The most accurate procedure for handling self-equilibrating secondary stresses in the elastic-plastic region is a numerical nonlinear finite-element formulation. However, it has been shown that an excellent approximation is possible in closed form knowing only the sum of the stress-intensity factors due to all stresses and the fully plastic J-integral expression for a flawed structure under non-self-equilibrating primary loading only. For the deformation plasticity failure assessment diagram (DPFAD) approach, this concept is impractical since each thermal transient or residual stress state would require a separate DPFAD curve. A simpler, more acceptable procedure is to generate the DPFAD curve for non-self-equilibrating primary loading (which is independent of the level of applied loading) and adjust the assessment points to reflect the effects of plasticity produced by the self-equilibrating secondary stresses. Two such simpler approaches are recommended, one based on adjusting K_r, while the other approach redefines S_r, where (K_r, S_r) is the assessment point to be evaluated. Comparisons of the two simpler procedures with the more accurate closed form procedure were made, and both simpler methods were found to be only slightly nonconservative in the region of small-scale yielding to elastic-plastic fracture. For the fully plastic region, both methods are conservative. An example problem illustrating the use of both simpler methods is presented.