356 Modern Physical Metallurgy and Materials Engineering several microns wide and fairly constant in width: they chemistry decides the character of individual molecules can scatter incident light and are visible to the unaided but it is the processing stage which enables them to be eye(e. g. transparent glassy polymers). As in the stress- arranged to maximum advantage. Despite the variety orrosion of metals, crazing of regions in tension of methods available for converting feedstock may be induced by a chemical agent(e. g. ethanol on ders and granules of thermoplastics into useful shapes. PMMA). The plane of a craze is always at right angles these methods usually share up to four common stages the principal tensile stress. Structurally, each craze of production; that is, (1)mixing, melting and homog consists of interconnected microvoids, 10-20 nm in enization,(2)transport and shaping of a melt, (3) size, and is bridged by large numbers of molecule- drawing or blowing, and(4)finishing orientated fibrils, 10-40 nm in diameter, The voidage Processing brings about physical, and often chemi- is about 40-50%, As a craze widens, bridging fibrils cal, changes In comparison with energy requirements xtend by drawing in molecules from the side walls. for processing other materials, those for polymers are Unlike the type of craze found in glazes on it is relatively low. Temperature control is vital because not a true crack, being capable of sustaining some load. it decides melt fluidity. There is also a risk of ther- Nevertheless, it is a zone of weakness and can initiate mal degradation because, in addition to having limited brittle fracture. Each craze has a stress-intensifying thermal stability, polymers have a low thermal cor tip which can propagate through the bulk polymer. ductivity and readily overheat. Processing is usuall Crazing can take a variety of forms and may even rapid, involving high rates of shear. The main methods beneficial. For instance, when impact causes crazes that will be used to illustrate technological aspects of to form around rubber globules in ABS polymers, processing thermoplastics are depicted in Figure 11.6 he myriad newly-created surfaces absorb energy and Injection-moulding of thermoplastics, such as PE toughen the material. Various theoretical models of and PS, is broadly similar in principle to the pressure craze formation have been proposed. One suggestion die-casting of light metals, being capable of produc- is that triaxial stresses effectively lower toane en ing mouldings of engineering components rapidly wit tensile strain has exceeded a critical value, induce a repeatable precision(Figure 11 6a). In each cycle, a glass-to-rubber transition in the vicinity of a flaw, or metered amount(shot)of polymer melt is forcibly similar heterogeneity. Hydrostatic stresses then cause injected by the reciprocating screw into a'cold'cavity microcavities to nucleate within this rubbery zone (cooled by oil or water channels). When solidifica As Figure 11.5 shows, it is possible to portray the tion is complete the two-part mould opens and the strength/temperature relations for a polymeric material moulded shape is ejected. Cooling rates are faster on a deformation map. This diagram refers to PMMa than with parison moulds in blow-moulding becaus and shows the fields for cold-drawing, crazing, viscous heat is removed from two surfaces. The capital out contours of strain rate over a range of ub composed lhy for injection-moulding tends to be high because of 11.2.2 Processing methods for thermoplastics multi-impression moulding dies. In die design, special Processing technology has a special place in the different flows coalesce, and of feeding gates. Com- remarkable history of the polymer industry: polymer puter modelling can be used to simulate the melt flow distributions of temperature and pressure Temperatute(C) the mould cavity. This prior simulation helps to lessen nal mo which are ostly. Microprocessors are used to monitor and d feed rates continuously during the io moulding process; for example the flow rates into a complex cavity can be rapid initially and then reduced to ensure that flow-dividing obstructions do not pro- duce weakening weld lines is wide n drawing nto continuous lengths of sheet, tube bar, filament, etc. with a constant and exact ci (Figure 11.6b). A long Archimedean screw (auger PAIVA rotates and conveys feedstock through carefully pro- Contours of portioned feed, compression and metering sections The polymer is electrically heated in each of the three barrel sections and frictionally heated as it is shear erature T/Tl tinned by the inally, it is forced through a .5 Deformation map for PMMA sh die orifice. Microprocessor control systems are avail tble to measure pressure at the die inlet and to keep us normalized temperature (from Ashby and Jones, stational speed of 1986: permission of Elsevier Science Ltd, UK) screw. Dimensional control of the product benefits
356 Modern Physical Metallurgy and Materials Engineering several microns wide and fairly constant in width: they can scatter incident light and are visible to the unaided eye (e.g. transparent glassy polymers). As in the stresscorrosion of metals, crazing of regions in tension may be induced by a chemical agent (e.g. ethanol on PMMA). The plane of a craze is always at right angles to the principal tensile stress. Structurally, each craze consists of interconnected microvoids, 10-20 nm in size, and is bridged by large numbers of moleculeorientated fibrils, 10-40 nm in diameter. The voidage is about 40-50%. As a craze widens, bridging fibrils extend by drawing in molecules from the side walls. Unlike the type of craze found in glazes on pottery, it is not a true crack, being capable of sustaining some load. Nevertheless, it is a zone of weakness and can initiate brittle fracture. Each craze has a stress-intensifying tip which can propagate through the bulk polymer. Crazing can take a variety of forms and may even be beneficial. For instance, when impact causes crazes to form around rubber globules in ABS polymers, the myriad newly-created surfaces absorb energy and toughen the material. Various theoretical models of craze formation have been proposed. One suggestion is that triaxial stresses effectively lower Tg and, when tensile strain has exceeded a critical value, induce a glass-to-rubber transition in the vicinity of a flaw, or similar heterogeneity. Hydrostatic stresses then cause microcavities to nucleate within this rubbery zone. As Figure 11.5 shows, it is possible to portray the strength/temperature relations for a polymeric material on a deformation map. This diagram refers to PMMA and shows the fields for cold-drawing, crazing, viscous flow and brittle fracture, together with superimposed contours of strain rate over a range of 10 -6 to 1 s -1. 11.2.2 Processing methods for thermoplastics Processing technology has a special place in the remarkable history of the polymer industry" polymer 10 0 10.~ 10.2 g E 10 "3 ~ 10 .4 Brittle fracture 11"I . Crozing and " shear yielding ~" PMMA E~; l S, OP. = 3?8 K ConlotJre of 10-$ :.., weln rite I Temperature (*C) -200 -100 0 100 200 300 1 I I 1 1 ! I ~ _~.vi,cou, I/~\\'!~ '~ 0 103 102 ,r 4, 10 ~ In 10 0 0.4 0.8 1.2 Normalised temperature (TITs ) 10 -I 1.( Figure 11.5 Deformation map for PMMA showing deformation regions as a fimction of normalized stress versus normalized temperature (from Ashby and Jones, 1986; permission of Elsevier Science Ltd, UK). chemistry decides the character of individual molecules but it is the processing stage which enables them to be arranged to maximum advantage. Despite the variety of methods available for converting feedstock powders and granules of thermoplastics into useful shapes, these methods usually share up to four common stages of production; that is, (1) mixing, melting and homogenization, (2) transport and shaping of a melt, (3) drawing or blowing, and (4) finishing. Processing brings about physical, and often chemical, changes. In comparison with energy requirements for processing other materials, those for polymers are relatively low. Temperature control is vital because it decides melt fluidity. There is also a risk of thermal degradation because, in addition to having limited thermal stability, polymers have a low thermal conductivity and readily overheat. Processing is usually rapid, involving high rates of shear. The main methods that will be used to illustrate technological aspects of processing thermoplastics are depicted in Figure 11.6. Injection-moulding of thermoplastics, such as PE and PS, is broadly similar in principle to the pressure die-casting of light metals, being capable of producing mouldings of engineering components rapidly with repeatable precision (Figure l l.6a). In each cycle, a metered amount (shot) of polymer melt is forcibly injected by the reciprocating screw into a 'cold' cavity (cooled by oil or water channels). When solidification is complete, the two-part mould opens and the moulded shape is ejected. Cooling rates are faster than with parison moulds in blow-moulding because heat is removed from two surfaces. The capital outlay for injection-moulding tends to be high because of the high pressures involved and machining costs for multi-impression moulding dies. In die design, special attention is given to the location of weld lines, where different flows coalesce, and of feeding gates. Computer modelling can be used to simulate the melt flow and distributions of temperature and pressure within the mould cavity. This prior simulation helps to lessen dependence upon traditional moulding trials, which are costly. Microprocessors are used to monitor and control pressure and feed rates continuously during the moulding process; for example, the flow rates into a complex cavity can be rapid initially and then reduced to ensure that flow-dividing obstructions do not produce weakening weld lines. Extrusion is widely used to shape thermoplastics into continuous lengths of sheet, tube, bar, filament, etc. with a constant and exact cross-sectional profile (Figure l l.6b). A long Archimedean screw (auger) rotates and conveys feedstock through carefully proportioned feed, compression and metering sections. The polymer is electrically heated in each of the three barrel sections and frictionally heated as it is 'shearthinned' by the screw. Finally, it is forced through a die orifice. Microprocessor control systems are available to measure pressure at the die inlet and to keep it constant by 'trimming' the rotational speed of the screw. Dimensional control of the product benefits
Plastics and composites 357 Nonie from an annular die is drawn upwards and with air to form thin film: stretching and ease when crystallization is complete at abou m 「州画是霄 Similarly, in the blow-moulding of bottles and air- ducting, etc, tubular extrudate(parison) moves ver- ically downwards into an open split-mould. As the ould closes, the parison is inflated with air at a pres movement ure of about 5 atmospheres and assumes the shape of the cooled mould surfaces. Relatively inexpensive alu minium moulds can be used because stresses are low Thermoforming( Figure 116c)is another secondary method for processing extruded thermoplastic sheet, being particularly suitable for large thin-walled hol- low shapes such as baths, boat hulls and car bodies (e.g. ABS, PS, PVC, PMMA). In the basic version of the thermoforming, a frame- held sheet is located above D·Hdra the mould, heated by infrared radiation until rubbery and then drawn by vacuum into close contact with the mould surface. The hot sheet is deformed and thinned Kev:口 pastic Es cooling by biaxial stresses. In a high-pressure version of ther- moforming, air at a pressure of several atmospheres heater acts on the opposite side of the sheet to the vacuum and improves the ability of the sheet to register fine mould detail. the draw ratio, which is the ratio of plastic mould depth to mould width, is a useful control parar eter. For a given polymer, it is possible to construct a plot of draw ratio versus temperature which can be used as a'map to show various regions where there mould table risks of incomplete corner filling, bursts and holes. Unfortunately, thinning is most pronounced at vulnerable corners. Thermoforming offers an econom- ical altermative to moulding but cycle times are rather long and the final shape needs trimming. 11.2.3 Production of thermosets Development of methods for shaping thermosetting able raised materials is restricted by the need to accommodate a uring reaction and the absence of a stable viscoelas- state Until fairly recently, these restrictions tended limit the size of thermoset products. Compres ion moulding of a thermosetting P-F resin(Bakelite) vithin a simple cylindrical steel mould is a well-known boratory method for mounting metallurgical samples. vacuum Resin granules, sometimes mixed with hardening or lectrically-conducting additives, are loaded into the table locked up ould, then heated and compressed until crosslinking actions are complete. In transfer moulding, which can produce more intricate shapes, resin is melted in a primary chamber and then transferred to a vented sheet(from MilLs, 1986; by permission o/ Tawara or auction moulding chamber for final curing In the car indus- plastic pipe by extrusion and (c) thermoforming ic try, body panels with good bending stiffness are pro duced from thermosetting sheet-moulding compounds (SMC). A composite sheet is prepared by laying do layers of randomly-oriented, chopped glass fibres, ca from this device. On leaving the die, the continuously. cium carbonate powder and polyester resin. The sheet formed extrudate enters cooling and haul-off sections. is placed in a moulding press and subjected to heat an Frequently, the extrudate provides the preform for a pressure. Energy requirements are attractively low second operation. For example, in a continuous melt Greater exploitation of thermosets for large car parts inflation technique, tubular sheet of LDPE or HDPE has been made possible by reaction injection-moulding
Plastics and composites 357 (a) Moving Nozzle mould ! Heater bands half / ! , /Screw rotation I ~_ i] I ~ / .Screw Non-return Injection unit valve movement Key:- II hydraulic :.: polymer system (b) m, ~ ~ Cooling water OUt -- ' 9 " I C~176 I / DIe spicier legs water i;r L mixing Fl/~ting tube plug Key: r'n plastic F~ cooling water (c) heater /l I I I I i2" .,..,,c l IIIII I I table ir table raised -:'?:us-- table locked up Figure 11.6 (a) Injection-moulding machine, (b) production of plastic pipe by extrusion and (c) thermoforming of plastic sheet (from Mills, I986; by permission of Edward Arnold). from this device. On leaving the die, the continuouslyformed extrudate enters cooling and haul-off sections. Frequently, the extrudate provides the preform for a second operation. For example, in a continuous meltinflation technique, tubular sheet of LDPE or HDPE from an annular die is drawn upwards and inflated with air to form thin film: stretching and thinning cease when crystallization is complete at about 120~ Similarly, in the blow-moulding of bottles and airducting, etc., tubular extrudate (parison) moves vertically downwards into an open split-mould. As the mould closes, the parison is inflated with air at a pressure of about 5 atmospheres and assumes the shape of the cooled mould surfaces. Relatively inexpensive aluminium moulds can be used because stresses are low. Thermoforming (Figure 11.6c) is another secondary method for processing extruded thermoplastic sheet, being particularly suitable for large thin-walled hollow shapes such as baths, boat hulls and car bodies (e.g. ABS, PS, PVC, PMMA). In the basic version of the thermoforming, a frame-held sheet is located above the mould, heated by infrared radiation until rubbery and then drawn by vacuum into close contact with the mould surface. The hot sheet is deformed and thinned by biaxial stresses. In a high-pressure version of thermoforming, air at a pressure of several atmospheres acts on the opposite side of the sheet to the vacuum and improves the ability of the sheet to register fine mould detail. The draw ratio, which is the ratio of mould depth to mould width, is a useful control parameter. For a given polymer, it is possible to construct a plot of draw ratio versus temperature which can be used as a 'map' to show various regions where there are risks of incomplete corner filling, bursts and pinholes. Unfortunately, thinning is most pronounced at vulnerable comers. Thermoforming offers an economical alternative to moulding but cycle times are rather long and the final shape needs trimming. 11.2.3 Production of thermosets Development of methods for shaping thermosetting materials is restricted by the need to accommodate a curing reaction and the absence of a stable viscoelastic state. Until fairly recently, these restrictions tended to limit the size of thermoset products. Compression moulding of a thermosetting P-F resin (Bakelite) within a simple cylindrical steel mould is a well-known laboratory method for mounting metallurgical samples. Resin granules, sometimes mixed with hardening or electrically-conducting additives, are loaded into the mould, then heated and compressed until crosslinking reactions are complete. In transfer moulding, which can produce more intricate shapes, resin is melted in a primary chamber and then transferred to a vented moulding chamber for final curing. In the car industry, body panels with good bending stiffness are produced from thermosetting sheet-moulding compounds (SMC). A composite sheet is prepared by laying down layers of randomly-oriented, chopped glass fibres, calcium carbonate powder and polyester resin. The sheet is placed in a moulding press and subjected to heat and pressure. Energy requirements are attractively low. Greater exploitation of thermosets for large car parts has been made possible by reaction injection-moulding
358 (RIM). In this process, polymerization takes place dur- Figure 11.7 shows the typical fall in apparent shear cal reactants are pumped at high velocity into a mixing If Newtonian flow prevailed, the plotted line would chamber. The mixture bottom-feeds a closed chamber be horizontal. This type of diagram is plotted for rhere polymerization is completed and a solid forms. fixed values of temperature and hydrostatic pressure. A Mouldings intended for high-temperature service are change in either of these two conditions will displace stabilized, or post-cured, by heating at a temperature the flow curve significantly. Thus, either raising the of 100C for about 30 min. The reactive system in RIM temperature or decreasing the hydrostatic(bulk)pres- can be polyurethane, nylon- or polyurea-forming. sure will lower the apparent shear viscosity. The latter The basic chemical criterion is that polymerization in increases with average molecular mass. For instance the mould should be virtually complete after about fluidity at a low stress, as determined by the standard 30 s. Foaming agents can be used to form compo- melt flow index(MFI) test, is inversely proportional nents with a dense skin and a cellular core. when glass to molecular mass. At low stress and for a giver fibres are added to one of the reactants, the process is molecular mass, a polymer with a broad distribution of RIM now competes with the injection-moulding of than one with a narrow distribution. However, at high thermoplastics. Capital costs, energy requirements and stress, a reverse tendency is possible and the version moulding pressures are lower and, unlike injection- with a broader distribution may be less pseudo-plastic are not su Figure 11.8 provides a comparison of the flo problems (sinks'and voids ). Cycle times for RIM behaviour of five different ther thermosets are becoming comparable with those for for comparing the suitability of different processes. It indicates that acrylics are relatively difficult to extrude ingent control is necessary during the rim changing in the fluid stream and there is a cha sition and viscosity a need to develop appropriate dynamic models nass transport and reaction kinetics 11.2. 4 viscous aspects of melt behaviour Melts of thermoplastic polymers behave in a highly iscous manner when subjected to stress during pro- essing. Flow through die orifices and mould chan nels is streamline (laminar), rather than turbulent with shear conditions usually predominating. Let us now adopt a fuid mechanics approach and conside e effects of shear stress, temperature and hydro static pressure on melt behaviour. Typical rates of strain(shear rates)range from 10-10s(extrusion) to 10-10-s(injection-moulding). When a melt is being forced through a die the shear rate at the die wall is calculable as a function of the volumetric flow ate and the geometry of the orifice. At the necessarily high levels of stress required, the classic Newtonian is not obeyed: an increase in shear stress produces Shear stress(N/m?) other words, the shear stress/shear rate ratio, which is now referred to as the 'apparent shear viscosity, falls. Figure 11.7 Typical plot of apparent shea Terms such as'pseudo-plastic'and'shear-thinning'are shear stress for LDPE ar 210C and atmo applied to this non-Newtonian fow behaviour. I The effects of increasing temperature T and hy general working range of apparent shear viscosity for Imperial Chemical Industries Plc!oA m extrusion, injection-moulding, etc is 10-10 Ns m-2. (Shear viscosities at low and high stress levels are IThis important test, which originated in ICI laboratories measured by cone-and-plate and capillary extrusion techniques, respectively during the development of PE, is used for most hermoplastics by polymer manufacturers and processors The MFI is the mass of melt extruded through a standard IIn thixotropic behaviour, viscosity decreases with increase cylindrical die in a prescribed period under conditions of in the duration of shear (rather than the shear rate) constant temperature and compression load
358 Modern Physical Metallurgy and Materials Engineering (RIM). In this process, polymerization takes place during forming. Two or more streams of very fluid chemical reactants are pumped at high velocity into a mixing chamber. The mixture bottom-feeds a closed chamber where polymerization is completed and a solid forms. Mouldings intended for high-temperature service are stabilized, or post-cured, by heating at a temperature of 100~ for about 30 min. The reactive system in RIM can be polyurethyane-, nylon- or polyurea-forming. The basic chemical criterion is that polymerization in the mould should be virtually complete after about 30 s. Foaming agents can be used to form components with a dense skin and a cellular core. When glass fibres are added to one of the reactants, the process is called reinforced reaction injection-moulding (RRIM). RIM now competes with the injection-moulding of thermoplastics. Capital costs, energy requirements and moulding pressures are lower and, unlike injectionmouldings, thick sections are not subject to shrinkage problems ('sinks' and voids). Cycle times for RIMthermosets are becoming comparable with those for injection-moulded thermoplastics and mouldings of SMC. Stringent control is necessary during the RIM process. Temperature, composition and viscosity are rapidly changing in the fluid stream and there is a challenging need to develop appropriate dynamic models of mass transport and reaction kinetics. 11.2.4 Viscous aspects of melt behaviour Melts of thermoplastic polymers behave in a highly viscous manner when subjected to stress during processing. Flow through die orifices and mould channels is streamline (laminar), rather than turbulent, with shear conditions usually predominating. Let us now adopt a fluid mechanics approach and consider the effects of shear stress, temperature and hydrostatic pressure on melt behaviour. Typical rates of strain (shear rates) range from 10-10 3 s -! (extrusion) to 10 3-10 5 s-l (injection-moulding). When a melt is being forced through a die, the shear rate at the die wall is calculable as a function of the volumetric flow rate and the geometry of the orifice. At the necessarily high levels of stress required, the classic Newtonian relation between shear stress and shear (strain) rate is not obeyed: an increase in shear stress produces a disproportionately large increase in shear rate. In other words, the shear stress/shear rate ratio, which is now referred to as the 'apparent shear viscosity', falls. Terms such as 'pseudo-plastic' and 'shear-thinning' are applied to this non-Newtonian flow behaviour. ~ The general working range of apparent shear viscosity for extrusion, injection-moulding, etc. is 10-10 4 Ns m -2. (Shear viscosities at low and high stress levels are measured by cone-and-plate and capillary extrusion techniques, respectively.) ]In thixotropic behaviour, viscosity decreases with increase in the duration of shear (rather than the shear rate). Figure 11.7 shows the typical fall in apparent shear viscosity which occurs as the shear stress is increased. If Newtonian flow prevailed, the plotted line would be horizontal. This type of diagram is plotted for fixed values of temperature and hydrostatic pressure. A change in either of these two conditions will displace the flow curve significantly. Thus, either raising the temperature or decreasing the hydrostatic (bulk) pressure will lower the apparent shear viscosity. The latter increases with average molecular mass. For instance, fluidity at a low stress, as determined by the standard melt flow index (MFI) test, ~ is inversely proportional to molecular mass. At low stress and for a given molecular mass, a polymer with a broad distribution of molecular mass tends to become more pseudo-plastic than one with a narrow distribution. However, at high stress, a reverse tendency is possible and the version with a broader distribution may be less pseudo-plastic. Figure 11.8 provides a comparison of the flow behaviour of five different thermoplastics and is useful for comparing the suitability of different processes. It indicates that acrylics are relatively difficult to extrude 10 5 . ~ 10 ~ i, '7 m > 10 3 I,. r0 t- o'} .,.., t- 0 2 < 10 -- ,, r / \. X" i / \ ! 1 IAIll I I II!1| 1 _.1.._ I I till 10 3 10 4 10 s 10 6 Shear stress (N/m 2) Figure 11.7 Typical plot of apparent shear viscosi~ versus shear stress for LDPE at 210~ and atmospheric pressure: effects of increasing temperature T and hydrostatic pressure P shown (after Powell, 1974; courtesy of Plastics Division, bnperial Chemical Industries Plc). 1This important test, which originated in ICI laboratories during the development of PE, is used for most thermoplastics by polymer manufacturers and processors. The MFI is the mass of melt extruded through a standard cylindrical die in a prescribed period under conditions of constant temperature and compression load
Plastics and composites 359 to tensile strain rate. At low stresses, tensile viscosity is independent of ter As the level of tensile stress rises tensile either remains constant (nylon 6,6), rises(LDPE)or falls(PP, HDPE). This characteristic is relevant to the stability of dimensions and form. For example, during blow-moulding, thin ning walls should have a tolerance for local weak spots E26>8 or stress concentrations. PP and hdpe lack this tol erance and there is a risk that tension-thinning,will lead to rupture. On the other hand the tensile viscos- ity of LDPE rises with tensile stress and failure during wall-thinning is less likely 11.2.5 Elastic aspects of melt behaviour While being deformed and forced through an extru- sion die, the melt stores elastic strain energy. As xtrudate emerges from the die, stresses are released, some elastic recovery takes ce and the extrudate swells. Dimensionally, the degree of swell is typically expressed by the ratio of extrudate diameter to die 10 diameter; the elastic implications of the shear process are expressed by the following modulus: A=t/yR (11.3) where u is the elastic shear modulus, t is the shear DPE at I70°C;B stress at die wall, and yr is the recoverable shear strain. The magnitude of modulus u depends upon the poly 230C; D moulding-grade acet er, molecular mass distribution and the level of shear moulding-grade nylon at 285C(after 1974; stress. (Unlike viscosity, dependency of elasticity upon courtesy of Plastics Division, Imperial Chemical industries mperature, hydrostatic pressure and average molec ular mass is slight. )If the molecular mass distribution is wide, the elastic shear modulus is low and elastic and that pP is suited to the much faster deformation ecovery is appreciable but slow. For a narrow distribu rocess of injection-moulding. In all cases, Newtonian on, with its greater similarities in molecular lengths How is evident at relatively low levels of shear stress ecovery is less but faster. With regard to stress level the modulus remains constant at low shear stresses but The following type of power law equation has been usually increases at the high stresses used commer- found to provide a reasonable fit with practical data and cially, giving ap le recovery. has enabled pseudo-plastic behaviour to be quantified The balance n elastic to viscous behaviour (11.2) deformation time with the relaxation time or 'natural of the polymer where C and n are constants. Now t= ny, hence the viscosity to elastic shear modulus(n/u), and derives viscosity n=Cym-l. The characteristic term (n-1) from the Maxwell model of deformation. The term vis can be derived from the line gradient of a graphical coelasticity originated from the development of such plot of log viscosity versus log shear rate. In practice, models(e.g. Maxwell, Voigt, standard linear solid he power law index n ranges from unity(Newtonian (SLS)). The Maxwell model is a mechanical analogue that provides a useful, albeit imperfect, simulation of ecreases in magnitude as the shear rate increases viscoelasticity and stress relaxation in linear polymers and the thermoplastic melt behaves in an increasingly above Tg(Figure 11.9). It is based upon conditions pseudo-plastic manner of constant strain. A viscously damped *Newtonian So far attention has been concentrated on the vis- dashpot, representing the viscous component of defor- cous aspects of melt behaviour during extrusion and mation, and a spring, representing the elastic compo- jection-moulding, with emphasis on shear process nent, are combined in series. at time t the stress g is In forming operations such as blow-moulding and exponentially related to the initial stress oo, as follows: filament-drawing, extensional fow predominates and tensile stresses become crucial: for these conditions O= Oo exp(-1/A) it is appropriate to define tensile viscosity, the coun- A is the relaxation time terpart of shear viscosity, as the ratio of tensile stress is sufficient time for viscous movement of chain
Plastics and composites 359 10 5 I- X .~y- "~ i 04 ~,~ p, "~ i0 ~ < I0 z I0 10 ~ 10" 105 100 Shear stress (N/m 2 ) Figure 11.8 Typical curves of apparent shear viscosity versus shear stress for five thermoplastics at atmospheric pressure. A Extrusion-grade LDPE at 170~ B extrusion-grade PP at 230 ~ C; C moulding-grade acrylic at 230~ D moulding-grade acetal copolymer at 200~ E moulding-grade nylon at 285~ (after Powell, 1974; courtesy of Plastics Division, Imperial Chemical Industries Plc.). and that PP is suited to the much faster deformation process of injection-moulding. In all cases, Newtonian flow is evident at relatively low levels of shear stress. The following type of power law equation has been found to provide a reasonable fit with practical data and has enabled pseudo-plastic behaviour to be quantified in a convenient form: r = Cy" (11.2) where C and n are constants. Now r -- r/y, hence the viscosity 0 = CY "-~. The characteristic term (n- 1) can be derived from the line gradient of a graphical plot of log viscosity versus log shear rate. In practice, the power law index n ranges from unity (Newtonian flow) to <0.2, depending upon the polymer. This index decreases in magnitude as the shear rate increases and the thermoplastic melt behaves in an increasingly pseudo-plastic manner. So far, attention has been concentrated on the viscous aspects of melt behaviour during extrusion and injection-moulding, with emphasis on shear processes. In forming operations such as blow-moulding and filament-drawing, extensional flow predominates and tensile stresses become crucial; for these conditions, it is appropriate to define tensile viscosity, the counterpart of shear viscosity, as the ratio of tensile stress to tensile strain rate. At low stresses, tensile viscosity is independent of tensile stress. As the level of tensile stress rises, tensile viscosity either remains constant (nylon 6,6), rises (LDPE) or falls (PP, HDPE). This characteristic is relevant to the stability of dimensions and form. For example, during blow-moulding, thinning walls should have a tolerance for local weak spots or stress concentrations. PP and HDPE lack this tolerance and there is a risk that 'tension-thinning' will lead to rupture. On the other hand, the tensile viscosity of LDPE rises with tensile stress and failure during wall-thinning is less likely. 11.2.5 Elastic aspects of melt behaviour While being deformed and forced through an extrusion die, the melt stores elastic strain energy. As extrudate emerges from the die, stresses are released, some elastic recovery takes place and the extrudate swells. Dimensionally, the degree of swell is typically expressed by the ratio of extrudate diameter to die diameter; the elastic implications of the shear process are expressed by the following modulus: # = r/t'R (11.3) where /z is the elastic shear modulus, r is the shear stress at die wall, and ~ is the recoverable shear strain. The magnitude of modulus/1, depends upon the polymer, molecular mass distribution and the level of shear stress. (Unlike viscosity, dependency of elasticity upon temperature, hydrostatic pressure and average molecular mass is slight.) If the molecular mass distribution is wide, the elastic shear modulus is low and elastic recovery is appreciable but slow. For a narrow distribution, with its greater similarities in molecular lengths, recovery is less but faster. With regard to stress level, the modulus remains constant at low shear stresses but usually increases at the high stresses used commercially, giving appreciable recovery. The balance between elastic to viscous behaviour during deformation can be gauged by comparing the deformation time with the relaxation time or 'natural time' (Z) of the polymer. ~, is the ratio of apparent viscosity to elastic shear modulus (r///z), and derives from the Maxwell model of deformation. The term viscoelasticity originated from the development of such models (e.g. Maxwell, Voigt, standard linear solid (SLS)). The Maxwell model is a mechanical analogue that provides a useful, albeit imperfect, simulation of viscoelasticity and stress relaxation in linear polymers above Tg (Figure 11.9). It is based upon conditions of constant strain. A viscously damped 'Newtonian' dashpot, representing the viscous component of deformation, and a spring, representing the elastic component, are combined in series. At time t, the stress cr is exponentially related to the initial stress or0, as follows: cr = o% exp(-t/~.) (11.4) where ~. is the relaxation time. When t >> Z, there is sufficient time for viscous movement of chain