5. Basics of Model of Random Fracture Resistance of Grain Boundaries

In this chapter elucidates modeling and simulation methods of one-dimensional and three-dimensional models of random fracture resistance of grain boundaries for an initiation and propagation of multiple small cracks in creep-fatigue. In the one-dimensional model of random fracture resistance of grain boundaries, the concept of the model is explained, and it is shown that the one-dimensional model can be used to simulate the behavior of small cracks from the early to mid-life. The three-dimensional model incorporates both the microstructural sensitivity of small cracks and the interaction of initiation and propagation of multiple cracks, and thus, enables the simulation up to the later stage of the life, which cannot be conducted by the one-dimensional model. The crack initiation and propagation under a slow-tensile fast-compressive creep-fatigue at 923 K (650 °C) in a vacuum were simulated using the heat-resistant steel with the grain boundaries which were created based on a nucleation-growth model and subsequently whose fracture resistance was set by the model of random fracture resistance. Consequently, it became evident that the experimental results on the crack density, angular distribution of the initiated crack, crack length distribution, and crack growth rate were well simulated.