A combined cyclic viscoplasticity and entropy generation approach for modelling fatigue crack growth behavior of a nickel-based superalloy at high temperature

•Finite element method for calculating material entropy generation based on the viscoplastic UMAT.•An entropy-based crack driving force was proposed within defined fracture process zone (FPZ).•A crack growth criterion based on cumulative entropy generation as crack grows a length of FPZ.•An entropy-based model was proposed to predict fatigue crack growth in GH4169 at high temperature. This paper developed an entropy-based approach to estimate the fatigue crack growth (FCG) behavior of GH4169 at high temperature. Firstly, systematic FCG experiments of GH4169 at 650 °C were conducted to obtain the experimental data. Then, a finite element analysis combined with Chaboche viscoplasticity and node release technology was developed to obtain cyclic stress–strain responses and entropy generation fields. Based on thermodynamic analysis, numerous discrete material elements as sub-systems were divided along the crack growth direction in simplified representative 2D middle section. Fracture process zone (FPZ) was defined equal to the size of discrete material elements (ρ) which can be determined by distribution of normal stress perpendicular to the crack plane. Subsequently, an effective cyclic entropy generation related to ρ was defined as the crack driving force. Effective cumulative entropy generation was calculated when crack increment was ρ and the results indicated that effective cumulative entropy generation float within a certain range. The average of all effective cumulative entropy generation values was defined as crack growth entropy. Finally, an entropy-based FCG rate model was established to estimate the FCG behavior of GH4169, and a good correlation between experimental results and model predictions are achieved for all the high temperature FCG tests.