In this paper, a superposition method is proposed to compute the stress field due to a dislocation loop in a heterogeneous thin film–substrate system. The problem is decomposed into two sub-problems: the stresses due to a dislocation loop in an infinitely extended bi-material space and the stresses induced by equivalent tractions on the free surface. The area-integral expression of the former is further reformulated in a line-integral form. Taking advantage of the Galerkin potential method and the Fourier transform, this paper then derives the elastic field in a heterogeneous thin film–substrate system due to surface loading. Numerical results demonstrate that both the free surface and the material heterogeneity have great influence on the stress field due to a dislocation loop.
We use charge exchange recombination spectroscopy to make the first localized measurements of impurity ion flow velocity profiles in the reversed field pinch. Measurements in improved confinement plasmas reveal an intrinsic flow profile that is peaked on the axis and mostly parallel to the equilibrium magnetic field. The toroidal flow decreases in time at off-axis locations where tearing modes are resonant, giving rise to a highly sheared flow profile near the axis. The tearing mode phase velocity correlates strongly with toroidal flow near the resonant surface and weakly with flow in other locations, providing an opportunity to verify the commonly held assumption that the plasma and mode move together at the resonant surface. Mechanisms for the observed momentum loss during the improved confinement period are evaluated, and it is found that eddy currents in the conducting shell caused by the rotation of the dominant tearing mode dominate over other losses.
Taking advantage of the generalized Galerkin potential function and the Fourier transform, the research presented in this paper first derives the Green's function for a multilayered heterogeneous thin film system. The area-integral expression for the stresses induced by a dislocation loop in the heterogeneous thin film system is formulated into a line-integral representation on the basis of a corollary of the Green's theorem, which makes the accurate calculation of the dislocation stress field feasible and practical. A decomposition scheme is further presented to address the numerical singularity issue encountered in the calculation of dislocation stresses on the slip plane. Numerical results demonstrate that the layered heterogeneity of materials has considerable influence on the stress field induced by dislocation loops.
Dislocation dynamics has been an intensive research subject in materials science and engineering due to the significant roles it plays in plastic deformation and the hardening of metals, fracture mechanics, and the fabrication of semiconductor thin films. However, a long-standing problem from the three-dimensional dislocation dynamics is that the motion and interaction of dislocation loops heavily depend on the loop-segment sizes, which substantially reduces the accuracy of simulation. We herein propose a new three-dimensional dislocation dynamics model together with its physical background. The proposed model incorporates the inherent interactions among differential dislocation segments. The simulation results on motion of Frank–Read sources demonstrate that the proposed model can resolve the paradoxical segment-dependent phenomenon in dislocation dynamics.
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