PPT07-notes_probs - ME4 Polymer Processing Technology 7...

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7 Creep and relaxation SPAP notes described qualitatively how injection moulding locks in residual strains because adjacent regions cool at different rates. During cooling, the stresses set up by these strains vary in quite a complex way: the stiffness increases with decreasing temperature but the material creeps with increasing time. A common result is warpage, sometimes immediately after ejection but usually later on in service — usually when the temperature changes yet again. Before investigating warpage, we need to consider viscoelasticity in greater depth. After defining the isochronous modulus of a time-dependent material, we go on to recall the way in which this modulus depends on temperature in an amorphous polymer. Noticing that the modulus depends in a similar way on log(time) leads to the concept of an ‘equivalence’ between time and temperature. In particular it leads to the WLF equation, already mentioned in the context of polymer melt rheology (§2.4.3). Learning outcomes After completing this section you should be able to… 1 Apply the ‘equation of state’ approach to derive solutions for the strain (or stress) response of a specified time-dependent material under simple stress (or strain) histories; and demonstrate an understanding of the shortcomings of this approach for viscoelastic materials. 2 Recognise cases in which the principle of time-temperature equivalence and the WLF equation could be used to transform modulus/temperature data into modulus/time data, and vice versa; and apply this principle in simple cases using ‘master curve’ data. 3 Demonstrate understanding and make appropriate use of the following terminology: creep (c. compliance), equation of state, isochronal (=isochronous curve), master curve (creep, relaxation), power-law creep, recovery, reference time, relaxation, relaxation modulus, rubbery polymer/phase/régime, secant modulus, tangent modulus, tensile modulus, transition, viscoelasticity (linear/non-linear). ME4 Polymer Processing Technology PSL 12 December 2009
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7.1 Viscoelasticity Viscoelastic phenomena were introduced in SPAP. A viscoelastic material combines: 1 viscous behaviour — e.g. linear, Newtonian viscosity, and 2 elastic behaviour — e.g. linear, Hookeian elasticity. Simple linear spring-dashpot models (e.g. the Standard Linear Solid, §10) reproduce all of the basic phenomena of linear viscoelasticity. The combination of elastic behaviour and rate-dependent behaviour makes behaviour time-dependent . To analyse viscoelasticity in any depth, linear viscoelasticity must be assumed. However, even metals show only Hookeian elasticity over only a restricted range, and we already know that polymer melts are non-Newtonian. It is therefore not surprising that polymer viscoelasticity is actually non -linear.
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