The ratio of the amplitude-dependent decrement, to the amplitude-dependent modulus defect, was analyzed within the framework of theories of dislocation hysteresis which were based upon the Granato-Lücke string model. Two conclusions were drawn from all variations of this model. Firstly, in the general case, the ratio was a function of the vibrational amplitude but the value of the ratio was not expected to exceed two. Secondly, the amplitude independence of the ratio was a specific case of a power law having the same exponent for both the decrement and the modulus defect. In this case, the ratio was a function of the exponent alone. A relationship between the ratio and the exponent was derived such that, when the exponent was lower than 6, the ratio was less than unity. But in most experiments, the ratio was a constant greater than unity while the exponent was between 1 and 4.

Amplitude-Dependent Decrement to Modulus Defect Ratio in Breakaway Models of Dislocation Hysteresis. A.B.Lebedev: Philosophical Magazine A, 1996, 74[1], 137-50. See also: Journal de Physique IV, 1996, 6[8], 325-8