Derivation of novel creep-integrated fatigue equations

•A novel model that integrates creep damage into fatigue.•Embedded creep damage is formulated from the constitutive equation of creep.•Capable of modelling creep fatigue from pure creep to pure fatigue.•Fundamentally sound, easy to use, valid over wide range of creep fatigue conditions.•Validated using two metals of vastly different creep and fatigue characteristics.