Stress isochronous

ISOMETRIC STRESS ISOCHRONOUS STRESS VS LOG TIME VS STRAIN... 

Strain and constant time can give respectively isometric stress-log time curves and isochronous stress-strain curves Figure 9.10). Whilst not providing any new information, such alternative presentations of the data may be preferred for certain purposes. 

ISOCHRONOUS STRESS - STRAIN CURVE CREEP MODULUS - TIME CURVE... 

Figure 9.10. Presentation of creep data sections through the creep curves at constant time and constant strain give curves of isochronous stress-strain, isometric stress-log (time) and creep modulus-log (time). (From ICI Technical Service Note PES 101, reproduced by permission of ICI...

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. 

These latter curves are particularly important when they are obtained experimentally because they are less time consuming and require less specimen preparation than creep curves. Isochronous graphs at several time intervals can also be used to build up creep curves and indicate areas where the main experimental creep programme could be most profitably concentrated. They are also popular as evaluations of deformational behaviour because the data presentation is similar to the conventional tensile test data referred to in Section 2.3. It is interesting to note that the isochronous test method only differs from that of a conventional incremental loading tensile test in that (a) the presence of creep is recognised, and (b) the memory which the material has for its stress history is accounted for by the recovery periods. 

Quite often isochronous data is presented on log-log scales. One of the reasons for this is that on linear scales any slight, but possibly important, non-linearity between stress and strain may go unnoticed whereas the use of log-log scales will usually give a straight-line graph, the slope of which is an indication of the linearity of the material. If it is perfectly linear the slope will be 45°. If the material is non-linear the slope will be less than this. 

As indicated above, the stress-strain presentation of the data in isochronous curves is a format which is very familiar to engineers. Hence in design situations it is quite common to use these curves and obtain a secant modulus (see Section 1.4.1, Fig. 1.6) at an appropriate strain. Strictly speaking this will be different to the creep modulus or the relaxation modulus referred to above since the secant modulus relates to a situation where both stress and strain are changing. In practice the values are quite similar and as will be shown in the following sections, the values will coincide at equivalent values of strain and time. That is, a 2% secant modulus taken from a 1 year isochronous curve will be the same as a 1 year relaxation modulus taken from a 2% isometric curve. 

The maximum stress or strain is not specified so an iterative approach is needed. From the 1 year isochronous for PP the initial modulus is 370 MN/m2... 

From the 1 day isochronous curve, the maximum stress at which the material is linear is 4 MN/m. TTiis may be converted to an equivalent shear stress by the relation... 

Example of isochronous stress-strain curves for PCs resulting from stress relaxation. 

Figure 4 shows stress-strain curves measured at an extension rate of 94% per minute on the TIPA elastomer at 30°, —30°, and —40°C. With a decrease in temperature from 30° to -40°C, the ultimate elongation increases from 170% to 600%. The modulus Ecr(l), evaluated from a one-minute stress-strain isochrone, obtained from plots like shown in Figure 1, increases from 1.29 MPa at 30°C to only 1.95 MPa at —40°C. This small increase in the modulus and the large increase in the engineering stress and elongation at fracture results from viscoelastic processes. 

Here m is the usual small-strain tensile stress-relaxation modulus as described and observed in linear viscoelastic response [i.e., the same E(l) as that discussed up to this point in the chapter). The nonlinearity function describes the shape of the isochronal stress-strain curve. It is a simple function of A, which, however, depends on the type of deformation. Thus for uniaxial extension,... 

The isochronous stress-strain curves for the creep of PP bead foams (254) were analysed to determine the effective cell gas pressure po and initial yield stress do as a function of time under load (Figure 11). po falls below atmospheric pressure after 100 second, and majority of the cell air is lost between 100 and 10,000 s. Air loss is more rapid than in extruded PP foams, because of the small bead size and the open channels at the bead boundaries, do reduces rapidly at short yield times <1 second, due to proximity of the glass transition, and continues to fall at long times. 

For example, the volume change of an acrylonitrile-butadiene rubber (NBR)40 sample at X = 2 relative to the volume of its undeformed state was about 5 x 10 4, and the values for the other vulcanizates were less than this. We therefore assumed that the use of Eqs. (34) and (35) is warranted for the computation of dW/dlt for our rubber samples, except at very small deformations for which// < 3.02. In most cases, stress relaxation was allowed to proceed at given stretch ratios and 1- and 10-min isochronal stress values were taken for the calculations. 

Figures 29 A and B show the original data from general biaxial extension measurements on the NR sample. Here the measured stresses at and a2 at a series of fixed Xx are plotted against X2. All these values are isochronal (10 min). The graphs have been displayed to illustrate the accuracy of our measurements. In Fig. 30, the observed at are compared with the predictions from other stress-strain relations.

For practical applications empirically determined creep data are being used, such as D(t) or, more often, E(t) curves at various levels of stress and temperature. The most often used way of representing creep data is, however, the bundle of creep isochrones, derived from actual creep curves by intersecting them with lines of constant (log) time (see Figure 7.7). These cr-e-curves should be carefully distinguished from the stress-strain diagram discussed before, as generated in a simple tensile test ... 

From a bundle of creep isochrones the tendency of a material to creep, can be read-off in a glance, namely from their mutual distance. Along horizontal lines of constant stress, the increase of deformation by creep can be detected. When the isochrones are straight lines, the superposition principle holds. Compliances at certain combinations of cr and t follow from the (reciprocal) slopes of connection lines to the origin. 

Creep isochrones are, sometimes, used to obtain information on stress relaxation the stresses are then read-off on a vertical line (constant strain). In general this is, however, not allowable, since E(t) in relaxation is not equal to 1 /D(t) in creep. In a linear region this objection is not too stringent for want of something better, the procedure can be used as a first approximation (data on stress relaxation are very scarce ). 

Creep at different temperatures can be represented by separate bundles of isochrones. A simple time-temperature shift could mean that for higher temperatures shorter time values could be written at each curve. It is, however, easier to transform the stress scale. Sometimes this is possible with sufficient accuracy in those cases only one bundle of isochrones is given with different stress scales for a number of temperature levels (Figure 7.9) (see also Qu. 7.13). 

Detection of crazes is very difficult yet craze formation should be avoided in critical applications (such as gas pipes). In order to achieve that, one uses the expression critical strain , which is based on the observation that, as long as a certain level of strain is not exceeded, no crazes are formed. It would be convenient if this critical strain would be independent of the applied stress this is, unfortunately, not the case, as illustrated in the bundle of isochrones in Figure 7.23... 

For practical purposes the lower limit of the critical strain can be used as a criterion. This value appears, moreover, to be not much dependent on temperature, so that it can be considered as a material constant. It varies from -03% for PS to 2.2 % for PP. From creep isochrones a stress level can now quite easily be detected at which, within a given time of usage, no damage to the material is to be expected. This stress level is, of course, much lower than the one we found from Figure 7.20. 

Dynamic Mechanical Properties. Figure 15 shows the temperature dispersion of isochronal complex, dynamic tensile modulus functions at a fixed frequency of 10 Hz for the SBS-PS specimen in unstretched and stretched (330% elongation) states. The two temperature dispersions around — 100° and 90°C in the unstretched state can be assigned to the primary glass-transitions of the polybutadiene and polystyrene domains. In the stretched state, however, these loss peaks are broadened and shifted to around — 80° and 80°C, respectively. In addition, new dispersion, as emphasized by a rapid decrease in E (c 0), appears at around 40°C. The shift of the primary dispersion of polybutadiene matrix toward higher temperature can be explained in terms of decrease of the free volume because of internal stress arisen within the matrix. On the other... 

Figure 2. Failure envelope for Sample A. Log percent elongation vs. log stress (engineering) for various isochrones obtained from creep data. Line a corresponds to necking, line p to the fully necked condition, and line y to fracture.

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