Elastic range, defined

The concept of a welt defined elastic range to large strain is not realistic. The concept of well defined stress at which mechanical yielding occurs leading to well defined elastic-inelastic conditions is not realistic. Actually, such conclusions could well be anticipated from strength studies at atmospheric pressure, but there has been little explicit reason to consider the nonideal effects from the mechanical-response shock studies. 

Differences in Network Structure. Network formation depends on the kinetics of the various crosslinking reactions and on the number of functional groups on the polymer and crosslinker (32). Polymers and crosslinkers with low functionality are less efficient at building network structure than those with high functionality. Miller and Macosko (32) have derived a network structure theory which has been adapted to calculate "elastically effective" crosslink densities (4-6.8.9). This parameter has been found to correlate well with physical measures of cure < 6.8). There is a range of crosslink densities for which acceptable physical properties are obtained. The range of bake conditions which yield crosslink densities within this range define a cure window (8. 9). 

The lower limit of the elastic range, the glass transition temperature, can be easily determined by refractometric, volumetric, or other well known methods. The upper limit suffers from an exact definition the transition from the fixed liquid to the liquid state occurs without transformation. But as the viscosity decreases exponentially with the temperature it is very convenient to define a 1 flow-temperature by penetrometer measurements. If the rate of temperature rise is kept constant, this temperature is reproducible within 1° or 2°C. The penetrometer indicates a temperature where macroscopically one would call the substance liquid. ... 

Plasticity causes blunting of the crack tip, as illustrated in Figure S.IS. The resulting crack tip separation defines both 8, the CTOD, and S, the critical CTOD at the onset of crack growth, which may be used as a measure of toughness. Where fracture is within the linear elastic range, can be correlated with Giq through the equation ... 

The easiest way to locate the source of acoustic emissions is the so-called zone location method, where the exact source coordinates are not determined. Here, localization means detecting a signal and the radius (or in plate structures, the zone) of the sensor sensitivity range defines the localization accuracy. However, this is also the most imprecise localization method. The principal of zone localization is simple. For a particular sensor distribution, the sensor that records the arrival of the elastic wave first is the sensor closest to the source. An example for such a case is shown in Fig. 6.4. 

The first of the concepts of broad applicability is the existence of a yield surface in stress space this same quantity is known by a variety of names, including yield locus, the elastic limit surface and yield function. The function defining the surface is denoted by and its role is to identify the boundary of the elastic range in a space spanned by the stress components (7jj. In the most general circumstances to be considered here, this function takes the form... 

The two results in (9.49) and (9.50) provide the basis for an extremum principle which can be expressed as either a minimum principle or a maximum principle the two forms are equivalent and the latter option is adopted here. For a given surface shape and elastic field, define a functional over the range of all trial surface flux fields j as... 

The aim for tree breeders and forest managers is to define and grow a plantation which will be elastic in its response to the large stresses induced by high wind speeds. Petty Swain (1985) have established models of the stress-strain responses of forest trees which may be used to define the sizes and morphologies of trees, for a defined range of wind speeds and elastic responses. A typical response of a plantation grown spruce tree to wind speed is shown on Fig. 2. This is a classic stress/strain curve, with an... 

The constrained-junction model was formulated in order to explain the decrease of the elastic moduli of networks upon stretching. It was first introduced by Ronca and Allegra [39], and Flory [40]. The model assumes that the fluctuations of junctions are diminished below those of the phantom network because of the presence of entanglements and that stretching increases the range of fluctuations back to those of the phantom network. As indicated by the second part of Equation (26), the fluctuations in a phantom network are substantial. For a tetrafunctional network, the mean-square fluctuations of junctions amount to as much as half of the mean-square end-to-end vector of the network chains. The strength of the constraints on these fluctuations is measured by a parameter k, defined as... 

The reduced stress is defined as the force per cross-sectional area of the undeformed sample, divided by the term X-X- with X being the relative elongation L/L0. With undiluted rubber, this is not found experimentally. In most cases, however, the elastic behaviour in a moderate elongation range is satisfactorily described fcy the empirical Mooney-Rivlin equation, which predicts a linear dependence of on reciprocal elongation X- (32-34)... 

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