Creep in polymers

As with other types of material it is important when designing for 

The characteristic of most plastics, and especially unfilled thermoplastics, is that under load they exhibit creep. When a component is subjected to a load stresses are created in it and it will deform or deflect, i.e. a strain will result. In traditional materials like metals, stone, concrete, etc., these quantities are easily manipulated because the 

If this notion is extended to include a number of different loads a family of curves may be drawn. These curves show that  

It is important to note also that, of course, different polymers have different families of curves, and that for each polymer, the properties also vary with temperature. Fig. 1.9. 

A development of the isometric creep curves is the creep rupture curve A constant load is applied, straining is continued until failure occurs and the time for this is noted, i.e. the isometric element is the failure strain at that load. The experiment is repeated with another load and so on for several more loads. From these data a plot can then be made of rupture stress against time. Fig, 1,10. 

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In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

These equations predict a continuously diminishing rate of creep. Many empirical and semi-empirical models of creep-strain have been made and are described by Ward [24], One of these has been used successfully to describe the later stages of creep in polymers such as oriented polyethylene. The Arrhenius equation was modified by Eyring to apply to the rate of creep (deJdt) in the following way ... 

Note 5 The retardation spectrum (spectrum of retardation times) describing creep in polymers may be considered as arising from a group of Voigt-Kelvin elements in series. 

Dharmarajan, N., Kumar, S. and Armeniades, C.D. A constitutive equation for creep in polymer concretes and their resin binders. The Production, Performance and Potential of Polymers in Concrete (Ed. Staynes, B.W.), ICPIC 87, Brighton, Sept. 1987. 

Accuracy To ensure good balance in the impellor the moulding must be dimensionally stable. Thus there should not be undue mould shrinkage, nor must the product creep appreciably when rotating. (See PST 1 for an account of creep in polymers.)... 

Creep is the time-dependent change in strain following a step change in stress. Unlike the creep discussed by metallurgists, creep in polymers at low strains (1... 

Several polymers combine excellent ultraviolet resistance with good tensile and elongation at break properties (Table 11.3). The storage modulus, alpha relaxation, and creep in polymers are influenced by electron irradiation. Thus, the creep of some polymers increased upon exposure to electron beam irradiation below 4 Mrad. Neutron/gamma irradiation also had an adverse effect on some polymer properties. Thus, some glass fiber-reinforced plastics lose 20%-40% of their flexural strength after exposure to neutron/gamma irradiation doses above 1 x 10 Gy [3]. 

It remains to be investigated whether this concept is correct, and if so whether the resulting flow is that of a solid (similar to ductility in metals or creep in polymers) or that of other (extremely viscous) fluids [12]. Until this... 

Creep of polymers is a major design problem. The glass temperature Tq, for a polymer, is a criterion of creep-resistance, in much the way that is for a metal or a ceramic. For most polymers, is close to room temperature. Well below Tq, the polymer is a glass (often containing crystalline regions - Chapter 5) and is a brittle, elastic solid -rubber, cooled in liquid nitrogen, is an example. Above Tq the Van der Waals bonds within the polymer melt, and it becomes a rubber (if the polymer chains are cross-linked) or a viscous liquid (if they are not). Thermoplastics, which can be moulded when hot, are a simple example well below Tq they are elastic well above, they are viscous liquids, and flow like treacle. 

Polymers are a little more complicated. The drop in modulus (like the increase in creep rate) is caused by the increased ease with which molecules can slip past each other. In metals, which have a crystal structure, this reflects the increasing number of vacancies and the increased rate at which atoms jump into them. In polymers, which are amorphous, it reflects the increase in free volume which gives an increase in the rate of reptation. Then the shift factor is given, not by eqn. (23.11) but by... 

Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or "creep" in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122], Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5] ... 

When dash pot and spring elements are connected in parallel they simulate the simplest mechanical representation of a viscoelastic solid. The element is referred to as a Voigt or Kelvin solid, and it is shown in Fig. 3.10(c). The strain as a function of time for an applied force for this element is shown in Fig. 3.11. After a force (or stress) elongates or compresses a Voigt solid, releasing the force causes a delay in the recovery due to the viscous drag represented by the dash pot. Due to this time-dependent response the Voigt model is often used to model recoverable creep in solid polymers. Creep is a constant stress phenomenon where the strain is monitored as a function of time. The function that is usually calculated is the creep compliance/(f) /(f) is the instantaneous time-dependent strain e(t) divided by the initial and constant stress o. ... 

In polymers the time dependence of an modulus plays a more important role than in metals. If polymers are loaded with a constant stress they undergo a deformation e, which increases with time. This process is named creep. Conversely, if a test specimen is elongated to a certain amount and kept under tension, the initial stress s decreases with time. This decay is called stress relaxation. 

The concentration of hydrogen in the polymer during irradiation is low, on the order of 10"6 mole per cc. This is far lower than the concentrations of plasticizers required to cause any significant changes in polymer creep behavior. 

This differential equation states that the creep rate during irradiation is directly related not only to the deflection of the unstressed sample which has occurred up to that time (D2, which may be related to the increase in polymer free volume) but also to the rate of increase of D2 with time. The reason for the dependence of the creep rate on dDo/dt is not apparent but may be related to the fact that gas is being generated at an increasing rate as time progresses (as in the case of PVC). This relationship emphasizes the strong dependence of the ac-... 

Tschoegl,N. W. Stress relaxation and creep in dilute polymer solutions. J. Chem. Phys. 44,2331-2334(1966). 

Methyl methacrylate impregnated concrete-polymer specimens subjected to creep tests exhibited expansion under sustained load (negative creep), in contrast to contraction in length (positive creep) shown by ordinary concrete. If confirmed, this property could influence significantly the design of concrete-polymer structural and prefabricated members. 

There is strong interest to analytically describe the fzme-dependence of polymer creep in order to extrapolate the deformation behaviour into otherwise inaccessible time-ranges. Several empirical and thermo-dynamical models have been proposed, such as the Andrade or Findley Potential equation [47,48] or the classical linear and non-linear visco-elastic theories ([36,37,49-51]). In the linear viscoelastic range Findley [48] and Schapery [49] successfully represent the (primary) creep compliance D(t) by a potential equation ... 

The model represents a liquid (able to have irreversible deformations) with some additional reversible (elastic) deformations. If put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components as per the Maxwell Model. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. It is important to note limitations of such a model, as it is unable to predict creep in materials based on a simple dashpot and spring connected in series. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time. However, polymers for the most part show the strain rate to be decreasing with time [23-26],... 

In polymer processing, we frequently encounter creeping viscous flow in slowly tapering, relatively narrow, gaps as did the ancient Egyptians so depicted in Fig. 2.5. These flows are usually solved by the well-known lubrication approximation, which originates with the famous work by Osborne Reynolds, in which he laid the foundations of hydrodynamic lubrication.14 The theoretical analysis of lubrication deals with the hydrodynamic behavior of thin films from a fraction of a mil (10 in) to a few mils thick. High pressures of the... 

Creep in Structural Design A pendulum clock manufacturer wants to replace the metal pendulum arm of the clocks with a polymer rod. Is his idea a good one Use the answer to Problem 3.20. 

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