A FAILURE OF A CLASS OF K-BKZ EQUATIONS BASED ON PRINCIPAL STRETCHES

The invariants in the K-BKZ constitutive equation for an incompressibl e viscoelastic fluid are usually taken to be the trace of the Finger s train tensor and its inverse. The basis for this choice of invariants is not derived from the K-BKZ theory, but rather is due to the percept ion that this is the most natural choice. Research into using other se ts of invariants in the K-BKZ equation, such as the principal stretche s or the eigenvalues of the Finger strain tensor (i.e., the squares of the principal stretches) is relatively new. We attempt here to derive a K-BKZ equation based on the squares of the principal stretches that models the behavior of a low-density polyethylene melt in simple shea r and uniaxial elongational deformation. In doing so, two assumptions are made as to the form of the strain-dependent energy function: first , that there is a function f(q) such that the energy function can be w ritten as the sum of f(q(i)), i = 1, 2,3, where the q(i)'s are the squ ares of the principal stretches, and second that f is a power law. We find that the K-BKZ equation resulting from these two assumptions is i nadequate to describe both the shear and elongational behavior of our material and we conclude that the second of the above assumptions is n ot valid. Further investigation, including predictions of the second n ormal stress difference and some finite element calculations reveals t hat the first assumption is also invalid for our material.