Initial modulus

Each type of propellant has specific mechanical characteristics, but the influence of test parameters (temperature, strain rate, and pressure) is the same for all propellants (11). Tensile tests are widely used to analyze propellant behavior as well as examine the manufacturing controls of the propellants. Because their behavior is not linear-elastic, it is necessary to define several parameters that allow a better representation of the experimental tensile curve. The stylistic experimental stress-strain response at a constant strain rate from a uniaxial tensile test is shown in Figure 7, where E is the elastic modulus (initial slope), Sr P is the tensile strength (used later for a failure criterion), and eXj> is the strain at tensile strength. 

PLA/starch ratio. For the blends without MDI, modulus initially increased slightly with the addition of starch, reaching a maximum at a PLA/starch ratio of about 80/20 wt%. Any further increase in starch content resulted in a reduction in the modulus value. A similar pattern was observed for... 

Modulus, initial The slope of the initial straight portion of a stress-strain or load-elongation curve. 

A number of metrics can be assessed from stress-strain behavior (Dowling 2007). Properties that are often evaluated include the modulus (initial modulus, or secant modulus evaluated to some specific strain), the yield stress, the yield strain, the ultimate strength, and the strain at break, as have been discussed in O Chap. 19. The area under the curve is known as the modulus of toughness, as this area has physical units of energy per unit volume, which are equivalent to force per unit area, the units of stress and modulus. 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

Here is tire tensile stress and = lL-/L-, where is tire initial lengtli of tire sample and AL is tire sample elongation. In shear experiments, tire shear relaxation modulus G(t) is defined as where... 

Returning to the Maxwell element, suppose we rapidly deform the system to some state of strain and secure it in such a way that it retains the initial deformation. Because the material possesses the capability to flow, some internal relaxation will occur such that less force will be required with the passage of time to sustain the deformation. Our goal with the Maxwell model is to calculate how the stress varies with time, or, expressing the stress relative to the constant strain, to describe the time-dependent modulus. Such an experiment can readily be performed on a polymer sample, the results yielding a time-dependent stress relaxation modulus. In principle, the experiment could be conducted in either a tensile or shear mode measuring E(t) or G(t), respectively. We shall discuss the Maxwell model in terms of shear. 

This result shows that the highest modes of response have the shortest relaxation times and influence the initial response of the sample. Conversely, the longest relaxation time is ti, which we can identify with the terminal behavior of the sample. For example, in Fig. 3.9 the final collapse of the modulus at long times occurs at Ti. An example will show how we can use this idea. 

The ratio of stress to strain in the initial linear portion of the stress—strain curve indicates the abiUty of a material to resist deformation and return to its original form. This modulus of elasticity, or Young s modulus, is related to many of the mechanical performance characteristics of textile products. The modulus of elasticity can be affected by drawing, ie, elongating the fiber environment, ie, wet or dry, temperature or other procedures. Values for commercial acetate and triacetate fibers are generally in the 2.2—4.0 N/tex (25—45 gf/den) range. 

Fiber Tenacity, N /tex Initial modulus, N/tex Elongation at break, %... 

In the derivation of equations 24—26 (60) it is assumed that the cylinder is made of a material which is isotropic and initially stress-free, the temperature does not vary along the length of the cylinder, and that the effect of temperature on the coefficient of thermal expansion and Young s modulus maybe neglected. Furthermore, it is assumed that the temperatures everywhere in the cylinder are low enough for there to be no relaxation of the stresses as a result of creep. 

In the coupled process (Fig. 7c), the draw ratio, which affects the tenacity and elongation, lowers with increasing spinning speed. As draw ratio is increased, tenacity and initial modulus increase and elongation decreases. 

---