mathematical and statistical fatigue life estimation models

How the mathematical and statistical fatigue life estimation models, based on microplastic strain energy accumulation, correlate between static test results and the cyclic loading condition?

The old Esin and John's model [1], which uses a mathematical procedure, together with the Probability Density Function, defines the limits for the estimation of microplastic strain accumulation from the point as the onset of plasticity to the point close to the fracture of the specimen, or the point at which the last element yields, in a tensile test. The question arises, where he considers this microplastic strain energy, accumulated in this period, as the half cycle energy accumulation in a fatigue cyclic test. Does anyone have an explanation for this?

[1] Esin, A., and W.J. Derrick Jones. "A Theory of Fatigue Based on the Microstructural Accumulation of Strain Energy ☆." A Theory of Fatigue Based on the Microstructural Accumulation of Strain Energy. Elsevier B.V., Oct. 1966. Web. 10 June 2016.