Tension modulus

Fig. 2 Temperature-dependence of the modulus of elasticity (Young s modulus) of plastics (diagram). As an alternative to this modulus, tension a can also be plotted against constant elongation e or viscosity i), or other properties [2]. MSRe x,d- main softening range of elastomers, thermoplastics, duroplastics, Tgt associated glass transition temperature, Tfi flow point of the amorphous thermoplastic, //////// application range, application range...

Stress Temperature (°C) Stiffness (MPa) Shear Compression/ modulus Tension Strength (MPa)... 

Modulus, tension The ratio of tensile stress to the strain in the material over the range for which this value is constant. 

Alloy Ultimate tensile strength (MPa) 1 (ksi) Yield strength (0.2% offset) (MPa) II (ksi) Elongation in 50 mm (2 in) (%) Elastic modulus (tension) (GPa) (10Vi) Hardness... 

This result is the shear equivalent to Eq. (3.42) for tensile deformation. Note the modulus is a constant independent of strain for shear, while this is only true for a = 1 in the case of tension as shown by Eq. (3.43). 

The situation is not so simple when these various parameters are time dependent. In the latter case, the moduli, designated by E(t)and G(t), are evaluated by examining the (time dependent) value of o needed to maintain a constant strain 7o- By constrast, the time-dependent compliances D(t) and J(t)are determined by measuring the time-dependent strain associated with a constant stress Oq. Thus whether the deformation mode is tension or shear, the modulus is a measure of the stress required to produce a unit strain. Likewise, the compliance is a measure of the strain associated with a unit stress. As required by these definitions, the units of compliance are the reciprocals of the units of the moduli m in the SI system. 

We shall follow the same approach as the last section, starting with an examination of the predicted behavior of a Voigt model in a creep experiment. We should not be surprised to discover that the model oversimplifies the behavior of actual polymeric materials. We shall continue to use a shear experiment as the basis for discussion, although a creep experiment could be carried out in either a tension or shear mode. Again we begin by assuming that the Hookean spring in the model is characterized by a modulus G, and the Newtonian dash-pot by a viscosity 77. ... 

An important part of solving any differential equation is the specification of the boundary conditions. In the present case these can correspond to tension or shear and can be solved to give either a modulus or a compliance. 

Table 3.5 Rouse Theory Expressions for the Modulus (entries labeled 1) and Compliances (entries labeled 2) for Tension and Shear Under Different Conditions ...

When shear is appHed, the total area of the thin films increases, and the surface tension results in a restoring force, providing the shear modulus of the... 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

Fig. 4. The immediate effect of temperature on the modulus of elasticity of clear wood, relative to the value at 20°C. The plot is a composite of studies on the modulus as measured in hen ding, in tension parallel to grain, and in compression parallel to grain. VariabiUty in reported results is illustrated by the...

Another commonly used elastic constant is the Poisson s ratio V, which relates the lateral contraction to longitudinal extension in uniaxial tension. Typical Poisson s ratios are also given in Table 1. Other less commonly used elastic moduH include the shear modulus G, which describes the amount of strain induced by a shear stress, and the bulk modulus K, which is a proportionaHty constant between hydrostatic pressure and the negative of the volume... 

Fibers produced from pitch precursors can be manufactured by heat treating isotropic pitch at 400 to 450°C in an inert environment to transform it into a hquid crystalline state. The pitch is then spun into fibers and allowed to thermoset at 300°C for short periods of time. The fibers are subsequendy carbonized and graphitized at temperatures similar to those used in the manufacture of PAN-based fibers. The isotropic pitch precursor has not proved attractive to industry. However, a process based on anisotropic mesophase pitch (30), in which commercial pitch is spun and polymerized to form the mesophase, which is then melt spun, stabilized in air at about 300°C, carbonized at 1300°C, and graphitized at 3000°C, produces ultrahigh modulus (UHM) carbon fibers. In this process tension is not requited in the stabilization and graphitization stages. 

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

Modulus of elasticity (E) the ratio of the unit stress to the unit strain within the proportional limits of a material in tension or compression. Refer to Figure 30.1. 

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