Stress-strain behaviour different polymers

The mechanical and thermal properties of a range of poly(ethylene)/po-ly(ethylene propylene) (PE/PEP) copolymers with different architectures have been compared [2]. The tensile stress-strain properties of PE-PEP-PE and PEP-PE-PEP triblocks and a PE-PEP diblock are similar to each other at high PE content. This is because the mechanical properties are determined predominantly by the behaviour of the more continuous PE phase. For lower PE contents there are major differences in the mechanical properties of polymers with different architectures, that form a cubic-packed sphere phase. PE-PEP-PE triblocks were found to be thermoplastic elastomers, whereas PEP-PE-PEP triblocks behaved like particulate filled rubber. The difference was proposed to result from bridging of PE domains across spheres in PE-PEP-PE triblocks, which acted as physical crosslinks due to anchorage of the PE blocks in the semicrystalline domains. No such arrangement is possible for the PEP-PE-PEP or PE-PEP copolymers [2]. 

In the case of (a), since there can be substantial variations in both compliance and strength (creep rupture) with angle, this may result in creep in some directions involving extremely low strains, and therefore presenting severe measurement problems, whilst in other directions very rapid large creep or rupture may occur thus limiting the information available. It has therefore been found preferable to employ (b) and to choose stress levels in different directions so as to produce equal strains after a specified creep time in all directions. Furthermore if correlation of creep behaviour with deformation mechanisms is sought it may well be desirable to compare the polymer response when the different mechanisms produce similar strains. Selection of appropriate stress-levels is achieved by use of the isochronous stress-strain curves. 

Many studies of the yield behaviour of polymers have bypassed the question of strain rate and temperature and sought to establish a yield eriterion as diseussed in Section 11.2 above. In very general terms sueh studies divide into two eategories (1) those that attempt to define a yield eriterion on the basis of determining yield for different stress states (2) those that eonfine the experimental studies to an examination of the influence of hydrostatie pressure on the yield behaviour. 

This classification is based on differences in mechanical performance specifically, differences in the strain response to applied stress. Elastic behaviour is defined by the deformation being proportional to the stress, and fully recoverable when the stress is removed. True plastic behaviour implies continuing flow under load, without recovery afterwards. In practice, polymers are viscoelastic , their behaviour being partly plastic and partly elastic, with the balance between the two extremes varying with the temperature and time under load. 

The important point to note from this Example is that in a non-symmetrical laminate the behaviour is very complex. It can be seen that the effect of a simple uniaxial stress, or, is to produce strains and curvatures in all directions. This has relevance in a number of polymer processing situations because unbalanced cooling (for example) can result in layers which have different properties, across a moulding wall thickness. This is effectively a composite laminate structure which is likely to be non-symmetrical and complex behaviour can be expected when loading is applied. 

Al-Saidi LF, Mortensen K, Almdal K (2003) Environmental stress cracking resistance behaviour of polycarbonate in different chemicals by determination of the time-dependence of stress at constant strains. Polym Degradat Stabil 82(3) 451—461... 

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. 

The yield stresses of several polymers at low temperatures and high strain-rates have been found to increase more rapidly with increasing strain-rate and decreasing temperature than predicted by equation (8.17). This behaviour can often be described by the addition of terms representing two activated processes with different activation volumes. 

Oriented thermoplastics can show large anisotropy in creep behaviour, expecially in partially crystalline polymers. Significantly different patterns of behaviour occur in different materials. Not only is there anisotropy of isochronous stiffness, but also of creep rate and non-linearity. If stiffoess is regarded as a function of time, direction and stress or strain, the behaviour is such that the variables are not normally separable. 

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