Fatigue crack growth characteristics of Fe and Ni under cyclic loading using a quasi-continuum method

A quasi-continuum (QC) method based on the embedded atom method (EAM) potential was employed to investigate the fatigue crack growth and expansion characteristics of single-crystal Fe and Ni under cyclic loading modes I and II. In particular, the crack growth and expansion characteristics of Fe and Ni under cyclic loading were evaluated in terms of atomic stress fields and force–distance curves. The simulation results indicated that under cyclic loading, the initially damaged area of the crack will coalesce again after compression or shear to the initial geometry leading to a strengthening of the material. If no coalescence appears, the crack spreads rapidly and the material breaks. Moreover, under the cyclic loading of shear at any orientation, the slip dislocation observed in the materials considerably affects the release of stress. Introduction When materials undergo cyclic loading, the growth of cracks in the material finally leads to fracture, which is referred to as fatigue. The fatigue behavior of structures is an important topic in fracture mechanics as fatigue failure is one of the major causes of accidents. Hence, it is imperative to investigate the fatigue cracking mechanism of nanocrystals for developing good, strong materials. Considerable attention has been focused on the investigation of the fatigue crack growth behavior in single crystals under cyclic loading using molecular dynamics (MD), which is an effective tool for analyzing the mechanical deformation and mechanical properties of materials at the microscopic scale [1-13]. For facecentered cubic (FCC) metallic systems, Wu et al. [10] have investigated the fatigue crack growth in single-crystal Ni under different cyclic loading regimes. They found that different crack propagation and stress distributions lead to changes in fatigue crack growth rates and crack opening displacements. Ma et al. [11] have examined the effect of orientation on the fatigue crack propagation in single-crystal iron under cyclic loading, leading to differences in the crack growth rates and slip directions. The plastic deformation and double slip in single-crystal Ni and Cu Beilstein J. Nanotechnol. 2018, 9, 1000–1014. 1001 under different loading orientations, including [111], [100], [110] and [101], have been reported by Potirniche et al. [12]. In addition, the fatigue crack growth of body-centered cubic (BCC) metallic systems under cyclic loading was analyzed by some MD simulations. Zhang et al. have examined the effect of the phase boundary on the fatigue crack propagation in an α/βiron biphasic system under cyclic tensile loading [13]. They found that the nucleation of new cracks typically appears at the phase boundary because of dislocation pile-ups. However, most of these studies using MD simulations have only focused on the fatigue fracture mechanisms. The relationship between the loading force and microstructure variation around the crack tip during the fatigue crack growth for BCCFe and FCC-Ni in different orientations has rarely been discussed simultaneously. In our previous study [14], the variation of the crack propagation in Fe and Ni during tensile processes with single orientation and different crack lengths and orientations is described. Hence, it is interesting to investigate the comparison of the crack growth behavior and slip system in Fe and Ni under a cyclic loading of tension or shear. To completely analyze the crack growth and expansion characteristics of single-crystal Fe and Ni, the quasi-continuum (QC) method as proposed by Miller and Tadmor [15], instead of the traditional MD method, was employed as its computational efficiency is considerably better than that of the MD method for large-scale materials [16-22]. The results were discussed in terms of the atomic stress field and force–distance curves. Methodology The QC method, which is a multiscale method that couples MD and the finite element method to analyze the mechanical characteristics of the material, was employed as the simulation method to examine the crack growth and expansion characteristics of single-crystal Fe and Ni under cyclic loading [19]. In the QC method, representative atoms are primarily used for calculation instead of all atoms, considerably decreasing the degrees of freedom and enhancing the simulation efficiency [14,19]. The energy calculation in the QC method is different from the other atomic calculation methods. In the system composed of N atoms without any external force, the total energy η(u) of the system can be expressed as follows [16]: