Stress-strain curves characteristic shape

Figure 18.17 shows that the characteristics of the stress-strain curve depend mainly on the value of n the smaller the n value, the more rapid the upturn. Anyway, this non-Gaussian treatment indicates that if the rubber has the idealized molecular network strucmre in the system, the stress-strain relation will show the inverse S shape. However, the real mbber vulcanizate (SBR) that does not crystallize under extension at room temperature and other mbbers (NR, IR, and BR at high temperature) do not show the stress upturn at all, and as a result, their tensile strength and strain at break are all 2-3 MPa and 400%-500%. It means that the stress-strain relation of the real (noncrystallizing) rubber vulcanizate obeys the Gaussian rather than the non-Gaussian theory. 

The most common type of stress-strain tests is that in which the response (strain) of a sample subjected to a force that increases with time, at constant rate, is measured. The shape of the stress-strain curves is used to define ductile and brittle behavior. Since the mechanical properties of polymers depend on both temperature and observation time, the shape of the stress-strain curves changes with the strain rate and temperature. Figure 14.1 illustrates different types of stress-strain curves. The curves for hard and brittle polymers (Fig. 14.1a) show that the stress increases more or less linearly with the strain. This behavior is characteristic of amorphous poly-... 

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 stress-strain curves in Fig. 4.39 to 4.41 have the characteristic shape for elastomers containing reinforcing particles. There is a rate-dependent flow stress associated with stress-activated segmental diffusion at the surface or interior of reinforcing particles, superimposed on the strain-stiffening hyperelastic stress response of the elastomeric matrix. Such a system is amenable to a quantitative description in terms... 

The shape of the stress-strain curves obtained in tensile tests differs between the different material classes. The characteristic shapes are summarised in figure 3.5. 

Finite element modelling on a macroscopic scale using the Tresca criterion matches the observed size and shape of the plastic zone and also the shape of the indentation stress-strain curves indicating that the physical characteristics of the microstructure determine its yield strength. The use of the Tresca criterion implies a zero coefficient of friction on the microstructural scale. The range of macroscopic yield stresses for the materials studied here is 750 MPa to 2000 MPa. 

All of these properties can be determined from the stress/strain characteristics of a plastic by plotting its stress/strain curve. Stress is defined as the intensity (measured per unit area) of the internal distributed forces, or components of force, which resist a change in the form of a body. Strain is the change per unit length in a linear dimension of a body accompanying a stress and is measured in metres per metre or in percent. When under tension or compression, strain is measured along the dimension under consideration. Many plastics have stress/strain characteristics that can be represented by a curve with the general shape shown in Fig. 1.1. 

When the stress is increased above the proportional limit a value is reached at which permanent extension occurs the original size and shape are not recovered completely on removal of the applied forces. The stress at which a permanent extension is first detected is called the yield stress, and the corresponding point on the stress-strain curve is called the yield point. Usually the proportional limit and yield stress have almost the same value and cannot readily be distinguished. The yield stress is characteristic of the material, but also depends on grain size and temperature. 

If the stress-strain curve extends considerably beyond the yield point one speaks of a tough polymer the shape of the curve depends on the strain hardening behavior of the polymer and on the tendency to neck formation. Curve d) is characteristic for soft polymers, e.g. for thermoplastics at a temperature close to their glass transition temperature or plasticised polymers, which do not yet show rubber elastic behavior. 

Other differences in the mechanical properties of superfibers are most clearly manifested in their operating characteristics. The stress-strain diagram of Kevlar-29 fibers at different temperatures and rates of deformation is shown in Fig. 10.14 [88]. The strength of the fibers decreases by 14% on average with an increase in the rate of deformation from 0.167 to 8000%/sec. The elongation at break virtually does not change. The shape of the curves is almost linear. 

In compression creep tests, a flat disk-shaped membrane sample (i.e., 6.3 mm diameter and 0.9-1.2 mm thickness) is positioned between two sample holder plates of a dynamic mechanical analyzer (DMA) [25]. The creep compliance [Pa ] is obtained by dividing the strain with the applied stress (i.e., 0.1 MPa), and is usually displayed as a plot against the testing time. The creep rate is the slope of the resulting curve. Low compliance and creep rate are characteristics for a material with good creep resistance. Molleo et al. [25] found that the conditioning of the samples is vital for reproducible results, and recommend to store the samples sandwiched between two solid blocks at 180 C (same as the test temperature) for about 24 h prior to the measurements, to get flat samples in which the PA is well distributed. 

The age-related viscoelastic properties of the ocular lens have not been fully characterized. Most of the attempts have been at elucidating only the elastic modulus, since the lens has been treated as an elastic substance (19,26). The process of accommodation however is mechanically analogous to a stress-relaxation experiment, where the stress is allowed to decay at constant strain (refractive power). Hence, the lens is truly viscoelastic. Researchers investigating the viscoelastic characteristics of the lens performed creep-recovery or frequency scan techniques ex-vivo ( 1 8). Ejiri et al. (28) investigated creep properties of a decapsulated dog lens by compression and fitted the time-displacement curve with three Kelvin units. The time constants for the three units were 0.09 s, 7.0 s, and 106 s. The elastic modulus could not be obtained, as the applied stress was unknown due to the aspheric geometry of the lens. In this article, we have investigated the creep behavior of cylindrical disc shaped hydrogels in order to obtain the time constants as well as the elastic modulus of the viscoelastic units. 

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