Creep logarithmic

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

When creep curves are plotted on logarithmic strain and time scales they are approximately straight lines so that the creep strain, edO may be expressed as... 

Tests have shown that when total strain is plotted against the logarithm of the total creep time (ie NT or total experimental time minus the recovery time) there is a linear relationship. This straight line includes the strain at the end of the first creep period and thus one calculation, for say the 10th cycle allows the line to be drawn. The total creep strain under intermittent loading can then be estimated for any combinations of loading/unloading times. 

The total creep strain after the stress of 10.5 MN/m has been applied for the 11th time would be 0.121 -I- 0.747 = 0.868%. Now tests have shown that a plot of total creep strain plotted against the logarithm of the total creep time (i.e. ignoring the recovery times) is a straight line which includes the point edT). 

Sato et al. " measured the viscosities of some binary and ternary alkali carbonates. Since melt creep must be prevented, a highly sintered alumina crucible was used instead of a gold-plated nickel crucible. Homogeneity of a mixture sample was achieved by gas bubbling. A laser beam is combined with a computer-assisted time counter to obtain the logarithmic decrement. Roscoe s equationi3i has been used for calculation of the viscosity, while it has been claimed by Abe et al. that the viscosities calculated from Roscoe s equation are 0.6-1.5% lower than those from more rigorous equations. 

Figures 5 and h show how the shape of the creep curve is modified by changes in the constants of the model. The values of the constants are given in Table I. Curve I is the same as shown in Figure 4, curve II shows onlv a small amount of viscous creep, and in curve 111, viscous flow is a prominent part of the total creep. The same data were used in Figures 5 and 6, but notice the dramatic, change in the shapes of the curves when a linear time scale is replaced by a logarithmic time scale. In the model, most of the recoverable creep occurs "Within about one decade of the retardation time.

Figure 6 Creep of a four-element model with the same constants as in Figure 5 but with a logarithmic time scale.

A distribution obtained by the use of equation (13) is only a first approximation to the real distribution. The corresponding distribution of retardation times is designated as L(T). It may be estimated from the slope of a compliance curve D(0 or J(t), for tensile or shear creep, respectively, plotted on a logarithmic time scale according to the equation (for shear creep)-... 

Plot the creep compliance (cm /dyn) as a function of time using a logarithmic time scale. Would the curve show the upward curvature on a linear time scale ... 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

By adopting a logarithmic creep function j(t)=j110log(t), Eq. Ill yields the following equation for the lifetime of a fibre... 

Assuming logarithmic creep, j(f)=j110log(f), Eqs. 118 and 119 allow the calculation of the creep curves up to fracture. The results are depicted in Fig. 62. Note that for increasing creep stress the slope of these curves decreases. 

Figure 8.8 Second stage of SIM. Creep modulus (load/strain) is plotted against the logarithm of the time measured from the respective temperature change.

Fig. 6.1.8. Hardness-testing time relation—logarithmic creep curve.

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) ... 

These differences in the mechanical behavior are not reflected, within the experimental error, in the temperature dependence of the mechanical properties. As shown by the examples of Figures 1 and 3, the relaxation modulus and creep compliance data showed very little scatter and could be shifted smoothly into superposition along the logarithmic time axis. The amounts of shift, log Or, required to effect superposition are plotted against the temperature, T, in Figure 5 for the relaxation data, and in... 

Values from tables of friction coefficients always have to be used with caution, since the experimental results not only depend on the materials but also on surface preparation, which is often not well characterized. In the case of plastic deformation, the static coefficient of friction may depend on contact time. Creeping motion due to thermally activated processes leads to an increase in the true contact area and hence the friction coefficient with time. This can often be described by a logarithmic time dependence... 

Yano et al. [53] studied acoustic properties of acetylated Sitka spruce by specific dynamic Young s modulus and by logarithmic decrement. For oven-dried specimens, both the modulus and the decrement have been found to increase. Meanwhile, mechanical properties are generally unchanged and adhesive strength is reduced by acetylation [2]. Furthermore, creep deformation of wood under humidity change is remarkably reduced by acetylation [54]. 

Figure 5.11 Schematic representation of the double logarithmic plot of shear creep compliance in the time domain.

Figure 8.2 Double logarithmic plots of the creep compliance function in the time domain at various temperatures for solutions of polystyrene in tri-m-tolyl phosphate the weight fraction of polymer in the solution is 0.70. The subscript p in Jp t) indicates that the values of this function have been reduced to a common temperature.

Figure 8.5 Double logarithmic plots of the creep compliance function versus t/a-p, where ap = (ri/Tio)(Po7b/p70 and the subindex 0 refers to 100°C. (From Ref. 5.)...

Figure 8.26 Double logarithmic plots showing the concentration dependence of both the creep compliance and the relaxation modulus at the plateau. (From Ref. 8.)...

The values of Jg, m, and were obtained by determining the value of Jg that best fits the double logarithmic plots of [Jg — Jit)]/J t) vs. t to a straight line. It has been found that the values of Jg, from creep and 3/Eg from the stress relaxation are in rather good agreement for several rubbers. 

Figure 12.26 Double logarithmic plot showing the creep rupture time, tf, as a function of the applied stress, a, for poly(methyl methacrylate) at 24°C. Data obtained for (A) freshly quenched samples and (O) samples aged at 24°C for 5 years. (From Ref. 30.)...

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