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

The amplitude-dependent defect of the elastic modulus has been calculated f or the three main dislocation-hysteresis models: (i) breakaway hysteresis o f Granato-Lucke, (ii) Davidenkov hysteresis, and (iii) friction hysteresis without restoring force (WRF). The ratio r of the amplitude-dependent decre ment 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 ampli tude. In the particular case of power-law amplitude dependences of the decr ement and the modulus defect, r does not depend on amplitude and depends on ly on the exponent n. Expressions have been obtained for the r(n) dependenc e for the three hysteresis-loop types, and it is demonstrated that r can se rve to identify the loop shape. A comparison of calculated curves with expe rimental data accumulated to date shows that most of them lie closer to the Davidenkov and WRF hystereses. An analysis has been made of the applicabil ity of the secant modulus-defect approximation used to derive the dislocati on strain from internal-friction measurements. (C) 1999 American Institute of Physics. [S1063-7834(99)01807-9].