Strain behaviour

Fig. 8.1. Stress-strain behaviour for a linear elastic solid. The axes are calibrated for a material such as steel.

Fig. 1.3 Effect of material temperature on stress-strain behaviour of plastics...

Fig. 2.1 Stress-strain behaviour of elastic and viscoelastic materials at two values of elapsed...

The reinforcing filler usually takes the form of fibres but particles (for example glass spheres) are also used. A wide range of amorphous and crystalline materials can be used as reinforcing fibres. These include glass, carbon, boron, and silica. In recent years, fibres have been produced from synthetic polymers-for example, Kevlar fibres (from aromatic polyamides) and PET fibres. The stress-strain behaviour of some typical fibres is shown in Fig. 3.2. 

Fig. 3.4 Stress-strain behaviour for several types of fibre reinforcement...

Fig. 2. Stress-strain behaviour of materials prepared with 50 wt% TEOS, 100% water content, and PTMO with various numbers of tri-EOS groups TEOS(50)-PTMO(58-X)-100. X = 3 ...

Comparison with Statistical Theory, Small-strain Behaviour. Calculations of theoretical moduli, using the phantom theory and the affine theory as limiting cases, were carried out in order to compare the theoretical predictions with values found experimentally (Table IV). 

The deviations from Gaussian stress-strain behaviour introduce uncertainties into the values of Mc/M discussed previously in this paper. However, such uncertainties have been shown to be of secondary importance compared with the ranges of Mc/Mc values found for networks from different reaction systems(25,32). 

The observed deviations from Gaussian stress-strain behaviour in compression were in the same sense as those predicted by the Mooney-Rivlin equation, with modulus increasing as deformation ratio(A) decreases. The Mooney-Rivlin equation is usually applied to tensile data but can also be applied compression data(33). According to the Mooney-Rivlin equation... 

The deviations from Gaussian stress-strain behaviour for the tetrafunctional polyurethane networks of Figure 9 are qualitatively similar to these found for the trifunctional polyester networks (Z5), and the error bars on the data points for systems 4 and 5 in Figure 9 indicate the resulting uncertainties in Mc/Mc. It is clear that such uncetainties do not mask the increases in Mc/Mc with amount of pre-gel intramolecular reaction. 

Interesting deviations from Gaussian stress-strain behaviour in compression have been observed which related to the Me of the networks formed, rather than their degrees of swelling during compression measurements. 

Dynamic properties are taken to mean the results from mechanical tests in which the plastic is subjected to a deformation pattern from which the cyclic stress-strain behaviour is calculated. These do not include cyclic tests in which the main objective is to fatigue the material. 

Stress/strain behaviour in the elastic region, i.e. below the yield stress, as a function of volume fraction, 4>, contact angle, 0, and film thickness, h, was examined [51]. The yield stress, t , and shear modulus, G, were both found to be directly proportional to the interfacial tension and inversely proportional to the droplet radius. The yield stress was found to increase sharply with increasing <(>, and usually with increasing 6. A finite film thickness also had the tendency to increase the yield stress. These effects are due to the resulting increase in droplet deformation which induces a higher resistance to flow, as the droplets cannot easily slip past one another. 

Below the yield point, however, stress/strain behaviour was found to be independent of initial cell orientation, due to the threefold symmetry of the hexagonal cellular array [54], This allows a correlation between shearing and extensional deformations to be made [55], namely that shear can be considered as elongation followed by rotation. Thus, information on one type of deformation can be obtained by solving expressions for the other. 

In a later study [56], the effect of gas volume fraction (foam rheology was investigated. Two models were considered one in which the liquid was confined to the Plateau borders, with thin films of negligible thickness and the second, which involves a finite (strain-dependent) film thickness. For small deformations, no differences were observed in the stress/strain results for the two cases. This was attributed to the film thickness being very much smaller than the cell size. Thus, it was possible to neglect the effect of finite film thickness on stress/strain behaviour, for small strains. 

It was found that increasing Ca caused the yield stress and yield strain to increase, along with cell deformation at the yield point. At sufficiently high values of Ca, cell distortion is so severe that film thinning and rupture can occur, resulting in mechanical failure of the foam (Fig. 6). This implies the presence of a shear strength for foams and HIPEs. The initial orientation of the cells was also found to affect the stress/strain behaviour of the system in the presence of viscous forces [63]. For some particular orientations, periodic flow was not observed for any value of Ca. 

In an earlier state of the art report (1) various properties of sulphur concretes were outlined. In the last few years, researchers have concentrated on the topics of durability (moist environment, biological and chemical attack, cycles of freezing and thawing), stress-strain behaviour and mix proportioning. 

Sulphur concrete (without additives) will typically have a near-linear stress-strain curve up to failure, which occurs explosively at a strain usually between 0.0005 and 0.002. The peak stress varies from 20 to 70 MPa depending on the mix design. Sulphur concrete is thus a strong but brittle concrete material the brittleness need not necessarily be a grave disadvantage cast iron was used for a long period of time as a construction material. Any modification to the stress-strain behaviour should be evaluated carefully to see whether the modification is potentially useful. Two different approaches have been used to modify stress-strain behaviour. The modifications are (a) polymerization of the binder 04, j>, 17) and (b) use of the thermodynamically stable orthorhombic sulphur as the binder with alteration of the bond behaviour (3, 18). The matrices of both types of concrete are thus "modified" sulphur. 

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. 

Sulphur concretes appear well suited for use in environments corrosive to Portland cement concretes. The extensive work by the U.S. Bureau of Mines shows their material performs admirably in such environments. When used as a lining, the initial stress-strain behaviour will allow the material to adapt to the main structural element and relieve internal stresses without cracking. Corrosion resistance will be maintained by the material thereafter, even though the stress strain behaviour alters. On its own, the material retains sufficient strength to withstand typical loads involved in this type of application (eg. liquid container). Sudicrete has not been tested much in this area, although laboratory tests show similar promise. 

Sulphur concretes have undergone substantial development in the last six years. Recent effort has been directed towards improved durability and less brittle stress-strain behaviour has been achieved. A technology has been developed to produce a material (Sudicrete) with the same stress strain behaviour after three years as that observed soon after casting. Other materials show a consistent reversion to brittle behaviour with time. Nevertheless, there is considerable room for improvement in mix design. 

The stress-strain behaviour of thermoelastoplastics is as a rule a nonlinear onell7> 118). It strongly depends on many factors, the most important being the volume... 

Theories based on these concepts all have to take into account the phenomenology of the stress-strain behaviour of networks. In unilateral extension as well as compression one observes, even at moderate extension (1.1 deviations from the Gaussian behaviour, which can be empirically described by the so-called Mooney-Rivlin equation ... 

In the following sections we will discuss the various theories which have been proposed and confront them with the general phenomenology of the stress-strain behaviour. 

Blokland (14) recently also considered the stress-strain behaviour of structured networks. His approach is schematically illustrated in Fig. 29. Consider a cubical lattice on which the chain configurations are laid out in a partially obstructed random walk. Of the N steps of each chain there will be on the average m steps which participate in a bundle structure... 

Determination of degree of crosslinking in natural rubber vulcanizates. IV. Stress-strain behaviour at large extensions. J. Appl. Pol. Sci. 2, 257 (1959). 

Rather surprisingly, all these kinds of deformation can be described in terms of a single modulus. This is a result of the assumption that rubber is virtually incompressible (i.e. bulk modulus much greater than shear modulus). Young s modulus E = 3G (for fdled rubbers the numerical factor may be in fact as high as 4). Indeed, these relationships by no means fully describe the complete stress strain behaviour of real rubbers but may be taken as first approximations. The shear stress relationship is usually good up to strains of 0.4 and the tension relationship approximately true up to 50% extension. 

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