Amplitude dependent internal friction under torsion

Abstract

The Granato-Lucke expression for the strain amplitude dependent damping capacity due to stress induced unpinning of dislocation, is modified for the case of torsion. The final expression is in the form of an integral which can be evaluated only numerically. A differential equation and an integral equation involving the mean damping capacity and the maximum strain amplitude have been derived, which enable straight line plots and evaluation of the G-L parameters from them. With suitable examples it has been shown that the pinning point density is exaggerated by a factor of 1.3 when uniform strain amplitude is assumed. Numerical evaluation of the integral has been made using Simpson's Rule for different ε₀. Plots of the mean damping capacity \^-gD and \^-gD/ε₀ⁿ vs ε₀, have been made for different n values; all of which show maxima. It has been shown that the G-L parameters can be calculated from the positions of the maxima.