Dislocation Structure Evolution in Thin Single Crystal Plates Under Cyclic Loading
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ABSTRACT The effect of cyclic uniaxial loading applied to surfaces of thin single crystal plates on dislocation structure is analyzed analytically and numerically. This work investigates detailed changes in dislocation structure near surfaces and in size and concentration of dislocation loops inside the crystal. The results may be helpful in choosing the optimum regime for material processing and in predicting material properties.
INTRODUCTION It was shown in [1-3] that thin crystal plates under cyclic uniaxial compression or tension have hysteresis effects of under- and over-saturation of samples with vacancies, which significantly influence the dislocation structure. There are two types of changes in dislocation structure: 1. Appearance and growth or dissolution and disappearance of dislocation loops. 2. Overcreeping of edge dislocations. Both effects are connected with the interaction of dislocations with vacancies that move from sources or to drains with cyclic loading. For calculational purposes, only thin single crystal plates with front surface area far exceeding the cross-sectional area are considered. In this case it is possible to disregard the diffusion of vacancies from (or to) the lateral surfaces, so that the problem becomes one-dimensional.
THEORY AND MODEL OF THE PROCESS Cyclic uniaxial loading with uniform surface distribution of compression or tension is applied to front surfaces of the sample. Undersaturation of a crystal with vacancies appears under tension-unloading, vacancy loops in the crystal become the sources of vacancies, which leads to dissolution of the loops. But as soon as loading stops, over- saturation of sample with vacancies appears, which leads to dislocation loops' growth and even new dislocation loops can appear in places of substantial over-saturation. During the compression stage, the appearance and growth of dislocation loops takes place. On the other hand, unloading is observed to cause dissolution and subsequent disappearance of loops. The process of dislocation loops growth and dissolution can be described by the following equation, which can be solved numerically [1,2]: aR at
21rDAc bln(8R/ro)
)
DGV(In(R/ro)+ao) + 2(l-v)RkTln(8R/r 0 )
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Mat. Res. Soc. Symp. Proc. Vol. 399 ©1996 Materials Research Society
where R is the radius of the loop, Ac = c - C, where c - current concentration of vacancies, C,-equilibrium concentration of vacancies, variables R, C, c depend on time t and coordinate x, which is the distance from the front surface. D-coefficient of vacancies diffusion, G - displacement modulus, k -Boltzmann constant, U-Poisson's ratio, Va-weight of the atom, b- module of Burger's vector, r0-radius of the loop nucleus, a =2.2 We consider only isothermal processes with absolute temperature T.
THE RESULTS OF NUMERICAL MODELING Numerical modeling shows, that in cyclic tension-unloading process the dissolution of the dislocation loops occurs. The radius of the dislocation loop decreases monotonously after each cycle, and the more intense this decrease is, the f
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