Creep behaviour time dependence

Creep and Recovery Behaviour. Plastics exhibit a time-dependent strain response to a constant applied stress. This behaviour is called creep. In a similar fashion if the stress on a plastic is removed it exhibits a time dependent recovery of strain back towards its original dimensions. This is illustrated in... 

For a linear viscoelastic material in which the strain recovery may be regarded as the reversal of creep then the material behaviour may be represented by Fig. 2.49. Thus the time-dependent residual strain, Sr(t), may be expressed as... 

In this book no prior knowledge of plastics is assumed. Chapter 1 provides a brief introduction to the structure of plastics and it provides an insight to the way in which their unique structure affects their performance. There is a resume of the main types of plastics which are available. Chapter 2 deals with the mechanical properties of unreinforced and reinforced plastics under the general heading of deformation. The time dependent behaviour of the materials is introduced and simple design procedures are illustrated. Chapter 3 continues the discussion on properties but concentrates on fracture as caused by creep, fatigue and impact. The concepts of fracture mechanics are also introduced for reinforced and unreinforced plastics. 

Stress relaxation tests are alternative ways of measuring the same basic phenomenon in viscoelastic polymers as creep tests, Le. the time-dependent nature of their response to an applied stress. As such, they have also been of value in understanding the behaviour of these materials. The essence of stress relaxation tests is that strain increases with time for a given stress, so that if stress is decreased with time in a controlled manner ( relaxed ), a state... 

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. 

For a semi-crystalline polymer the E-modulus shows between Tg and (in which region it is already lower than below Tg), a rather strong decrease at increasing T, whereas with amorphous polymers, which are used below Tg, the stiffness is not much temperature dependent (apart from possible secondary transitions). The time dependency, or the creep, shows a similar behaviour. 

Relaxation processes are universal. They are found in all branches of physics mechanical relaxation (stress and strain relaxation, creep), ultrasonic relaxation, dielectric relaxation, luminescence depolarisation, electronic relaxation (fluorescence), etc. Also the chemical reaction might be classified under the relaxation phenomena. It will be readily understood that especially in polymer science this time-dependent behaviour is of particular importance. 

Dimensional stability is one of the most important properties of solid materials, but few materials are perfect in this respect. Creep is the time-dependent relative deformation under a constant force (tension, shear or compression). Hence, creep is a function of time and stress. For small stresses the strain is linear, which means that the strain increases linearly with the applied stress. For higher stresses creep becomes non-linear. In Fig. 13.44 typical creep behaviour of a glassy amorphous polymer is shown for low stresses creep seems to be linear. As long as creep is linear, time-dependence and stress-dependence are separable this is not possible at higher stresses. The two possibilities are expressed as (Haward, 1973)... 

Several successive sets of creep tests were carried out between 1996 and 2002. The tests results show that the argillites has a time-dependent behaviour even in undrained conditions. That observation confirms that the time-dependent behaviour of the argilites is thus dependent on both... 

Before the models are described, the two simple aspects of viscoelastic behaviour already referred to - creep and stress-relaxation - are considered. For the full characterisation of the viscoelastic behaviour of an isotropic solid, measurements of at least two moduli are required, e.g. Young s modulus and the rigidity modulus. A one-dimensional treatment of creep and stress-relaxation that will model the behaviour of measurements of either of these (or of other measurements that might involve combinations of them) is given here. Frequently compliances, rather than moduli, are measured. This means that a stress is applied and the strain produced per unit stress is measured, whereas for the determination of a modulus the stress required to produce unit strain is measured. When moduli and compliances are time-dependent they are not simply reciprocals of each other. 

Boltzmann extended the idea of linearity in viscoelastic behaviour to take account of the time dependence He assumed that, in a creep experiment ... 

The term time dependency involved in squeezing ground behaviour, is mainly due to the creep caused by exceeding a limiting shear stress creep and consolidation processes taking place around the tunnel (Deere. 1981, Aydan et al. 1993, Anagnostou Kovari 2005). 

High performance polyethylene fibres such as Dyneema (a reinforcing polyethylene fibre from DSM) show a pronounced time-dependent behaviour under static loading conditions. An increase in strain rate and/or decrease in temperature results in an increase in fibre modulus and strength, but a decrease in work of fracture [33]. It is also known that creep can be observed even in unidirectional PE-fibre reinforced laminates. How far this specific behaviour influences the fatigue behaviour is of great interest and has to be investigated in order to find the appropriate applications for PE-composites. 

The theory outlined above is rigorous only for infinitesimal elastic deformation. Creep of polymeric materials is explicitly concerned with time dependence and implicitly with finite strains and therefore nonlinear behaviour. The nature of the non-linear behaviour is complex and varies not only from material to material but also with direction within a given sample of material, i.e. the non-linearity of behaviour is anisotropic. It is found, therefore, that on a particular definition of strain the behaviour of a sample may appear to be linear in one direction and significantly non-linear in another. Such a phenomenon is demonstrated in results presented below. 

So far the parameters defined, compliances, moduli and contraction ratios, are in forms which can be rigorously interpreted for infinitesimal time dependent deformation under constant stress, thus creep moduli E 9, r) are functions of angle and time. Extension to accommodate nonlinear behaviour at finite strain is obtained by allowing the quantities to become also functions of stress or strain. Thus modulus has the form E 6,t,%) and compliance functions Si/t.t). Such an extension is not rigorous but is useful. 

A major problem in data presentation for anisotropy of creep behaviour arises from the dependence of behaviour on many parameters. In Section 10.2 the modulus for a given degree of molecular orientation under given environmental conditions for a single material was given as a function of angle, time and either stress or strain whilst the material compliance functions for these conditions were functions of time and stress or strain. Changes of temperature, composition, orientation, structure, etc., will of course affect the whole pattern of behaviour. 

The value of the simplified technique for producing isochronous stress-strain curves for non-linear isotropic materials by successive loading and unloading of a single sample have been amply demonstrated over many years and fully described elsewhere.These techniques become even more valuable in studies of anisotropy, where samples may be difficult to obtain in large numbers and where the scope of the problem is much larger. A considerable proportion of work on oriented materials reported in the literature is essentially confined to this measurement and does not include studies of time dependence of behaviour. Detailed work has been carried out validating this procedure for oriented materials by comparison of the isochronous stress-strain data with isochronous sections from families of creep curves. ... 

In studying time dependence, Le. creep behaviour, it is necessary to carry out tests at several stress levels in each direction of interest in the oriented material. I his can involve a prohibitive amount of experimental work and, in practice, little is generally lost by reducing the tests to, say, one creep curve and one isochronous stress-strain curve in each direction. The problem then becomes one of selection of the absolute value of stress for each of the creep curves and is most severe when non-linearity and its anisotropy are well developed. The choice of stress levels is arbitrary but interesting special cases are (a) equal stress levels at all angles and (b) equal strain ranges at all angles. 

The behaviour of the lateral compliance, S13, is similar to that of 533 but the behaviour of S12 at low draw ratio is worthy of note. Thus, on applying the creep load, an initial decrease in specimen thickness is followed first by a slight time dependent thickening and then the more usual time dependent decrease in thickness. No explanation has yet been offered for this unexpected effect. It has also been observed in LDPE drawn at 90°C and is completely reproducible and experimentally significant. ... 

From the dynamic mechanical measurements of Stachurski and Ward this process is seen to occur at 50°C in the region of 150 Hz. Clayton et al. concluded therefore that the tensile creep behaviour observed at low draw ratio could be the result of the cone easy shear process occurring in their time scale at 20°C. The observed anisotropy of time dependence of S33 and S22 dS33/dt > dS22/dt) leads to a low value of (0) compared with (90), which is consistent with the above conclusion. Furthermore, calculation of the variation of volume strain with time during tensile creep at 0° and 90° (made possible by the measurement of both lateral and axial strains) showed that at 0° the... 

The tensile creep behaviour of specially oriented sheets of LDPE was studied by Gupta and Ward. However, their data took the form of a dependence of isochronous modulus on temperature time dependence and non-linearity being ignored. The interpretation of such data is reviewed elsewhere in this book. 

Inspection of this equation shows that it models reasonably well, on a very superficial level, a stress-strain curve of the type shown in Fig. 1(b), curve (4). In other words it raises the question as to whether the deviations from linear stress-strain relationships observed in constant strain-rate tests might not be merely resulting from the intrinsic time-dependence of the linear viscoelasticity, which can be more clearly studied in creep or stress-relaxation and not due to some new process starting at high stresses. It does not take long to show that at the strain-levels of 3-5% experienced at yield, the response of most polymers is highly non-linear (r(t)/ is a function of strain-rate S as well as t, and so eqn. (14) cannot adequately describe the behaviour. However, it is also clear that at... 

During loading time t), the bituminous mixture deforms the deformation (51) and, thus, the strain (e) increase rapidly at the beginning and then become quasi-constant. After removal of applied stress (rest period), part of the total deformation is recovered instantaneously (the elastic deformation), another part of deformation is recovered gradually and is time dependent (viscoelastic deformation) and another part of the deformation cannot be recovered (viscous or plastic or permanent deformation). Figure 7.15 explains the above, in terms of strain, which is known as creep behaviour. As it can be seen, the above behaviour is similar to the viscoelastic behaviour of the bitumen (see Section 4.21.1). 

Creep. In general, polymers exhibit a degree of visco-elastic behaviour and thus for full characterisation of such a material a knowledge of its rate dependent response is necessary. To determine the long-term behaviour of a material either stress relaxation or creep tests may be used. The former involves monitoring the time-dependent change in stress which results from the application of a constant strain to a specimen at constant temperature. Conversely,... 

Creep curves in shear were measured at different stages of the gelation process. At temperatures above 0°C the rate of gelation was too small for a reasonable measurement. Initially, the creep curves showed liquidlike behaviour, whereas after some time, depending on temperature, rubberlike behaviour... 

The modified series model shown in Fig. 21 has been extended to include the viscoelastic behaviour. 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 fibre 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 CTq... 

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