Complex modulus tensile

Compliance n The degree to which a material deforms under stress the reciprocal of the modulus. Thus, in each mode of stress, the material is characterized by three moduli and their reciprocals, three compliances. However, when the stress is varying, the real and imaginary parts of the complex compliances are not equal to the reciprocals of their counterparts in the Complex Modulus. Tensile compliance the reciprocal of Young s modulus shear compliance the reciprocal of shear modulus. 

Dynamic Mechanical Properties. Figure 15 shows the temperature dispersion of isochronal complex, dynamic tensile modulus functions at a fixed frequency of 10 Hz for the SBS-PS specimen in unstretched and stretched (330% elongation) states. The two temperature dispersions around — 100° and 90°C in the unstretched state can be assigned to the primary glass-transitions of the polybutadiene and polystyrene domains. In the stretched state, however, these loss peaks are broadened and shifted to around — 80° and 80°C, respectively. In addition, new dispersion, as emphasized by a rapid decrease in E (c 0), appears at around 40°C. The shift of the primary dispersion of polybutadiene matrix toward higher temperature can be explained in terms of decrease of the free volume because of internal stress arisen within the matrix. On the other... 

Figure 15. Temperature dispersion of isochronal complex, dynamic tensile modulus function at a fixed frequency of 10 Hz, observed for the SBS-PS specimen at unstrethed and stretched (330% elongation) states...

The viscoelastic properties of the crystalline zones are significantly different from those of the amorphous phase, and consequently semicrystalline polymers may be considered to be made up of two phases each with its own viscoelastic properties. The best known model to study the viscoelastic behavior of polymers was developed for copolymers as ABS (acrylonitrile-butadiene-styrene triblock copolymer). In this system, spheres of rubber are immersed in a glassy matrix. Two cases can be considered. If the stress is uniform in a polyphase, the contribution of the phases to the complex tensile compliance should be additive. However, if the strain is uniform, then the contribution of the polyphases to the complex modulus is additive. The... 

Mixing, solution/latex Modulus, bulk Modulus, complex, G Modulus, loss, G Modulus, measurements Modulus, plateau Modulus, storage, G Modulus, tensile/flexural... 

Right-hand plots in the same Fig. 13.6 allows to conclude the well-optimized material performance from the macroscopic up to the mesoscales by the correspondence between the elastic modulus component obtained from the tensile tests and the elastic component of complex modulus from the DMA measurements performed at room temperature and which ratio results to be independent of the grafting level in the interfacial modifier (32,55). 

Figure 13.6 Examples of correlation between responses from different scales when the interfacial modifier is changed Left, tensile strength at break point (up) and relative crystalline variation for the polypropylene matrix (down) versus the grafting level in the interfacial modifier right, elastic moduli (tensile/DMA) ratio (up) and components of the complex modulus from DMA tests (down) versus the grafting level in the interfacial modifier. (From References 32 and 55 with permission of John Wiley Sons, Inc. and Elsevier, respectively.)...

E, elastic modulus 5, complex modulus G, shear moduli ultimate tensile strength e, elongation at break. 

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. 

P = proportional rut depth, determined in accordance to CEN EN 12697-22 (2007), large device. S = stiffness, determined by either the complex modulus test (trapezoidal or parallelepiped specimen) or the uniaxial tensile test (cylindrical or parallelepiped specimens), according to CEN EN 12697-26(2012). 

Dynamic mechanical spectrum n. The information obtained from testing with a mechanical spectrometer. A plot or tabulation of complex modulus or its components versus frequency of oscillation or temperature or both. The mode of stress may be tensile/compressive, flexural, or torsional (shear). Because both abscissa (frequency) and ordinates can range widely, bilog-arithmic plots are usual. Sepe MP (1998)... 

The DMA characterization was made of the series of polymers denoted PU 1 to PU 5 as listed in Table 3.11. The samples were tested in the tensile mode with a starting distance between the clamps of 45 mm. The cooling conditions were room temperature till -60°C cooling rate of 10 K/minute, -60°C to -120°C 3.5 K/min and -120°C to -140°C 2 K/min. The test started at -140°C and the complex modulus , storage modulus loss modulus E" and the loss factor were measured as function of temperature at a heating rate of 1 K/min. The instrument was operated with controlled sinusoidal force with a frequency of 1 s ... 

The effects of high humidity on the dynamic mechanical properties and thermal transitions of a commercial nylon-epoxy adhesive have been reported by Butt and Cotter." Exposure of the cured adhesive to 43°C and 97% RH for times ranging from 142 h to 2,040 h resulted in a substantial decrease (as much as 82%) in the complex dynamic tensile modulus. Some of the results of these authors are shown in Table I. The thermal transitions... 

Table I. Effect of Exposure to High Humidity on the Complex Dynamic Tensile Modulus (E ) of a Cured Nylon-Epoxy Adhesive"...

DMA experiments are performed under conditions of very small strain so that the material response is in the linear viscoelastic range. This means that the magnitude of stress and strain are linearly related and the deformation behavior is completely described by the complex modulus function, which is a function of time only. The theory applies both for the case of a tensile deformation or simple extension and for shear. In the latter case the comparable modulus is with components G ico) and G" co). As a first-order approximation, E = 3G. The theory is developed assuming deformation under isothermal conditions, and temperature does not appear (nor is implicit) as a variable. 

The flexural modulus is of most interest in many applications. This is much more complex than tensile, compressive or shear moduli. It not only has elements of both tensile and compression, but is very much influenced by particle orientation and by the surface layers. These are often polymer rich, an effect that becomes greater as the filler size increases. 

Material functions must however be considered with respect to the mode of deformation and whether the applied strain is constant or not in time. Two simple modes of deformation can be considered simple shear and uniaxial extension. When the applied strain (or strain rate) is constant, then one considers steady material functions, e.g. q(y,T) or ri (e,T), respectively the shear and extensional viscosity functions. When the strain (purposely) varies with time, the only material functions that can realistically be considered from an experimental point of view are the so-called dynamic functions, e.g. G ((D,y,T) and ri (a), y,T) or E (o),y,T) and qg(o),y, T) where the complex modulus G (and its associated complex viscosity T] ) specifically refers to shear deformation, whilst E and stand for tensile deformation. It is worth noting here that shear and tensile dynamic deformations can be applied to solid systems with currently available instruments, whUst in the case of molten or fluid systems, only shear dynamic deformation can practically be experimented. There are indeed experimental and instrumental contingencies that severely limit the study of polymer materials in the conditions of nonlinear viscoelasticity, relevant to processing. 

As an alternative, one can employ as well the complex dynamic tensile modulus E (u)j defined as... 

An extensional deformation is also known as a tensile deformation. If an oscillatory deformation is applied to a viscoelastic material, a complex modulus with components E and E" can be defined, in analogy to the dynamic shear moduli G and G" (cf. Eq. 1.37). 

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