Interrelations, between shear

The conclusion is that Lodge s rheological constitutive equation results in relationships between steady shear and oscillatory experiments. The limits y0 0 (i.e. small deformation amplitudes in oscillatory flow) and q >0 (i.e. small shear rates) do not come from Lodge s equation but they are in agreement with practice. These interrelations between sinusoidal shear deformations and steady shear flow are called the relationships of Coleman and Markovitz. 

LDPE, and with polypropylene, PP, was studied In steady state shear, dynamic shear and uniaxial extenslonal fields. Interrelations between diverse rheological functions are discussed In terms of the linear viscoelastic behavior and Its modification by phase separation Into complex morphology. One of the more Important observations Is the difference In elongational flow behavior of LLDPE/PP blends from that of the other blends the strain hardening (Important for e.g. fllm blowing and wire coating) occurs In the latter ones but not In the former. 

In a similar way as the Young modulus E and the Poisson ratio V are connected to the uniaxial extension test, the shear modulus G and the bulk modulus K are connected to simple shear and isotropic deformation (i.e. dilatation or compression). Note that, accidentally, it turns out that the shear modulus G equals the second Lame constant ju. Since for isotropic materials only two of the elastic constants are independent, the knowledge of any pair of them is sufficient to calculate the other constants and thus to describe the elastic behavior of isotropic materials completely. For easy reference in this chapter we list the most important interrelations between the elastic constants ... 

It is possible to define other small strain material functions, such as stress growth under constant rate of straining (Example 3.2.1) or recoverable strain after constant strain rate. However, these deformation histories are better suited for large strain studies and are discussed in Section 3.2. The small strain material functions will be seen as limits of the large strain ones. Table 3.3.2 lists some of the interrelations between the various experiments for linear viscoelastic behavior. Note that the limiting low shear rate viscosity rio can be calculated from... 

In this section three topics are discussed (1) the molecular weight dependence of the rheological properties (2) the interrelation between steady shear and dynamic oscillatory shear measurements and (3) the effect of branching. The importance of the second topic rests on the fact that dynamic oscillatory properties are easier to measure and can be obtained at higher equivalent shear rates than are possible for the steady shear flow properties obtained by means of rotary rheometers. 

Elastic constant n. Any of the several constants of a constitutive relationship between stress (of any mode) and strain in a material. For an isotropic material stressed in its elastic range, there are (at any temperature) four interrelated constants tensile modulus , shear modulus G, bulk modulus By and Poisson s ratio ji. Two expressions of the relations are... 

In most cases the material cannot be regarded as one-dimensional, and forces and deformations in all three principal directions must be taken into account. The normal and shear stresses are interrelated by the equations of mechanical equilibrium. The relationship between stresses and deformations can be described by the generalized Hooke s law in the case of linear elastic behavior. The stress-strain relationship of materials showing more complicated behavior can often be described by advanced theories based on the generalized Hooke s law. All models contain constants that must be determined experimentally, on materials equilibrated in moisture content and temperature. 

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