Strain Amplitude Dependent Damping Research Articles

A hysteretic loop phenomenon at strain amplitude dependent damping curves of pre-strained pure Mg during cyclic vibration

In this study, twins were introduced into pure Mg by pre-deformation, the strain amplitude dependent damping in pre-strained pure magnesium was investigated using cyclic vibration. The strain amplitude dependent damping curve exhibited a hysteretic loop as the strain amplitude was cycled. The damping value was greater during the high strain amplitude regime when the strain amplitude increased than when strain amplitude decreased. For the low strain amplitude regime, the opposite trend was observed. The results point to the damping behavior transitions between the two regimes occurring at a specific strain amplitude, increasing commensurately with increased pre-strain. This hysteretic loop phenomenon is attributed to the difference in mechanical energy consumed by the motion of the twin boundaries during cyclic vibration. The hysteretic loop indicates that twin dampening already exists. Therefore, the strain amplitude value of the intersection may be used as a reference parameter to detect twin damping.

Anelastic and Microplastic Damping of an Mg–Zn–Y–Al Alloy

In this study, the Mg97Zn1Y2–Al alloy was selected as a high damping material, anelastic and microplastic damping were analyzed by studying strain amplitude-dependent damping curves of the alloy. The C1 and C2 values of the Granato–Lucke (G–L) model, the theoretical basis of anelastic damping, can be calculated for each alloy, then, the corresponding numbers of strong and weak pinners are deduced. However, since the occurrence of microplastic damping in a high strain amplitude cannot be explained by the G–L model, a new microplastic damping theory was introduced, by comparing the activation volume of the material dislocation slip, the microplastic damping capacity of the Mg97Zn1Y2–xwt%Al (x = 0.3, 1, 3) alloys at the microplastic stage are compared. The elastic and plastic deformation of the materials could be sensitively reflected by studying the damping behavior of these two stages.

Simultaneously enhanced mechanical and damping properties of Mg–Zn–Y alloys reinforced with LPSO phase

The microstructure, mechanical properties and damping capacities of Mg-Zn-Y alloys were investigated and compared systematically. The results showed that strength and damping of the alloy were increasing markedly with the increase of the volume fraction of long period stacking ordered (LPSO) phase (8%, 16%, 32%, 64%, respectively) on the whole. The corporate effect of LPSO phase and solid solution atoms was beneficial to the strengths. The Mg-1.36Zn-2.28Y can be classified as high damping metals (Q−1≧0.01) at strain amplitudes surpassing 1×10-3. With increasing of the LPSO phase, the critical strain amplitudes of alloys gradually decreased so that alloys can break away from pinning points more easily, thus, achieving a more superior damping performance. In addition, the strain amplitude-independent damping and strain amplitude-dependent damping of the Mg–Zn–Y alloys both increased. The damping capacities of the alloys cannot be explained by the Granato–Lücke theory exclusively.

Effect of long period stacking ordered structure on the damping capacities of Mg–Ni–Y alloys

Abstract The microstructure and damping capacities of the Mg–Ni–Y alloys were researched and compared synthetically. This study showed that long period stacking ordered (LPSO) structures were conducive to the overall damping capacities. Mg–8.51%Ni–15.25%Y can be classified as high damping metals ( Q −1 ≥0.1) at strains exceeding 1×10 −3 . With increased LPSO phase, the critical strain amplitudes of alloys gradually decreased so that the alloys could more easily break away from pinning. In addition, the strain amplitude-independent damping and strain amplitude-dependent damping of the Mg–Ni–Y alloys both increased. The damping capacities of the alloys cannot be explained by the Granato–Lucke theory alone.

Microstructures and Damping Capacity of Mg-6Zn-0.5Zr Alloy

The dynamic mechanical analyzer (DMA) was applied to investigate the damping properties of Mg-6Zn-0.6Zr alloys. The results show that the as-cast Mg-6Zn-0.6Zr alloy exhibits higher strain amplitude independent damping performance than that of as-homogenized. The strain amplitude dependent damping of the as-homogenized has the best damping performance with the strain amplitude from 3×10-5 to 6×10-4, and the as-extruded is the lowest. When the strain amplitude exceeded 6×10-4, the as-extruded has the best damping capacity all the time within the experimental strain amplitude, and all the alloys reach the high damping capacity. Two critical strain amplitude points were detected in the alloy as-extruded and as-homogenized. The damping peak value is 0.0192 with the strain amplitude of 1.5×10-3 presented in the alloy as-extruded.

High damping capacities of Mg-Cu based alloys

The dynamic mechanical analyzer (DMA) was applied to investigate the damping properties of Mg-Cu based alloys. The results show that the as-cast hypoeutectic Mg-Cu binary alloys exhibit ultra-high damping capacities, while the eutectic Mg-Cu alloy exhibits low damping capacity. The strain amplitude dependent damping performance reveals that the dislocation damping mainly dominates in Mg-Cu alloys. Furthermore, the influence of eutectic phase on damping mechanisms of Mg-Cu binary alloys was discussed in detail and the effect of Si addition on the damping of Mg-1%Cu based alloy was also reported. Two damping peaks are observed on the temperature dependent spectrum of Mg-Cu based alloys. One is located at room temperature, which is dislocation related peak; and the other is located at moderate temperature, which is caused by the grain boundary sliding.

A study of the effect of Y on the mechanical properties, damping properties of high damping Mg–0.6%Zr based alloys

The effect of Y content on the mechanical properties, damping properties of high damping Mg–0.6%Zr based alloys was carried out both using tensile testing and dynamic mechanical analysis (DMA) methods. The results show that the mechanical properties of the high damping Mg–0.6%Zr alloy can be significantly improved by Y addition. The as-cast Mg–0.6%Zr–0.5%Y alloy, with excellent mechanical properties, σ b = 160 MPa, σ 0.2 = 69 MPa, δ = 14.5%, and good damping capacities, tan ϕ = 0.01 at ɛ = 3.2E−5 or even better damping capacity than Mg–0.6%Zr at high strain amplitude, could be considered a promising damping magnesium alloy. In addition, the strain amplitude dependent damping capacities of the alloys were discussed in detail.

Precipitation and responding damping behavior of heat-treated AZ31 magnesium alloy

Microstructure observation and dynamic mechanical analysis were carried out to investigate the precipitation and responding damping behaviors of AZ31 magnesium alloy. All the strain amplitude-dependent damping curves of the aged alloys are located between the curves of solutionized and as-cast alloys, although they have different critical strain amplitudes. The G-L theory is employed to explain the damping mechanism involving the interaction between the dislocation and the precipitated phase. In addition, a damping peak is observed at temperatures close to 330 °C for AZ31 magnesium alloy, which is related to the β-Mg 17 Al 12 phase dissolution.

Effect of eutectic phase on damping and mechanical properties of as-cast Mg-Ni hypoeutectic alloys

Dynamic mechanical analysis (DMA) was applied to systematically investigate the low frequency damping properties of as-cast hypoeutectic Mg-Ni alloys. The results show that the as-cast hypoeutectic Mg-Ni alloys exhibit high damping capacities. The strain amplitude dependent damping curve has its own special characteristic, in which the damping is strongly related to the strain amplitude. The effect of the eutectic phase on damping and the mechanical properties of as-cast hypoeutectic Mg-Ni alloys were also discussed in detail.

Application of G-L Dislocation Model in Low Frequency Damping Capacities of AZ91D and SiCw/AZ91D Composites

The low frequency damping capacities of commercial cast AZ91D, squeeze cast AZ91D alloy and SiCw/AZ91D composite were studied using dynamic mechanical analyzer (DMA). The obtained strain amplitude dependent damping could be divided into two regions. In the region of small strain amplitude, the damping capacity was independent of the amplitude. While at high strain region, the damping capacity increased rapidly with increasing of strain amplitude. The G-L dislocation model was used to explain the damping capacity, and the differences of the distance between the weak and strong pinning points were discussed. The microstructures of the alloys and composites were observed and coincided with the analysis results according to G-L dislocation model.

Damage in fiber reinforced and unreinforced AZ91 studied by internal friction

The influence of load cycling on the amplitude dependent damping and possible causes of fatigue in unreinforced and Saffil fibre reinforced magnesium alloy AZ91 was investigated. The unreinforced AZ91 alloy was investigated in the as cast and in the homogenized state. For an increasing number of cycles N, the amplitude dependent component of the logarithmic decrement decreases until a critical N (= N C). For higher cycle numbers ( N > N C), a maximum in the strain amplitude dependent damping curves increases and shifts to lower strain amplitudes with increasing N, which is attributed to the growth of cracks. These findings are consistent with the decrease of the resonant frequency during crack growth.

Amplitude-dependent damping of PSZ with sinter defects

Samples of 3Y-PSZ (with yttria partially stabilized zirconia) ceramics were produced in a form of rectangular bar by uniaxial pressing with subsequent sintering and grinding. In some samples crack-type defects were induced under the larger surfaces by green-body pressing with very high pressure. The strain amplitude-dependent damping of these samples was measured in a single cantilever arrangement as the logarithmic decrement of free decaying bending vibrations. An increase of damping with strain amplitude was found. Compared to the samples without induced defects the samples with induced defects showed higher damping for all strain amplitudes and their damping increases strongly with increasing strain amplitude. Moreover, in the samples with induced defects, the damping for bending vibrations perpendicular to the defect-affected surfaces is much lower than parallel to those. Damping of the samples could be increased by bending fatigue performed in the apparatus by which the damping was measured. After a heat treatment up to 300 °C a decrease of damping was found which could possibly indicate healing of cracks. The results demonstrate that the measurement of internal friction is a powerful tool for detection of typical flaws such as pressing or sintering defects or cracks and can be used for non-destructive testing of ceramics.

Mechanical Damping and Dynamic Modulus Measurements in Continuous Fiber-Reinforced Composite Materials: Al/Al2O3 and Al/W

AbstractMeasurements of mechanical damping, or internal friction (Q−1), and dynamic Young's modulus (E) have been made near 80 kHz and at strain amplitudes (ε) in the range of 10−8 to 10−4 on small specimens of the following two continuous fiber-reinforced metal matrix composites (MMCs): 6061 aluminum reinforced with alumina (Al/A12O3) and 6061 aluminum reinforced with tungsten (AI/W). Baseline experiments were also performed on 99.999% aluminum (pure Al) for comparison puposes. The temperature (T) dependence of modulus up to 475°C was determined for AI/A12O3 and pure Al. The rate of modulus decrease with increasing temperature for AI/A12O3 and Al was the same, that is, dE/dT was essentially the same for both materials. Thus, the reduction in modulus observed for the Al/Al2O3 was attributed to the reduction in modulus of the Al matrix and not that of the Al2O3 fibers. The strain amplitude dependence of damping was examined for all three materials. The pure Al exhibited classical dislocation damping behavior with strain amplitude dependent damping starting at a strain of 2 × 10−5. The Al/Al2O3 specimens showed only mild dependence of damping on strain amplitude starting at strains near 10−5. The AI/W exhibited significant amplitude dependence of damping starting at strains of 2 × 10−6 with the fiber diameter being a major factor in determining the damping behavior. The Q−1 versus ε data for Al/Al2O3, when analyzed in terms of the Granato-Lücke (GL) theory for dislocation damping, yielded minor pinning lengths of dislocations near 10−8 m and mobile dislocation densities near 1011 m−2. The same analysis for the Al/W data gave values near 10−8 m for the minor pinning lengths and 1012 M−2 for the dislocation density. Relative to the results for pure Al, the minor pinning lengths for Al/Al2O3 and AL/W are comparable (10−8 m for pure Al), but the dislocation densities are much higher (109 m−2 found in the pure Al). The relatively high dislocation densities calculated for these aluminum matrix MMCs agree with previous findings of other researchers and may be associated with the fiber/matrix interface.

Amplitude dependent internal friction under torsion

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 ε 0. Plots of the mean damping capacity \\ ̄ gD and \\ ̄ gD ε 0 n vs ε 0, 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.

Instrumentation and techniques for the measurement of low frequency internal friction

An instrumentation system for measuring the amplitude and period of oscillation of low frequency internal friction pendula is described. It can be constructed from commercially available operational amplifiers and functional modules and includes a small computer to record data. It can be used to provide an amplitude feedback signal for a pendulum amplitude control system. Measurement techniques and estimation of errors are discussed, with particular emphasis on the measurement of strain amplitude dependent damping. A method of correcting low frequency strain amplitude dependent damping for the strain distribution in the specimen is outlined.

The strain amplitude dependent damping in iron

Abstract The strain amplitude dependent damping in pure polycrystalline iron has been determined as a function of grain size at a frequency of approximately 1 HZ, and has been shown to consist of two stages. At low strain amplitudes the damping follows the Granato–Lucke law but at higher strain amplitudes the damping can be explained in terms of the model postulated by Peguin, Perez and Gobin (1967). The strain amplitude at which stage one gives way to stage two decreases with increasing grain size. From an analysis of the second stage of damping an activation volume of 1·3 × 10−21 cm3 has been calculated.

The strain amplitude damping in metals

The Granato-Lücke theory of strain amplitude dependent damping is only applicable over a limited range of strain amplitude, which is dependent on the material. In 1967 Peguin and co-workers developed a model to explain the damping at higher strain amplitudes. This note shows how their model can be applied to the results of Hutchison and Rogers (in 1962), Niblett and Wilks (in 1959) and Caswell (in 1958). The results are in agreement with theory, and values of activation volumes agree with the ideas for the initiation of plastic flow.