Question

All normally ductile polymers can also craze even in the absence of solvents, given the right circumstances. The crazing stress of each polymer is slightly sensitive to temperature but insensitive to strain rate. Ductile to brittle transition temperature (Tb) are often found at low temperatures for such polymers; explain why Tb shifts to higher temperatures at increasing strain rates. (Hint: the easiest way to explain this is to use diagrams. If you do, be sure the label the curves and explain briefly what they mean.)

Answer 1

Sol. All normally ductile polymers do crazing.The crazing stress is sensitive to temperature and insensitive to strain rate. At the increasing rate of strain the ductile to brittle transition temperature (T_b) shifts to higher temperature.

At the lower rate of strain the Tb values remain low in ductile polymer. This can be easily explained by the basic properties of ductile materials. The ductile materials possess crazing and provides curved crack surface. They possess necking and are normally related to shear yielding. The following figure presents the basic behavior of ductile polymers.

The diagram of stress versus strain rate presented below is used to explain the process of increase in ductile to brittle temperature in ductile polymers. The behaviour of variation in stress with increasing strain rate is presented, this suggests as brittle to ductile temperature towards the ductile to brittle temperature, the strain rate increases and needs more stress. Which will lead to increase in T_b temperature.

In ductile polymers, a semicircle kind patterned behavior is seen for the variation in stress with strain. It is observed that in ductile zone as the strain rate increases the temperature transits from brittle to ductile temperature (T_BD) to ductile to brittle temperature (T_DB or T_b). And the stress versus strain rate curve for the ductile polymers materials present the increase in Tb with the increase in strain rate.

As the strain rate is increased the Tb becomes directly proportional to strain rate, due to the quick variation in impact energy in the ductile polymers. The ductile polymers in transition to ductile to brittle transition temperature becomes hard and needs high impact energy. That high impact energy is given by high strain rate given to ductile polymers, which in turn lead to high transition temperature values of T_b.

This behavior is presented in the figure below, that moving to ductile to brittle temperature, in ductile polymers, the high impact energy or high strain rate lead to high transition temperature.

Here with the increase in impact energy the strain rate increases and hence the transition temperature of ductile to brittle (T_b) is increasing.