Measurements of the first normal-stress difference in a new Rheo-dilatometer for molten polymers: Triple-step-shear-strain tests for all K-BKZ constitutive equations

Following the 3rd of a triple-step-shear-strain sequence, the relaxation of the first normal-stress difference,N ₁ (t), has been measured for a sample (IUPAC A) of low-density polyethylene at 150 °C over a range of shear-strain magnitudes up to 28 shear units. A new cone-plate Rheodilatometer was used, giving sample volume change data as well as thrust and torque data during cone rotation. At 130 °C, prior measurements (described elsewhere) gave an upper limit of 0.001% for the volume change with IUPAC A; this gave an estimated error of only 1.7% in determiningN ₁(t) from time-dependent thrust data. Wagner's network-rupture model (based on a postulated strain-induced irreversible network disentanglement process) gave quantitative agreement withN ₁(t) data for IUPAC A at 150 °C over some of the ranges of time and shear-strain investigated. Wagner's earlier constitutive equation (of K-BKZ type) gave no quantitative agreement. Using a special choice of strain magnitudes in which the 3rd is half that of the 1st and 2nd, it is shown that a critical test of all K-BKZ equations can be made on the basis ofN ₁ (t) data only. This test excludes all K-BKZ equations for IUPAC A under the conditions here used. In all the present investigations, the 1st and 3rd shears had the same sign while the 2nd had the opposite sign.