Extension of a Theory of Damping Due to Dislocations

Abstract

A theory of mechanical damping based on the model developed by Granato and LUcke was extended to small numbers of pinning points per network length and to streoses high enough to produce complete breakaway. The detailed response of a dislocation array to an applied stress was calculated using computer techniques in the low-frequency (kilocycle) range and both the viscous and hysteretic damping were computed. The amplitude dependence of the viscous and hysteretic damping was computed as a function of loop-length distribution, distribution of dislocation orientations, pinning point density, and stress distribution. The computation techniques allowed the,e calculations to be made without the usual mathematical approximations which are shown to result in a severe limitation on the previous analytic expressions. The results were applied to a discussion of the use of the damping theory to obtain parameters which describe the dislocation array and dislocation behavior. The time dependence of dislocation damping which results from diffusion of pins along the dislocation and in the lattice is discussed.

Effect of Ca addition on the damping capacity of Mg-Al-Zn casting alloys

“…However, in terms of protecting passengers or stored data from sudden accidents, impacts, noise, and irregular vibrations, the high damping characteristics of Mg alloys are also regarded as an important factor for their structural applications [4][5][6][7]. In the case of Mg alloys, it is generally difficult to obtain a combination of high strength and high damping capacity, because the damping mechanism is related to easy dislocation motion [8][9][10][11], whereas their hardening mechanisms usually involve grain refinement and dispersion of solutes, segregates, and secondary particles, which play a role in obstructing dislocation movement. In a previous work [12], it was reported that a small addition of Ca (~0.3%) to AM50 Mg alloy contributes to increasing its damping capacity.…”

Relationship between age-hardening by continuous precipitation and damping capacity in AZ91 alloy

“…According to the Granato-Lücke (G-L) theory [1][2][3][4], the total damping capacity (δ) can be divided into strain-amplitude-independent (δ o ) and strainamplitude-dependent (δ H ) damping components. The δ o component is attributed to the loss caused by forced vibrations of dislocation segments pinned by weak pinning points, such as vacancies and solute atoms.…”

“…The δ H values were obtained from the tan φ values according to the formula δ = π tan φ [22]. A linear relationship was established between ln( δ H × ε ) and 1/ ε , which demonstrates that the damping of the solutionised and aged AZ91 alloys occurred according to the dislocation damping mechanism [1-4]. In Figure 5, ln( C 1 ) and C 2 correspond to the y -axis intercept and the slope, respectively; the obtained C 1 and C 2 values are listed in Table 1.…”

“…It is well accepted that achieving a combination of high strength and high damping capacity of Mg alloys is difficult, because their damping mechanism is based on easy dislocation motion [1][2][3][4][5][6][7][8] whereas their hardening mechanisms generally involve grain refinement and dispersion of solutes, segregates, and precipitate particles, which play an important role in suppressing the movement of dislocations. AZ91 (Mg-9%Al-1%Zn-0.2%Mn) alloy is the most popular among various available cast Mg alloys, because it can offer beneficial combination of high room temperature mechanical properties, good die-castability, and high corrosion resistance [9][10][11][12].…”

Anelastic Relaxation in Crystalline Solids

“…division has some basis in theory, althoughas Trott and Birnbaum (1970) have emphasized, the amplitude independence of^breaks down with the onset of the disloca tion breakaway process that leads to the appearance of <^h.The first two sections deal with the theory and experiments related to <f>t, while the last two sections cover the same ground for <£h.…”