Mechanical properties sinusoidal

Dynamic mechanical properties, sinusoidal, intermittent Stiffness, rigidity (flexural modulus)... 

When a sinusoidal strain is imposed on a linear viscoelastic material, e.g., unfilled rubbers, a sinusoidal stress response will result and the dynamic mechanical properties depend only upon temperature and frequency, independent of the type of deformation (constant strain, constant stress, or constant energy). However, the situation changes in the case of filled rubbers. In the following, we mainly discuss carbon black filled rubbers because carbon black is the most widespread filler in rubber products, as for example, automotive tires and vibration mounts. The presence of carbon black filler introduces, in addition, a dependence of the dynamic mechanical properties upon dynamic strain amplitude. This is the reason why carbon black filled rubbers are considered as nonlinear viscoelastic materials. The term non-linear viscoelasticity will be discussed later in more detail. 

The mechanical properties of a linear, isotropic material can be specified by a bulk modulus, K, and a shear modulus, G. For an ideal elastic solid, these moduli are real-valued. For real solids undergoing sinusoidal deformation, these are best represented as complex quantities [49] K = K jA and G = G -I- jG". The real parts of K and G represent the component of stress in-phase with strain, giving rise to energy storage in the film (consequently K and G are referred to as storage moduli) the imaginary parts represent the component of stress 90° out of phase with strain, giving rise to power dissipation in the film (thus, K" and G" are called loss moduli). 

Rheovibron (dynamic) viscometer is widely used for measurements of dynamic mechanical properties such as loss modulus, storage modulus, and dissipation factor, each as a function of temperature. In this instrument, the test specimen is clamped between strain gauges and subjected to low order of sinusoidal strain at a specified frequency. The value of tan d is directly read and the storage and loss moduli are calculated using sample dimensions and instrument readings. 

Cyclic loads were applied to the specimens using a hydraulic feedback load system which could be either load-, stroke-, or strain-controlled. Sinusoidal and linear-ramp waveforms were generally used. Fatigue frequencies were varied from 0.1 to 15 Hz. Unless otherwise stated, mechanical property data were obtained at a fatigue frequency of 10 Hz. 

A very good way to characterize and differentiate between elastomers and rigid plastics is by the measurement of dynamic mechanical properties. A most convenient method to study dynamic mechanical properties is to impose a small, sinusoidal shear or tensile strain and measure the resulting stress. Dynamic mechanical properties are most simply determined for a small sinusoidally varying strain, for which the response is a sinusoidally varying stress. An increase in frequency of the sinusoidal deformation is equivalent to an increase in strain rate. 

In the dynamic mechanical tests, either a vibrational force or a deformation is applied to the specimen, and then the sinusoidal response of either the deformation or force is measured, respectively. The dynamic mechanical properties are measured as a function of frequency at a constant temperature or as a function of temperature. The temperature dependence of dynamic viscoelasticity is conveniently used by the plastic industry to characterize solid polymers. Recently, various kinds of equipment for measuring dynamic viscoelasticity are commercially available and widely used for scientific and practical purposes. 

Dynamic Mechanical Properties n (1) The stress-strain properties of a material when subjected to an applied sinusoidally varying stress or strain. For a perfectly elastic material the strain response is immediate and the stress and strain are in phase. For a viscous fluid, stress and strain are 90° out of phase. (2) The mechanical properties of composites as deformed under periodic forces such as dynamic modulus, loss modulus and mechanical damping or internal friction. (Sepe MP (1998) Dynamic mechanical analysis. Plastics Design Library, Norwich, New York)... 

The thermal-mechanical properties of these PBA-based, T -type SMPU fibers were studied with the DMA. A bundle of ten fibers was attached to the sample holder with a gauge length of 1 cm. The tensile gange was then driven by a sinusoidal signal with a minimnm force amplitnde of 100 mN. Liqnid nitrogen was used as a coolant and the temperatnre range was -70 to 200°C. The experiments stopped either when the eqnipment reached the target temperature or the fibers broke. 

Absolute values of shear modulus cannot be determined via TBA however, it is quite useful to follow the dynamic mechanical properties of reactive systems (e.g., epoxy curing) [21]. Forced vibration, almost exclusively employed today, fixes both ends of a sample and applies a sinusoidal tensile or shear strain, which yields sinusoidal stress response with a phase angle S lag. As with free vibration, Eqs. 5.13 to 5.16 apply. Typical instruments employed include Rheovibron viscoelastometer and various versions of dynamic mechanical analyzers. For forced vibration, the frequency range of 0.01 to 100 Hz is commonly available with a temperature range of —150 °C to >400°C. A discussion of the details and utility of dynamic mechanical analysis can be found in [19, 22]. The stress-strain response of forced vibration and free vibration is illustrated in Fig. 5.3. 

Later on, semi-soft elasticity concept has been extended to the dynamical case. The theory, which is based on the separation of time scales between the director and the network, describes the mechanical properties of monodomain NEs in the linear response regime, when the sample is subjected to a sinusoidal shear of small amplitude (Terentjev and Warner 2001). When the shear is applied in a plane containing the director, the theory predicts the existence of a low frequency semi-soft elastic plateau, in addition to the usual rubbery plateau observed at higher frequencies. 

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