Amplitude-dependent decrement to modulus defect ratio in breakaway models of dislocation hysteresis

The ratio r of the amplitude-dependent decrement delta(h) to the amplitude-dependent modulus defect Delta M/M has been analysed within the framework of theories of dislocation hysteresis based on the Granato-Lucke string model. For all variations of this model, two conclusions have been made: firstly, in the general case, r is a function of the vibrational amplitude sigma(o), but the value of r should not exceed two; secondly, the amplitude independence of r is the specific case of a power law with the same exponent n for both the decrement and the modulus defect: delta(h)=r(Delta M/M) proportional to sigma(0)(n). In this case, r is a function of n only. A relationship between r and n has been derived. For n < 6, r is shown to be less than unity. These theoretical requirements have been compared with the available experimental data. In the majority of cases, r is a constant; however, r > 1 while 1 < n < 4. The reasons for such disagreement are discussed.