Theory of Damping due to Thermally Assisted Unpinning of Dislocations

By algebraic methods, this paper obtains expressions for the decrement and modulus defect due to the breakaway of a dislocation from a row of equally spaced pinning points, using expressions for the activation energy given in an earlier paper. The model is that of Teutonico, Granato, and Lücke, but incorporating a pinning force of general shape. The plane, representing the complete range of values of temperature T and stress amplitude σ 0 , is found to consist of five regions (A to E) of qualitatively different behavior. In regions B, C, and D, breakaway (from the whole row) is activated at a single pin, as in the Granato–Lücke model; in A and E, breakaway is activated over a group of several pins. In A and B, few of the dislocations break away during a stress cycle; in C and E, nearly all do. As one moves from the "few-all" boundary into a "few" region (A or B) by decreasing T or σ 0 , the decrement decreases rapidly in an exponential fashion. As one moves into an "all" region (C or E), it decreases, but not rapidly. For [Formula: see text] (short loops), only two regions, A and E, exist; here, β = L c U 0 /Cr 2 , where L c is the distance between pins, U 0 is the maximum binding energy between a dislocation and a pin, C is the tension of the dislocation, and the pinning force has its maximum at a displacement of order r, the "range". Region D differs from the other regions in that there the activation energy for unpinning remains effectively constant during the cycle; the theoretical damping peak of Koiwa and Hasiguti lies in D. Region D exists only when [Formula: see text] (very long loops); here, ν t is the effective attack frequency for unpinning, ω is the angular frequency of the applied stress, and the pinning force varies as y −γ−1 at large displacements y. The peak decrement, which is constant along the "few-all" boundary except near region D, drops by a factor of 2.5 when D is entered. All the boundaries between the five regions are obtained. Within each region, expressions for the decrement and modulus defect are given, which are accurate at least in limiting cases; stresses near the mechanical breakaway stress are also discussed. Generalized forms of these expressions are also given, applying to a class of damping mechanisms possessing symmetry of the breakaway type. The theory is related to experimental results of Hutchison and Rogers, and Koiwa and Hasiguti.