Steady-state calculation from creep

A good diagnostic for creep and stress relaxation tests is to plot them on the same scales as a function of either compliance (J) or modulus (G), respectively. If the curves superimpose, then all the data collected is in the linear region. As the sample is overtaxed, the curves will no longer superimpose and some flow is said to have occurred. These data can still be useful as a part of equilibrium flow. The viscosity data from the steady-state part of the response are calculated and used to build the complete flow curve (see equilibrium flow test in unit hi.2). 

Basically, a constant stress cr is applied on the system and the compliance J(Pa ) is plotted as a function of time (see Chapter 20). These experiments are repeated several times, increasing the stress in small increments from the smallest possible value that can be applied by the instrament). A set of creep curves is produced at various applied stresses, and from the slope of the linear portion of the creep curve (when the system has reached steady state) the viscosity at each applied stress, //, can be calculated. A plot of versus cr allows the limiting (or zero shear) viscosity /(o) and the critical stress cr (which may be identified with the true yield stress of the system) to be obtained (see also Chapter 4). The values of //(o) and <7 may be used to assess the flocculation of the dispersion on storage. 

Also in this case, Y2O3 was added to the nanocomposite. The creep tests were performed by four-point bending at temperatures of 1200 and 1450 °C within a stress range of 50-150 MPa. The creep rate was calculated from the slope of the c versus t curve (Fig. 9.31) and steady-state creep was evaluated using Fq. (9.5), i.e., the Norton equation. An alternative explanation for the observed increase in creep resistance in the nanocomposite is that the SiC nanoparticles hinder the grain growth... 

From the slope of the linear portion of the creep curve (after the system reaches a steady state), the viscosity at each applied stress, is calculated. A plot of % versus (T (Figure 7.40) allows one to obtain the limiting (or zero shear) viscosity and the critical stress eta (which may be identified with the true yield stress of the system). 

Fig. 2.11. Creep-compliance measurements at several temperatures (indicated in the figure) on a polystyrene sample with molecular weight 46 900, reduced to 100 °C with shift factors calculated from the steady-state viscosity. Subscript p denotes multiplication by Tp/ TqPq). From Plazek [53], by permission.

The steady-flow viscosity qo and the steady-state compliance can easily be determined from creep data in the region of linear viscoelastic behavior as shown-in Fig. 1-12, from equation 40 of Chapter 1, provided steady-state flow has been attained. However, it is easy to be misled into believing prematurely that the linear portion of the creep curve has been reached in general, it cannot be expected to become linear until the flow term t/vo is at least as large as the intercept / . It is always desirable to perform the recovery experiment shown in Fig. 1-12 to conflrm the calculation. 

Any uncross-linked polymer system with a viscosity high enough to be studied by the methods described in this section will be very slow in coming to steady-state flow attempts to obtain jjo and 7° from linear plots such as Fig. 1-12 should be approached with caution and skepticism, and if possible tested by creep recovery experiments. From the methods described in Chapter 4, it is possible to calculate the retardation spectrum L from J t) even if one is not sure whether steady-state flow has been achieved. 

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