Elastic behavior Subject

Elastic Behavior. In the following discussion of the equations relevant to the design of thick-walled hoUow cylinders, it should be assumed that the material of which the cylinder is made is isotropic and that the cylinder is long and initially free from stress. It may be shown (1,2) that if a cylinder of inner radius, and outer radius, is subjected to a uniform internal pressure, the principal stresses in the radial and tangential directions, and <7, at any radius r, such that > r > are given by... 

Coating solutions often exhibit a mixture of viscous and elastic behavior, with the response of a particular system depending on the stmcture of the material and the extent of deformation. Eor example, polymer melts can be highly elastic if a polymer chain can stretch when subjected to deformation. 

Since Meyer ) introduced the concept of kinetic molecular chain into the physics of polymers in 1932, remarkable progress has been made in the molecular-theoretical interpretation of elastic behavior of rubber vulcanizates and polymer solids in general2- ), and one can appreciate the present status of knowledge on this subject by a number of review articles and reference books. On the other hand, the phenomeno-logic approach to rubber elasticity has not aroused much interest in the field of polymer research. This is understandable because polymer scientists are primarily concerned with affairs of the molecular world. 

From a technical standpoint, it is also important to note that colloids display a wide range of rheological behavior. Charged dispersions (even at very low volume fractions) and sterically stabilized colloids show elastic behavior like solids. When the interparticle interactions are not important, they behave like ordinary liquids (i.e., they flow easily when subjected to even small shear forces) this is known as viscous behavior. Very often, the behavior falls somewhere between these two extremes the dispersion is then said to be viscoelastic. Therefore, it becomes important to understand how the interaction forces and fluid mechanics of the dispersions affect the flow behavior of dispersions. 

Oscillatory measurements using the cone-and-plate viscometer are sometimes carried out to demonstrate the elastic behavior of a viscoelastic fluid [10]. The fluid in the viscometer is subjected to an oscillatory strain imposed on the bottom surface while the response of the shearing stress is measured on the top surface. If the phase shift between the input strain and the output stress is 90°, the sample is purely viscous if it is 0°, the sample is completely elastic. A measured phase shift between 0° and 90° demonstrates that the fluid is viscoelastic. 

Many composites are elastically anisotropic and, thus, more than the two elastic constants are needed to describe their elastic behavior. This is a very large topic and, for this text, just some of the basic ideas that apply to unidirectional fiber composites will be discussed. Consider a two-phase material, with the two geometries shown in Fig. 3.15, being subjected to a uniaxial tensile stress. For the structure in Fig. 3.15(a), the two phases are subjected to equal strain whereas. 

Plastics are materials that can be formed into various shapes, usually by the application of heat and pressure. Thermoplastic materials can be reshaped. For example, plastic milk containers are made from the polymer polyethylene. These containers can be melted down and the polymer recycled for some other use. In contrast, a thermosetting plastic is shaped through irreversible chemical processes and, therefore, cannot be reshaped readily. An elastomer is a material that exhibits rubbery or elastic behavior. When subjected to stretching or bending, an elastomer regains its original shape upon removal of the distorting force, if it has not been distorted beyond some elastic limit. Rubber is the most familiar example of an elastomer. 

The above-mentioned thermomechanical models only consider the elastic behavior of materials. Boyd et al. [13] reported on compression creep rapture tests performed on unidirectional laminates of E-glass/vinylester composites subjected to a combined compressive load and one-sided heating. Models were developed to describe the thermoviscoelasticity of the material as a function of time and temperature. In their work, the temperature-dependent mechanical properties were determined by fitting the Ramberg-Osgood equations and the temperature profiles were estimated by a transient 2D thermal analysis in ANSYS 9.0. 

High elasticity behavior is different to that one what is usually observed in reversible (or elastic) deformations of soUds (e.g. metals). Stress subjected to a specimen causes deformation. If the stress is removed and the specimen returns to its original shape, the deformation is called elastic or reversible. Hooke s law is the base law of deformation of a perfect elastic body (Chapter 7, Equation 15) deformation (strain) stress... 

Various elastic behaviors. The domain of elastic properties of solids is a broad subject because the number of dimensions of space allows a great variety of application modes of a force for provoking a deformation. 

Hard elastic behavior is a manifestation of a bulk-microfibril superstructure. A substantial surface energy component of the stress exists in these materials, independent of strain at high tension. As a result, significant changes in the equilibrium stress occurs when the polymers, under load, are subjected to changes in environmental surface tension. An apparent requirement for this surface tension component is load bearing microfibrils with sufficiently small radii. Evidently, a maximum average fibril diameter exists whereby hard elastic behavior may occur in polymers with these structures. 

An elastomer is a material that exhibits rubbery or elastic behavior. When subjected to stretching or bending, it regains its original shape upon removal of... 

Unfortunately, Hooke s Law does not accurately enough reflect the stress-strain behavior of plastics parts and is a poor guide to good successful design. Assuming that plastics obey Hookean based deformation relationships is a practical guarantee of failure of the part. What will be developed in this chapter is a similar type of basic relationship that describes the behavior of plastics when subjected to load that can be used to modify the deformation equations and predict the performance of a plastics part. UnUke the materials that have been used which exhibit essentially elastic behavior, plastics require that even the simplest analysis take into account the effects of... 

Gere, J. M. 2004. Mechanics of Materials, 6th ed. London Brooks/Cole. Describes the fundamentals of mechanics of materials. Principal topics are analysis and design of structural members subjected to tension, compression, torsion, and bending as well as stress, strain, elastic behavior, inelastic behavior, and strain energy. Transformations of stress and strain, combined loadings, stress concentrations, deflections of beams, and stability of columns are also covered. Includes many problem sets with answers in the back. 

Besides the brittle elastic behavior, when a gel is subjected to a tensile load, under a compressive load the porous network can be irreversibly transformed. This plasticity effect depends strongly on the volume fraction of pores, but is also clearly affected by macropores and by the OH content. In fact, either under tension or compression, the gel material is not stable and its structure and mechanical features evolve. 

In practice polymeric materials are often subjected to mechanical loads. Therefore, it is essential to know how polymers respond to the mechanical load. Figure 1.3 presents the common behavior of thermoplastic polymers under uniaxial deformation. On the stress(a)-strain(e) curve four regions [7] can be distinguished in region I the material shows an elastic behavior. In this region the material is characterized by its Young s modulus of elasticity. In region II the material yields. The slope of... 

As shown in Figure 12.13, we have performed the pressure dependence study of the Ge-Ge modes of the NCs for one pressure cycle and there is no hysteresis observed. This confirms that the pressure-induced strain in the NCs is reversible. With this elastic behavior of our Ge/Si02 NCs-matrix system, we assume both the NCs and the matrix as isotropic elastic continua [46]. We modeled the NC as a sphere of radius ri in a spherical Si02 matrix of radius t2, where r2 2> ri. The system is subjected to a hydrostatic pressure P. Using spherical co-ordinates with the origin at the center of the NC sphere, our system has a spherical symmetry where the displacement vector u is everywhere radial and can be written d u = ar + b/r. The components of the strain tensor are Urr = a — and uee = =... 

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

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