Polymer properties exhibit time-dependent behavior, meaning that the measured properties are dependent on the test conditions and polymer type. Figure 1.7
shows a typical viscoelastic response of a polymer to changes in testing rate or temperature. Increases in testing rate or decreases in temperature cause the material to appear more rigid, while an increase in temperature or decrease in rate will cause the material to appear softer. This time-dependent behavior can also result in long-term effects such as stress-relaxation or creep.2 These two time-dependent behaviors are shown in Fig. 1.8.
Under a fixed displacement, the stress on the material will decrease over time, termed stress relaxation. This behavior can be modeled using a spring and dashpot in series as depicted in Fig. 1.9.
The equation for the time dependent stress using this model is (1.5)
where t is the characteristic relaxation time (./k). Under a fixed load, the specimen will continue to elongate with time, a phenomenon termed creep, which can be modeling using a spring and dashpot in parallel as seen in Fig. 1.9. This model predicts the time-dependent strain as (1.6)
For more accurate prediction of the time-dependent behavior, other models with more elements are often employed. In the design of polymeric products for long-term applications, the designer must consider the time-dependent behavior of the material. If a series of stress relaxation curves is obtained at varying temperatures, it is found that these curves can be superimposed by horizontal shifts to produce a master curve.3 This demonstrates an important feature in polymer behavior: the concept of time-temperature equivalence. In essence, a polymer at temperatures below room temperature will behave as if it were tested at a higher rate at room temperature. This principle can be applied to predict material behavior under testing rates or times that are not experimentally accessible through the use of shift factors (aT) and the equation below: (1.7)
where Tg is the glass transition temperature of the polymer.
shows a typical viscoelastic response of a polymer to changes in testing rate or temperature. Increases in testing rate or decreases in temperature cause the material to appear more rigid, while an increase in temperature or decrease in rate will cause the material to appear softer. This time-dependent behavior can also result in long-term effects such as stress-relaxation or creep.2 These two time-dependent behaviors are shown in Fig. 1.8.
Under a fixed displacement, the stress on the material will decrease over time, termed stress relaxation. This behavior can be modeled using a spring and dashpot in series as depicted in Fig. 1.9.
The equation for the time dependent stress using this model is (1.5)
where t is the characteristic relaxation time (./k). Under a fixed load, the specimen will continue to elongate with time, a phenomenon termed creep, which can be modeling using a spring and dashpot in parallel as seen in Fig. 1.9. This model predicts the time-dependent strain as (1.6)
For more accurate prediction of the time-dependent behavior, other models with more elements are often employed. In the design of polymeric products for long-term applications, the designer must consider the time-dependent behavior of the material. If a series of stress relaxation curves is obtained at varying temperatures, it is found that these curves can be superimposed by horizontal shifts to produce a master curve.3 This demonstrates an important feature in polymer behavior: the concept of time-temperature equivalence. In essence, a polymer at temperatures below room temperature will behave as if it were tested at a higher rate at room temperature. This principle can be applied to predict material behavior under testing rates or times that are not experimentally accessible through the use of shift factors (aT) and the equation below: (1.7)
where Tg is the glass transition temperature of the polymer.
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