Stress-strain curve viscoelastic polymers

The effect of gas compression on the uniaxial compression stress-strain curve of closed-cell polymer foams was analysed. The elastic contribution of cell faces to the compressive stress-strain curve is predicted quantitatively, and the effect on the initial Young s modulus is said to be large. The polymer contribution was analysed using a tetrakaidecahedral cell model. It is demonstrated that the cell faces contribute linearly to the Young s modulus, but compressive yielding involves non-linear viscoelastic deformation. 3 refs. 

PP bead foams of a range of densities were compressed using impact and creep loading in an Instron test machine. The stress-strain curves were analysed to determine the effective cell gas pressure as a function of time under load. Creep was controlled by the polymer linear viscoelastic response if the applied stress was low but, at stresses above the foam yield stress, the creep was more rapid until compressed cell gas took the majority of the load. Air was lost from the cells by diffusion through the cell faces, this creep mechanism being more rapid than in extruded foams, because of the small bead size and the open channels at the bead bonndaries. The foam permeability to air conld be related to the PP permeability and the foam density. 15 refs. 

The influence of temperature on the stress-strain behavior of polymers is generally opposite to that of straining rates. This is not surprising in view of the correspondence of time and temperature in the linear viscoelastic region (Section I l.5.2.iii). The curves in Fig. 11-23 are representative of the behavior of a partially crystalline plastic. 

Ideal yielding behaviour is approached by many glassy polymers well below their glass-transition temperatures, but even for these polymers the stress-strain curve is not completely linear even below the yield stress and the compliance is relatively high, so that the deformation before yielding is not negligible. Further departures from ideality involve a strain-rate and temperature dependence of the yield stress. These two features of behaviour are, of course, characteristic of viscoelastic behaviour. 

Inspection of this equation shows that it models reasonably well, on a very superficial level, a stress-strain curve of the type shown in Fig. 1(b), curve (4). In other words it raises the question as to whether the deviations from linear stress-strain relationships observed in constant strain-rate tests might not be merely resulting from the intrinsic time-dependence of the linear viscoelasticity, which can be more clearly studied in creep or stress-relaxation and not due to some new process starting at high stresses. It does not take long to show that at the strain-levels of 3-5% experienced at yield, the response of most polymers is highly non-linear (r(t)/ is a function of strain-rate S as well as t, and so eqn. (14) cannot adequately describe the behaviour. However, it is also clear that at... 

The problems of exact design for a viscoelastic polymer with non-linear properties are severe. For example, in Figure 8.1 a) the stress-strain curve is linear only at the smallest strains (below 0.2%). Most plastic parts are designed to operate at strains well above 0.2%, and in this case exact stress analysis is impossible. In practice, a safe approximate procedure known as the pseudo-elastic design method is used. The salient features of the method, which is veiy straightforward to apply, are as follows ... 

Schematic stress strain curve for a viscoelastic polymer. The tensile force is applied at a uniform rate...

Many polymers are viscoelastic and recover elastically following deformation. Figure 6.11 shows a schematic stress strain curve where a tensile force is applied at a uniform rate to a viscoelastic sample at a constant temperature. The shape and characteristic parameters of the stress strain curve are strongly influenced by the temperature and the sample processing conditions. 

The discussions above focus on the small strain as a response of polymer materials to the small stress. Large stress brings large strain and even destroys the inherent structure of the solid materials, causing permanent deformation. Under the constant strain rates, the stress-strain curve reflects the structural and viscoelastic characteristic features of materials. For polymer materials, there occur five typical curves, as illustrated in Fig. 6.18 (1) hard and brittle, such as PS and PMMA, eventually brittle failure (2) hard and tough, such as Nylon and PC, most of semi-crystalline polymers. 

The molecular theory of extensional viscosity of polymer melts is again based oti the standard tube model. It considers the linear viscoelastic factors such as reptation, tube length fluctuations, and thermal constraint release, as well as the nonlinear viscoelastic factors such as segment orientations, elastic contractimi along the tube, and convective constraint release (Marrucci and lannirubertok 2004). Thus, it predicts the extensional stress-strain curve of monodispersed linear polymers, as illustrated in Fig. 7.12. At the first stage, the extensional viscosity of polymer melts exhibits the Newtonian-fluid behavior, following Trouton s ratio... 

The discussion of mechanical properties comprises the various contributions of elastic, viscoelastic and plastic deformation processes. Often two characteristic stress levels can be defined in the tensile curve of polymer fibers the yield stress, at which a significant drop in slope of the stress-strain curve occurs, and the stress at fracture, usually called the tensile strength or tenacity. In this section the relation is discussed between the morphology of fibers and films, made from lyotropic polymers, and their mechanical properties, such as modulus, tensile strength, creep, and stress relaxation. 

Polymers deform viscoelastically. Under cyclic loads, the stress-strain curve upon unloading is not the same as upon loading. Therefore, there is a hysteresis between stress and strain, causing energy dissipation during the deformation, thus producing heat. This hysteresis is discussed in detail in exercise 26. 

A polymer responds to a pulling force (tensile stress) by being stretched (tensile strain). The mechanical properties of a polymer can be described partly by the values derived from the tensile stress-strain curve (Figure 2.10). Polymers are viscoelastic materials - that is, they can behave simultaneously as liquids with viscous flow and as elastic solids. When a polymer is stretched, the sample goes throngh varions stages. The first part of the curve describes the elastic properties of the polymer, when the sample can be stretched without permanent distortion. 

Fillers of various dimensions are added to polymers to alter its processability, properties and uses. Such micro and nano composites obtained may have tremendous possibilities in industries and information on their viscoelasticity is very necessary as far as their processing and applicability are concerned. The dynamic properties of filled elastomers have been a subject of active research since they affect the performance of tyres such as skid, traction, and rolling resistance. Elastomer nanocomposites are most important materials characterized by excellent elasticity and flexibility, and are widely used in various applications such as cables, tyres, tubing, dielectric materials and sensors [1-5]. The non linear features observed in filled elastomers upon a simple shear are as follows. The dynamic storage and loss moduli of the composites are only dependent on the dynamic strains and not on the static strain. In the same way the stress strain curves also do not depend on static strain. Moreover the initial modulus under constant strain rate is highly rate dependent whereas the terminal modulus is independent of strain rate. This initial to terminal modulus ratio in the stress-strain curves is the same as the ratio of the dynamic storage moduli obtained at low and high strains. 

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