Cycle-dependent multiaxial stress relaxations under non-proportional creep-fatigue conditions

• Conducted multiaxial creep-fatigue tests under non-proportional strain paths. • Proposed a unified visco-plastic model for cyclic deformation behaviors. • Incorporated triaxiality and Tanaka’s parameter to capture stress relaxation. • Validated energy-based model predicting creep-fatigue life within a factor of 1.5. A series of non-proportional creep-fatigue tests under different strain paths were performed for type 304 stainless steel at 873 K. Among these strain paths, the holding period was applied at peak axial strain or peak shear strain to introduce creep damage under different multiaxial stress states. A unified visco-plastic model was developed for describing the cyclic deformation behaviors. More specifically, the Tanaka’s non-proportional parameter was introduced to consider the additional hardening effect, and stress triaxiality was used to modified the static recovery term for multiaxial stress relaxation behaviors. Furthermore, the cycle-dependent relaxed stress was described by a simple evolution equation, which constructed the relationship between hardening coefficient in static recovery term and equivalent plastic strain rate. The cycle-dependent hardening and stress relaxation behaviors were correlated with the equivalent plastic strain rate through three evolution equations with a consistent form, avoiding the introduction of additional material parameters when considering new deformation behaviors, which was more conducive to engineering applications. After obtaining precise stress/strain response, an energy-based creep-fatigue damage evaluation method was used to predict the non-proportional creep-fatigue life, which showed good agreement with the experimental data within a factor of 1.5.