Deformation behaviour creep

Since the tensile test has disadvantages when used for plastics, creep tests have evolved as the best method of measuring the deformation behaviour of... 

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. 

Mechanical properties per se concerns with the qualities which determine the behaviour of a material towards applied forces. The ability to support weight without rupture or permanent deformation, to withstand impact without breaking, to be mechanically formed into different shapes - all these depend upon a combination of mechanical properties characteristic of metals. Four types of behaviour of a material under stress are very important linear or elastic behaviour, plastic behaviour, creep behaviour and fatigue behaviour. 

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 ... 

G. Sauthoff High Temperature Deformation and Creep Behaviour of BCC Based Interme-tallics. In O. Izumi (ed.) Proceedings of the International Symposium on Intermetallic Compounds - Structure and Mechanical Properties - (JIMIS-6). The Japan Institute of Metals, Sendai (1991)371-378. 

Under static loading conditions where either the stress or strain is keeping constant polymer materials (especially thermoplastics) show non-linear viscoelastic deformation behaviour to appear as retardation (creep) or relaxation. Long-term investigations to analyse creep or relaxation can be accomplished at flexural, indentation, or uniaxial tensile or compression loading as a function of time and loading level as well as environmental conditions such as temperature, media etc. (see [13Gre], p. 171 - 183). 

Target values for the required mechanical strength and the deformation behaviour of the adhesive layer are derived. We describe how adhesive formulahons can be developed and tested for their potential application based on shear, delamination and creep tests. With a limited number of suitable adhesive systems, large scale bending tests were carried out to verify the theoretical predictions. A fully satisfactory behaviour of a single adhesive layer demonstrated the enhanced strength of the glulam beam. 

The simplest test used to study the deformation behaviour of asphalts was the static unconfined uniaxial compression test, termed the creep test, developed in the 1970s by Shell Bitumen (Hill 1973). The specimen was subjected to static axial compressive load over a long period (1 h). The test procedure was very simple and required low-cost equipment. In addition. Shell Bitumen developed a rut prediction procedure based on results of the creep test but soon realised that it underestimated rut depths measured in trial pavements (Hill et al. 1974). This was attributed to the effects of dynamic loading producing higher deformation in the wheel-tracking test (Van de Loo 1974). 

Polymers undergo deformation under an applied stress over their lifetime some deformations which are irrecoverable once the source of stress is removed are referred to as creep. An understanding of the mechanical response of a polymer can be obtained by investigating the viscoelastic properties using creep experiments, where the behaviour is monitored under small deformational stress. Creep behaviour is an important consideration if the properties and dimensions are to be maintained. Experimental creep behaviour can be quantified using the four-element model with some limitations evident in the viscoelastic transitional region. ... 

Various deformation, however, are imposed unavoidably on geomembranes during the installation and operational phase, even if they are handled and installed correctly. The imposed deformations also result in stresses which are partially relieved over the course of time by stress relaxation. Chapter 4 deals with creep, relaxation and deformation behaviour of HDPE geomembranes in more detail. Since imposed deformations represent a frequent and a likely event, not only particularly stress crack resistant resins should be chosen but the relaxation behaviour of the geomembranes should be checked as well. 

The term creep is used in the literature primarily in connection with the delayed deformation behaviour of solid materials due to sudden mechanical loading [359]. Very similar behaviour can be observed to different degrees in the relationship between the respective physical parameters in ferromagnetic and ferroelectric materials as well as in magnetostrictive and - even more pronounced - in piezoelectric actuators. And so the term creep came to stand for more than just the delayed response between mechanical input... 

Time-dependent creep can be accurately modelled using the viscoelastic theory, which inherently assumes that all deformation is eventually recovered. However, when considering the long-term deformational behaviour of polymers it is important to realise that all polymers are subject to physical ageing, which not only affects the polymer s stiffness but has a profound influence on its creep deformation. Physical ageing of the matrix material should therefore be considered in order to make the investigation of the delayed failure of the composite meaningful. 

This competition between mechanisms is conveniently summarised on Deformation Mechanism Diagrams (Figs. 19.5 and 19.6). They show the range of stress and temperature (Fig. 19.5) or of strain-rate and stress (Fig. 19.6) in which we expect to find each sort of creep (they also show where plastic yielding occurs, and where deformation is simply elastic). Diagrams like these are available for many metals and ceramics, and are a useful summary of creep behaviour, helpful in selecting a material for high-temperature applications. 

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. 

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. 

The Kohlrausch formula is well suitable to represent the creep at small stresses and strains. Do is then the compliance at f = 0, and is a measure of the immediate elastic deformation. The formula, however, fails when the creep behaviour is nonlinear this is, in general, the case with stresses occurring in practice. 

The plastic deformation characteristics yield stress, ay, plastic flow stress, crpf, and strain softening, have been studied under uniaxial compression at a strain rate of 2 x 10-3 s-1 [53] in a temperature range from - 110 °C to typically Ta - 20 K. Indeed, for temperatures closer to Ta, the experimental results are less reliable, some creep behaviour occurring. 

For second-phase sintered ceramics, these phases control the plasticity and they are responsible for the asymmetric behaviour when deformed in tension or compression, because there is a crucial difference in the microstructure evolution associated with tension and compression creep. There are few explanations for this asymmetry. 

Both models, the Maxwell element and the Kelvin-Voigt element, are limited in their representation of the actual viscoelastic behaviour the former is able to describe stress relaxation, but only irreversible flow the latter can represent creep, but without instantaneous deformation, and it cannot account for stress relaxation. A combination of both elements, the Burgers model, offers more possibilities. It is well suited for a qualitative description of creep. We can think it as composed of a spring Ei, in series with a Kelvin-Voigt element with 2 and 772. and with a dashpot, 771... 

With all these models, the simple ones as well as the spectra, it has to be supposed that stress and strain are, at any time, proportional, so that the relaxation function E(t) and the creep function D(t) are independent of the levels of deformation and stress, respectively. When this is the case, we have linear viscoelastic behaviour. Then the so-called superposition principle holds, as formulated by Boltzmann. This describes the effect of changes in external conditions of a viscoelastic system at different points in time. Such a change may be the application of a stress or also an imposed deformation. 

We should realize that the values of the moduli of elasticity, as discussed so far, are only applicable to short-term loading situations. The creep, already mentioned several times before, renders these values unsuitable to characterize the behaviour of a polymer under stress over a longer time. In 4.5 we already met the example of two polymers, where POM, at a certain stress, initially deforms less than PC, but, later on, its deformation exceeds that of PC. 

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