Non-linear creep

Various models have been proposed to account for the non-linear creep of polymers, such as the Eyring model this model explains some aspects, but fails with other ones, and will not be discussed here. 

Ivanov, A., Potapov, Yu., and Alimov, S. About the Equation of Non-linear Creep of Some Plastics and Wood, Proceedings of Higher Institutes of Learning no. 6 (1968), (in Russian). 

In order to verify some of the long term predictive capabilities of the finite element model described in the previous sections, the transverse creep of a IM7/5260 [90]i6 specimen subjected to cyclic thermomechanical loading investigated in an earlier study [8] was used as a benchmark. The authors of that study performed creep and recovery tests to characterize the non-linear creep behavior of the composite and then subjected the composite specimens to cyclic thermomechanical loading for up to 6 months. 

In a follow-up of the integral equation approach Croll made a preliminary study of the non-linear creep behaviour of the same oriented PET sheet in other orientations, and also of amorphous and crystallised isotropic PET. He discovered that whereas for the oriented material at 0 = 90° and for the amorphous isotropic sheet, the creep modulus versus stress graphs were linear, as suggested by eqn. (22), a more complicated form of non-linearity was evident both for the oriented material at 6 = 45° and 0°, and for the highly crystalline isotropic material. An example of this is shown schematically in Fig. 22 where the creep modulus/stress graph for oriented PET sheet in tension at 0 = 0°, can be seen to have three distinct regimes. 

Figure 7 Non-linear creep properties of oil-in-water emulsions with various amoimts of oil [7],...

Service lifetime prediction of polymers and/or polymer based materials may be undertaken from different types of tests, such as creep behavior tests (linear and non-linear creep, physical aging, time-dependent plasticity), fatigue behavior tests (stress transfer and normalized life prediction models, empirical fatigue theories, fracture mechanics theory and strength degradation) and standard accelerated aging tests (chemical resistance, thermal stability, liquid absorption) [32]. 

The creep deformation of complex plastic products in which non linear creep occurs can be predicted using commercial FEM programs. 

Occasionally, materials are tested in tension by applying the loads in increments. If this method is used for plastics then special caution is needed because during the delay between applying the load and recording the strain, the material creeps. Therefore if the delay is not uniform there may appear to be excessive scatter or non-linearity in the material. In addition, the way in which the loads are applied constitutes a loading history which can affect the performance of the material. A test in which the increments are large would quite probably give results which are different from those obtained from a test in which the increments were small or variable. 

For crb 0 the lifetime fb °°,so Eq. 115 presents a non-linear relation between log( b) and the creep stress crb, which is different from the Coleman relation. According to Eq. 115, at constant load the lifetime of a fibre decreases with increasing orientation parameter. Figure 61 compares the observed data for a PpPTA fibre by Wu et al. with the calculated lifetime curve using the parameter values /J=0.08, tan =0.1483, g= 1.6 GPa, j O.032 (GPa)-1, which implies a fibre with a sonic modulus of 91.8 GPa [30]. As shown by Wu et al., fibres that were tested at high stresses had shorter lifetimes than those calculated from the experimental lifetime relation. 

Note 5 Creep is sometimes described in terms of non-linear viscoelastic behaviour, leading, for example, to evaluation of recoverable shear and steady-state recoverable shear compliance. The definitions of such terms are outside the scope of this document. 

The mechanical response of polypropylene foam was studied over a wide range of strain rates and the linear and non-linear viscoelastic behaviour was analysed. The material was tested in creep and dynamic mechanical experiments and a correlation between strain rate effects and viscoelastic properties of the foam was obtained using viscoelasticity theory and separating strain and time effects. A scheme for the prediction of the stress-strain curve at any strain rate was developed in which a strain rate-dependent scaling factor was introduced. An energy absorption diagram was constructed. 14 refs. 

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 ... 

According to the change of strain rate versus stress the response of the material can be categorized as linear, non-linear, or plastic. When linear response take place the material is categorized as a Newtonian. When the material is considered as Newtonian, the stress is linearly proportional to the strain rate. Then the material exhibits a non-linear response to the strain rate, it is categorized as Non Newtonian material. There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. This kind of materials are known as thixotropic deformation is observed when the stress is independent of the strain rate [2,3], In some cases viscoelastic materials behave as rubbers. In fact, in the case of many polymers specially those with crosslinking, rubber elasticity is observed. In these systems hysteresis, stress relaxation and creep take place. 

The reduced creep curves in Figure 7.6 (e/o or D(t)) should coincide if Boltzmann s superposition principle would hold for each level of stress, D(t) should be the same. However, creep behaviour is non-linear, linearity only occurs at very low values of <7 and , as a limiting case. Therefore, D(t) is D(t, a). 

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)... 

As previously noted, this chapter has been concerned mainly with those models for the creep of ceramic matrix composite materials which feature some novelty that cannot be represented simply by taking models for the linear elastic properties of a composite and, through transformation, turning the model into a linear viscoelastic one. If this were done, the coverage of models would be much more comprehensive since elastic models for composites abound. Instead, it was decided to concentrate mainly on phenomena which cannot be treated in this manner. However, it was necessary to introduce a few models for materials with linear matrices which could have been developed by the transformation route. Otherwise, the discussion of some novel aspects such as fiber brittle failure or the comparison of non-linear materials with linear ones would have been incomprehensible. To summarize those models which could have been introduced by the transformation route, it can be stated that the inverse of the composite linear elastic modulus can be used to represent a linear steady-state creep coefficient when the kinematics are switched from strain to strain rate in the relevant model. 

If you step back and think about it, the mechanical and rheological properties of many solids and liquids can be modeled fairly well by just two simple laws, Hooke s law and Newton s law. Both of these are what we call linear models, the stress is proportional to the strain or rate of strain. If we examine viscoelastic properties like creep, the variation of strain with time appears decidedly non-linear (see Figure 13-75). Nevertheless, it is possible to model this non-linear time dependence by the assumption of a linear relationship between stress and strain. By this we mean that if, for example, we measure the strain as a function of time in a creep experiment, then for a given time period (say 1 hour) the strain measured when the applied stress is 2o would be twice the strain measured when the stress was o. 

Y]sf Findlay, JS Lai, K Onaran. Creep and Relaxation of Non-Linear Viscoelastic Materials. Amsterdam, North-Holland, 1976, 71. 

While IPNs can be and have been made extremely tough and impact resistant, many of the proposed applications involve such diverse fields and sound and vibration damping, biomedical materials, and non-linear optics. This is because the presence of crosslinks in both polymers reduces creep and flow, allowing relatively stable materials with a wide range of moduli to be prepared. Thus, those materials with leathery mechanical behavior, combinations of elastomers and plastics, are especially interesting to scientists, inventors, and engineers. 

Ferguson, R., paper presented at lUPAC, Montreal, 1991. Findley, W. N., Lai, S. S., and Onaran, K., Creep Relaxation of Non Linear Viscoelastic Materials , North Holland, Amsterdam (1976). 

Not all such flows, however, are linear—as, for example, in the case of non-Newtonian creeping flows around spherical particles (B4a, B4b, Cl, D3, F9, FIO, G5, L8, LIO, Rl, S2, SIO, T4, T7, W2, W3, W3a, W3b, W4, W5, W6, Zl). Similarly, owing to the unknown shape of the interface at the outset, free-boundary problems involving liquid droplets in nonuniform flows (Section II, C, 2, b) are intrinsically nonlinear despite the possible linearity of the equations of motion (and boundary conditions) inside and outside of the droplet. 

Abstract Based on the theory of irreversible process thermodynamics, non-linear stress-strain-temperature equations are derived, together with an expression for time-temperature equivalence. In addition, an equation of shift factor for time-temperature equivalence is also obtained. The parameters in the equations are experimentally determined and the main curves for creep compliance and cohesion of TOP granite are obtained by a series of creep tests. As a result, it is proved that both deformation and strength of the TOP granite follow the time-temperature equivalent principle. 

In this paper time-temperature equivalence for rocks is investigated for non-linear behaviours of rocks, based upon inner-variable theory of irreversible process and creep tests. 

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