Material characteristics elastic deformation

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. 

In an elastic material medium a deformation (strain) caused by an external stress induces reactive forces that tend to recall the system to its initial state. When the medium is perturbed at a given time and place the perturbation propagates at a constant speed (or celerity) c that is characteristic of the medium. This propagating strain is called an elastic (or acoustic or mechanical) wave and corresponds to energy transport without matter transport. Under a periodic stress the particles of matter undergo a periodic motion around their equilibrium position and may be considered as harmonic oscillators. 

The phenomenological approach does not preclude a consideration of the molecular origins of the characteristic timescales within the material. It is these timescales that determine whether the observation you make is one which sees the material as elastic, viscous or viscoelastic. There are great differences between timescales and length scales for atomic, molecular and macromolecular materials. When an instantaneous deformation is applied to a body the particles forming the body are displaced from their normal positions. They diffuse from these positions with time and gradually dissipate the stress. The diffusion coefficient relates the distance diffused to the timescale characteristic of this motion. The form of the diffusion coefficient depends on the extent of ordering within the material. 

Elastic and viscous characteristics of materials can be visualized using a Cartesian material element, as shown in Fig 3.2. For this visualization the square shape in the x-y plane is deformed into a parallelogram. A force is applied to the material element parallel to one axis, in this case along the x axis at a distance H up the y axis. The material element is deformed away from they axis by a distance a by the force F. 

The book contains two parts each part comprises six chapters. Part I deals with basic relationships and phenomena of gas-solid flows while Part II is concerned with the characteristics of selected gas-solid flow systems. Specifically, the geometric features (size and size distributions) and material properties of particles are presented in Chapter 1. Basic particle sizing techniques associated with various definitions of equivalent diameters of particles are also included in the chapter. In Chapter 2, the collisional mechanics of solids, based primarily on elastic deformation theories, is introduced. The contact time, area, and... 

The dependence of rf, rf, G, and G" on frequency reflects the ability of macromolecular systems to flow like Newtonian fluids if the experimental time allowed them, feXp = 1 /< , is very large compared to the time that they require to fully respond macromolecularly. This temperature-dependent, material-characteristic time is commonly called the relaxation time, X, although it is actually a relaxation spectrum (7). Conversely, when /exp is very short, that is, co is very high compared to X, the macromolecular system can only respond like an elastic solid, able only to undergo deformation and not flow. In... 

Although a key characteristic of the mechanical behavior of rubber-like materials is their ability to undergo large elastic deformations, we will present here some important results from the theory of linear elasticity [1], which is valid only for small deformations. These serve our present purposes better than the nonlinear theory, because of their simpler character and physical transparency. 

Considering a mass of ceramic powder about to be molded or pressed into shape, the forces necessary and the speeds possible are determined by mechanical properties of the diy powder, paste, or suspension. For any material, the elastic moduli for tension (Young s modulus), shear, and bulk compression are the mechanical properties of interest. These mechanical properties are schematically shown in Figure 12.1 with their defining equations. These moduli are mechanical characteristics of elastic materials in general and are applicable at relatively low applied forces for ceramic powders. At higher applied forces, nonlinear behavior results, comprising the flow of the ceramic powder particles over one another, plastic deformation of the particles, and rupture of... 

The compressive strain is given at 10 % compression, since for semi-rigid foamed plastics there is no sudden rupture of the cell structure. In the characteristic compressive force-compression set line for foamed PS material, the curve rises linearly at the beginning. Here foamed PS material behaves elastically. As the strain increases, an irreversible deformation occurs (compressive set). The limit of elasticity lies in the range 1.5-3.5% compression. This limit is shifted toward lower compression levels as the temperature increases. The compressive strain at 10% compression depends on the degree of fusion of the pre-foamed beads. Compressive set increases linearly with increasing density (Figure 9.16). 

A key characteristic of plastic deformations is that they are irreversible. The difference between a viscoelastic fluid and a plastic material is the presence of a yield stress. The yield stress is the stress at which the deformation becomes irreversible and once the yield stress has been exceeded then the deformation is irreversible (Figs. 14 and 15). For example, brittle materials often behave elastically until the yield point has been reached once this point has been exceeded, the material will irreversibly deform or fracture like a piece of chalk (Fig. 15A). The key feature of a brittle material is that there is little deformation after the yield point. In contrast to a brittle material are a ductile materials (Fig. 15B) ductile materials undergo a lot of deformation after the yield point. 

Along with this, plastification induces growth of highly elastic deformations on the background of reduced elasticity modulus and other strength characteristics of the polymer materials [103]. Impairment of breaking strength under tension of LDPE-based films takes place as the concentration of the non-polar plasticizer bis-(2-ethylhexyl)sebacate increases. The decrease in 06 reaches 25% at PI concentration of about 20 wt% [5,6]. 

Young s Modulus (sometimes referred to as Modulus of Elasticity, meaning "measure" of elasticity) is an extremely important characteristic of a material. It is the numerical evaluation of Hooke s Law, namely the ratio of stress to strain (the measure of resistance to elastic deformation). To calculate Young s Modulus, stress (at any point) below the proportional limit is divided by corresponding strain. It can also be calculated as the slope of the straight-line portion of the stress-strain curve. (The positioning on a stress-strain curve will be discussed later.)... 

Drawing is a process similar to dry-spinning, in which nanofibres are drawn slowly from the droplet of a polymer solution by a micropipetter. The polymer solution is made from a viscoelastic material (i.e., one exhibiting both viscous and elastic characteristics upon deformation) that can accommodate the extensive deformation caused by drawing and retain the integrated form of an ultrafine fibre (Ondarcuhu and Joachim, 1998). 

Both creep and stress relaxation is modeled using computer simulation software based on simple spring (elastic deformation) and dashpot (viscous flow) models. Many polymers, when they approach the Tg, will exhibit viscoelastic behavior in which the physical characteristics are best described by considering the material as having both solid- and liquid-like properties. Viscoelasticity is an important property to be found in polymeric materials (see Viscoelasticity). 

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