SUBJECTS elasticity

In order to avoid misinterpretations, it is advisable in certain cases to subject elastic materials to specific pre-treatments prior to the ozone chamber test ... 

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

A polymer chain can be approximated by a set of balls connected by springs. The springs account for the elastic behaviour of the chain and the beads are subject to viscous forces. In the Rouse model [35], the elastic force due to a spring connecting two beads is f= bAr, where Ar is the extension of the spring and the spring constant is ii = rtRis the root-mean-square distance of two successive beads. The viscous force that acts on a bead is... 

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). 

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... 

The residual shear stress distribution in the assembled cylinders, prior to the appHcation of internal pressure, may be calculated, from pressure P, generated across the interface. The resulting shear stress distribution in the compound cylinder, when subjected to an internal pressure may be calculated from the sum of the residual stress distribution and that which would have been generated elastically in a simple cylinder of the same overall radius ratio as that of the compound cylinder. 

Machine components ate commonly subjected to loads, and hence stresses, which vary over time. The response of materials to such loading is usually examined by a fatigue test. The cylinder, loaded elastically to a level below that for plastic deformation, is rotated. Thus the axial stress at all locations on the surface alternates between a maximum tensile value and a maximum compressive value. The cylinder is rotated until fracture occurs, or until a large number of cycles is attained, eg, lO. The test is then repeated at a different maximum stress level. The results ate presented as a plot of maximum stress, C, versus number of cycles to fracture. For many steels, there is a maximum stress level below which fracture does not occur called the... 

Piezoresistive Sensors. The distinction between strain-gauge sensors and pie2oresistive (integrated-circuit) sensors is minor. Both function by measuring the strain on an elastic element as it is subjected to pressure. A pie2oresistive transducer is a variation of the strain gauge that uses bonded... 

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. 

Elastic limit the maximum stress a test specimen may be subjected to and which may return to its original length when the stress is released. 

Whilst the origin of such turbulence (melt fracture) remains a subject of debate it does appear to be associated with the periodic relief of built-up elastic stresses by slippage effects at or near polymer-metal interfaces. 

Irwin [23] developed an expression for the mode I stress intensity factor around an elliptical crack embedded in an infinite elastic solid subjected to uniform tension. The most general formulation is given by ... 

For a component subjected to a uniaxial force, the engineering stress, a, in the material is the applied force (tensile or compressive) divided by the original cross-sectional area. The engineering strain, e, in the material is the extension (or reduction in length) divided by the original length. In a perfectly elastic (Hookean) material the stress, a, is directly proportional to be strain, e, and the relationship may be written, for uniaxial stress and strain, as... 

Solution The maximum strain in a cylinder which is subjected to an internal pressure, p, is the hoop strain and the classical elastic equation for this is... 

Example 2.14 A plastic is subjected to the stress history shown in Fig. 2.45. The behaviour of the material may be assumed to be described by the Maxwell model in which the elastic component = 20 GN/m and the viscous component r) = 1000 GNs/m. Determine the strain in the material (a) after u seconds (b) after 1/2 seconds and (c) after 3 seconds. 

---