Solutions Using Broadband Bulk, Shear and Poissons Ratio Measured Functions

7 Solutions Using Broadband Bulk, Shear and Poisson s Ratio Measured Functions 

As discussed in Chapter 7 real material properties extend over many decades of time and for realistic solutions of boundary value problems it is necessary to have methods to incorporate these real measured properties. When material properties can be represented by a Prony series composed of a number of terms, it is possible to obtain solutions for more practical representation of polymers. Examples of the use of Laplace transforms for 

However, it is also necessary to discuss how broadband bulk, shear and Poisson s ratio are measured. The measurement of the broadband shear modulus is easily accomplished using the time-temperature-superposition-principle (TTSP) and a torsion test. See Kenner, Knauss and Chai (1982) for a description of a simple torsiometer and the measurement of a master curve for a structural epoxy adhesive, FM-73, at 20.5° C. 

The contradictions posed by use of a viscoelastic Poisson s ratio have been discussed by Flugge, (1975), Shames and Cozzarelli, (1992), Lake, (1998) and Tschoegl, et al., (2002). Some issues that arise are non-physical values for Poisson s ratio when simple mechanical models are used (e.g. Maxwell or Kelvin), and even the fundamental definition of a time-dependent Poisson ratio. Various definitions of Poisson s ratio and its measurement are discussed in depth by Tschoegl, et al., (2002). Therein the suggestion is given that the ratio is best measured in relaxation and that extreme four-digit accuracy is required which is presently not found in the literature. 

As a result, at the present time, use of one or more of the assumptions provided earlier in the chapter, together with broadband data for shear or extensional modulus, represent the most fruitful approach to the solution of viscoelastic boundary value problems. 

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