Influence of pipe diffusion of defects on the amplitude dependence of hysteresis internal friction

Abstract

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.

Determination of Dislocation Structure Parameters from Data on the Amplitude Dependence of Internal Friction

“…For small E , the attenuation ration a,, does not depend on the amplitude, for large amplitude o((c0) is approaching an amplitude independent value, a02 ' ao1. Table 1 The ascending branch of hysteretic dislocation IF is described by the Granato-Liicke formula [l] which follows from (2) when Eo/T 4 1 [7]. Fig.…”

“…The pipe diffusion of weak pinning points leads to a shift of the I F peak into the region of smaller e0 values and to a decrease in AH, [7]. This process can be taken into consideration by using formulae cited in [7] and one can find the functions a, (No, l), pl(NO, t), and yl (No, t) which are analogous to (7), (8), (10) and take into consideration the exciting time t.…”

“…The amplitude dependence of hysteretic IF is given by [7] where Here G is the shear modulus, b is the modulus of the Burgers vector, A is the density of dislocations, L is the distance between the major pinning points, No is the number of weak pinning points on the segment L , I, = L /(No + 1) is the mean distance between the pinning points, f, is the maximum value of the binding force between the point defect and a dislocation, C is the line tension of a dislocation. The function Po(z) determines the probability of breakaway of the dislocation segment L from weak pinning points under the influence of an external stress (T = zTC.…”

“…With No > 6 D0(z) x Po(z) can be used. The function A,(zo)/Al has a maximum whose coordinates A,,/A, and z , depend only on No [7]. The numerical calculations which were made by formula (2) for different N o made it possible to find the dependence of coordinat,es of the maximum on No, Em z, = -= tll ( N o ) , r (7) The plots of the functions tll(No) and P1(No) are shown in Fig.…”

“…1 (curve 3). Thus, by determining the parameters a, E,, and AH, from experiments and using formula (12) one can find N o and after that determine r and A , by (7), (8) (or (9)). It should be noted that only the descending branch of IF as well as the coordinates of the maximum point If the total damping decrement A(&,) is presented by (l), then AD(c0) can be found by subtracting the hysteretic IF AH(&,) calculated by means of formula (2) with the known values No, I', and A , from the experimentally obtained dependence A(c0).…”