Stress relaxation single-step experiments

The modes of operation of a DMA are varied. Using a multifrequency mode, the viscoelastic properties of the sample are studied as a function of frequency, with the oscillation amplitude held constant. These tests can be run at single or multiple frequencies, in time sweep, temperature ramp, or temperature step/hold experiments. In multistress/strain mode, frequency and temperature are held constant and the viscoelastic properties are studied as the stress or strain is varied. This mode is used to identify the LVR of the material. With creep relaxation, the stress is held constant and deformation is monitored as a function of time. In stress relaxation, the strain is held constant and the stress is monitored versus time. In the controlled force/strain rate mode, the tanperature is held constant, while stress or strain is ramped at a constant rate. This mode is used to generate stress/ strain plots to obtain Young s modulus. In isostrain mode, strain is held constant during a tanpera-ture ramp to assess shrinkage force in films and fibers. 

From equation (1), It can be seen that If the bar at time x=0 is subjected to a single step in strain, p(t), then the stress necessary to keep the bar stretched at time t is equal to H(p(t), t), where H(l,t) 0. From data obtained from single step stress-relaxation experiments carried out at different levels of strain. It is evident that one can determine the stress response for any other strain history in uniaxial extension. However, since equation (1) is nonlinear, one cannot determine the strain as a function of the stress, as for example In a creep experiment. Equation (1) applies to the type of experiment where, knowing the strain history, one can determine the stress response and the calculated values can then be compared with experimentally determined quantities. 

The utility of the K-BKZ theory arises from several aspects of the model. First, it does capture many of the features, described below, of the behavior of polymeric melts and fluids subjected to large deformations or high shear rates. That is, it captures many of the nonlinear behaviors described above for steady flows as well as behaviors in transient conditions. In addition, imlike the more general multiple integral constitutive models (108,109), the experimental data required to determine the material properties are not overly burdensome. In fact, the information required is the single-step stress relaxation response in the mode of deformation of interest (72). If one is only interested in, eg, simple shear, then experiments need only be performed in simple shear and the exact form for U I, /2, ) need not be obtained. Furthermore, because the structure of the K-BKZ model is similar to that of finite elasticity theory, if a full three-dimensional characterization of the material is needed, some of the simplilying aspects of finite elasticity theories that have been developed over the years can be applied to the behavior of the viscoelastic fluid description provided by the K-BKZ model. One such example is the use of the VL form (98) of the strain energy function discussed above (110). The next section shows some comparisons of the material response predicted by the K-BKZ theory with actual experimental data. 

The K-BKZ Theory Comparison with Experiment. The first data required to test the K-BKZ model is single-step stress relaxation data to determine the material parameters of interest. This is best seen from the following example for a simple shearing history. From equation 49, the shear stress for a simple shear deformation can be expressed as (see Ref 72)... 

In examining the single-step stress relaxation behavior of the DE model, one can also look at the normal stress responses in shearing experiments. The first and second normal stress differences are Niiy, t) and N2(y, i) respectively. The relevant equations are (56)... 

The consequences of this approximation have been extensively investigated and the results are outlined here. In terms of the orientation tensor, the lA approximation in a single-step stress relaxation experiment in simple shear is given by... 

Fig. 56. Values of the time and strain-dependent strain energy function derivatives dW/dli and 9W/9/2 for a glassy PMMA determined from torque and normal force measurements in single-step stress relaxation torsional experiments. After McKenna (114).

Fig. 57. Values of the time and strain-dependent strain energy function derivatives Wi = 9W/9/1 and W2 = 9W/9/2 for a glassy polycarbonate determined from torque and normal force measurements in single-step stress relaxation torsional experiments, (a) >/ 0.017 0.033 A 0.050 v 0.067 0.083 O 0.10. (b) y A 0.017 0.033 o 0.050 T 0.067 v 0.083 0.10. After Pesce and McKenna (146).

Whether a viscoelastic material behaves as a viscous Hquid or an elastic soHd depends on the relation between the time scale of the experiment and the time required for the system to respond to stress or deformation. Although the concept of a single relaxation time is generally inappHcable to real materials, a mean characteristic time can be defined as the time required for a stress to decay to 1/ of its elastic response to a step change in strain. The... 

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