Application of MD-Based Study of Fracture Analysis
The fracture of materials necessarily involves breaking of the atomic bonds in the material. Hence, the atomistic-scale study of the fracture behavior of the material is vital to characterize the toughness of the material and understand the fracture mechanism associated with it. In this regard, MD has proven to be quite useful in accurate modeling and estimation of cohesive zone and the identification of the fracture mechanism at the interface and the ductile fracture behavior using non-linear fracture mechanics (J-integral and crack tip opening displacement [CTOD]). Apart from accurate estimation of the local stress in the near vicinity of the crack, the atomistic simulation also aids in explaining the effects of various parameters such as temperature, crystallographic loading orientation, strain rate, initial nanovoid volume fraction, and geometry of the structural changes of the material leading to failure of the material. In this section, we have discussed briefly some of the atomistic aspects of the fracture behavior of the material (performed via MD simulation).
Role of Crack Tip Dislocations on the Crack Propagation Behavior of Metals
The orientation of the materials with respect to the crack plays a vital role in determining the plasticity of the material. The crack propagation behavior of the SC metallic systems with different orientations has been presented in Figure 7.13 . In case of orientation I, that is, the crack propagation, can be divided into two stages, and the crack propagation takes place in the <1 0 0> direction. In the first stage, crack propagation is rapid, the crack tip remains sharp, and no dislocation emissions are witnessed in the crack tip, indicating brittle behavior. However, in the second stage, partial dislocation emission eventuates, thereby blunting the crack shape and generating stacking faults, thus transitioning from brittle to ductile fracture behavior. As a result, the stiffness of the material also drops in the second stage as compared with the first stage. However,
FIGURE 7.13 Three orientations considered for the crack propagation behavior in SC Ni under Mode I loading: (a) Orientation I, (b) orientation II, and (c) orientation III.
in case of orientation II dislocation, emission occurs faster than the crack propagation, thereby leading to plastic behavior right from the beginning of the deformation process, leading to the blunting of the crack. Dislocation motion is more active in case of blunted tip as compared with the sharp tip. Extensive formation of stacking faults in case of orientation II leads to an interaction of stacking faults; as a result, the atoms corresponding to the intersection of stacking faults serve as a potential site for void nucleation. Under such conditions, in addition to atomic bond cleavage, void nucleation growth and coalescence also play a crucial role in the damage mechanism of the SC metallic system. Such observations are generally witnessed in case of ductile materials. However, in case of orientation III, twin partial dislocation emission is preceding to crack propagation. The twin partial dislocation has identical Burgers vector with the Shockley partial dislocation a/6(ll2). Dissimilar Shockley partial which leaves the stacking faults behind and an array of twin partial dislocations will form a micro twin behind, typically with several layers of (1 1 1) plane atoms. As opposed to dislocation, the formation of micro twins does not impede the crack propagation effectively. In a nutshell, the emission of dislocations at the crack tip will result in blunting of the crack, thereby slowing down the crack propagation process. However, the formation of micro twins does not have any such beneficial effect on the delaying of the crack propagation. The dislocation process greatly influences the brittle versus ductile behavior of materials. The nucleation of dislocation can be marked as the onset of brittle-to-ductile transition for metallic system, whereas for covalent materials, ductility is governed by the mobility of the dislocations.
The crack deformation mode is highly influenced by the crystallographic orientation of the crack. The crystallographic orientation of a crack can be defined by two parameters, that is, the inclination angle of the slip plane relative to the crack plane (0) and the twist angle of the slip plane (
FIGURE 7.15 Stress-strain curve for (a) SC Cu, (b) SC Al (100)  edge cracks with different lengths of cracks under Mode I loading conditions. (From Cui, C.B., and Beom, H.G.. Mater. Sci. Eng.: A, 609, 102-109, 2014. With permission.)
At 0 K, the nucleation of dislocation occurs only when the local stress overcomes a critical value, followed by a sudden burst of dislocation activities; therefore, a sharp brittle-to-ductile transition eventuates. However, as the temperature increases, the energy barrier for the nucleation of dislocation can be overcome by thermal fluctuations, thereby imparting crack tip plasticity more gradually . The SC Cu initially exhibits sharp crack with brittle crack propagation behavior, but after local threshold stress is achieved, a sharp brittle-to-ductile transition of the crack propagation occurs. In addition, the failure feature of Cu exhibits brittle behavior as the crack length of the edge cracks increases, as shown in Figure 7.15a . Although for short edge cracks, the dislocation emission eventuates prior to crack propagation, thereby blunting and imparting plasticity to the crack tip. However, attributed to large intrinsic stacking fault in Al, its directional bonding dislocations are nucleated right in the initial stages of loaded conditions, even at 0 K, eventually resulting in the formation of avalanche dislocation loops at the crack tip, thereby exhibiting crack tip plasticity even in the initial stages of crack deformation process. Moreover, lower vacancy-formation and surface energies associated with Al  result in extensive plastic crack deformation behavior of Al, as shown in Figure 7.15b.