Complex dynamic shear compliance

Before discussing tire complex mechanical behaviour of polymers, consider a simple system whose mechanical response is characterized by a single relaxation time x, due to tire transition between two states. For such a system, tire dynamical shear compliance is [42]... 

Dynamic mechanical results are generally given in terms of complex moduli or compliances (3,4), The notation will be illustrated in terms Of shear modulus G, but exactly analogous notation holds for Young s modulus F. The complex moduli are defined by... 

A general description of the fundamental relationships governing the dynamic response of linear viscoelastic materials may be found in several sources (28, 37, 93). In general, sinusoidally applied strains (stresses) result in sinusoidal stresses (strains) that are out of phase. Measurements may be made under uniaxial, shear, or dilational loading conditions, and the resultant complex moduli or compliance and loss-phase angle are computed. Rotating radius vectors are usually taken to represent the... 

We note that, in principle, the main physical discussions related to filler networking in this paper do not change if a sinusoidal tensile or uniaxial compres-sional stress (amplitude 0) is imposed on the rubber material. In some examples the complex dynamic modulus is then denoted with E = E + iE" and the compliance with C = C - iC". All theoretical considerations use the shearing modulus G. ... 

The complex modulus will be employed throughout this paper except that the dynamic viscosity >j (to) will be used in some cases. In order to describe the low frequency behavior of a material, the zero-shear viscosity rj and the steady shear compliance Je° are used. They are defined... 

Dynamic Modulus. The complex shear compliance is being obtained in a Periy-Fitzgerald transducer apparatus and preliminary results are illustrated here.f9) Figure 10 shows the real part of the compliance, reduced to 25 0 Figure 11, the imaginary part. 

Rheological properties of mayonnaise have been studied using different rheological techniques steady shear rate-shear stress, time dependent shear rate-shear stress, stress growth and decay at a constant shear rate, dynamic viscoelastic behavior, and creep-compliance viscoelastic behavior. More studies have been devoted to the study of rheological properties of mayonnaise than of salad dressings, probably because the former is a more stable emulsion and exhibits complex viscous and viscoelastic rheological behavior. 

Having established the properties of the single-time relaxation process, we have now also a means to represent a more complex behavior. This can be accomplished by applying the superposition principle, which must always hold in systems controlled by linear equations. Considering shear properties again, we write for a dynamic compliance J (uj) with general shape a sum of Debye-processes with relaxation times ti and relaxation strengths AJi... 

---