Stress Relaxation and Creep

Reliable creep and stress relaxation data are obtainable only if the specimens are well defined and strictly comparable. As deformations and deformation rates are usually quite small, if linearity is to hold then precision measurements are required conditions that may be difficult to attain throughout the highly significant short-time regime. 

The creep of polymer fibers is composed of the primary creep, which is recoverable with time, and of the non-recoverable or secondary 

The secondary creep is almost negligible if a fiber has been 

Creep measurements on single PpPTA filaments have been performed by Walton and Majumdar. They observed creep strains amounting to less than 20% of the initial elastic strain after several years under stress. The graphs of the creep plotted against the logarithm of time were not linear but showed an increasing slope. Ericksen observed logarithmic creep curves and, in addition, found that the strain after recovery from creep also 

The modified series model shown in Fig. 6.21 has been extended to include the viscoelastic behavior. To this end the simple assumption is made that the time-dependent part of the creep strain arises solely from the rotation of the chains towards the direction of the fiber axis as a result of the shear deformation of the crystallites. This yields for the fiber extension as a function of the time t during creep caused by a stress (Tq  

At any time the orientation parameter is given by the equation for the dynamic compliance (6.15) and we obtain 

During the last few years, most attention has been paid to the blending of PLCs with less expensive thermoplastic engineering polymers (EPS). Addition of PLCs to such polymers not only enhances mechanical properties (strength and stiffness) of the resulting composites obtained due to the orientation of the PLC phase, but also improves their processing properties. Even relatively small amounts of a PLC may induce a reduction in the melt viscosity and thus improve the processability. In most cases, under appropriate processing conditions the dispersed PLC phase can be deformed into a fibrillar one. The 

Mechanical and Thermophysical Properties of Polymer Liquid Crystals Edited by W. Brostow 

Despite this large volume of results, there are almost no papers on the thermoviscoelastic behavior of PLCs and their blends with EPs under conditions of creep or stress relaxation. At the same time, it is known that the time dependence of the mechanical behavior of these materials is significant, i.e. they are distinctly viscoelastic. Thus creep and stress relaxation studies can give important information for better understanding of the peculiarities of this type of polymer material and for the application conditions of PLCs as engineering materials. 

The only data on creep and stress relaxation of PLCs and their blends available at present are those obtained by the present authors and their colleagues. In the following sections we analyze those results, noting possible general features. 

There are two further related sets of tests that can be used to give information on the mechanical properties of viscoelastic polymers, namely creep and stress relaxation. In a creep test, a constant load is applied to the specimen and the elongation is measured as a function of time. In a stress relaxation test, the specimen is strained quickly to a fixed amount and the stress needed to maintain this strain is also measured as a function of time. 

In creep tests, the parameter of interest is the creep compliance, J, defined as the ratio of the creep strain to the applied stress, i.e. 

Immediately the load is applied, the specimen elongates corresponding to an instantaneous elastic modulus. This is followed by a relatively fast rate of creep, which gradually decreases to a smaller constant creep rate. Typically this region of constant creep in thermoplastics essentially corresponds to 

Since the stress is constant, it follows that so also is the creep rate. The creep compliance at time t, 7, can be considered to consist of three terms, an instantaneous compliance, Jq, a term covering a variety of retardation processes, xj/it), and a viscous term, t/rj. These are related by  

The last term represents irrecoverable flow which occurs in these polymers such that there is a permanent deformation which remains in the specimen after the load is removed. 

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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. 

Snap-Fit and Press-FitJoints. Snap-fit joints offer the advantage that the strength of the joint does not diminish with time because of creep. Press-fit joints are simple and inexpensive, but lose hoi ding power. Creep and stress relaxation reduce the effective interference, as do temperature variations, particularly with materials with different thermal expansions. 

Tensile Testing. The most widely used instmment for measuring the viscoelastic properties of soHds is the tensile tester or stress—strain instmment, which extends a sample at constant rate and records the stress. Creep and stress—relaxation can also be measured. Numerous commercial instmments of various sizes and capacities are available. They vary greatiy in terms of automation, from manually operated to completely computer controlled. Some have temperature chambers, which allow measurements over a range of temperatures. Manufacturers include Instron, MTS, Tinius Olsen, Apphed Test Systems, Thwing-Albert, Shimadzu, GRC Instmments, SATEC Systems, Inc., and Monsanto. 

A typical stress—strain curve generated by a tensile tester is shown in Eigure 41. Creep and stress—relaxation results are essentially the same as those described above. Regarding stress—strain diagrams and from the standpoint of measuring viscoelastic properties, the early part of the curve, ie, the region... 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

Dynamic loading in the present context is taken to include deformation rates above those achieved on the standard laboratorytesting machine (commonly designated as static or quasi-static). These slower tests may encounter minimal time-dependent effects, such as creep and stress-relaxation, and therefore are in a sense dynamic. Thus the terms static and dynamic can be overlapping. 

Long time dynamic load involves behaviors such as creep, fatigue, and impact. T vo of the most important types of long-term material behavior are more specifically viscoelastic creep and stress relaxation. Whereas stress-strain behavior usually occurs in less than one or two hours, creep and stress relaxation may continue over the entire life of the structure such as 100,000 hours or more. 

The rate of creep and stress relaxation of TPs increases considerably with temperature those of the TSs (thermoset plastics) remain relatively unaffected up to fairly high temperatures. The rate of viscoelastic creep and stress relaxation at a given temperature may also vary significantly from one TP to an-... 

Creep and stress relation Creep and stress relaxation behavior for plastics are closely related to each other and one can be predicted from knowledge of the other. Therefore, such deformations in plastics can be predicted by the use of standard elastic stress analysis formulas where the elastic constants E and y can be replaced by their viscoelastic equivalents given in Eqs. 2-19 and 2-20. 

Creep and stress-relaxation tests measure the dimensional stability of a material, and because the tests can be of long duration, such tests are of great practical importance. Creep measurements, especially, are of interest to engineers in any application where the polymer must sustain loads for long periods. Creep and stress relaxation are also of major importance to anyone interested in the theory of or molecular origins of Viscoelasticity. 

Very simple models can illustrate the general creep and stress-relaxation behavior of polymers except that the time scales are greatly collapsed in the models compared to actual materials. In the models most of the in-... 

Thus (he time scale / at /, divided by an is equivalent to the scale at On a log scale, log a, is thus the horizontal shift factor required for superposition. An important consequence of equation (22) is that a, or log (ii is the same for a given polymer (or solution) no matter what experiment is being employed. Thai is. creep and stress-relaxation curves are shifted by the same amount. 

At temperatures well below 7K where polymers are brittle, their molecular veight has a minor effect on creep and stress relaxation. This independence... 

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