Strain double-step

Though the BKZ-type constitutive equation has been quite successful in many phenomena, it has been reported that under certain flow history, the equation gives unsatisfactory predictions. One such experiment is tte stress relaxation after application of double step strain. The flow history of this experiment is illustrated in Fig. 7.23. 

STRESS RELAXATION AFTER DOUBLE STEP STRAIN... 

We consider the inextensible chain model. Figure 7.24 eiqilains the change of polymer conformation under the double step strain. Figure 7.24a shows the undeformed state just before the first deformation. Figure 7.24h represents the state immediately after the deformation the primitive chain is deformed by the shear Yi. Figure 7.24c indicates the state just before the second deformation the inner part AB still remains in the deformed tube, while the outer parts are in the undeformed tube. Now when the second deformation is applied, the inner part AB is deformed by the shear Yi + Yi from the equilibrium state, while the outer part is deformed by the shear Yi- It is important to note that the second shear stretches the contour length of the outer part by the factor < (72), but that of the inner part by the factor... 

Once the single-step data are known, then integration of equation 56 (or eq. 53) for different strain histories leads to predictions for the material response in any deformation history of interest. A very powerful method of evaluating constitutive equations is the double-step strain history in which the second-step response should be able to be predicted by the model in question. Figure 33 shows the set of two-step histories that is dealt with here and subsequently. Figures 34,... 

D. C. Venerus and H. Kahvand, Doi Edwards Theory Evaluation in Double-Step Strain Flows J. Polym. Sci., Part B Polym. Phys. 32, 1531—1542 (1994). 

K. Osaki, Y. Einaga, M. Kurata, N. Yamada, and M. Tamura, Stress Relaxation of Polymer Solutions under Large Strain Application of Double-Step Strain Polym. J. 5, 283-287 (1973). 

E. F. Brown and W. R. Burghardt, First and Second Normal Stress Difference Relaxation in Reversing Double-Step Strain Flows Rheol. 40, 37—54 (1996). 

Factorization of the function concentrated polystyrene solution, time-strain factorability is not valid at short times after the imposition of the step shear. An accurate K-BKZ constitutive equation for shearing flows of this material will be much more complex than that for melt I. Furthermore, in strain histories in which a strain reversal takes place, such as constrained recoil (Wagner and Laun, 1978) or double-step strains with the second strain of sign opposite the first (Doi, 1980 Larson and Valesano, 1986), good agreement... 

One may also subject a solution to a series of strains at timed intervals. Venerus, et al. observe that double-step strains using strains in opposite directions have proven particularly effective at testing different models of polymer dynamics(21). They provide an example, combining optical and mechanical measurements to determine not only the stress but also the two normal stress differences Ni and N2 during double-strain experiments. 

A deformation history that provides a critical test of constitutive equations is stress relaxation following double-step strain. In this experiment, a strain of is introduced at f = 0, and a second strain is introduced at t = such that the final total strain is The resulting stress is a function of four parameters, i.e., a= and is reported only for f > fj. If it... 

Brown, E. F., Burghardt, W. R. First and second normal stress difference relaxation in reversing double-step strain flows./. RheoL (1996) 40, pp. 37 54... 

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