Yield and fracture of polymers

When polymers are applied for any practical purpose it is necessary to know, among other things, what maximum loads they can sustain without failing. Failure under load is the subject of the present chapter. 

In chapter 7 the phenomenon of creep in a viscoelastic solid is considered. For an ideal linear viscoelastic medium the deformation under a constant stress eventually becomes constant provided that in equation (7.4) is zero. If the load is removed at any time, the ideal material recovers fully. For many polymers these conditions are approximately satisfied for low stresses, but the curves (b) and (c) in fig. 6.2 indicate a very different type of behaviour that may be observed for some polymers under suitable conditions. For stresses above a certain level, the polymer yields. After yielding the polymer either fractures or retains a permanent deformation on removal of the stress. 

Just as linear viscoelastic behaviour with full recovery of strain is an idealisation of the behaviour of some real polymers under suitable conditions, so ideal yield behaviour may be imagined to conform to the following for stresses and strains below the yield point the material has time-indepen-dent linear elastic behaviour with a very low compliance and with full recovery of strain on removal of stress at a certain stress level, called the yield stress, the strain increases without further increase in the stress if the material has been strained beyond the yield stress there is no recovery of strain. This ideal behaviour is illustrated in fig. 8.1 and the differences between ideal viscoelastic creep and ideal yield behaviour are shown in table 8.1. 

Ideal yielding behaviour is approached by many glassy polymers well below their glass-transition temperatures, but even for these polymers the stress-strain curve is not completely linear even below the yield stress and the compliance is relatively high, so that the deformation before yielding is not negligible. Further departures from ideality involve a strain-rate and temperature dependence of the yield stress. These two features of behaviour are, of course, characteristic of viscoelastic behaviour. 

Just as real materials may have behaviour close to ideal yielding behaviour but with some features similar to those of viscoelastic materials, materials that exhibit behaviour close to the ideal linear viscoelastic may exhibit features similar to those of yield, particularly for high stresses and long times of application. If the term e i) in equation (7.4) is not zero, a linear viscoelastic material will not reach a limiting strain on application of a fixed stress at long times the strain will simply increase linearly with time. The material may also depart from linearity at high or even moderate stresses, so that higher stresses produce disproportionately more strain. These are features characteristic of yield. 

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