening mechanisms is analyzed. Considering that the superposition can be written as a sum to which each mechanism contributes through function f, that the dependence of the critical resolved shear stress on the density of obstacles to dislocation motion is given by function g, and that f and g have the same functional form for all strengthening mechanisms considered, it is shown that these two function are necessarily power functions, and their exponents are related. Furthermore, requiring that the superposition law is valid both at finite temperatures and at 0 K leads to an equivalent expression for the strain rate sensitivity and imposes restrictions on the way in which contributions of various mechanisms to the flow stress are evaluated at finite temperatures.