As for the nano-mechanical phase transformation, the five most important factors are the phase transformation temperature, cooling rate, cooling rate of previous heating cycles, rate of heating, and the phase transformation at zero load. According to the Shockley-Read-Hall (SRH) theory, laser was used to make plastic deformation to induce dislocation generation and subsequently device failure by manufactured cracks [40,41,42]. As far as crack initiation and development in GBM can be controlled, it will be an effective method to suppress device failure by mis-alignment during the manufacturing process. However, due to the wavelength limitation, the shrinking of the GBM in plastic deformation to induce the local structure variation is hard to achieve the dislocation absorption in the crack-initiation region. The crystal stress field was induced to absorb the generated dislocations from the substrate and the intact bulk region [43,44, 45]. The stress field not only affects the dislocation nucleation and growth process, but also avoids device failure.
The main aim of this study is to simulate the crack propagation in GBM, which can be considered as a probabilistic system and the crack is assumed to follow the first-order Markov random process (MORP). Therefore, the development of the crack follows the most likely gradient and the directional ratio is equivalent to the elemental probability of the first-order natural transition of the crack [46,47,48]. Using the combination of the Monte Carlo (MC) simulation and the atomistic simulation of the GBM, the MORP (MJO) can be successfully proposed to explain the effect of the structural variation on crack propagation. The minimum of the degree of misorientation is lower than the critical one for the crack to appear. d2c66b5586