Tensile creep compliance

Figure 3 shows the plot of the reduced tensile creep compliance, Dp(t), against t in logarithmic coordinates for the creep tests on Sheet I. A similar plot was made for the data obtained from Sheet II, and, in addition, for the relaxation data shown in Figure 1 after conversion to creep data using the relation (7) ... 

Figure 3. Reduced tensile creep compliance, DD(t), of Kraton 102 cast from benzene solution, at different temperatures as a function of time, t (Sheet I)...

Figure 13. Master curves of the extra tensile creep compliance, ADD(t), of Kraton 102, cast from benzene solution at 0°C...

Changes in properties of materials during aging form the crux of much research. Changes in thermal and mechanical properties are the most commonly used parameters in studying aging because they are easily detectable. For example, Struik (I) studied the effect of physical aging on torsional and tensile creep compliance of about 40 totally amorphous materials, Chapman (9) examined the effect of physical... 

We will first consider the parameters we are trying to model. Let us start with stress relaxation, where it is usual to describe properties in terms of a relaxation modulus, defined in Table 13-5 for tensile [ (r)] and shear [G(r)] experiments. The parameter used to describe the equivalent creep experiments are the tensile creep compliance [D(r)] and shear creep compliance [7(0]. It is important to realize that the modulus and the compliance are inversely related to one another for linear, tune-independent behavior, but this relationship no longer holds if the parameters depend on time. 

Consider the tensile experiment of Fig. 11 -12a as a creep study in which a steady stress To is suddenly applied to the polymer specimen. In general, the resulting strain c(t) will be a function of time starting from the imposition of the load. The results of creep experiments are often expressed in terms of compliances rather than moduli. Tlie tensile creep compliance D(t) is... 

Creep experiments are often carried out by hanging a weight on a strip of material of rectangular or cylindrical cross section (ref. 4, page 132 and 162). In this case, the tensile creep compliance D t) is calculated as... 

The evolution of the tensile creep compliance of a glassy epoxy resin at different aging times is shown, as an example, in Figure 12.22. The glasses were obtained by quenching the resin from Tg -I- 22°C to Tg — 9°C and were kept at this temperature for different intervals of time. The results obtained show that as the aging time increases, the values of J t) for comparable... 

The corresponding experiment in extension results in the tensile creep compliance D(t) defined by... 

Also from the results of Chapter 2, Section A, it is clear that the left side of equation (3-8) is simply the tensile creep compliance, D(t). Thus the response of the Maxwell model to a creep experiment is... 

A straight rod of polymer is 10 mm in diameter (2r) and 1 m long. The pol5aner behaves in a linear viscoelastic manner with a tensile creep compliance that can be well approximated by J t) = (2 — ) GPa ,... 

Fig. 12. Variation of tensile creep compliance with time for specimens cut at armies of 0°, 45° and 90° to the fibre axis of hot-drawn (H) and cold-drawn (C) LDPE (from...

Figure 12.2 Experimental tensile creep compliance data in logarithmi. coordinates at the same temperatures as in Figure 12 1 (After [36])...

A bar of polypropylene is of length 200 mm and has a rectangular cross-section of dimensions 25 mm X 3 mm. It is subjected to a constant tensile load of 250 N acting along its length. 100 s after the load was applied the length is measured and is found to have increased by 0.5 mm. Determine the 100 s tensile creep compliance. 

A spherical vessel is moulded from a pofymer whose one-month tensile creep compliance D(1 month) is 2 GPa . The vessel is of diameter 400 mm and wall thickness S mm. A constant internal pressure is applied to the vessel, giving rise to a tensile stress 1.6 MPa acting uniform in all directions in the plane of the vessel wall. Find (a) the change in diameter, and (b) the change in wall thickness, after 1 month of pressurization, assuming the polymer to be linearly viscoelastic with constant Poisson ratio v = 0.41. 

Let 3S°C be taken as reference temperature Tg and 40°C as temperature T. Then, applying eqn 4.72 to the tensile creep compliance yields... 

Rearranging, the required tensile creep compliance at 40°C is given by... 

A straight rod of solid polymer is of length 1 m and diameter 10 mm. The polymer is linearly viscoelastic with a tensile creep compliance... 

Show that, for a linear viscoelastic beam under a constant bending moment Mg, the curvature of the beam 1/R (R is the radius of curvature) increases with time t according to an equation similar to that for a linear elastic beam, except that the reciprocal tensile creep compliance (or creep modulus ) takes the place of Young s modulus ... 

Diffusion coefficient Tensile compliance Tensile creep compliance... 

A grade of polypropylene is found to have the following tensile creep compliance when measured at 35 C. 

Figure 10.13 (29) illustrates typical creep compliance results for poly(vinyl chloride), which has a glass transition temperature of about 80°C. The most important conclusion obtained from such studies is that the rate of creep slows down as the sample ages. Note that in the first and last curves in Figure 10.13, the polymer reaches a tensile creep compliance of 5 x 10 m /N after about 10 s after being aged for 0.03 days, but after an aging period of 1000 days, 10 s are required to reach the same tensile creep compliance level. 

Next, a model joint (or thick adherend specimen) problem presented in Reference 49 is analyzed using the present program, NOVA. In this case, a linear viscoelastic finite-element analysis was carried out on the model joint under a constant applied load of 4448 N giving an average adhesive shear stress of 13.79 MPa. The specimen geometry, descretization, and boundary conditions are shown in Figure 5. The thickness of the adhesive layer is taken to be 0.254 mm. A nine-parameter solid model was used to represent the tensile creep compliance of FM-73 at 72 °C and is given by... 

Fig. 2.10. The small-strain tensile-creep compliance versus creep time of poly(vinyl chloride) quenched from 90 °C to 20 °C and aged at 20 dz 0.1 °C for a period of time in days (indicated above the curves), after which each individual creep measurement was performed. The reduced curve on the extreme right was obtained by shifting the individual creep data to the longest-aging-time (1000 days) response as indicated by the arrow. From Struik by permission [44].

FIG. 18-11. Tensile creep compliance plotted against time with a logarithmic scale for poly(vinyl chloride) quenched from 90°C to 40° and aged for varying periods as shown up to 1000 days. Curve at right contains all points after shifts as in Fig. 18-10 (almost no vertical shift). (Struik. ) Reproduced, by permission, from Physical Aging in Amorphous Polymers and Other Materials, by L. C. a Struik, Elsevicr/North Holland Biomedical Press, 1978. 

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