Thermoelastic Internal Friction Research Articles

Special Issue on Multi-Scale Experimental Measurements in Mechanics

The development of micro/nano science and technology in recent years has created new challenges to the traditional macro-scale based experimental measurement. As such, multi-scale experimental measurements in mechanics have become a key area of research. Both the metrology and its applications have drawn great interest from researchers in related fields and have been progressing rapidly. It is our pleasure to present the nine papers in this special issue, entitled “Multi-Scale Experimental Measurements in Mechanics.” The special issue attempts to gather papers in the developments of multi-scale metrologies and related applications. It covers a range of topics to reflect the recent advances in optical measurement methods, non-destructive techniques, mechanical behavior characterization under different high resolution microscopes, fabrication techniques on micro-deformation sensor, etc. A brief introduction of these papers is as follows: In regard to multi-scale experiments including uniaxial tensile testing, in situRaman spectroscopy and scanning electron microscopy, Wei-Lin Deng et al. investigated the deformation in multi-scale and interfacial mechanical behavior of carbon nanotube fibers with multi-level structures. A twolevel interfacial mechanical model is presented to analyze interfacial bonding strengths of mesoscopic bundles and microscopic nanotubes. This study shows that properties of the multi-level interfaces are critical factors for determining fiber strength and toughness. With the aid of the atomic force microscopy (AFM) indentation system, Dongchuan Su et al. studied the near-surface elastic modulus via force-penetration curves acquired during indentation. An analysis algorithm is proposed based on the secant modulus method to extract the true penetration depths from force-displacement curves in AFM indentation testing. The results show that the AFM indentation method is capable of producing high spatial resolution maps of the elastic modulus with small forces and shallow indentations. MEMS sensors are typically fabricated out of materials that are mechanically sound at the microscale, but can be relatively poor electrical conductors. For this reason, areas ofMEMS are coated with various thin metal films to provide electrical pathways. These films, however, adversely alter resonant properties of a device. The paper by Pryputniewicz reviews a theoretical analysis of the effect that thermoelastic internal friction has on the Q-factor of microscale resonators and shows that the internal friction relating to TED is a fundamental damping mechanism in determination of quality of high-Q resonators over a range of operating conditions. As a method for measuring full-field out-of-plane displacement, projection moire provides high quality results with simple test setup. B. Gulker et al. implemented a projection moire system in low-velocity impact testing using an image processing program. Results from the projection moire experiments agree reasonably well with those obtained from the commonly used load cell method. The technique is further applied to composites with various microstructures. Y.R. Zhao et al. developed the electron grid fabricating technique by using a common scanning electron microscope (SEM). An error analysis for the multi-scanning grating was Y. Kang School of Mechanical Engineering, Tianjin University, Tianjin, China

Effect of Thin Films on Dynamic Performance of Resonating MEMS

Continued advances in microelectromechanical systems (MEMS) technology have led to development of a multitude of new sensors and their corresponding advanced applications. Great many of these sensors (e.g., microgyroscopes, accelerometers, biological, chemical, security, medical, etc.) rely on either sensing elements or elastic suspensions that resonate. Regardless of their applications, sensors are always designed to provide the most exact responses to the signals they are developed to detect and/or monitor. One way to quantify this exactness is to use the Quality factor (Q-factor). MEMS sensors are typically fabricated out of materials that are mechanically sound at the microscale, but can be relatively poor electrical conductors. For this reason, areas of MEMS are coated with various thin metal films to provide electrical pathways. These films, however, adversely alter resonant properties of a device. To facilitate our study, microcantilever configurations were selected to test influence that thin metal films have on resonators. This paper reviews a theoretical analysis of the effect that thermoelastic internal friction has on the Q-factor of microscale resonators and shows that the internal friction relating to TED is a fundamental damping mechanism in determination of quality of high-Q resonators over a range of operating conditions. Using silicon microcantilevers coated with aluminum films from 5 nm to 30 nm thick, on one as well as both sides, Q-factors were experimentally determined using the ring-down method. From the ring-down curve, the Q-factor of each microcantilever was determined. Experimental results show that as thickness of the aluminum film increases, Q-factor of the device decreases. Comparison of analytical and experimental results indicates good correlation, well within the limits based on uncertainty analysis. In addition, preliminary results also show a significant temperature dependence of the Q-factor of aluminum coated microcantilevers.

Thermal diffusivity measurement of 2.25Cr–1Mo steel with internal friction

In this work, the internal friction of 2.25Cr–1Mo steel measured on a dynamic mechanical analyzer (DMA) was used to evaluate its thermal diffusivity at elevated temperatures. With the dual cantilever clamp, the internal friction of 2.25Cr–1Mo steel at high temperatures was obtained, which was mainly composed of the thermoelastic relaxation with a peak of 15 Hz and the broad spectrum of relaxation processes especially at low frequencies. According to the deconvolution of these results, the thermoelastic internal friction of 2.25Cr–1Mo steel at high temperatures was achieved. Then, the thermal diffusivity of 2.25Cr–1Mo steel at high temperatures was quantitatively estimated, which confirmed the validity of present method.

Intrinsic damping, relaxation processes, and internal friction in vibrating systems.

Vibrations lose energy because of (1) coupling of the system to other systems or to the environment or of (2) intrinsic damping within the system itself. The present paper attempts to survey the current state of understanding for the principal mechanisms of the latter type with explicit physics (rather than purely phenomenological considerations), as simply as practical. Some mechanisms are evidenced in the attenuation of waves in unbounded homogeneous media, others are caused by the presence of boundaries. Some explicitly require quantum-mechanical concepts for their explanation, others can be explained in terms of classical mechanics and thermodynamics. Specific mechanisms that are to be discussed include those associated with thermal conductivity, grain and domain boundary effects, interstitial atom diffusion, relaxation by diffusion, inter-grain diffusion, micro-eddy current losses, hysteresis losses, thermoelastic internal friction, thermal damping associated with transverse vibrations of thin bodies, phonon-phonon interactions, phonon-electron interactions, internal fluids, and dislocations. The concept of relaxation often provides a convenient unified description. Rather than use the local averaged particle displacement as a sole description of the local vibrations, one considers additional local variables, loosely referred to as hidden variables. Each such variable, when disturbed, relaxes to its equilibrium value with a characteristic relaxation time.

Thermoelastic damping of the low density metals AZ91 and DISPAL

Light metals have high thermoelastic internal friction due to high coefficients of thermal expansion which has to be considered for various structural damping investigations. The thermoelastic effect of a powder metallurgically produced aluminium composite DISPAL™ and a magnesium casting alloy AZ91 (9 wt.% Al, 1 wt.% Zn) was investigated by measurements of the logarithmic decrement of free vibrations of bending beams. Because of inhomogenous stress distribution, a temperature gradient occurs between the compressed and the extended surface of the specimen, which leads to a transverse heat flow. This causes damping that is sensitive to the frequency of vibration. When the time of stress reversal equals the time necessary for heat flow from the compressed to the extended regions, a maximum of the logarithmic decrement occurs. The damping was measured as a function of the specimen thickness and the frequency of vibration ranging from 10 to 130 Hz. The frequency range was realised by both, a variation of the thickness and the mass at the end of the bending beams. By drawing the logarithmic decrement versus the product of the frequency and the quadratic thickness, a Debye peak is obtained which overlays all other damping mechanisms. The thermal diffusivity was calculated by determining the position of the maximum of the peak. The height of the peak, Young's modulus and the specific heat of each sample were used to calculate the coefficient of thermal expansion of the specimens. The values agree, within the limits of scatter, with values measured by a dilatometer and taken from the literature, respectively.

Attenuation of elastic waves in granular mediums

Experimental evidence that Fourier components of wave pulses are attenuated at the same rate as sinusoidal waves of the same frequency suggests that the mechanism which attenuates elastic waves in a granular medium is linear. Thermoelastic internal friction as proposed by Zener is considered as the source of attenuation. As a stress wave propagates through a granular medium, strain concentrations will be induced about pore spaces, cracks, and isolated points of contact between angular grains; even entire grains may become strain concentrations by virtue of either composition or orientation. The dilatations and compressions associated with these strain concentrations generate localized temperature fluctuations. The diffusion of these temperature fluctuations by conduction constitutes the loss mechanism. The associated Q for the medium will be essentially constant if a particular relationship obtains between the size of the strain concentration, the strain level within it, and the number of concentrations of that size. Subject to this constraint, an order-of-magnitude calculation indicates that the theory yields an estimate of Q consistent with the frequency dependence and magnitude observed in rocks. The theory also suggests the form of the observed pressure dependence of Q but appears to predict a temperature dependence which is not observed in rocks.

Internal Friction in Solids II. General Theory of Thermoelastic Internal Friction

Stress inhomogeneities in a vibrating body give rise to fluctuations in temperature, and hence to local heat currents. These heat currents increase the entropy of the vibrating solid, and hence are a source of internal friction. The general theory of this internal friction is here developed. The simplest example of stress inhomogeneity is that occurring in the transverse vibrations of reeds and wires. Explicit formulae are obtained for reeds and wires, and the effect is calculated of crystal orientation in single crystal specimens. Microscopic stress inhomogeneities arise from imperfections, such as cavities, and from the elastic anisotropy of the individual crystallites. The internal friction due to spherical cavities is calculated. The internal friction due to elastic anisotropy is investigated for cubic metals, and is found to be greatest for lead, least for aluminum and tungsten.

Internal Friction in Solids III. Experimental Demonstration of Thermoelastic Internal Friction

In order to demonstrate the presence of thermoelastic internal friction, the authors measured the internal friction of a copper reed over a wide frequency range (50 to 4000 cycles/sec.). They obtained a maximum precisely at the predicted frequency. The observed variation of internal friction with frequency proves that, over a wide frequency range, the internal friction due to the flow of heat back and forth across a reed is of a larger order of magnitude than that due to all other causes. Independent experiments of Bennewitz and R\"otger on wires of silver, aluminum, brass, steel, and glass are shown to furnish an equally striking demonstration of thermoelastic internal friction.