Physical-Mechanism Exploration of the Low-Cycle Unified Creep-Fatigue Formulation

Background—Creep-fatigue behavior is identified as the incorporated effects of fatigue and creep. One class of constitutive-based models attempts to evaluate creep and fatigue separately, but the interaction of fatigue and creep is neglected. Other models treat the damage as a single component, but the complex numerical structures that result are inconvenient for engineering application. The models derived through a curve-fitting method avoid these problems. However, the method of curving fitting cannot translate the numerical formulation to underlying physical mechanisms. Need—Therefore, there is a need to develop a new creep-fatigue formulation for metal that accommodates all relevant variables and where the relationships between them are consistent with physical mechanisms of fatigue and creep. Method—In the present work, the main dependencies and relationships for the unified creep-fatigue equation were presented through exploring what the literature says about the mechanisms. Outcomes—This shows that temperature, cyclic time and grain size have significant influences on creep-fatigue behavior, and the relationships between them (such as linear relation, logarithmical relation and power-law relation) are consistent with phenomena of diffusion creep and crack growth. Significantly, the numerical form of “1 − x” is presented to show the consumption of creep effect on fatigue capacity, and the introduction of the reference condition gives the threshold of creep effect. Originality—By this means, the unified creep-fatigue equation is linked to physical phenomena, where the influence of different dependencies on creep fatigue was explored and relationships shown in this equation were investigated in a microstructural level. Particularly, a physical explanation of the grain-size exponent via consideration of crack-growth planes was proposed.