Example 3 A polymer rod is tested to determine its viscoelastic response. The ro

Question

Example 3 A polymer rod is tested to determine its viscoelastic response. The rod's cross section is square with the side of 5mm. The rod's length before loading is 500mm. A tensile force of 500N is applied to the rod and the rod's length under load was measured as a function of time. Instantly after applying the load, the rod is stretched to 508mm. After 24 and 48 hour under load, the rod's length was measured as 550mm and 570mm, respectively. The load was then removed and the rod's length was measured as 525mm after a long time after the removal of the force (consider this as the permanent length). Determine the parameters of the Burger's model for describing this type of mechanical behavior. -500 N 5 mm 5 mm 500 mm

Explanation / Answer

For Burgers model to determine viscoelastic behaviour of polymers it is important to remember that it is a combination of a KELVN-VOIGT and MAXWELL model, which are serial bonded in order to generate the BURGERS model.

So we have two E-modulus and two damping factors. Therefore the parameters are E1 and E2 as well as d1 and d2.

The Burgers model has the constitutive equation have four rheological constants a1,a2,a3,a4

sigma + a1*sigma+a2*sigma = a3*gamma+a4*gamma

where sigma = stress and gamma is rate of deformation or strain

stress = Force/ area, strain = change in length/original length

therefore, stress = 500/25 =20N//mm2, strain = 525/500 = 1.05

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