Formulae are obtained which describe the damping decrement of hysteresis dislocation internal friction with due account of pipe diffusion of mobile pinning points. The amplitude dependence of a damping decrement is described by a non‐monotoneous function which has maximum at some value of the applied stress amplitude. The asymptotic formulae are obtained for the damping decrement at low and high amplitudes. The pipe diffusion of pinning points results in the displacement of both the beginning of an amplitude dependence and the point of maximum into the region of low amplitudes. The question is dicsussed about the influence of a number of mobile pinning points and the energy of dislocation interaction with point defect on the amplitude dependence of internal friction.
A method is proposed of determination of the number of weak pinning points on a dislocation and other dislocation structure parameters, on the basis of the amplitude dependence of the internal friction maximum and some characteristics of the descending branch. Using the parameters obtained one can divide the dislocation internal friction into dynamic and hysteretic ones. The proposed method is used for the analysis of the internal friction peak in lead. The influence of various parameters on the position and height of the peak is discussed.
Formulae are obtained which make it possible to find the distribution function of dislocation loop lengths P(l, t) for a given concentration of mobile pinning points n(x, t). In explaining these formulae the equation of pipe diffusion in the external stress field σ(t) is obtained. The distribution of mobile pinning points in a constant external stress field is found. A study is made of the internal friction when the dislocation is under the action of constant, σ1 = const, and variable, σ2 = σ0 cos ωt, external stresses, while σ0 ≪ σ1. The dependence of damping decrement on time t and on stress σ1 is investigated.
By minimizing the Gibbs free energy of a crystal containing dislocations and impurity atoms, formulae are obtained which describe the equilibrium distribution of impurities pinning dislocations in a field of external stress σ It is shown that when stresses reach a critical value σc the number of impurity atoms pinning the dislocation diminishes sharply. After further increase in the value of the applied stress, the decrease in the number of minor points is accompanied by pipe diffusion. An expression for the distribution function of dislocation loop lengths is obtained when external stress is applied. An estimate is made of the contribution made to the distribution function by two mechanisms of redistribution of minor pinning points: impurity diffusion along the dislocations and exchange of impurity atoms between the dislocation core and the volume of the crystal.
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