Amplitude-dependent elastic-modulus defect in the main dislocation-hysteresis models

The amplitude-dependent defect of the elastic modulus has been calculated for the three main dislocation-hysteresis models: (i) breakaway hysteresis of Granato-Lücke, (ii) Davidenkov hysteresis, and (iii) friction hysteresis without restoring force (WRF). The ratio r of the amplitude-dependent decrement to the modulus defect has been considered for all three types of loops, and it is shown that, in a general case, r depends on the vibration amplitude. In the particular case of power-law amplitude dependences of the decrement and the modulus defect, r does not depend on amplitude and depends only on the exponent n . Expressions have been obtained for the r ( n ) dependence for the three hysteresis-loop types, and it is demonstrated that r can serve to identify the loop shape. A comparison of calculated curves with experimental data accumulated to date shows that most of them lie closer to the Davidenkov and WRF hystereses. An analysis has been made of the applicability of the secant modulus-defect approximation used to derive the dislocation strain from internal-friction measurements.