Truly Mechanism Based Develop Creep Damage Constitutive Equations for Wide Range of Stress

This paper represents the development of novel creep damage constitutive equations applicable across a wide stress range. This framework integrates: (i) a modified hyperbolic sine law, ε ̇_min=A*sin⁡h(B〖*σ〗^q ), tailored to capture minimum creep strain rates under varying stress; (ii) a time-temperature-stress dependent cavitation damage function, w(t,T,σ)=U'(T,σ)*t^m, tailored to capture minimum creep strain rates under varying stress; and (iii) a power law function, 1/(1-w)^P , representing creep cavitation influence on creep deformation. The modified hyperbolic sine law was designed to capture minimum creep strain rate over a wide range of stress; the cavitation damage model, w(t,T,σ), is calibrated directly from cavity for a given stress and temperature, w(t,T)=U'(T)*t^m, then mapped over stresses as w(t,T,σ)=U^' (σ,T)*t^m. Together, these three components reflect an early observable-driven and transformation-aware modeling. P91 steel was selected for its practical relevance and its well-characterized cavitation behavior, enabling mechanism-resolved calibration. Preliminary validation demonstrates strong alignment with experimental deformation profiles and rupture lifetimes. Full datasets and comparative model assessments, including residual analysis and stress-regime sensitivity, will be reported in forthcoming work.