H S = Hashin-Shtrikman lower bound of bulk modulus, N/mm 2 K U G L G U. H = Hashin-Shtrikman lower bound of shear modulus, N/mm 2

Transcription

1 Arup uar Nandi and hubhabrata Datta Arup uar Nandi entral Mechanical ngineering Research Institute (IR-MRI Advance Design and Optiization 79 Durgapur, West Bengal, India hubhabrata Datta Birla Institute o Technology, Deoghar 844 Deoghar, Jharkhand, India Iproveent o ot Tooling Process Through Particle Reinorceent with Polyurethane Mould Use o conventional lexible polyeric ould aterials yields to longer solidiication tie o (wax/plastic patterns in sot tooling process, thereby reducing the rapidity o the process to a great extent, which is not desirable in present copetitive arket. In this work, approach o particle-reinorceent with ould aterials is introduced to reduce the cycle tie o ot tooling process and the resulting cooling tie is experientally investigated in considering a case o anuacturing o a typical wax pattern with aluiniu particle illed polyurethane. It is observed that cooling tie is signiicantly reduced particularly with higher loading condition o aluiniu iller. This happens due to the increase o eective theral conductivity o ould aterial. owever, it is also ound that the stiness o ould becoes siultaneously high due to increase o eective odulus o elasticity o ould aterial. Realizing these acts, an extensive study is carried out to ind the eect on equivalent theral properties and odulus o elasticity o polyurethane coposite ould aterials with the reinorceent o aluiniu and graphite particles independently through rigorous experientation and correlation o experiental indings with the odels cited in literatures. eywords: sot tooling process, lexible polyeric ould aterial, particle reinorceent, cooling tie, equivalent theral conductivity, equivalent odulus o elasticity Introduction Aong dierent rapid tooling processes, sot tooling (T is the one where polyeric lexible aterials are used or aking ould (Rosochowski and Matuszak,. T process is particularly suitable to produce wax patterns in sall batch by vacuu assisted or gravity casting ethod based on RP (rapid prototype/others pattern. This wax coponent is used in investent casting process as a pattern to ake ceraic slurry and inally etallic coponents are produced by using the wax pattern. Developent o etal coponent through rapid prototyping (RP-sot tooling-investent casting process is illustrated in Fig.. Noenclature φ, axiu packing raction o disperse phase α theral diusivity, /sec k theral conductivity, W/-k k x theral conductivity in x-direction, W/-k k z theral conductivities in z direction, W/-k ρ density o aterial c speciic heat o aterial T(x, y, z, t teperature at point (x, y, z and tie, t Q(x, y, z, t aount o heat released at (x, y, z, t per unit volue and unit tie, J/ -s P power output o hot disk sensor per unit tie Q heat released per unit length o hot disk sensor ring source, J/ -s δ Dirac delta unction a radius o the largest ring o concentric spiral hot disk sensor, v hal thickness o concentric spiral hot disk sensor, µ nuber o concentric rings o spiral hot disk sensor L total length o rings o spiral hot disk sensor, σ an integration variable τ characteristic tie ratio (diensionless paraeter D(τ diensionless tie unction T(τ average teperature increase o hot disk sensor c theral conductivity o coposite, W/-k p theral conductivities o polyer/atrix, W/-k theral conductivities o iller aterial, W/-k k instein coeicient, φ voluetric raction o iller in the coposite odulus o elasticity, N/ shear odulus, N/ bulk odulus, N/ odulus o elasticity o atrix/polyer, N/ odulus o elasticity o iller aterial, N/ c odulus o elasticity o coposite, N/ shear odulus o atrix/polyer, N/ shear odulus o iller aterial, N/ c shear odulus o coposite, N/ bulk odulus o atrix/polyer, N/ bulk odulus o iller aterial, N/ c bulk odulus o coposite, N/ L lower bound o odulus o elasticity, N/ U upper bound o odulus o elasticity, N/ L ashin-htrikan lower bound o bulk odulus, N/ U L U ashin-htrikan upper bound o bulk odulus, N/ ashin-htrikan lower bound o shear odulus, N/ ashin-htrikan upper bound o shear odulus, N/ PU polyurethane Al aluiniu RP rapid prototyping T sot tooling LA stereo-lithography Apparatus T theral conductivity T equivalent theral conductivity TP transient plane heat source Paper received May. Paper accepted October. Technical ditor: Anselo Diniz / ol. XXXIII, No., July-epteber ABM

2 Iproveent o ot Tooling Process Through Particle Reinorceent with Polyurethane Mould Figure. Developent o etal coponents through RP-T-wax pattern -investent casting. The coon polyeric lexible ould aterials used in sot tooling process are polyurethane (PU, silicone rubber, etc. owever, the conventional ould aterials possess poor theral conductivity (T. Thereore, the solidiication tie o wax/plastic pattern produced in T process is long because o poor heat low rate through the ould wall. As a result, the rapidity o sot tooling process is reduced to a great extent. In order to increase the heat low rate through ould wall, enhanceent o theral conductivity o ould aterial is an essential issue which can be achieved either by olecular orientation o polyeric ould aterial itsel in order to synthesize new (highly conductive polyeric aterial or by the reinorceent o high conductive illers into existing ould aterials. In the present work, approach o particle-reinorceent with existing ould aterials is adopted, because reinorceent o conductive illers (particularly in the or o particles into the ould aterial is the siplest ethod that ay be easily ipleented in practical application. Furtherore, the degree o increasing eective theral conductivity and other ould properties can be easily controlled by deciding proper aount o iller content in the polyer. The resulting cooling tie in T process is experientally investigated in considering a case o anuacturing o a typical wax pattern with aluiniu illed polyurethane. Through experientation, it is observed that cooling tie is signiicantly reduced particularly with higher loading condition o aluiniu iller, due to the increase o eective theral conductivity o ould aterial. But siultaneously it is also ound that the stiness o ould becoes high due to increase o odulus o elasticity o ould aterial. igh stiness o ould is not desirable in sot tooling process, because releasing pattern and wax coponent ro the ould box becoes diicult. Thereore, it is iportant to carry out an extensive experiental study to ind the eect on equivalent theral properties and odulus o elasticity o polyurethane coposites by reinorcing aluiniu and graphite particles independently with dierent loading conditions. A signiicant aount o research works was ound where particulate iller aterials were introduced in polyer to increase its eective theral conductivity (Agrawal et al., ; Boudenne et al., 4; Miller et al., 6; Mu, Feng and Diao, 7; ubodh et al., 8; inod, arghese and uriakose, 4; undstro and hen, 97; i et al., 8; Pal, 7. The equivalent theral conductivity (T o particulate illed polyer coposites was also investigated with the variation o various orphological properties o conductive iller particles (Ye, hentu and Weng, 6, ulti-odal particle size ixing (Yung and Lie, 7 as well as using hybrid iller aterials (Lee et al., 6. Moreover, addition o iller particles in ould aterial increases the eective odulus o elasticity o ould aterials (Tavan, 997; Rusu, oian and Rusu, ; Papanicolaou and Bakos, 99. In the present work, equivalent theral and echanical properties o particle reinorced polyurethane coposites are analysed through rigorous experientation. In addition, various predictive odels o equivalent theral conductivity and odulus o elasticity reported in the literature are tried to validate based on the experiental results which will be highly helpul in industry or estiation o tie requireent or anuacturing a coponent in T process. The rest o the article is organized as ollows: the second section describes the aterials and orphology o iller particle. Details o experientation with results o cooling tie in T process are presented in the third section. Measureent procedures, discussions on experiental results and validation o odel(s o equivalent theral conductivity and odulus o elasticity o Al and graphite particle reinorced polyurethane are illustrated in the ourth and ith sections, respectively. Finally, concluding rearks are drawn in the sixth section. Flexible Mould Material and Particulate Fillers Flexible ould aterials In the present study on the eect o cooling tie in T process using particle reinorceent with lexible ould aterials, we have considered polyurethane (o type PM /5 produced by ooth-on, Inc. UA. The polyurethane (PU ould aterial has two parts, Part A (liquid polyer and hardener/part B. Both Part A and Part B are ixed in the ratio o : either in weight or volue and norally cured in roo teperature. The value o theral conductivity (kp o cured PU ould aterial as experientally ound is.65 W/-k. Filler particle The iller aterials, aluiniu ine powder and graphite granules having theral conductivities 7 and 9.4 W/-k, respectively, are taken in this study. Measureents o granuloetric paraeters o both the illers are ade using M4, WILD eerbrugg Microscope. The particle size and shape distributions o both iller aterials are enlisted in Table. The (arithetic ean size o particles is deterined by taking the average o iniu and axiu lengths o the particles. For (near spherical shape, the particle size is equivalent to the diaeter o sphere. For (near cylindrical shape, the size o particle is equal to (length diaeter/. In order to ind the size distribution o particles, a sall aount o saple is taken at rando or bulk. We have counted the nuber o particles in that aount as well as easured the size o each particle in an approxiate approach and inally deterined the particle size distributions arithetically in our dierent ranges. The average particle sizes (calculated based on weighted average ethod o aluiniu and graphite illers are. icron and 96 icron, respectively. The axiu volue ractions o graphite and aluiniu particles ound experientally are.56 and.6, respectively. J. o the Braz. oc. o Mech. ci. & ng. opyright by ABM July-epteber, ol. XXXIII, No. /

3 Arup uar Nandi and hubhabrata Datta Table. Filler particle size and shape distributions. Filler type ize distributions hape distributions Fro. to Above. to Above.5 to Above. pherical ylindrical Irregular raphite..5. 7% 8% 8% % % 7% 4% Fro µ to Above µ to Above µ to Above 5 µ pherical ylindrical Irregular Al µ µ 5 µ 66% 4% 8% % 46% % % xperientation o ooling Tie in T Process The eect o cooling tie in sot tooling process using particle reinorced ould aterial is experientally investigated. In this experiental study, we have considered PU as ould aterial and Al particle is taken as iller aterial. We have copared the cooling tie required using Al illed PU coposite ould aterial with that o using only PU or producing a cubical shaped (size: 5 x 5 x 5 wax coponent. The experientation is carried out with the aounts o Al iller content in PU ould aterial as.8% o volue raction. Wax aterial In the present study, Investent casting wax (A7- supplied by Blayson Oleines Ltd, U, is used. The wax consists o natural wax, synthetic wax and natural resins. The elting point o wax is 55º-7º and the boiling point/lash point is greater than º. The elt wax possesses viscosity o.6 Pas at around º. Preparation o ould and anuacturing o wax coponent A cubical shaped RP coponent ade using tereo Lithography Apparatus (LA is used as a pattern or aking the ould. The pattern is inished to a desired quality as required or the inal wax coponent. The RP pattern is suspended by Telon rod in an enclosed box (using thin sheet preerably ade o Perspex aterial and necessary arrangeent is ade to provide passage in the ould box or pouring the olten wax into the ould box. The weights o part-a and part-b o liquid PU and Al iller are calculated based on the respective densities o these coponents or a certain volue raction o iller in the coposite. Part A (liquid polyer is irst ixed with iller particles in a container. To assure a unior ixing, stirring o liquid polyer and gradual pouring o iller particles is done siultaneously. Once the unior ixing o liquid polyer and iller particles is achieved, the hardener (Part B will be poured into the ixture o liquid polyer and iller, and stirred properly or soe tie to attain the particle reinorced ould aterial. Beore pouring the ould aterial into ould box, release agent is sprayed thoroughly inside the ould box. In the box, the (liquid ixture o Al particle reinorced PU is poured all around the pattern. Ater that, the box with coposite ould aterial is placed inside the vacuu casting achine to eliinate any traces o entrapped air in the ould, later it is allowed to cure in roo teperature. radually, it sets with tie and becoes a solid rubbery ass with the pattern inside. Now the ould box is cut along a suitable parting line and the RP pattern is reoved ro within the ould box. Two therocouple wires are placed on the upper part o the ould box or easuring the teperatures. Then, both the parts o ould box are assebled in the proper position with the help o adhesive tape (as shown in Fig.. Once the ould is prepared, liquid wax is poured into the ould and cooling/solidiication o liquid wax is done in roo teperature. Figure. Mould box prepared with Al illed PU. xperiental setup Once the liquid wax solidiies, both the parts o ould box are disassebled by reoving the adhesive tape and the wax coponent is taken out. Ater cleaning the ould box, it becoes ready or another casting. It was noticed that the surace o wax coponent solidiies aster than the core (inside o the coponent. Depending on the size/shape o coponent, a certain depth o solidiication ro the surace ay be suicient so that the wax coponent can be taken out ro the ould box without any daage. Many ties, industrial people ollow such technique or shortening the processing tie to increase the productivity. Thus, in this experiental study, the easureents o teperature are taken at two distinct positions o the wax coponent, at the centre and at a depth o 5 ro the surace o the coponent. Measureent o teperatures is taken through the therocouple syste (as shown in Fig.. The readings o teperatures are collected in an interval o sec through data acquisition syste. Results and discussions The behaviours o cooling rate o the cubical shaped wax coponent where the ould wall thickness is kept as and the outside teperature o ould box is the abient condition (5º are deonstrated here. The variation o teperatures with tie at the location o 5 deep ro the surace and the core o wax coponent using PU ould aterial are plotted in Fig.. In Fig. 4, variations o teperatures at the sae positions o wax coponent using Al particle reinorced PU ould aterial are shown. In both Fig. and Fig. 4, it is noticed that, initially, cooling rate near to surace o coponent is uch aster than that at the core. This is because heat near the surace o wax pattern dissipated only through the ould wall. Whereas heat at the core o wax pattern lows through the ould wall as well as (solidiied wax and the theral conductivity o wax is quite lower than the ould aterial. Ater a long tie, both the teperatures gradually coe to the atospheric one. The teperature o liquid wax during pouring in both the oulds ade o PU and Al particle reinorced PU was kept alost the sae as 85º. Figure deonstrates that to reach the teperature, or instance 4º at a depth o 5 ro the surace o wax coponent, it takes around 8 in in case o PU ould, whereas only 5 in is required in case o particle 4 / ol. XXXIII, No., July-epteber ABM

4 Iproveent o ot Tooling Process Through Particle Reinorceent with Polyurethane Mould reinorced PU. Thus, it is revealed that the cooling tie is reduced signiicantly in sot tooling process using particle-reinorceent with ould aterials. This happens due to the increase o eective theral conductivity o ould aterial. owever, besides the theral conductivity o ould aterial, the cooling tie also depends on the teperature dierence between the inside and outside o the ould box, and thickness o the ould wall. experientation is carried out to ind the eect on equivalent theral conductivity and odulus o elasticity o polyurethane coposites due to reinorceent o iller particles, naely, aluiniu and graphite with dierent loading conditions. The existing odels o equivalent theral conductivity and odulus o elasticity o coposites are also tried to validate based on the experiental indings which will be helpul to decide the optiu aount o iller content to be reinorced with ould aterial. quivalent Theral Properties o Particle-Reinorced PU Mould Materials Figure. ooling rate o wax pattern using PU ould o (d wall thickness at roo teperature. Figure 4. ooling rate o wax pattern using Al particle reinorced PU ould o (d wall thickness at roo teperature. The iniu thickness o ould box is decided based on the shape and size o the wax coponent to be anuactured. On the other hand, cooling/solidiication o wax carried out in abient teperature is the ost desirable technique in industry due to no additional expenditure. Thereore, the only controllable paraeter in T process is the theral conductivity o ould aterial which practitioners can iprove in order to solidiy the wax coponent with a iniu tie. owever, it has been ound that though the cooling tie is signiicantly reduced by conductive iller reinorceent with ould aterial, the stiness o ould is becoing high. This is happening due to the increase o odulus o elasticity o ould aterial as a result o particle reinorceent. igh stiness o ould is not desirable in sot tooling process because releasing pattern and wax coponent ro the ould box becoes diicult. Moreover, the values o eective theral conductivity and odulus o elasticity o a particle reinorced polyeric ould aterial depend on the type o iller aterial. By realizing it, in the ollowing section, an extensive xperiental easureents: Procedures Theral properties o dierent coposites are easured based on transient plane heat source (TP hot disk ethod (ustasson, 99 ollowing the standard IO 7-: 8(. We have used the instruent TP 5 Theral onductivity yste associated with the sotware otdisk Theral onstant Analyser (solids, liquids, powders and paste. The TP 5 Theral onductivity yste utilizes a hot disk sensor in the shape o a double spiral o nickel wire. The hot disk sensor (design nuber: 55 with 4 concentric rings is used here or easuring theral properties. The sensor eleent is ade o µ thick nickel wire and the spiral is supported by µ thick apton aterial to protect its particular shape by providing echanical strength and also keeping it electrically insulated. The relaxation tie o the probe is less than s, and the required tie to reach a constant teperature dierence is kept as 5 in. The sensor used in the experients has a diaeter o a (a is the radius o the largest ring, 6.4 and total thickness (apton-nickel-apton o v (7 µ and was placed between two saples o 5 square and thickness 5-6. The probing depth o the sensor used or all the saples is around 6. In hot disk ethod, easureents o theral properties are ade based on the average teperature increase in hot disk sensor. In the ollowing, derivation o average teperature increase in hot disk sensor and the ethod o coputing theral properties are ade. The dierential equation o heat conduction in an isotropic aterial whose theral conductivity is independent o teperature is given by (arslaw and Jaeger, Q T α T ( ρc t where α (k/ρc is the theral diusivity, k is the theral conductivity, ρ and c are the density and speciic heat o aterial, respectively. ρc is called voluetric speciic heat o the aterial. ( x y, z t ( x y, z t T,, is the teperature at point (x, y, z and tie, t. Q,, (J/ -s is the aount o heat released at (x, y, z, t per unit volue and unit tie. The undaental solution o q. (, assuing that heat source switched at tie t, is r T ( r,t ( 4 k ( t r ξ Q ξ,t T e ( t t d ξdt 4α ρc [( t t ] In cylindrical coordinates, any position in the saple is ( r,θ,θ r, any position in the source is ξ ( r,θ,z and ( J. o the Braz. oc. o Mech. ci. & ng. opyright by ABM July-epteber, ol. XXXIII, No. / 5

5 Arup uar Nandi and hubhabrata Datta ( θ ( zz r ξ r r rr cos θ. For continuous single ring source with radius a in the z plane, the heat source strength can be expressed as ( r a δ( z u( t Q Q δ ( in which δ is the Dirac delta unction (where α ( x δ( x p ( p and u ( t (where u ( t or t < and α u ( t or t is the eaviside unit step unction. Q is the heat released per unit length o ring source. A hot disk sensor is considered to have nuber concentric rings o heat source that are equally spaced (ustasson, 99. Assuing the source is continuous and it is switched on at t, the strength o heat source can be deined as la Q Q δ r δ ( z u( t (4 l i where a is the radius o the largest ring and that o the sallest ring is a, and the total length (heating ilaent ring (L is na n (i.e., ( a. Thus, the total heat released by the sensor in tie t is obtained as t ( ξ, t Q d dt α la α t Q δ r δ ( z r dr dθ dz u( t dt l α Q (5 t a Pt (6 where P is the power output o the hot disk sensor per unit tie. Now, the teperature increase caused by hot disk sensor can be obtained by carrying out the integration in q. ( and with the help o q. (4: T r ( r,t T Q ρc l la r e [ r r rr ( θ ϑ ] α ( tt r dr α cos δ 4 Q la e ρc l aq ρc u( t [ 4 α( t t ] α ( zz t e4α ( tt δ ( z dz dθ α la r z t dt rla ( ( ( cos θ θ 4α t t θ e α t t d l e l [ 4 α( tt ] la r z t dt 4α ( tt I rla [ 4 α( tt ] α ( t t x cosθ x sinθ I e e odiied Bessel unction o the th order. where ( x dθ dθ (7 is the irst kind In a hot disk easureent, as the teperature change near the surace o the sensor is concerned, z, and by considering the power output o the hot disk sensor per unit tie (P instead o Q, q. (7 ay be written as T ( r,t ρc t dt P l ( (8 e α tt I 4 l α t t 4 α( t t [ ] la r quation (8 ay be rewritten by introducing soe new paraeters as ollows T ( r τ ( τ dσ l e αρc σ l ( r ( l a P, 4 σ I a where σ is an integration variable deined as α rla rl (9 aσ ( t t a and the (diensionless paraeter, τ ( αt is called the characteristic a tie ratio. Thus the teperature increase at any point on the sensor surace (i.e., z-plane is described by the q. (9. But to deterine the teperature increase o the sensor itsel, it is required to deterine the average teperature increase over the length o the concentric rings. Thereore, the average teperature increase o the sensor is deined as T na δr rdθ L n ( τ T ( r, τ By replacing the expressions o T ( r,τ (as cited above in q. (, T ( τ dσ na T ( τ P a( a k n l τ σ ( (ro q. (9 and L ay be expressed as l e ( r ( l a 4σ ( r ( l τ a P dσ 4 ( n le ak σ n l P I nl σ nl σ I σ D( τ ( ak where k is theral conductivity o aterials. ( τ D is a diensionless tie unction. Fro q. (, it can be seen that average teperature increase in hot disk sensor, T ( τ diensionless tie unction, ( τ is linearly proportional to the D and exhibit straight-line curve by plotting their values. The slope o this straight-line curve is equal to P ro which the value o k ay be evaluated. But the ak D ay be obtained or a proper value o τ that is again dependent on the value o α (or a given value o a and tie t. Thereore, it is required to ind the proper value o α and, norally, this ay be done by aking a straight line curve between T ( τ and ( τ 6 / ol. XXXIII, No., July-epteber ABM

6 Iproveent o ot Tooling Process Through Particle Reinorceent with Polyurethane Mould series o coputational plots o T ( τ versus ( τ D or a range o α values. The correct value o α will be reached once the straight-line plot o T ( τ versus ( τ D is obtained. Once the correct value o α is obtained, the value o k can be deterined ro the slope o the straight-line plot o T ( τ versus D ( τ. Another way to deterine the value o k is to easure the density (ρ and the speciic heat (c o the aterial separately. Then, the value o k can be obtained by ultiplying the value o k by the density and speciic heat o the aterial. This ethod is generally applied or anisotropic aterials. I the properties along x- and y- axes are the sae, but dierent ro those along the z- axis and i the plane o the hot disk sensor is apped out by x- and y- axes, q. ( will be expressed as P T τ x D τ x ( a k x k z where k x and k z are the theral conductivities in the x (or y and z t directions respectively and k x. The value o k τ x can be x a deterined by the above stated iteration process until a straight-line T D is reached and the value k x is τ x τ x plot o versus equivalent to αρ c. On the other hand, ro the slope o the τ x τ x straight-line plot o T versus D, the value o k x k be ound out. Thereore, the value o k z is calculated by dividing the value o by obtained value o k x. x z k k z can oposite saple preparation The sae procedure as described in Preparation o ould and anuacturing o wax coponent subsection is adopted here to prepare the coposite saples or theral property easureents. As per the standard, IO 7-: 8(, the coposite saples are ade in the size o 5 square and thickness is kept as 5-6. xperiental results and discussions The equivalent theral conductivity (T, theral diusivities and voluetric heat capacity o particulate illed PU coposites with Al and graphite particles or dierent aount o illing ractions as obtained through experientations at roo teperature ( are illustrated in Fig. 5. Fro the experiental results, it is quite evident that theral conductivities o particulate illed PU and R are increasing (around ties with increasing aount o iller and the increasing rate starts ore drastically at around -% volue raction o iller or soe coposites. This is due to the oration o theral conductive chain in coposite whose tendency is high in elevated iller content. In Fig. 5, another point noticed is that increasing rate o theral conductivity is coparatively higher or any level o iller content when graphite iller is used or both the ould aterials. The reason is: large particles which are equivalent as the coposed o aggregates o iller particles are ore capable o oring conductive chains than ine particles. Moreover, the aount o heat scattered around the contact points in case o coarse particles is saller than in ine particles, since less nuber o contact points are required to or the sae length o conductive chain (Agari and Uno, 985. Figure 5. quivalent theral properties o PU coposites with aluiniu and graphite particles: (a theral conductivity, (b theral diusivity and (c voluetric heat capacity. J. o the Braz. oc. o Mech. ci. & ng. opyright by ABM July-epteber, ol. XXXIII, No. / 7

7 Arup uar Nandi and hubhabrata Datta ( ln k c ln k ln k p (4 where, the actor o the eect on crystallinity and crystal size o polyer, does not depend on particle size. is the actor o ease in oring conductive chains o particles, which is aected by iller particle size. Figure 6. Morphological structure o PU and aluiniu coposites with volue raction levels: a 9.9% and b %. On the other hand, it is worth entioning that anuacturing process o coposite is an iportant aspect to achieve a axiu value o T o lexible ould aterial coposites. Because there is ore possibility o the presence o voids in ould due to ault(s in anuacturing, which will reduce eective theral conductivity. This phenoenon is observed in the results o PU-Al coposites (Fig. 5(a. It is ound that though the coposite contains higher iller (48.66%, it exhibits lower T than that having lower (9.9% iller due to presence o ore voids (as seen in Fig. 6. alidation o xisting Models Based on xperiental Results The experiental results o T o the coposites have been explained by several epirical/sei-epirical odels, naely Maxwell-ucken (Maxwell, 954, Bruggean (Bruggean, 95, Lewis-Nielsen (Lewis and Nielsen, 97, heng-ackon (heng and achon, 969, Ziebland (Butta and Migliaresi, 996, Torquato (Torquato, 985 and Agari-Uno (Agari and Uno, 986, as shown in Fig. 7. It is observed that Lewis-Nielsen odel (which is deined by epirical expression as shown in q. ( provides closer estiations (average % error 9. than other epirical odels in all our coposites. k AB B ϕ c k p ( where k k p B k A k p φ and ϕ ; φ k c, k p, and k represent the equivalent theral conductivities o coposite, polyer, and iller, respectively, and is the voluetric raction o iller in the coposite. The constant A depends on the shape and orientation o disperse particles in the coposite, and is deined by A (where k k is the instein coeicient. φ is the axiu packing raction o disperse phase (or randoly distributed spherical particles, φ.67. The value o A is equal to.5 or randoly distributed spherical particles, while in case o randoly distributed aggregates o spherical particles, A. Moreover, a better it is observed with the sei-epirical odel o Agari-Uno (expressed by q. (4 whose controlling paraeters are deterined based on the experiental data. The average % errors o Agari-Uno odel are ound as.5 and. by individually itting the coposite systes o PU-Al and PU- raphite, respectively. owever, it was ound that the average % error o Agari-Uno odel by itting all the data o two coposite systes is considerably high (6.95%, though still lower than Lewis-Nielsen odel. Figure 7. Theral conductivities o coposites (a PU-Al and (b PU- raphite: experiental values and various odel predictions. In looking at the Agari-Uno odels, it was ound that values o (.9594 and. are nearer/equal to. and the values are.65 and.8595 or the suspension systes, PU-Al and PUgraphite, respectively. alue o close to. indicates that eect 8 / ol. XXXIII, No., July-epteber ABM

8 Iproveent o ot Tooling Process Through Particle Reinorceent with Polyurethane Mould o crystallinity and crystal size o polyer on the changing theral conductivity o polyer (atrix aterial is negligible due to the inclusion o iller. uch kind o eect is observed in lexible ould aterial coposites with both the graphite and Al particles. The value o close to. indicates ore ease in oring conductive chains o iller particles in coposite. In the present coposites, it is observed that the value o is greater or large particle size iller (graphite than the saller one (Al which agrees well with the results o Boudenne et al. (4. coparatively saller than graphite particles. This phenoenon is speciically observed when the iller content is ore than 4%. Whereas, adhesion between PU and graphite particles is not as critical as copared to polyer atrix and etallic iller coposite systes. The eective odulus o elasticity o particle illed lexible (polyeric ould aterial coposite also depends on the odulus o elasticity o the polyer, odulus o elasticity o iller aterial, and the volue/weight raction o iller particle in the coposite. quivalent Modulus o lasticity o Particle-Reinorced PU Mould Materials xperiental easureents: Procedures Modulus o elasticity o a aterial ay be tested using dierent standard test ethods, naely tensile testing, our-point loading test (ere, 984, ultrasonic easureent (Moore, 7, etc. The tensile testing ethod we have adopted here to ind the equivalent Young's odulus o lexible ould aterial coposites is based on the standard ATM D 9M-8. According to this standard, a constant rectangular cross-section shaped specien o thickness,.5 ±4%, 5 ±% o width and 7 o length in the or o sheet is prepared using the ethod as described in Preparation o ould and anuacturing o wax coponent. Tensile tests are perored on an Instron testing achine (ade o DART. The testing achine is equipped with a recording syste (load sensor or easuring the applied orce within ±% and is capable o easuring elongation o the test specien in iniu increents o %. The achine has two grips, one o which is connected to the load sensor. The grips (constant pneuatic and wedged type are tighten autoatically and exert a unior pressure (o axiu bar across the gripping suraces which is increasing as the tension increases in order to prevent slippage and to avour ailure o the specien in the straight iddle section. At the end o each grip, a positioning device is placed in order to insert specien to the sae depth in the grip and to ake the specien aligned with the direction o pull. An extensoeter (Made o MT, Model No. 64.5F-4, erial No A is used to easure the strain o test specien. The extensoeter was calibrated by M/s MT. The extensoeter was attached to the specien at two points o 5 apart (extensoeter gauge length syetrically about the id-span and id-width location. During experientation, a value o constant head-speed o 5 /in is applied and the orce applied to the specien until a axiu value o elongation, 5% or ailure o the specien whichever is occurred earlier. The values o displaceent, orce and strain are recorded through data acquisition syste at a constant interval o. sec. Ater plotting the data o stress vs. strain, a linear curve is ound which indicates the elastic region o the stress-strain diagra o the aterial. The slope o this linear curve is evaluated, which represents the tensile odulus o elasticity o coposite oulds. xperiental results and discussions Fro the experiental results as illustrated in Fig. 8, increase o odulus o elasticity is observed in all kinds o lexible ould aterials reinorced with conductive iller particles. In PU coposite syste, increase o odulus o elasticity is ore-or-less siilar in nature or both the reinorceents, Al and raphite, especially when the iller concentration label is below 4%. But a sudden rise o odulus o elasticity is observed with Al iller at above 4% volue raction, unlikely to that illed with graphite particles. This ay be due to the act that Al particles are securely ebedded with polyer atrix since the size o particles is Figure 8. quivalent odulus o elasticity o PU coposites with aluiniu and graphite particles. alidation o existing odels based on experiental results The experiental results o equivalent odulus o elasticity o the particulate illed polyurethane and silicone rubber coposites, as illustrated in Fig. 8, are explained using various existing epirical odels available in the literature. The ost coonly used odels or predicting equivalent odulus o elasticity o a coposite aterial in a straightorward way, ro its nuerical expressions are the ollowing: Model proposed by Paul (Paul, 96: ( c (5 ( ( where, and c are the odulus o elasticity o the atrix, particle and coposite, respectively. Model proposed by Ravichandran (Ravichandran, 994: L c ( ( ( ( (6 J. o the Braz. oc. o Mech. ci. & ng. opyright by ABM July-epteber, ol. XXXIII, No. / 9

9 Arup uar Nandi and hubhabrata Datta 4 / ol. XXXIII, No., July-epteber ABM [ ] U c (7 where Model proposed by Wu (Wu, 965: λ (8 where ( - is volue raction o atrix aterial. λ is the paraeter, which reains ixed or any relative concentration o a given coposite aterial. Through experiental study, it has been ound that the value o λ is quite close to unity or <<. Besides the above odels, there are any epirical expressions proposed by various researchers, naely ashin-htrikan bounds (ashin and htrikan, 96, alpin-tsai odels (alpin, 969; alpin and ardos, 976, Walpole bounds (Walpole, 966a; Walpole, 966b, ethods based on ean-iled (such as oigt odel (oigt, 889, Reuss odel (Reuss, 99, Mori-Tanaka s odels (Benveniste, 987, etc., sel-consistent ethod based odels (roner, 958, odels based on dierential ethod (McLaughlin, 977, Lielens odels (Lielens et al., 998 ro which the equivalent odulus o elasticity (or its upper bound (UB & lower bound (LB o a particulate illed coposite can be deterined based on the conventional expressions (q. (9 o isotropic aterial properties by assuing the coposite to be (quasi isotropic and (quasi hoogeneous. 9 (9 where, and are the odulus o elasticity, shear odulus and bulk odulus, respectively. I the Lielens odel is orulated based on a noralization o the upper and lower bounds suggested by ashi-htrikan, it can be written as U L c ( U L c ( where, and L, U, L and U are the ashin-htrikan lower and upper bounds o bulk odulus and shear odulus, respectively, which are expressed by the ollowing epirical expressions: L 4 ( U 4 ( L (4 U (5 Figure 9. quivalent odulus o elasticity o coposites (i PU-Al and (ii PU-raphite: experiental values and various odels. In Fig. 9, the equivalent odulus o elasticity o particle reinorced PU coposites obtained using various odels are illustrated. Through rigorous coparative study aong the experiental results with that obtained ro various odels, it is ound that the odel proposed by Lielens, with noralization o the upper and lower bounds suggested by ashi-htrikan (deined in q. ( and q. (, provides close agreeents with experiental data copare to other odels, particularly up to a volue raction o. o the particulates. Fro Fig. 9(i to Fig.

10 Iproveent o ot Tooling Process Through Particle Reinorceent with Polyurethane Mould 9(ii, it has been observed that ost o the experiental data o all the suspension systes lie in the region enclosed by the ashi- htrikan upper and lower bounds. The odel sees to be eicient enough to predict the odulus o elasticity o the PU coposites with varying atrix as well as reinorceent particles. onclusions In the present work, an experiental study is carried out to ind the equivalent theral properties and eective odulus o elasticity o particle reinorced PU ould aterial using hot disk technique and tensile testing ethod, respectively. The easureents o theral properties using hot disk technique and odulus o elasticity using tensile testing ethod are presented. A signiicant increase o theral conductivity as well as odulus o elasticity o PU coposite ould aterial (reinorced with Al and graphite particulate illers is observed. As a result, it has been ound that the cooling tie in sot tooling process is uch reduced, but siultaneously increase o stiness o ould box is observed. Thereore, deterination o an optiu aount o iller content with ould aterial is iportant. Presence o voids in the coposite due to anuacturing ault(s reduces the eective theral conductivity considerably. By coparing the experiental results o equivalent theral conductivity o PU coposites with the existing odels, it is observed that data driven odel by Agari-Uno and nuerical odel by Lewis-Nielsen provide better estiations than other odels. On the other hand, odel proposed by Lielens shows better trade-o with experiental indings o equivalent odulus o elasticity o particle reinorced PU copared to other odels. Acknowledgeents The authors are thankul to DT (Departent o cience and Technology, New Delhi, India, or supporting this research work under the BOYAT ellowship prograe. 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11 Arup uar Nandi and hubhabrata Datta oigt, W., 889, Uber die Beziehung zwischen den beiden lasticitatsconstanten isotroper korper, Annals o Physics, ol. 8, pp Walpole, L.J., 966a, On bounds or the overall elastic oduli o inhoogeneous syste I, Journal o the Mechanics and Physics o olids, ol. 4, No., pp Walpole, L.J., 966b, On bounds or the overall elastic oduli o inhoogeneous syste II, Journal o the Mechanics and Physics o olids, ol. 4, No. 5, pp Wu, T.T., 965, On the paraetrization o the elastic oduli o twophase aterials, Journal o Applied Mechanics, ol., pp. -4. Ye,.M., hentu, B.Q. and Weng, Z.X., 6, Theral conductivity o high density polyethylene illed with graphite, Journal o Applied Polyer cience, ol., No. 6, pp Yung,.. and Lie,., 7, nhanced theral conductivity o boron nitride epoxy-atrix coposite through ulti-odal particle size ixing, Journal o Applied Polyer cience, ol. 6, No. 6, pp / ol. XXXIII, No., July-epteber ABM