Stress-time curves

With thermoplastic materials, above a certain stress, the stress-strain curve shows a marked departure from linearity that is, above such values, further increases in stress lead to disproportionately greater increases in elongation. By study of the isochronous stress-train curves of a material, it is possible to decide upon a certain strain that should not be exceeded in a given application. The stress required to produce this critical strain will vary with the time of application of the load, so that the longer the time of application, the lower will be the permissible stress. 

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Long-term deformation such as shown by creep curves and/or the derived isochronous stress-strain and isometric stress-time curves, and also by studies of recovery for deformation. 

For time-dependent fluids (thixotropic or rheopectic) there are no simple relations now available for showing the stress-strain-rate-time. dependence. Figure 15.2 is, a typical stress-time curve for a thixotropic fluid, showing lines of... 

Stress-time curve for various strain rates for a typical thixotropic fluid, obtained in an apparatus like that shown in Fig. 15.1. [Courtesy of the late E. B. Christiansen.]... 

Figure 4. Typical stress-time curve for determining loading rate...

Calculation of the final dimensions based on the stress-time curve for the design life of the part. 

The above type of data can be conveniently summarised by the presentation of stress-time curves corresponding to different levels of permissible strain. Such curves enable the time dependency of different materials to be conveniently compared. Where possible, rupture data should also be included on such plots so that at longer times an adequate safety margin over the rupture strength is always maintained. 

Figure 18.5 Stress-time curve. Source Author s own files)...

One convenient method is to combine the information available from either isochronous stress-strain curves or stress-time curves obtained on the same materials at different temperatures. For example, suppose the performance criterion for a particular application is that the total strain should not exceed 2% in 1000 hours. Using the 1000 hour isochronous stress-strain curve for each temperature, and erecting an ordinate at the 2% point on the strain axis, the individual working stresses for each temperature can be obtained. Alternatively, by erecting an ordinate at the 1000 hour point on the stress-time curve for 2% strain for each temperature investigated, the individual working stresses can be similarly obtained. From these interpolated results the stress-temperature curve can be drawn. 

As has already been mentioned, stress-time curves on a double logarithmic scale are also linear and can be easily extrapolated. In both cases, however, over-extrapolation should be avoided (i.e., one decade and preferably not more than two). 

To a first approximation, such data can be obtained from the basic family of creep curves by sectioning through them at the relevant strain value parallel to the time axis. That is to say, similar procedures are used as for obtaining stress-time curves. 

Figure 18.12 Interpolated stress-time curves of various grades of polypropylene at 23 °C (2% total strain). KMT 61 and GMT 61 = polypropylene copolymers. KM 61, GM 61 and DE 61 = polypropylene homopolymer. Source Author s own files)...

Figures 18.19, 18.20, 18.21 and 18.22 show creep curves, isochronous stress-strain curves, and stress-time curves, for a typical acrylonitrile-butadiene-styrene (ABS) terpolymer and a typical unplasticised polyvinyl chloride (PVC).

The data in Figure 2.9 demonstrate the marked influence of density on the creep behavior of polyethylene. The curves in Figure 2.9 are relevant to a total strain of 1%, but similar plots for other permissible strains can be readily derived from the isochronous stress-strain curves. The linear relationship between creep and density for polyethylene at room temperature, irrespective of the melt index over the range investigated (i.e., 0.2-5.5), has enabled the stress-time curve of Figure 2.10 to be interpolated for the complete range of polyethylene. In this case, the data have been based on a permissible strain of 2%, but as previously explained, data for other permissible strains can be similarly interpolated from the creep curves. 

FIGURE 2.10 Interpolated stress-time curves of PE of various densities (2% total strain). 

Of further note is the fact that constant true stress levels are rarely achieved in creep tests as the cross-section of the sample decreases as the sample extends, thus increasing stress levels (Figure 9.20). Information from a family of creep curves can be rearranged to give an isometric stress-time curve. A line drawn at constant strain across the curves will intercept them at a number of stress-time combinations, and these are used to plot the curve. This information can be used to determine the maximum stress that can be accepted for a specified time. 

Figure 9.20 Creep test results, (a) Series of creep curves, (b) Isometric stress/time curve, (c) Isochronous stress/strain curve, (d) Creep modulus/time curve. After Whelan and Craft [26].

Figure 2-35. Stress-time curve. (Courtesy of Instron Corporation.)...

Typical results obtained from dynamic tensile tests on concrete and fibre reinforced concrete are shown in Fig.4. The values of stress and strain are plotted with respect to time. The stress-time curves for specimens for which records of the deformation failed, are shown in Fig.5. 

Figure 4. Recorded stress-time curves (continuous lines) and strain-time curves (dashed lines) for concrete and fibre reinforced concrete specimens.

Figure 5. Recorded stress-time curves for concrete and fibre reinforced...

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