13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Monte Carlo Simulation of Fatigue Crack Initiation at Elevated Temperature Feifei He1,*, Cher Ming Tan1,2, Shuai Zhang1, Shuguang Cheng3 1 School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 2 SIMTech-NTU Joint Lab on Reliability, Singapore 3 School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798 * Corresponding author: ffhe@ntu.edu.sg Abstract In this paper, a novel way that simulated the micro-crack initiation due to void nucleation under thermal fatigue was proposed using the combination of finite element modeling and Monte Carlo method. A 3D model that simulated the dynamic void nucleation process was constructed using the commercial FEA software ANSYS. The strain and thermal energies of the model due to the applied loads at elevated temperature are calculated. After manually including the grain structures, surface and bonding energies, a number of vacancies were randomly generated and they moved and nucleated according to the energy distributions of the model. To consider the problem at microscopic scale while still maintaining acceptable accuracy, two models are constructed, namely a real-sized full model and a micro-scale sub-model that included the microstructure. The impurities and the residue stresses that may affect the void nucleation process were included in the sub-model as well. The simulation results showed that the vacancies tended to nucleate at the “weak spots”. Keywords Metal fatigue, micro-crack initiation, finite element modeling 1. Introduction Fatigue is the progressive damage to the material under cyclic loading and unloading. Cracks initiate at the stress concentration centers such as the surfaces, persistent slip bands or grain boundaries. The material eventually fractures even if the load is below its yield strength limit [1]. The initiation of the crack is due to the nucleation of tiny voids during the fatigue process [2]. Many simulation and experimental work had been conducted in the literature to study the crack initiation process using various approaches. For example, Piques et al. proposed a crack initiation model in 316L stainless steel based on the intergranular damage accumulation in the crack tip stress-strain field [3]. Nowack et al. studied the crack initiation and propagation of a Al 7475 sample under biaxial loading using the modified EVICD approach [4]. Haddar et al. developed a 2D model that simulated the crack initiation and shielding effects under thermal fatigue using the linear accumulation damage model [5]. Fine et al. predicted the fatigue crack initiation in single crystal iron and copper using the continuum models [6]. However, all the above-mentioned methods are modeled at macroscopic scale (i.e. mm scale). In fact, the voids inside the metal become visible at the size of 1 µm [7], which means the nucleation of the tiny voids start at microscopic scale. Such small crack is outside the regime of the conventional Paris’s law and thus the traditional lifetime prediction cannot be applied. Furthermore, at micrometer scale, the change in lattice orientation affects the anisotropic stress distributions near the grain boundaries and this effect should not be ignored. There is a number of reported works that studied the impact of microstructures on fatigue crack initiation. Vehoff et al. predicted the crack initiation at the grain boundary interfaces using the combination of the EBSD methods and the finite element stress analysis [8]. A microstructure sensitive crack nucleation criterion based on the local effective stresses and the non-local plastic strains and strain gradients was proposed by Kirane et al. [9]. Manonukul et al. developed a polycrystal plasticity finite element model that simulated the fatigue crack initiation based on the
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