Solid material elasticity

Due to the particle size, a colloidal crystal is much weaker than a nonnal solid material—the elastic moduli are... 

By measuring V z), which includes examining the reflectance function of solid material, measuring the phase velocity and attenuation of leaky surface acoustic waves at the liquid-specimen boundary, the SAM can be used indetermining the elastic constants of the material. 

Rheology deals with the deformation and flow of any material under the influence of an applied stress. In practical apphcations, it is related with flow, transport, and handling any simple and complex fluids [1], It deals with a variety of materials from elastic Hookean solids to viscous Newtonian liquid. In general, rheology is concerned with the deformation of solid materials including metals, plastics, and mbbers, and hquids such as polymer melts, slurries, and polymer solutions. 

Application to heterogeneous polymer solids, and elastic composites, is presented in the Section 7 (Gusev, Suter), which is followed by a summary and the outlook for the various methods reviewed here. It will be apparent to the reader that this review thus assembles several building blocks for the difficult task to bridge the gaps from the atomistic to the macroscopic scales in space and times for the simulation of polymeric materials. Integrating these building blocks into one coherent framework still is not fully solved and a matter of current research. 

The final main category of non-Newtonian behaviour is viscoelasticity. As the name implies, viscoelastic fluids exhibit a combination of ordinary liquid-like (viscous) and solid-like (elastic) behaviour. The most important viscoelastic fluids are molten polymers but other materials containing macromolecules or long flexible particles, such as fibre suspensions, are viscoelastic. An everyday example of purely viscous and viscoelastic behaviour can be seen with different types of soup. When a thin , watery soup is stirred in a bowl and the stirring then stopped, the soup continues to flow round the bowl and gradually comes to rest. This is an example of purely viscous behaviour. In contrast, with certain thick soups, on cessation of stirring the soup rapidly slows down and then recoils slightly. 

Polymers are viscoelastic materials meaning they can act as liquids, the visco portion, and as solids, the elastic portion. Descriptions of the viscoelastic properties of materials generally falls within the area called rheology. Determination of the viscoelastic behavior of materials generally occurs through stress-strain and related measurements. Whether a material behaves as a viscous or elastic material depends on temperature, the particular polymer and its prior treatment, polymer structure, and the particular measurement or conditions applied to the material. The particular property demonstrated by a material under given conditions allows polymers to act as solid or viscous liquids, as plastics, elastomers, or fibers, etc. This chapter deals with the viscoelastic properties of polymers. 

Fillers are solid materials that are dispersed in plastics and elastomers. One distinguishes between inactive fillers that are used in the first place to make the plastics less expensive and active fillers (reinforcing fillers) that improve specific mechanical properties and thus effect a reinforcement . With the aid of these fillers, the elastic modulus, hardness, and thermostability are enhanced predominantly, whereas the impact strength of thermoplastic niaterials is re-... 

Detonation, Elastic Properties of Solid Materials in. See A.H. Eschenfelder in BRL (Ballistics Research Lab) Memo 521(1950)... 

Physical properties of solid materials which are greatly influenced by the presence of defects of lattice order in real single crystals are called structural-sensitive properties, and are distinguished from intrinsic properties, which are determined by the elements constituting the crystal, for example the chemical bonds, the structure, etc. Color, plasticity, glide, and semiconductor properties are structural-sensitive properties, whereas density, hardness, elasticity, and optical, thermal, and magnetic properties are the intrinsic properties. Structural-sensitive... 

The elastic stiffness depends on the relative density. In general the dependence of relative stiffness, E /E, where E is the elastic modulus of the structure and E is the modulus of the solid material on relative density, is of the form... 

Table 1.6. Elastic Properties of Some Solid Materials...

Any solid material has its own upper limit of elastic deformation under either normal or tangential stresses. Once the stresses exceed this limit, plastic deformation will occur. In this section, collisions of inelastic spheres are presented. The degree of inelastic deformation is characterized by the restitution coefficient. 

It should be noted that the elasticity modulus E is not merely a property of the solid material in the bed. In general, is a complex function of the structure of packing, material properties of packing particles, particle size, and particle contact and cohesion forces between particles. 

As Meyers el al. [3] point out, polymers remain as solid material even when these parts of their chains are rearranging in order to accompany the stress, and as this occurs, it creates a back stress in the material. When the back stress is of the same magnitude as the applied stress, the material no longer creeps. When the original stress is taken away, the accumulated back stresses will cause the polymer to return to its original form. The material creeps, which gives the prefix visco, and the material fully recovers, which gives the suffix elasticity. 

Abstract. In present work we propose the results of acoustomicroscopy investigation the physical properties of materials for fuel elements. In addition, we demonstrate that exposed structure of materials, observe its subsurface layers and determine level of elastic-mechanical characteristics are easy tasks with acoustic microscope defectoscopy methods. Experimental results confirm, that propose methods are effectively for exposing microdefects with different nature. V(Z)-curves methods gives us a possibility to research a nanopore density and to determine the criteria of limit state for hydrogen containing solid materials. 

The simplest model assumes ideal elastic behavior (Figure 7.12A). At a stress below the yield stress (Fy), the sample behaves perfectly elastically. In this region, a modulus of elasticity can be determined. At the yield stress, the sample flows. It continues to flow until the stress is lowered again to below the yield stress value. Therefore, both the elastic modulus and yield stress describe the behavior of a plastic material. They can be determined easily by compression testing. The continuous network of fat crystals in a fat bears the stress below the yield stress and therefore contributes solid or elastic properties to the material (Narine and Marangoni, 1999a). 

The Poisson ratio is a very important parameter. Its value varies from 0 for diamond to Vi for purely elastic incompressible solid materials. 

With elastically anisotropic materials the elastic behavior varies with the crystallographic axes. The elastic properties of these materials are completely characterized only by the specification of several elastic constants. For example, it can be seen from Table 10.3 that for a cubic monocrystal, the highest symmetry class, there are three independent elastic-stiffness constants, namely, Cn, C12, and C44. By contrast, polycrystalline aggregates, with random or perfectly disordered crystallite orientation and amorphous solids, are elastically isotropic, as a whole, and only two independent elastic-stiffness coefficients, C44 and C12, need be specified to fully describe their elastic response. In other words, the fourth-order elastic modulus tensor for an isotropic body has only two independent constants. These are often referred to as the Lame constants, /r and A, named after French mathematician Gabriel Lame (1795-1870) ... 

Other amorphous solids such as polymers, being rigid and brittle below. Tg, and elastic above it, also exhibit this behavior. Table 2.1 lists the glass transition temperatures of common solid materials. Although most solid-state textbooks deal almost exclusively with crystalline materials, this text will attempt to address both the crystalline and amorphous states, describing the structure/property relationships of major amorphous classes such as polymers and glasses. 

Chapter 4 outlines operations of symmetry on ideal solids that show how the number of independent components of the modulus tensor diminishes as the number of symmetry elements in the solid increases. This analysis leads to the formulation of the generalized Hooke s law utilizing both elastic modulus and elastic compliances for amorphous solid materials. These relationships, conveniently modified, are further used in viscoelasticity. In this chapter the generalized law of Newton for ideal liquids is also stated. 

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