Polymers stress—strain experiments

Many of the quoted physical properties of a polymer are derived from a stress-strain experiment. The polymer is cut into an appropriate shape. For instance, plastics are cut into the shape shown here (sometimes called a dogbone). They are placed in two jaws of a special instrument (Fig. 15.2). 

The shear component of the applied stress appears to be the major factor in causing yielding. The uniaxial tensile stress in a conventional stress-strain experiment can be resolved into a shear stress and a dilational (negative compressive) stress normal to the parallel sides of test specimens ofthe type shown in Fig. 11-20. Yielding occurs when the shear strain energy reaches a critical value that depends on the material, according to the von Mises yield criterion, which applies fairly well to polymers. 

Stress-strain experiments have traditionally been the most widely used mechanical test but probably the least understood in terms of interpretation. In stress-strain tests the specimen is deformed (pulled) at a constant rate, and the stress required for this deformation is measured simultaneously (Figure 13.1). As we shall see in subsequent discussions, polymers exhibit a wide variation of behavior in stress-strain tests, ranging from hard and brittle to ductile, including yield and cold drawing. The utility of stress-strain tests for design with polymeric materials can be greatly enhanced if tests are carried out over a wide range of temperatures and strain rates. 

We have developed the idea that we can describe linear viscoelastic materials by a sum of Maxwell models. These models are the most appropriate for describing the response of a body to an applied strain. The same ideas apply to a sum of Kelvin models, which are more appropriately applied to stress controlled experiments. A combination of these models enables us to predict the results of different experiments. If we were able to predict the form of the model from the chemical constituents of the system we could predict all the viscoelastic responses in shear. We know that when a strain is applied to a viscoelastic material the molecules and particles that form the system gradual diffuse to relax the applied strain. For example, consider a solution of polymer... 

Gas compression in closed-cell polymer foams was analysed, and the effect on the uniaxial compression stress-strain curve predicted. Results were compared with experimental data for a foams with a range of cell sizes, and the heat transfer conditions inferred from the best fit with the simulations. The lateral expansion of the foam must be considered in the simulation, so in subsidiary experiments Poisson s ratio was measured at high compressive strains. 13 refs. 

AFM is useful in identifying the nature and amount of surface objects. AFM, or any of its variations, also allows studies of polymer phase changes, especially thermal phase changes, and results of stress or strain experiments. In fact, any physical or chemical change that brings about a variation in the surface structure can, in theory, be examined and identified using AFM. 

From the viewpoint of the mechanics of continua, the stress-strain relationship of a perfectly elastic material is fully described in terms of the strain energy density function W. In fact, this relationship is expressed as a linear combination erf the partial derivatives of W with respect to the three invariants of deformation tensor, /j, /2, and /3. It is the fundamental task for a phenomenologic study of elastic material to determine W as a function of these three independent variables either from molecular theory or by experiment. The present paper has reviewed approaches to this task from biaxial extension experiment and the related data. The results obtained so far demonstrate that the kinetic theory of polymer network does not describe actual behavior of rubber vulcanizates. In particular, contrary to the kinetic theory, the observed derivative bW/bI2 does not vanish. 

Summary In this chapter, a discussion of the viscoelastic properties of selected polymeric materials is performed. The basic concepts of viscoelasticity, dealing with the fact that polymers above glass-transition temperature exhibit high entropic elasticity, are described at beginner level. The analysis of stress-strain for some polymeric materials is shortly described. Dielectric and dynamic mechanical behavior of aliphatic, cyclic saturated and aromatic substituted poly(methacrylate)s is well explained. An interesting approach of the relaxational processes is presented under the experience of the authors in these polymeric systems. The viscoelastic behavior of poly(itaconate)s with mono- and disubstitutions and the effect of the substituents and the functional groups is extensively discussed. The behavior of viscoelastic behavior of different poly(thiocarbonate)s is also analyzed. 

As it was mentioned above mechanical properties of polymers are strongly dependent on the temperature. Therefore, E and D, for a polymeric sample are dependent on the temperature at which the experiment is performed. On the other hand the mechanical properties of polymers are also dependent on time. Therefore E and D are not constant at one temperature but evolve with time i.e. E(t), D(t) [7], The complex relationship between the configurational distorsion produced by a perturbation field in polymers and the Brownian motion that relaxes that distorsion make it difficult to establish stress-strain relationships. In fact, the stress at that point in the system depends not only on the actual deformation but also on the previous history of the deformation of the material. 

The effect of temperature on the stress-strain properties of PMMA, its gradient polymers with various compositions, and an IPN are shown in Figures 7, 8, and 9. These experiments were performed at various strain rates at 60°C. Comparison with the 80°C data shows that the main effects of temperature are to increase the stress levels in the plateau regions at lower temperatures without significant differences in other aspects. 

Fig. 11). It is, therefore, highly probable that the bulky filler particles impose geometrical hindrances (entropy constraints) for the chain dynamics at the time scale of the NMR experiment (of the order of 1 ms). This effect may be compared with the effect of transient chain entanglements on chain dynamics in polymer melts. It should be remarked that the entanglements density estimated for PDMS melts by NMR is close to its value fi om mechanical experiments [38]. Therefore, it can be assimied that topological hindrances from the filler particles can also be of importance in the stress-strain behavior of filled elastomers. 

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