Stress-strain behavior change with time

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-... 

Figure 2. Change in stress-strain behavior with time, with dicyclopentadiene polymerized sulfur...

As a melt is subjected to a fixed stress (or strain), the deformation vs. time curve will show an initial rapid deformation followed by a continuous flow (Fig. 1-6). The relative importance of elasticity (deformation) and viscosity (flow) depends on the time scale of the deformation. For a short time, elasticity dominates over a long time, the flow becomes purely viscous. This behavior influences processes when a part is annealed, it will change its shape or, with post-extrusion (Chapter 5), swelling occurs. Deformation contributes significantly to process flow defects. Melts with small deformation have proportional stress-strain behavior. As the stress on a melt is increased, the recoverable strain tends to reach a limiting value. It is in the high-stress range, near the elastic limit, that processes operate. 

There are several other thermal analysis techniques. In thermomechanical analysis (TMA), mechanical changes are monitored versus temperature. Expansion and penetration characteristics or stress-strain behavior can be studied. In dynamic mechanical analysis (DMA), the variations with temperature of various moduli are determined, and this information is further used to obtain fundamental information such as transition temperatures. In thermogravimefric analysis (TGA), weight changes as a function of temperature or time (at some elevated temperature) are followed. This information is used to assess thermal stability and decomposition behavior. 

Example 12.1 A polymer sample is subjected to a constant tensile stress (Tq. How does the strain change with time Assume that the mechanical behavior of the polymer can be represented by a spring and dashpot in series, as shown in Figure 12.4. 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

Wave profiles in the elastic-plastic region are often idealized as two distinct shock fronts separated by a region of constant elastic strain. Such an idealized behavior is seldom, if ever, observed. Near the leading elastic wave, relaxations are typical and the profile in front of the inelastic wave typically shows significant changes in stress with time. 

When a viscoelastic material is subjected to a constant strain, the stress initially induced within it decays in a time-dependent manner. This behavior is called stress relaxation. The viscoelastic stress relaxation behavior is typical of many TPs. The material specimen is a system to which a strain-versus-time profile is applied as input and from which a stress-versus-time profile is obtained as an output. Initially the material is subjected to a constant strain that is maintained for a long period of time. An immediate initial stress gradually approaches zero as time passes. The material responds with an immediate initial stress that decreases with time. When the applied strain is removed, the material responds with an immediate decrease in stress that may result in a change from tensile to compressive stress. The residual stress then gradually approaches zero. 

Nonequilibrium conditions may occur with respect to disturbances in the interior of a system, or between a system and its surroundings. As a result, the local stress, strain, temperature, concentration, and energy density may vary at each instance in time. This may lead to instability in space and time. Constantly changing properties cannot be described properly by referring to the system as a whole. Some averaging of the properties in space and time is necessary. Such averages need to be clearly stated in the utilization and correlation of experimental data, especially when their interpretations are associated with theories that are valid at equilibrium. Components of the generalized flows and the thermodynamic forces can be used to define the trajectories of the behavior of systems in time. A trajectory specifies the curve represented by the flow and force components as functions of time in the flow-force space. 

Equation (4) can be used to compare the change in creep behavior at zero time and for an infinitely long time. Consider that a composite is initially loaded at an infinitely rapid rate to a constant creep stress strain-rate relation for the composite (crc, ec) becomes... 

The applied stress results in the shear strain of the cube, i.e. the top face becomes shifted with respect to the bottom one by distance y. This displacement is numerically equal to the tangent of a tilt angle of the side face, i.e. it is equal to the relative shear strain, y, and at small strains tany y. The relationship between shear stress, x, and shear strain, y, and the rates of change in these quantities with time, dx/dt=x, dy/dt=y, represent mechanical behavior, which is the main subject in rheology. One usually begins the description of mechanical behavior with three elementary models, namely elastic, viscous, and plastic behavior. 

---