An approximate theoretical treatment is given for small compressions of bonded rubber blocks. The component of the compressive force arising from the bonded condition at the loaded surfaces is obtained from a pressure distribution within the block, given by the solution of the corresponding torsion problem. The bending of blocks is treated in a similar way, the pressure distribution in this case being derived from the corresponding bending stress function. The apparent shear of relatively thick blocks is then treated as a combination of shear and bending displacements. The location of an internal rupture and the deformation at which it occurs are also derived from a critical (negative) value of the pressure developed within the block, at which a small cavity increases indefinitely in size. The corresponding critical deformations are calculated for extension and bending displacements. The shear stresses developed at the bonded surfaces under extension, compression or bending displacements are also evaluated.
It has been shown that it is possible to predict the viscoelastic response of elastomers and elastomeric engineering components under both load- and position-control conditions if one assumes: a) that the modulus of the materials increases with the strain amplification factor as given by the Guth and Gold equation, b) that the occluded rubber is taken into account when using this equation, and c) that the energy loss per cycle and unit volume of material is increasing with the square of the strain-amplification factor. These calculations were applied to an assembly where one unfilled section is in series with a filled one. The overall filler loading was kept constant, and it was found that the equations derived show completely different heat-generation rates for load- and position-control conditions. While the losses are the same in both sections and equal to that of the assembly as a whole under position-control conditions, they are quite different under load-control conditions. They increase with both filler loading and values of α and abnormally high local overheating in the unfilled section occurs. These considerations indicate that a uniform mixing quality is important for compounds which will be used in dynamically deformed engineering components. Under position-control conditions, poor filler dispersion will give rise to a decrease in the dynamic modulus and the energy loss per cycle, i.e., variations in the quality of the mix will cause variability of the dynamic properties. Under load-control conditions, the situation is even worse, since the energy dissipation increases with poor mixing, and local overheating of the sections containing less than the average amount of carbon black takes place. The model is obviously too oversimplified for qualitative predictions. But it still gives good qualitative indications regarding the heat-generation rate in structures made from two elastomers having different filler loadings or for imperfectly mixed compounds.
synopsisImpact behavior can be predicted for rate-dependent foams from constant rate ofThe response must be factorized into a rate-dependent modulus funcIn this way the rate-dependent modulus can vary strain response. t,ion and a strain-dependent function. throughout the impact as the velocity of the impactingobject decreases.
The influence of carbon black loading on the dynamic properties of statically deformed elastomers has been investigated. The energy loss per cycle was found to increase according to the square of the strain amplification factor as expressed by the Guth-Gold-Einstein equation. The dynamic complex modulus |E*| is approximately equal to the static modulus obtained from the slope of the static stress-strain curve. The influence of carbon black loading on E* can, therefore, be predicted from its influence on the static stress-strain curve which was found to be governed by the first power of the strain amplification factor. The tangent of the loss angle can thus be predicted from |E*| and the energy loss per cycle. It does not only depend upon the dynamic viscosity of the material; it also depends upon the shape of the stress-strain curve as well.
The overall crystallization rate of polypropylene fractions was studied dilatometrically, and the crystallization behavior was considered in relation to the stereoregularity of the samples. The study includes a photomicroscopic analysis of the nucleation, formation, and growth of spherulites, as well as an evaluation by means of rapid x‐ray scanning techniques of the increase of crystallinity within the spherulites. A theory was applied to the discussion of crystallization behavior in which two stages of growth were introduced: (a) growth at the spherulite interface, and (b) secondary crystallization within the spherulite. These were described in terms of Avrami‐type equations with differing parameters.
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