Dynamic specific modulus

Dynamic specific modulus E /y, the ratio of dynamic Young s modulus to specific gravity, and loss tangent tan 8 can be used to study the viscoelastic nature of wood. E /y is related to sound velocity and tan 8 to sound absorption or damping within the wood. A large E /y and small tan 8 characterize the acoustic quality of soundboard wood [3]. 

FIG. 13.87 Diagram of the specific tenacity (specific dynamic tensile modulus (Ea/p), for modern high-performance filaments. The diagonal lines have the indicated ratio, which is the theoretical elongation at break (fractional) high-performance yarns have refractory materials have values between 0.025 and 0.005. (ty = tire yarn). 

The Autovibron system is designed to measure the temperature dependence of the complex modulus (E ), dynamic storage modulus (E ), dynamic loss modulus (E") and dynamic loss tangent (tan 6) of viscoelastic materials at specific selected frequencies (0.01 to 1 Hz, 3.5, 11, 35, 110 Hz) of strain input. During measurement, a sinusoidal tensile strain is imposed on one end of the sample, and a sinusoidal tensile stress is measured at the other end. The phase angle 6 between strain and stress in the sample is measured. The instrument uses two transducers for detection of the complex dynamic modulus (ratio of maximum stress amplitude to maximum strain amplitude) and the phase angle 6 between stress and strain. From these two quantities, the real part (E ) and the imaginary part (E ) of the complex dynamic modulus (E ) can be calculated. 

The most commonly used stiffness modulus is the elastic or dynamic stiffness modulus. It is used for ranking bituminous mixtures (asphalts), for estimating their structural behaviour in the road, as data for compliance with specifications requirements and as a property of asphalt for pavement design analytical calculations or procedures. 

Fig. 5.54. PE studied by TMDSC and HWS Temperature dependence of the modulus of the dynamic specific heat measured for various frequencies [61]...

In the case of dynamic mechanical relaxation the Zimm model leads to a specific frequency ( ) dependence of the storage [G ( )] and loss [G"(cd)] part of the intrinsic shear modulus [G ( )] [1]. The smallest relaxation rate l/xz [see Eq. (80)], which determines the position of the log G (oi) and log G"(o>) curves on the logarithmic -scale relates to 2Z(Q), if R3/xz is compared with Q(Q)/Q3. The experimental results from dilute PDMS and PS solutions under -conditions [113,114] fit perfectly to the theoretically predicted line shape of the components of the modulus. In addition l/xz is in complete agreement with the theoretical prediction based on the pre-averaged Oseen tensor. 

Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or "creep" in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122], Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5] ... 

The dynamic viscoelastic properties of acetylated wood have been determined and compared with other wood treatments in a number of studies. Both the specific dynamic Young s modulus (E /j) and tan S are lower in acetylated wood compared with unmodified wood (Akitsu etal., 1991, 1992, 1993a,b Korai and Suzuki, 1995 Chang etal., 2000). Acetylation also reduces mechanosorptive creep deformation of the modified wood (Norimoto etal., 1992 Yano etal, 1993). In a study of the dynamic mechanical properties of acetylated wood under conditions of varying humidity, it was concluded that the rate of diffusion of moisture into the wood samples was not affected by acetylation (Ebrahimzadeh, 1998). 

Fig. 1 a,b. Strain amplitude dependence of the complex dynamic modulus E E l i E" in the uniaxial compression mode for natural rubber samples filled with 50 phr carbon black of different grades a storage modulus E b loss modulus E". The N numbers denote various commercial blacks, EB denotes non-commercial experimental blacks. The different blacks vary in specific surface and structure. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 1 Hz, and static pre-deformation of -10 %. The x-axis is the double strain amplitude 2eo... 

Under dynamic conditions, where equilibrium between the surface and the film bulk cannot be realised, some specific elasticity properties are expressed. This is Marangoni s effect. Assuming that under such conditions there is an equilibrium only in some parts between the film bulk and its surface, it is possible to employ Eq. (7.6) for the material balance to calculate the modulus of elasticity. Hence, instead of the whole film volume, only the zone where equilibrium with the film surface is established, should be considered. The faster the process of film thinning, the smaller this volume is and the larger the modulus of film elasticity. In the limiting case, when it is completely impossible to achieve equilibrium between the film bulk and its surface, the elasticity of the adsorption surfactant layers takes place. 

Dynamic mechanical properties of PO- or BO-treated wood were recently investigated in relation to their structure at both the cellular and the molecular level [43]. The chemical treatment reduced the specific dynamic Young s modulus E /y. 

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