A Stress-Space Reparameterization Framework for Unified Minimum Creep Strain-Rate Equations

For predictive structural integrity assessment and creep damage modelling (CDM), integrated constitutive descriptions are needed that remain consistent across stress levels and deformation mechanisms. This requirement was first identified and systematically addressed by Xu et al. through the mechanism-based time–temperature–stress (TTS) concept and TTS-integrate framework [1–4], in which prediction is achieved through a unified constitutive architecture rather than separate regime-based formulations. Accordingly, the minimum creep strain-rate equation must represent stress dependence continuously. Conventional power-law or piecewise approaches require stress-region identification and transition criteria, limiting their suitability for integrated prediction. To overcome this limitation, Qiang Xu originally proposed a modified hyperbolic sine law in 2015 [5, p. 6], which has since been widely applied in creep strain-rate and creep-life modelling. This formulation has become an effective basis for creep damage constitutive equations and lifetime prediction with the Monkman–Grant relationship because of its dislocation-creep basis, numerical stability, and mathematical consistency [6–9]. However, its effectiveness has remained largely empirical, and its theoretical origin has not been fully clarified. This paper provides a scientific interpretation through stress-space reparameterization. By introducing a transformed stress variable with a stress-dependent activation coefficient and closure, the framework shows that the effective stress exponent evolves continuously. Apparent piecewise behaviour is therefore interpreted as local slopes of a unified function. This work introduces stress-space reparameterization into creep damage modelling, theoretically justifies the modified hyperbolic sine law, and supports integrated TTS-based constitutive architectures for improved predictive capability.