We consider and analyze general methodological issues regarding the strength and endurance (life-time) of the materials and structure elements under a combined effect of various force, deformation and temperature factors. The Journal "Zavodskaya laboratoriya. Diagnostika materialov" (Industrial laboratory. Diagnostics of materials) has launched systematic publications on this problematic since 2018. For many decades, domestic and foreign laboratory studies have gleaned to a traditional methodology for obtaining initial curves of the long-term and cyclic strength that related the breaking stresses with time or number of cycles. These curves, with the characteristic sections and break points, separating the areas of elastic and inelastic (plastic strain or creep strain) strain, are used in analysis of long-term and cyclic damage. Using the elementary linear law of damage summation, it is possible to calculate at a first approximation the strength and endurance under varying conditions of loading. Stepping up the requirements to the accuracy of calculations necessitates a transition from force fracture criteria (at stresses a) to deformation criteria (in elastic and inelastic deformations e). Thus, it becomes possible to construct and use a unified expression for the curve of the long-term cyclic fracture (taking into account the temporal x and cyclic N factors) and a long-term cyclic damage. With such approach it is possible to remain the linear law of damage summation though those damages are obviously nonlinear. The goal of the study is to continue and support the discussion of the most complex problems of a comprehensive assessment of the strength, resource, survivability and safety of high-risk engineering equipment within the journal pages.