Impact resistance of thermoplastics Prediction from bulk properties

Transcription

1 Impat resistane of thermoplastis Predition from bulk properties P. S. Leevers, S. Hazra, and S. Hillmansen Although neither the impat strength nor the brittle tough transition temperature measured using nothed impat bend (Charpy and Izod) tests an be used for quantitative design, both are widely aepted as realisti indies on whih to assess and selet plastis. However, polymer suppliers annot easily tailor materials for impat strength, sine it is not a single property but a onvolution of several. The thermal deohesion riterion allows two of these properties resistane to the initiation and rapid propagation of brittle frature to be predited expliitly from bulk material properties. This paper demonstrates the strengths and the limitations of impat test simulation, using this riterion, to predit an inferred G. Methods of isolating and measuring a third property, shear lip resistane, and of evaluating its ontributions to toughness and transition temperature, are disussed. A potential sheme for building this into the simulation is assessed using a simplified analytial model. Using data from the inverted Charpy test, this model itself yields a useful aount of the brittle tough transition temperature in impat. PRC/ IoM Communiations Ltd. The authors are in the Department of Mehanial Engineering, Imperial College of Siene, Tehnology and Mediine, London SW7 2BX, UK. This paper is published as part of a speial issue of PRC devoted to urrent researh at Imperial College of Siene, Tehnology, and Mediine on the mehanial properties and performane of polymers and omposites. INTRODUCTION based on a sharp nothed Charpylike speimen Unless a mehanial property test an maintain redibility with both produers and users of the materials an instrumented test. However, the failure load of a geometry, ertainly allows G to be measured from it evaluates, it will fall into disuse. On this riterion struture an be predited from G or K only after the Charpy (ISO 179) and Izod ( ISO 180) tests have the position and geometry of a sharp initial rak proved fit to survive: the Charpy test, more widely have been presribed (whereas ohesive law formu- used in Europe, is about to mark its entenary. These lations an lead towards the predition of frature tests onfirm the aknowledged truth that many from stress analysis of the unflawed omponent). An unreinfored strutural thermoplastis, although additional problem for tough thermoplastis is that tough and dutile at normal loading rates, an fail neither G nor K turns out to be independent of in a brittle manner under impat, espeially at low geometry or impat speed, and neither an be temperatures and in the environment of a stress regarded as a basi material property.3 onentration. This is of great industrial importane In the present paper the fous is on the tough sine many load bearing plasti omponents must polyethylenes used for pressurised gas and water survive being dropped (e.g. mobile phone shell mould- pipelines. In these, as in many thermoplastis, a ings), impated (ar bumpers and interior omponents), oplanar raze extends from a rak tip when it is or subjeted to shok (water distribution loaded. Highly drawn and oriented fibrils survive to pipelines). span the ohesive surfaes of this raze. In ontinuing Despite their apparent redibility, Izod and Charpy to support a ohesive stress as they extend, sometimes test results annot be used in quantitative design; by several millimetres, the raze fibrils limit the stress it is an ahievement even to orrelate them with at the original rak tip. Frature begins only when eah other.1 Designers must instead resort to rules they break, or tear out from the raze/bulk interfae, of thumb, empirial orrelations, wasteful overspe- at this point. For raze forming thermoplastis a ifiation, and expensive ad ho produt tests. To model is available whih does allow impat frature guarantee impat resistant design, the automotive resistane to be predited from basi bulk properties.4 industry has developed a dependene on expensive Clutton and Channell5 and Harry and Marshall6 rubber toughened and glass reinfored plastis. Now, have done muh to identify the phenomena that our it faes problems in meeting tough diretives to reyle in impat bend tests on these materials (Fig. 1). them. Thus a better understanding of what impat Following impat, the load inreases at a rate orresponding strength is, and what material properties influene it, to the nothed ompliane of the speimen, an benefit both produers and users.2 with a superimposed osillation determined also by Linear elasti frature mehanis, whih allows the its mass and ontat stiffness. Then, if the impat impat frature load in any geometry to be related to speed is high enough and/or the temperature low that in a speimen via an alleged material property enough, a burst of brittle rapid rak propagation (frature resistane G or frature toughness K ), (RCP) follows. This unloads the speimen more rapidly than the striker an load it, leaving a offers a first step. The method of ISO/CD , learly 460 Plastis, Rubber and Composites 2000 Vol. 29 No. 9 ISSN

2 Leevers et al. Impat resistane of thermoplastis: predition from bulk properties 461 point of RCP initiation, whih aording to the newly standardised method ISO/CD defines the frature resistane G, it ahieves enouraging suess. The period that follows is usually dominated by the shear lips. In the present paper, the property tests available to haraterise shear lip properties are reviewed and it is shown, using an approximate analytial formulation, how they an be used to take the simulation forward. From this analysis emerges a simple potential method for prediting the impat transition temperature T bt. BRITTLE FRACTURE INITIATION UNDER IMPACT Plati and Williams9 showed that if the load displaement trae up to peak load in an impat test remained linear, the impat frature resistane G ould be alulated from the area U under it p G = U p (1) BW W(a) 1 Phenomena during impat bend test, as seen where B is the speimen (i.e. noth) width; a=a/w, on frature surfae and in load trae (After where a is the initial length of the rak and W the Ref. 5) total length of its path from one free surfae to the other; and W(a) is a dimensionless funtion of identifiable peak ( P in Fig. 1) on the load time trae, geometry. and a harateristially flat region on the frature surfae. Between the initial noth and the RCP sur- Frature mehanism fae, a stress whitened thumbnail marks what is In rystalline as well as glassy thermoplastis, the assumed to be stable raze growth during loading. rak tip plasti zone often takes the form of a raze, This stable raze growth aounts for at least some whih Williams10 represented as a Dugdale load displaement non-linearity during loading.7 It is Barenblatt zone bearing a uniform ohesive stress. If the breakdown of raze extension to initiate RCP, a rak with suh a raze at its tip either suffers an and the resistane to RCP itself, whih are aounted inreasing load without extending, or extends arrying for by the thermal deohesion model. the raze ahead of it, every raze fibril is extended. It Distintive features appear at eah verge of the is assumed in the present work that fibrils extend by RCP surfae: shear lips, indiating dutile drawing a Lauterwasser Kramer11 mehanism, old drawing from the surfae and usually a subsequent 45 shear polymer through the ohesive surfaes from the bulk separation. Shear lips also appear on frature surfaes material beneath them, so that these surfaes orrefrom pressurised pipe in whih a suffiiently aute spond to the shoulders of a propagating tensile nek impat has initiated RCP and a suffiiently high in a bulk speimen. Suh a proess onentrates shear initial pressure has sustained it. In pipe, these shear work at the ohesive surfae, and at high rates, owing lips typially onstitute only 10% of the surfae width to the low thermal diffusivity of polymers, traps shear but are redited with muh of the frature resistane. heating there. The shear heating effet is greatest at In both pipe and impat speimens they are redited the raze mouth, i.e. the rak tip. with determining the brittle tough transition temper- Using the Dugdale model, Leevers12 alulated the ature T, above whih RCP vanishes: this is a pro- bt onditions under whih the ohesive surfae in a perty of great industrial importane.8 In an impat rystalline thermoplasti ould melt, to a depth test, brittle frature resistane ontrols initiation of suffiient to liberate every polymer hain rossing it. the rak jump but shear lips ontrol arrest.6 The analysis was originally applied to a entral rak, If RCP does arrest and the striker does not (point in a large plate, with a small raze at eah end. For A in Fig. 1) RCP may subsequently reinitiate, some- this referene ase, frature riteria for both steady times repeatedly. Following the last arrest, an impat RCP and impat rak initiation emerge as managebend speimen may develop a dutile hinge: the able, losed form equations. If the ohesive stress is heavily nothed ligament is deformed by a ombi- assumed to be high enough for the raze to be small, nation of raze growth and gross plasti deformation its atual magnitude does not even appear. until the speimen an esape between the supports. The resistane G to RCP follows a bath tub This phenomenon is too terminal and of insuffiient D funtion of rak speed. Between low speed (isogenerality to be of great interest. thermal) and high speed (adiabati) onditions, at The present paper desribes the urrent status of whih rak resistane is high, lies a broad, flat Simpat, a simple omputer simulation of a Charpy minimum with a value of style, three point bend impat test. The aim of Simpat is to simulate impat frature from bulk mehanial G D,min =rs: [5C (T T)+2DH ]... (2) w p m f and physial properties; a set from whih frature where r is the mass density, s: is the weight average w properties have hitherto been exluded. Up to the hain ontour length, C is the speifi heat, DH is p f Plastis, Rubber and Composites 2000 Vol. 29 No. 9

3 462 Leevers et al. Impat resistane of thermoplastis: predition from bulk properties the latent heat of fusion, T is the melting temperature, The seond onstituent is a lumped parameter, m and T is the test temperature. This is assoiated with mass spring dynamial model. This transforms the the flat frature surfae seen in both pipe tests for steady motion of a pendulum or rosshead into a RCP resistane and in impat tests (Fig. 1). speimen load history, the harmoni ontent of whih The resistane to impat frature initiation is gener- usually beomes dominant at impat speeds above ally greater. It is a funtion not only of impat ~1ms 1. The hosen model3 has four parameters. displaement rate v, but also of speimen size W and Two of them (the effetive (moving) mass and stiffness shape (through another geometry fator Y, the deter- of the speimen) are predetermined by the speimen mination of whih has been outlined elsewhere4) geometry (inluding its rak and raze length) and G =E 1/3[J rc (T T)]4/3(pk)2/3Y(a)W 1/3v 2/3 the material density. A third parameter represents p m (3) the stiffness of the striker and support points; this an be measured using the method outlined in where E is the elasti modulus and k is the thermal ISO/CD The fourth represents a ontat diffusivity of the polymer. The 3/2 fator was omitted damping fator. In the simulations reported the onin error from some previous expositions. tat stiffness was hosen to be 10 that of the For rystalline polymers both s: and the melting w unraked speimen, and the ontat damping fator point T are learly definable but some of the other m to be parameters are not; E must represent both the bulk The simulation begins as the striker, moving at material and the rak tip zone (at whih strain rates onstant speed, ontats the speimen. The initial are muh higher) while both C and k vary strongly p stiffness of the speimen is determined by its bulk between a typial T and T. Nevertheless, equaelasti properties, size, thikness, and initial noth m tion (2) has proved to be remarkably suessful in length. After eah subsequent time step: determining the minimum brittle RCP resistane G D (i) the new striker displaement is alulated of a number of polymers.13 The simplest method of (ii) the mass spring model equations are solved to measuring G uses a tube or pipe speimen internally D determine the striker fore pressurised by an annular layer of liquid surrounding (iii) the striker fore determines the inrease in a solid mandrel.6 Using this method, the rak raze length, and hene the newly inreased hooses its own speed and an be assumed to run at G. Equation (3) provides both an aeptable rak tip rak opening displaement (COD) D,min aount of the magnitude of G for the polyethylenes d and the newly dereased speimen om- to whih it was initially applied. It also explains why pliane C G shows a linear dependene on v 2/3 in a number (iv) at the rak tip, the rate of opening determines of thermoplastis. the instantaneous rate of shear work done by ohesive stress on eah of the raze/bulk interfaes Computational simulation of impat bend test For Charpy type tests on polyethylene, the raze size is often too large and the speimen too ompliant for equation (3) to be reliable. Sine the work of Leevers and Morgan,14 the thermal deohesion failure riterion has been implemented using a semianalytial method in the Simpat program. Input parameters for a simulation are: (i) an elasti stress strain harateristi (usually assumed linear), representing the load displaement urve for a similar but unnothed speimen of the same material (ii) the dimensions of the nothed speimen (inluding the initial noth length) (iii) the parameters of a Williams mass spring model to represent the effets of ontat point ompliane (iv) the impat speed (v) bulk thermal properties of the polymer (vi) the raze stress s ; this an be derived from measurements of the final raze length and peak load.7 The simulation is based on two separate models of the speimen. The first is a two-dimensional, linear elasti model of speimen deformation, in whih the noth and raze are represented as a Dugdale rak. Analysis detailed in a ompanion paper7 determines, from a given external load, the raze dimensions (its length and the surfae separation or rak opening displaement at its mouth), and the orresponding redution in stiffness. Plastis, Rubber and Composites 2000 Vol. 29 No s dd dt (v) at the same point, the new temperature a distane (1/2)s: below the interfae is om- w puted; the interfae is assumed to experiene a heat input equal to the shear work done, i.e. the thermomehanial onversion fator is assumed to be unity; the temperature is om- puted arefully from the work input using the algorithm desribed by Leevers and Morgan14 (vi) the new raze length determines the new, redued speimen ompliane. The simulation ends at peak load, as determined by one of two riteria. If the thermal deohesion riterion (T attained at a ritial depth) is satisfied, the rak m is assumed to jump, sine rak extension from a short initial noth in the single edge noth bend (SENB) geometry is unstable under either displaement or load ontrol. The seond riterion is met in slow tests for whih the thermal deohesion riterion is never satisfied beause shear heat generation is overwhelmed by thermal ondution. The load on- tinues to inrease until a riterion for plasti ollapse of the ligament is satisfied: uniform tensile ohesive stress s on one side of the neutral axis is just balaned by uniform ompressive yield stress on the other. Output onsists primarily of the simulated load displaement plot up to the load maximum. By apply- ing the analysis of ISO/CD to this load trae,

4 Leevers et al. Impat resistane of thermoplastis: predition from bulk properties 463 These results represent a fair seletion and show typial behaviour. The tough, high moleular weight polyethylenes show very good onformity to the preditions of the model, while PE3 shows none. It has been argued15 that the ruial distintion between those materials whih onform to the model and those whih do not is suffiient hardening to sustain stable drawing (on a marosopi sale) even at rates for whih shear heating onditions beome quite adiabati. The PE3 shows little or no fratographi evidene of raze extension and a raze stress ould (a) not be determined; the simulation used an estimated value of 50 MPa. Of greater onern is the distintion between the two onformist materials, PE80 and PE100. The simulation sueeds in desribing their overall behaviour, in partiular explaining why G dereases linearly with v 2/3, where v is the impat speed, but it fails to resolve the essential differene between them. Up to peak load, the impat test itself does so only to some extent, G for PE100 being higher by ~30%. There is a omparable differene in strength lass (10 MPa ompared with 8 MPa for PE80) but this is probably fortuitous given that the strength lass is determined by long term strength and thus by a different separation mode.16 (b) Figure 3 ompares simulated and measured load time traes for a test on PE80 at 0 5 ms 1. Both end with a brittle rak jump, and the early part of the trae is well simulated, but the simulation parts ompany signifiantly from reality at higher loads, showing greater softening. This may be partly due to non-linear elastiity or to visoelasti effets, but it is at least partly due to subritial rak growth. Using a servohydrauli mahine, some tests were arrested from impat speed and setioned at the mid-thikness plane. Whereas Clutton,5 using a similar stop blok tehnique, observed survival of the raze up to the RCP initiation point, the present observations showed signifiant subritial rak growth. The proportional inrease in ompliane during loading also orresponds more losely to that expeted from rak () growth aross region 2 (Fig. 1) than by raze growth. A simulation method that an roll the rak tip forward aording to a thermal deohesion riterion 2 Impat frature resistane for a PE80, b PE100, requires a more omplex system than Simpat in its and PE3, as measured using ISO/CD urrent form. The rak tip advanes into material and as alulated using Simpat simulation; heated by surfae drawing in the raze ahead of it mm span Thus the surfae separation rate, heating rate, and resulting temperature depth profile must be omputed at every point within the raze rather than, as at inluding its harmoni ontent, the program also present, just at the raze mouth. As is demonstrated omputes a value of G. below, suh a propagation mode simulation an yield muh more than a further inrease in auray Experimental results and simulations for an already enouraging initiation predition: Figure 2a presents G results for two moderately useful results an be inferred in advane. high moleular weight pipe grade polyethylenes As mentioned above, impat frature initiation lassed as a PE80 (medium strength) and a PE100 resistane differs little between PE80 and PE100. ( high strength), and PE3, a 965 kg m 3 density linear However, in pratie the RCP resistane of PE100 polyethylene of lower weight average moleular greatly exeeds that of PE80, in the sense that there weight ( ). Impat tests were arried out using is a range of temperature, between about 10 C and a servohydrauli mahine, at a range of onstant at least +10 C, over whih PE100 pipe, unlike PE80, resists RCP at any sustainable pressure.8 This sub- stantial differene in the brittle tough transition temperature T is of great industrial importane. It is bt speeds, on mm speimens using a 72 mm support span. The raze stress for eah material was determined from the measured raze extension.7 Plastis, Rubber and Composites 2000 Vol. 29 No. 9

5 464 Leevers et al. Impat resistane of thermoplastis: predition from bulk properties (a) 4 Methods of measuring plane stress frature resistane: a sharp nothed Charpy test; b plane stress Charpy test; inverted Charpy test ing annot draw in material from the lateral surfaes. This onstraint against plasti flow generates high tensile hydrostati stress and favours avitation. In a thermoplasti under these plane strain onditions the flaw tends to invade the material ahead of it as a void sheet or menisus, initiating a raze. Towards the free surfaes, however, plasti flow relieves the hydrostati stress. The polymer yields at the uniaxial yield stress, flows, neks, and, if the material strain hardens as muh as these tough polyethylenes, draws in further material from above and below the frature plane. Harry and Marshall6 and Rithie et al.17 have eah devised variants of the Charpy test to measure the prodigious apaity of polyethylenes, in partiular, to absorb energy in this plane stress separation mode (Fig. 4). Harry and Marshall s method6 involves a Charpy type test on a nothed speimen just thin enough to onsist only, as it were, of two adjaent shear lips. The result is expressed as a plane stress G. Rithie s (b) inverted Charpy (IC) test17 also uses an impat bend speimen, but the noth is so deep that only a ligament as wide as a typial shear lip remains. This is struk in three point bending on the wrong side, 3 Individual load time traes as measured in i.e. adjaent to the noth mouth, so that the ligament ISO/CD impat frature resistane test is extended under almost pure uniaxial tensile impat and as predited by Simpat: a PE80 and b PE100 loading. at 23?C; mm span; 0 25W noth; Although both tests are very young and it is too impat speed 0 5 m s 1 early to attempt a fair omparison, there appear to refleted by the Charpy test only when total energy be several advantages for the IC test as a method for rather than peak energy performane is measured. In olleting geometry independent data: both pipe and SENB speimens, T depends strongly (i) the material is extended from initial onditions on geometry. In partiular, it inreases bt with thikness. that losely represent those within a The final part of this paper demonstrates a sheme developing shear lip; on one side is a perpenthat aounts for the shear lip effet in a propagation diular free surfae, on the other, a sharp mode simulation. The outline presented is an analytifree in their own plane oplanar noth, the surfaes of whih are stress al sheme based on simplifying assumptions. It arrives at a diret and useful predition for the impat (ii) the distane between these boundary on- transition temperature, in terms of bulk property ditions is determined by the ligament depth parameters and an additional measured property left after nothing and tests at several ligament introdued below. widths an be used to establish its effet (iii) sine the speimens used are muh thiker PLANE STRESS TOUGHNESS AND SHEAR than the ligament width, the gauge setion is LIP CONTRIBUTION Around the deepest region of a rak front in a moderately thik impat bend speimen, rak open- Plastis, Rubber and Composites 2000 Vol. 29 No. 9 essentially two-dimensional (iv) the Marshall test is also easily onduted at different thiknesses; however, it is not lear

6 Leevers et al. Impat resistane of thermoplastis: predition from bulk properties 465 at whih point, as thikness is redued, the rates of around <0 1ms 1 at room temperature, a relevant free onstrained free onditions are sharply nothed speimen fails instead by propagation lost and the onstraint is lost throughout. of a raze aross the entire net setion. Inreasing the Results from the IC tests on speimens with different temperature or dereasing the thikness at a higher ligament thiknesses s show that the total plasti displaement rate preipitates a seond transition, work required to separate a shear lip varies with s2. haraterised not by inability of RCP to initiate at Thus rather than representing the shear lip resistane point P in Fig. 1, but by the ability of shear lips to of eah material as Marshall does, using a G -like rearrest it at point A before it breaks the free surfae.6 energy absorbed per unit area, a volumetri energy The total energy absorbed in frature, rather than density w (whih has the units of stress) is used. Of the peak energy used in ISO/CD , provides an S partiular interest is the dependene of w on temper- effetive index for identifying the temperature T of S bt ature. There is evidene of an upper plateau but none the transition; Morgan18 desribed this as a nil of an abrupt transition. Nevertheless the IC test, dutility temperature. developed prinipally through problem oriented The predition of T developed in the present work bt industrial studies, has proven sensitive to hanges in is based on the idea that at the transition point, where the material that orrelate with shifts in the transition the rak just reahes the bak free surfae (i.e. (e.g. orientation, ooling rate, and rystallinity) while point A just lifts off the time axis), the rak propagation proess has been driven purely by the strain G remains little affeted. energy in the speimen at the point of rak initiation. This stored energy is given from G by rearranging Influene of shear lips on frature initiation equation (1), while the energy demands of the propa- Up to the point of deohesion, the two-dimensional gation proess an be inferred from the thermal ohesive model used by Simpat does not distinguish deohesion model and from shear lip resistane data. between a ohesive stress s ating on the plane strain The work needed to propagate two shear lips of ohesive surfae and a uniaxial tensile yield stress s y varying width s right aross the ligament is ating on the adjaent plane stress regions; in fat the underlying Dugdale model was originally applied to 2Ww S P 1 the latter. The distintion appears only in the opening s2 da (5) displaement that the material an survive. This is a 0 often muh greater for a shear lip, whih is able to while the energy to reate the RCP surfae area draw in a greater depth of material. Sine s and s between them is y are of the same order, the average ohesive stress taken aross the total thikness is little affeted by W P 1 G(B 2s) da (6) the presene of the shear lips. a The point of raze failure under impat loading, as 0 The total energy balane for the frature proess at predited by the thermal deohesion theory, is relathe brittle tough transition is therefore given, using tively insensitive to ohesive stress. It is therefore little equation (1), by affeted by the shear lips. When the raze reahes its failure length, the rak opening displaement is BW W(a )G =W P 1 typially still very small. Having attained only a small [G (B 2s)+2s2w ] da (7) 0 S fration of their extensibility, the shear lips have a 0 expended little of their apaity to absorb energy. Following Williams,10 s an be estimated as the size Behind a propagating rak tip, however, the shear of the plane stress plasti zone assoiated with the lips ontinue to exert a ohesive stress, while that rak as it propagates under a rak driving fore G exerted by the raze material vanishes. The drag effet of the shear lip on the rak driving fore during s=r = 1 p 2pA EG phase 3 (Fig. 1) does not register on the impat load s2 y B (8) displaement reord, whih shows only an almost whih, on substitution into equation (7), gives vertial load drop, but it ontrols the extent and ultimately the existene of the rak jump. In materials with fragile shear lips the rak jump uts the BW(a )G 0 speimen in half, unloading it without inreasing the = P 1 a 0 G BG+ C2p2A 1 E s2 y B 2 w 1 S pa E absorbed energy. In materials with highly resistant s2 y BD G2 H da shear lips, progressive redution of the rak driving (9) fore auses rak arrest. A period then follows during This integration an only be arried out properly by whih energy is absorbed by extension of material in a propagation mode analysis, governed by a riterion the two shear lips surviving behind the rak tip, and suh as thermal deohesion, as advoated here. As by hinge deformation. the rak propagates, the load, and hene the rak driving fore, dereases from its initial value orresponding to G. If arrest is only just avoided, it must Brittle tough transition Two distint brittle tough transitions an be dis- break the free surfae under the striker nose at the tinguished in impat frature tests on these materials.18 The first, whih ours as the impat speed less than G up to quite high impat speeds. It an minimum RCP resistane G, whih is normally D,min dereases, is haraterised by the disappearane of simply be assumed in the present work that G RCP initiation (phase 3 in Fig. 1). At displaement dereases linearly with rak extension Plastis, Rubber and Composites 2000 Vol. 29 No. 9

7 466 Leevers et al. Impat resistane of thermoplastis: predition from bulk properties G= G (1 a ) [(1 a)+g*(a a )] (10) where G*= G. G D,min (11) whih an be alulated diretly from equations ( 2) and (3). On evaluating the integrals and rearranging, equation (9) gives the ritial shear lip resistane w S needed to arrest a rak just before it reahes the free surfae w =2p s2 y S E G 1+ 3 ( 1+G* +G*2) C W(a 0 ) (1 a 0 ) 1 2 (1+G*) D B 2r p0 H (12) where r is the plane stress plasti zone size at impat p0 initiation r = 1 p0 2pA EG. s2 y B (13) Provided that the temperature dependenes of other relevant bulk properties are known, the transition temperature an now be estimated graphially, by plotting w results (from inverted Charpy tests) v. S temperature. Figure 5 shows data for two polyethylene grades. The PE80 is the same as that for whih impat data was presented in Fig. 2. The PE100 is not the same as that of Fig. 2, but to be qualified in this lass it neessarily has a similar transition temperature. These results have been alulated using both the total energy absorbed ( by analogy with a lassial, non-instrumented Charpy impat analysis) and only the energy absorbed beyond the peak load point (as originally advoated by Rithie et al.17). Equation (12) (b) has been evaluated for impat tests at 1 m s 1 on speimens having an initial noth length of 0 25W, a span/depth ratio of 6, a width of 12 mm, and thiknesses of 3, 6, and 12 mm. 5 Use of inverted Charpy data (experimental points) to infer impat brittle tough transition temperature, and its speimen thikness DISCUSSION AND CONCLUSIONS dependene for a PE80 and b PE100 resins (23?C) A brittle tough transition point appears on Fig. 5 as an intersetion between a w data set and a line S representing w as given by equation (12). For Although this aount of the transition temperature S w >w, behaviour is dutile and for w <w it is seems unontroversial and the trends it implies are S S S S brittle. This simple onstrution aounts qualitat- orret, it is important to reognise the limitations of ively both for thikness effets and for the differene its implementation in equation (12). In partiular, the in T between PE80 and PE100. The latter arises role of impat speed is by no means fully aounted bt prinipally from their widely differing shear lip resistane, G is little different, so that ISO/CD mines the rak speed at whih RCP is subsequently for. As well as affeting G, the impat speed deter- frature mehanis analysis of impat tests hides the driven. At low rak speeds G is very muh higher; D distintion. For PE100 G is signifiantly higher, but this is both predited by the thermal deohesion D this property is diffiult to measure and it seems to model and witnessed by the impossibility of driving ontribute little to the behaviour of the material at RCP at muh less than ~100 m s 1. Aounting fully the brittle tough transition. However, its role is for this effet using a propagation analysis would amplified by the surfae plasti zones that it generates: inrease w and hene the predited transition temperatures. This is signifiant sine whereas S shear lip energy absorption inreases with the square agreement of their size. The brittle surfae and these larger shear lips ooperate to exhaust the strain energy stored by resistane to initiation. Plastis, Rubber and Composites 2000 Vol. 29 No. 9 with experimental values is urrently better for the post-peak shear lip resistane values, there is little real justifiation for proessing the data in this way. (a)

8 Leevers et al. Impat resistane of thermoplastis: predition from bulk properties 467 Inverted Charpy data is valid only where the load 4. P. S. LEEVERS: Polym. Eng. Si., 1996, 36, 18, trae shows a dutile tail, indiating that all of the 5. E. Q. CLUTTON and A. D. CHANNELL: in Impat and energy stored up to peak load has been dissipated in dynami frature of polymers and omposites, (ed. shear lip extension as well. J. G. Williams and A. Pavan), ; London, MEP. In summary, a framework for prediting the impat 6. P. G. HARRY and G. P. MARSHALL: Plast. Rubber Int., 1991/1992, De./Jan., strength of raze forming thermoplastis has been 7. P. S. LEEVERS: Plast. Rubber Compos., 2000, 29, 453. demonstrated using bulk properties and a thermal 8. P. S. LEEVERS, G. P. VENIZELOS, and R. E. MORGAN: in deohesion riterion. Given an additional measure- Buried plasti pipe tehnology, (ed. D. Ekstein), Vol. 2, ment of shear lip resistane, the method has the STP 1222; 1993, Philadelphia, PA, ASTM. inherent property of indiating a brittle tough trans- 9. E. PLATI and J. G. WILLIAMS: Polym. Eng. Si., 1975, ition. Installation of this method in a propagation 15, mode version of the existing impat test simulation 10. J. G. WILLIAMS: Frature of polymers ; 1984, London, seems to present no speial diffiulty. Ellis Horwood. 11. B. D. LAUTERWASSER and E. J. KRAMER: Philos. Mag. A, ACKNOWLEDGEMENTS 1979, 39, (4), P. S. LEEVERS: Int. J. Frat., 1995, 73, (2), Sumit Hazra was supported by a grant from BP 13. P. S. LEEVERS, M. DOUGLAS, M. CHONG, and J. G. WILLIAMS: Chemials Ltd while engaged on this researh. Stuart Pro. 10th Int. Conf. on Deformation, yield and frature Hillmansen is supported by a Projet Researh of polymers, April 1997, Cambridge,UK, Institute of Studentship from the Engineering and Physial Materials, Siene Researh Counil. 14. P. S. LEEVERS and R. E. MORGAN: Eng. Frat. Meh., 1995, 52, (6), REFERENCES 15. P. S. LEEVERS, R. N. HAWARD, S. HAZRA, and 1. M. P. MANAHAN Sr, C.A.CRUZJr, and H. E. YOHN: in S. HILLMANSEN: presented at 2nd TC4 Conf. on Frature Limitations of test methods for plastis, (ed. J. S. of polymers, omposites and adhesives, September Peraro), STP 1369; 2000, West Conshohoken, PA, 1999, Les Diablerets, Switzerland, ESIS. ASTM, pp E. Q. CLUTTON, L. J. ROSE, and G. CAPACCIO: Plast. 2. D. T. KNIGHT, N. ZABLAN, A. BACKHOUSE, and I. ROBINSON: Rubber Compos. Pro. Appl., 1998, 27, Pro. ABAQUS Users Conferene, May 1999, Chester, 17. S. J. K. RITCHIE, P. DAVIS, and P. S. LEEVERS: Polymer, UK, pp , 39, J. G. WILLIAMS and G. C. ADAMS: Int. J. Frat., 1987, 18. R. E. MORGAN: Dutile brittle transitions in pipe grade 33, polyethylene, PhD thesis, University of London, Plastis, Rubber and Composites 2000 Vol. 29 No. 9