Time-dependent mechanical behaviour

This model was proposed in the 19th century by Maxwell to explain the time-dependent mechanical behaviour of viscous materials, such as tar or pitch. It consists of a spring and dashpot in series as shown in Fig. 5.7(a). Under the action of an overall stress cr there will be an overall strain e in the system which is given by... 

Recognizing the importance of the coupled hydro-mechanical effects on the performance of civil engineering structures involving fractured rocks, the stress-flow coupling mechanism of the dam-foundation system at Longyangxia site was simulated using a three-dimensional Finite Element code, supported by two visco-elastic constitutive models to represent the time-dependent material behaviour of the dam concrete and the foundation rock. The calculated results were concord with the measured ones and helped to interpret the causes of this continuous displacement at the 13" dam section of the Longyangxia hydropower project, towards the left bank. 

It has long been recognised that the mechanical properties of polymers are time-dependent. The behaviour at very small strains (less than 0 5%) can be described by the theory of linear viscoelasticity. Conventionally the stress a at time t is related to the strain e at all previous instants by the equation... 

As clearly discussed, the mechanical behaviour of polymers changes rapidly as the temperature is reduced or the strain rate increased. Brooks et al. have shown that for polyethylene there is a sudden transition in the yield strain at temperatures below ambient, the exact temperature depending on the sample morphology. Figure 12.31 shows results for linear PE. It was also found that this temperature marks the change from classical elastic-plastic behaviour to time-dependent viscoelastic behaviour where the yielded samples show... 

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. 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

The above models are all rather unsatisfactory, because they involve somewhat arbitrary assumptions about the time-dependence of the cosmic-ray flux and spectrum and because they predict a secondary-like behaviour for Be and B abundances, whereas the overall trend indicated by the data is more like a primary one and there are the energetic difficulties pointed out above. In the case of nB, there is a possible primary mechanism for stellar production in supemovae by neutrino spallation processes (Woosley et al. 1990 Woosley Weaver 1995), but the primary-like behaviour of beryllium in metal-poor stars, combined with a constant B/Be ratio of about 20 fully consistent with cosmic-ray spallation (Garcia Lopez et al. 1998) in the absence of any known similar process for Be, indicates that this does not solve the problem unless a primary process can be found for Be as well. Indeed,... 

The properties of a material must dictate the applications in which it will best perform its intended use. All materials made to date with polymerized sulphur show time-dependent stress-strain behaviour. The reversion to the brittle behaviour of orthorhombic sulphur is inevitable as the sulphur transforms from the metastable polymeric forms to the thermodynamically stable crystalline structure. The time-span involved of at most 15 months (to date) would indicate that no such materials should be used in applications dependent on the strain softening behaviour. Design should not be based on the stress-strain relationships observed at an age of a few days. Since the strength of these materials is maintained, however, uses based on strength as the only mechanical criterion would be reasonable. 

At the time this mechanism was proposed it was considered that boron fluoride catalysis showed rather similar kinetics and activation energy, differing from the stannic chloride only in that chain transfer could occur but termination apparently was very slow or absent (13). Subsequent work with boron fluoride suggests however (14) that the apparent fractional order dependence on monomer may be spurious and thus tends to discredit the data for stannic chloride in spite of the fact that the rate expressions give an excellent account of the rate of disappearance of epoxide both within and between the individual experiments. The difference in behaviour between stannic chloride und boron fluoride remains one of the unsolved problems in this field. 

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. 

Thixotropy of casting slips is characterized by the time dependence of both viscosity and yield point. This phenomenon is caused by reversible sol-gel transition in the clay component, which can be affected by mechanical means (stirring, vibration). The effect is much more distinct with enamel slips than with ceramic casting slips. A more marked yield point is required with the former, while ceramic casting suspensions are usually characterized by a pseudoplastic rheological behaviour without a distinct yield point. 

Patermarakis, G. (2003) The parallel dehydrative and dehydrogenative catalytic action of y-A1203 pure and doped by MgO kinetics, selectivity, time dependence of catalytic behaviour, mechanisms and interpretations. Appl. Catal. A-General, 252, 231-241. 

Figure 2 shows a model/measurement comparison from a butenedial photolysis experiment in the absence of NOx. The loss of butenedial is well predicted by MCMvS.l. However, the HO2 concentration is over-estimated by MCMv3.1 by almost an order of magnitude during the early part of the experiment. The time-dependent behaviour is also not well reproduced by the simulation as in the experiment an initial fast increase in concentration is followed by a slower linear increase until the chamber closes, while the simulation shows a fast rise followed by a fall in the HO2 concentration even while the photolysis continues. The photolysis mechanism for butenedial in the absence of NOx as implemented in MCMvS.l is shown schematically in Figure 4. This indicates fliat two HO2 radicals should be formed for each molecule of maleic anhydride and glyoxal produced, and while both these product concentrations are over-estimated this is not sufficient to account for the large over-prediction ofH02.

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