Stress-strain behaviour yield

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. 

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 the category of deformation properties the phenomena of stress-strain behaviour, modulus and yield, stress relaxation and creep have been discussed already in Chap. 13. Here we want to give special attention to the long-term deformation properties. For a good design we need sufficiently reliable creep data (or stress-strain curves as a function of time and temperature). 

Under tensile loading, the stress concentrating effect of an unbonded spherical particle is dmilar to that of a void. Nicolais and co-workers have studied the tensile stress-strain behaviour of composites based on SAN, ABS, PPO, and epojgr resins " 4-36) jjj jj g g polymers, unbonded glass beads cause yielding... 

Figure 2 Stress-strain behaviour of rock. Initially any deformation can be recovered when stress is removed. When yield point is reached further stress produces non-recoverable deformation of the rock, usually fracturing...

A typical uniaxial stress-strain behaviour of an HDPE geomembrane is also shown in Fig. 8.29. While maximum elongation is several hundred per cent, yield occurs at 10-15% strain. A safety factor of 1.5-2.5 is usually taken into account when employing geomembranes, which brings any allowable strain down to 5-6.5%. Geomembranes are viscoelastic materials and their stress-strain behaviour is time dependent, so over the long term, applied stresses could lead to their creep failure. 

Medium- and high-molecular-weight linear PE shows pronounced plastic flow even at 4.2 K. The stress-strain behaviour below the yield point is nonlinear, but elastic. The fracture stress at 4.2 K is about 20 to 30% higher than is usually found for epoxy resins. 

Tensile tests on different HDPE resins indicate that the stress-strain behaviour below the yield point can generally be described by the following empirical relationship (Fig. 4.2) ... 

There have been a number of detailed investigations of the influence of hydrostatic pressure on the yield behaviour of pol3maers. Because it illustrates clearly the relationship between a yield criterion, which depends on hydrostatic pressure, and the Coulomb yield criterion, an experiment will be discussed where Rabinowitz, Ward and Parry [23] determined the torsional stress-strain behaviour of isotropic PMMA under hydrostatic pressures up to 700 MPa. The results are shown in Figure 11.17. 

The stress-strain behaviour of models such as that of Figure 11.16 can be explored by solving the associated equations using numerical techniques. In the work of Sweeney et al. on PET fibres [62], a model similar to that of Figure 11.16 but with the Eyring dashpot restrained by a Gaussian network, was solved in this way. The strain at which yield occurs, the general shape of the stress-strain curve, and the stability of the deformation were predicted and found to compare well with experiment. 

Cellular materials can collapse by another mechanism. If the cell-wall material is plastic (as many polymers are) then the foam as a whole shows plastic behaviour. The stress-strain curve still looks like Fig. 25.9, but now the plateau is caused by plastic collapse. Plastic collapse occurs when the moment exerted on the cell walls exceeds its fully plastic moment, creating plastic hinges as shown in Fig. 25.12. Then the collapse stress (7 1 of the foam is related to the yield strength Gy of the wall by... 

The phenomena of brittle and tough fracture give rise to fairly characteristic stress-strain curves. Brittle fracture in materials leads to the kind of behaviour illustrated in Figure 7.1 fairly uniform extension is observed with increasing stress, there is minimal yield, and then fracture occurs close to the maximum on this graph. 

Tough fracture, which is alternatively known as ductile fracture, by contrast, gives the type of behaviour illustrated in Figure 7.2. After the maximum in the stress-strain plot has been reached, there is a substantial amount of yielding, before the sample eventually breaks. 

Atomic force microscopy and attenuated total reflection infrared spectroscopy were used to study the changes occurring in the micromorphology of a single strut of flexible polyurethane foam. A mathematical model of the deformation and orientation in the rubbery phase, but which takes account of the harder domains, is presented which may be successfully used to predict the shapes of the stress-strain curves for solid polyurethane elastomers with different hard phase contents. It may also be used for low density polyethylene at different temperatures. Yield and rubber crosslink density are given as explanations of departure from ideal elastic behaviour. 17 refs. 

Fig. 7 a and b. Scheme of the thermomechanical behaviour of a well phase-separated thermoelasto-plastic. Stress-strain (or time) curves. Plots of heat effects versus time. First loading (ABC) and unloading (CD) cycle. Second loading (AC) and unloading (CD) cycle. The yielding point occurs at B. AD indicates the residual deformation after the first cycle. AB on the dQ/dT-time curve is the endo-effect resulting from the initial small-strain deformation AB U9)... 

Fig. 2 Typical stress-strain curves for amorphous polymers, a Elastic, anelastic, strain softening, and plastic flow regions can be seen, b Plastic flow occurs at the same stress level as required for yielding so strain softening does not exist, c Strain hardening occurs very close to yielding, suppressing both strain softening and plastic flow behaviour...

First, it is important to notice that the stress-strain curves and, consequently, the derived characteristics (yield stress, cry, plastic flow stress, crpf, and strain softening) have been studied in a temperature range extending to, typically, Ta - 20 K. Indeed, for temperatures closer to Ta, the experimental results are less reliable, as some creep behaviour can occur. 

A combination of Eqs. (13.167) and (13.168) yields the typical concave shape of the elastic stress-strain curve of well-oriented fibres. In Fig. 13.98 the calculated stress-strain curve is compared with the experimental curve at decreasing stress of a Twaron 1000 fibre. It shows almost elastic behaviour. By including the simple theory the tensile curve with yield can be calculated as shown in Fig. 13.99. 

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