13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Here, r is the distance between two atoms; D, α, and r0 are controllable parameters and are closely related to the cohesive energy, elastic moduli, and lattice constant, respectively. Moreover, to introduce the cut-off distance, rc, φ(r) is modified into the shifted-force potential φs(r) as follows: s(r)= (r) − (rc) − r −rc d dr rc , r ≤ rc 0 , r > rc (2) Here, we set rc to 0.6 nm. It has been shown that the dimensionless value of µb/γs can roughly determine the inherent mechanical properties of single-phase materials, i.e., ductile or brittle properties [3]. Here, µ, b, and γs are the shear modulus, Burgers vector, and surface energy, respectively. If µb/γs is greater than 10, the material generally exhibits brittle properties. On the other hand, if µb/γs is smaller than 10, the material shows ductile deformation. There are two physical descriptions for the threshold value of µb/γs. One is the relationship between the ideal tensile strength and ideal shear strength, and the other is the relationship between the stress intensity factors for brittle cleavage and dislocation nucleation from the crack tip. Table 1 shows the material parameters for two designed virtual materials. The dimensionless values of µb/γs are 6.5 for the virtual material “M-D” and 17.7 for “M-B.” Therefore, we can consider the M-D material as a ductile phase and the M-B material as a brittle phase. To simplify the mechanical phenomena around the interface between the brittle and ductile phases, we set the same value for the lattice constant of each model; it is not necessary to consider the lattice mismatch influence. Table 1. Parameters of designed virtual materials with ductile and brittle properties. 2.2. Mechanical Properties of Virtual Materials To confirm the mechanical properties of the single-phase material described by the designed Morse potential, tensile deformation tests were performed at a strain rate of 4 × 108 1/s and 10 K. Figure 1(a) shows stress–strain curves of the two designed virtual materials, M-B and M-D. Defects in the form of micro-cracks are initially introduced into each material by removing three atoms from the perfect structure. The number of micro-cracks is 1 for M-B and 12 for M-D. After relaxation before tensile loading, all initial cracks of M-D changed into dislocation dipoles. This transition should be closely related to the large value of the surface energy of M-D. In the case of M-B, the micro-crack begins to propagate at the peak stress and M-B shows the brittle fracture mode with small elongation. On the other hand, in the case of M-D, yielding occurs by dislocations moving from the dislocation dipoles, and then, M-D displays ductile properties with large elongation. Therefore, it
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