Experimental studies on equivalent thermal properties of particle-reinforced flexible mould materials

Transcription

1 Coposites: Advances in Manufacture and Characterisation 199 Experiental studies on equivalent theral properties of particle-reinforced flexible ould aterials A. K. Nandi, C. Cingi & J. Orkas Foundry Engineering, Helsinki University of Technology, Finland Abstract The investent casting process uses wax patterns which ay be produced using the soft tooling process where the coon flexible (polyer) ould aterials used are polyurethane rubber, silicone rubber, etc. of a typical kind. However, due to poor theral conductivity of these aterials, solidification tie of (wax) patterns takes longer leading to reduced rapidity of the process to a great extent. This proble ay be overcoe by increasing theral conductivity of ould aterial that can be achieved either by olecular orientation of polyer itself or by addition of conductive fillers into polyer. The ethod of controlled addition of theral conductive (particulate) fillers into ould aterial ay be adopted by realizing it as the siplest and easiest to ipleent technique in industry. In this article, an experiental study has been carried out to find the effects on equivalent theral properties of flexible ould aterials reinforced with conductive filler particles. Two different types of particles (aluiniu and graphite) with different orphological characteristics are considered as fillers. The easureent of theral properties is carried out by a transient plane heat source technique. As uch as 1-fold increases in theral conductivity and theral diffusivity values of ould aterials reinforced with conductive fillers are found. In explaining the experiental results by several epirical/seiepirical odels, it is observed that the Lewis Nielsen odel provides a good estiation, while the Agari Uno odel (fitted with experiental data) shows better agreeent than other odels. Keywords: soft tooling process, flexible ould aterial, particle reinforced polyer coposite, equivalent theral properties, transient plane heat source technique. WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press doi:1.495/ /

2 Coposites: Advances in Manufacture and Characterisation 1 Introduction Aong different rapid tooling processes, soft tooling (ST) is the one where polyeric flexible aterials (such as polyurethane (PU) rubber and silicone rubber (SR) of typical kind) are used for aking ould [1]. The ST process is particularly suitable to produce wax patterns (used in investent casting processes) in sall batch by vacuu assisted or gravity casting ethod based on rapid prototype (RP)/others pattern. Developent of a etal coponent through rapid prototyping-soft tooling-investent casting process is illustrated in fig. 1. Rapid prototype pattern Wax pattern ade in ST process Investent casting shell preparation Investent casting product Figure 1: Developent of etal coponents through RP-ST-wax patterninvestent casting. However due to poor theral conductivity (TC) of flexible ould aterials, the solidification tie of wax coponent in ST process takes longer leading to reduced rapidity of the process to a great extent. This proble ay be overcoe by increasing the theral conductivity of ould aterial that can be achieved either by olecular orientation of the polyer itself or by addition of conductive fillers in the polyer. The ethod of controlled addition of theral conductive (particulate) fillers into ould aterial (to for polyer coposite) is adopted by any practitioners by realizing it as the siplest and easiest to ipleent technique in industry. However, the presence of filler particles in ould aterial will affect other properties of ould (naely, stiffness of ould, flow ability of elt ould aterial, etc.); those are iportant for the ST process to obtain various advantages fro the oulding process. Thus, it is very uch iportant to have a prediction on equivalent theral conductivity of coposite prior to the addition of certain aount of given filler into ould aterial in order to keep various advantages of ST process obtained in the ould up to the desired levels. In the past, various researchers studied the effect of equivalent theral /electrical conductivity of polyer by inclusion of etallic/ceraic powders. A significant aount of work has been conducted by varying the aount of conductive fillers in coposite aterials [ 5]. The ai of the present research work is to analyse the effect on equivalent theral properties (theral conductivity, theral diffusivity and specific heat) of flexible ould aterials, PU and SR by addition of high theral conductive filler particles, aluiniu and graphite. In addition, various equivalent theral conductive odels reported in literature are used to explain the experiental results of theral conductivities. WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

3 Coposites: Advances in Manufacture and Characterisation 1 Materials and coposite anufacturing.1 Flexible ould aterials Aong different ould aterials, in this study two flexible ould aterials, extensively used in industries, have been chosen, naely polyurethane (PU) produced by Sooth-ON, Inc. USA and silicone rubber (SR) (Silicones ELASTOSIL RT 61 A) anufactured by Wacker-Cheie GMBH, Gerany. Both PU and SR consist of two parts (part A and part B) ixing at the ratio of 1:1 and 9:1 by weight or volue, respectively and cured in roo teperature.. Filler particle The filler aterials that have been considered in this work are aluiniu fine powder and graphite granules having theral conductivities 37 and 9.34 W/-k, respectively. The average filler particle size and shape distributions that are investigated through experientation are described next...1 Filler particle size and shape distributions Measureents of granuloetric paraeters of both fillers are ade using a M4, WILD Heerbrugg Microscope. The particle size and shape distributions of both filler aterials are listed in table 1. The (arithetic ean) size of particles is deterined by taking the average of iniu and axiu lengths of the particles. For (near) spherical shape, the particle size is equivalent to the diaeter of sphere. For (near) cylindrical shape, the size of particle is equal to (length + diaeter)/. In order to find the size distribution of particles, a sall aount of saples is taken at rando fro bulk. The nuber of particles has been counted in that aount, the size of each particle easured by an approxiate approach and, finally, the particle size distributions arithetically deterined in four different ranges. The average particle sizes (calculated based on weighted average ethod) of aluiniu and graphite fillers are 1.3 and 96, respectively. The axiu volue fractions of graphite and aluiniu particles found experientally are.516 and.63, respectively. Filler type Graphite Aluiniu Table 1: Fro.1 to.3 Filler particle size and shape distributions. Size distributions Above.3 to.5 Above.5 to 1. Shape distributions Above Spherical Cylindrical Irregular 1. 7% 18% 8% % 3% 7% 43% Fro 1 μ to 1 μ Above 1 μ to 3 μ Above 3 μ to 5 μ Above 5 µ Spherical Cylindrical Irregular 66% 4% 8% % 46% % 3% WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

4 Coposites: Advances in Manufacture and Characterisation.3 Coposite anufacturing In order to prepare the coposite saples (5 square and 5 6 thick) used for theral property easureents, the weights of part-a and part-b of liquid polyer (PU/SR) and filler are calculated based on the densities of these coponents for a certain volue fraction of filler in the coposite. Then the part A (liquid polyer) is first ixed with filler particles in a container using anual stirring. To assure a unifor ixing, stirring of liquid polyer and gradual pouring of filler aterial is done siultaneously. Once, the unifor ixing of liquid polyer and filler aterial is achieved, the hardener (Part B) is poured into the ixture of liquid polyer and filler, and stirred properly for another 5 1 inutes. Before pouring the ixture aterial into ould box, a release agent is sprayed thoroughly inside the ould box. After curing the polyer coposite at roo teperature, it is taken out fro the ould box and the latter is reused for preparing another saple. Different saples are prepared by varying the aount of (volue fraction) filler ixed with PU and SR. The aount of filler to be ixed with ould aterial has been restricted up to the axiu packing fraction of filler particles since this indicates the axiu loading level of particles to be ixed into a fluid. 3 Measureent of theral properties The theral properties of different coposites are easured based on transient plane heat source (TPS) hot disk ethod [6] following the standard, ISO 7-: 8(E). The instruent TPS 5 S Theral Conductivity Syste, associated with the software HotDisk Theral Constant Analyser V (solids, liquids, powders and paste), has been used [7 9]. The TPS 5 S Theral Conductivity Syste utilizes a hot disk sensor in the shape of a double spiral of nickel wire. The hot disk sensor (design nuber: C551) with 14 concentric rings is used here for easuring theral properties. The sensor eleent is ade of 1 μ thick nickel wire and the spiral is supported by 3 μ thick Kapton aterial to protect its particular shape by providing echanical strength and also keeps it electrically insulated. The relaxation tie of the probe is less than 1 s and the required tie to reach a constant teperature difference is kept at 15 in. The sensor used in the experients has a diaeter of a (a is the radius of largest ring, 6.43 ) and total thickness (Kapton-nickel-Kapton) of v (=7 μ) was placed between two saples 5 square and 5 6 thick. The probing depth of the sensor used for all the saples is around 6. In the hot disk ethod, easureents of theral properties are ade based on the average teperature increase in the hot disk sensor. In the following, derivation of average teperature increase in the hot disk sensor and the ethod of coputing theral properties are ade. The differential equation of heat conduction in an isotropic aterial whose theral conductivity is independent of teperature is given by [1] Q T k T (1) c t WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

5 Coposites: Advances in Manufacture and Characterisation 3 where k (=K/ρc) is the theral diffusivity, K is the theral conductivity, ρ and c are the density and specific heat of aterial, respectively. ρc is called voluetric specific heat of the aterial. T(x,y,z,t) is the teperature at point (x,y,z) and tie t. Q(x,y,z,t) (J/ 3 -s) is the aount of heat released at (x,y,z,t) per unit volue and unit tie. The fundaental solution of eqn (1), assuing that heat source was switched at tie t =, is rξ 1 t Q ( ξ,t) 4 ( ) e ktt d d V T r,t T ξ t () ρc(4π k) ( t t) In cylindrical coordinates, any position in the saple is at coordinates r = (r,,z), any position in the source is at = (r',',z') and r x = r +r' rr'cos( ') + (z z'). For a continuous single ring source with radius a in the z = plane, the heat source strength can be expressed as Q Q ( r a) ( z) u( t), (3) in which ( ) is the Dirac delta function where f ( x) ( x p) f( p) and u(t') is the Heaviside unit step function where u(t') = for t and u(t') =1 for t. Q is the heat released per unit length of ring source. A hot disk sensor is considered to have nuber of concentric ring (heat) sources that are equally spaced [6]. Assuing the source is continuous and switched on at t' =, the strength of heat source can be defined as la Q Q r ( z) u( t) li (4) where a is the radius of the largest ring, a/ that of the sallest ring and the total length (heating filaent) ring is na L = π (i.e., ( + 1)a). n1 Thus, the total heat released by the sensor in tie t is obtained as t la t H Q(, t)dvdt Q r ( z ) rdr d dz u( t) dt V l1 π a ( 1) Qt (5) P t (6) where P is the power output of the hot disk sensor per unit tie. Now, the teperature increase caused by the hot disk sensor can be obtained by carrying out the integration in eqn () and with the help of eqn (4), [ r r rrcos( )] la 4 kt ( t) Q T r,tt r e rdr ρc l1 WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

6 4 Coposites: Advances in Manufacture and Characterisation where ( zz) 4 kt ( t) π t ut ( ) e ( z)dz d dt 3 [4π kt ( t)] la r z rla t π cos( ) d k ( tt ) e 4 kt ( t) e 3 l1 Q la t c [4π kt ( t)] la r z πaq t 4 kt ( t) dt rla le I 3 c l1 k( t t) [4π kt ( t)] 1 π π xcos 1 xsin d I( x) e d e d π π is the first kind odified Bessel function of the th order. In a hot disk easureent as far as the teperature change near the surface of the sensor is concerned, z and by considering the power output of the hot disk sensor per unit tie (P ) instead of Q, eqn (7) ay be written as la r 4 kt ( t) P t dt rla Trt (,) le I ( 1) 3 c l1 4[π kt ( t)] k( t t ) Eqn (8) ay be rewritten by introducing soe new paraeters as follows l r a P d rl 4 3 l1 a Tr (, ) le I π a( 1) kc where σ is an integration variable that defined as k( t t) σ = a and the diensionless paraeter τ ( kt a (7) (8) (9) ) is called the characteristic tie ratio. Thus the teperature increase at any point on the sensor surface (i.e., z- plane), is described by the eqn (9). But to deterine the teperature increase of the sensor itself, it is required to deterine the average teperature increase over the length of the concentric rings. Therefore, the average teperature increase of the sensor is defined as T π 1 na r rd L Tr, n1 (1) WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

7 Coposites: Advances in Manufacture and Characterisation 5 By replacing the expressions of T(r,) (fro eqn (9)) and L (as cited above) in eqn (1), T ay be expressed as l r a P d na 4 nl 3 n1 l1 1 T( ) le I π π a ( 1) π a 1 K l r a P 1 d e 4 nl n l 3 I ( 1) n1 l1 π ak P D( ) (11) 3 π ak where K is the theral conductivity of aterials. D() is a diensionless tie function. A ore detailed derivation of average teperature increase in hot disk sensor can be found in [11]. Fro eqn (11), it is seen that the average teperature increase in hot disk sensor, T ( ) is linearly proportional to the diensionless tie function, D() and exhibited straight-line curve by plotting these values. The slope of this straight-line curve is equal to P /( 3/ ak) fro which the value of K ay be evaluated. But, the straight line curve between T ( ) and D() ay be obtained for a proper value of τ that is again depended on the value of k (for a given value of a and tie, t). Therefore, it is required to find the proper value of k and norally this ay be done by aking a series of coputational plots of T ( ) versus D() for a range of k values. The correct value of k will be reached once the straight-line plot of T ( ) verses D() is obtained. Once the correct value of k is obtained, the value of K can be deterined fro the slope of the straight-line plot of T ( ) versus D(). Another way to deterine the value of K is to easure the density (ρ) and the specific heat (c) of the aterial separately. Then, the value of K can be obtained by ultiplying the value of k with the density and specific heat of the aterial. This ethod is generally applied for anisotropic aterials. If the properties along x- and y- axes are the sae, but different fro those along the z-axis and if the plane of the hot disk sensor is apped out by x- and y- axes, eqn (11) will be expressed as P T( x ) D( ) 3 x (1) π a KxKz where K x and K z are the theral conductivities in the x (or y) and z directions, respectively, and x = k x t / a. The value of k x can be deterined by the above stated iteration process until a straight-line plot of T ( x ) versus D( x ) is WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

8 6 Coposites: Advances in Manufacture and Characterisation reached and the value K x is equivalent to kc. On the other hand, fro the slope of the straight-line plot of T ( x ) versus D( x ), the value of K x K z can be found. Therefore, the value of K z is calculated by dividing the value of by the obtained value of K x. 4 Results and discussion K x K z The equivalent theral conductivity (ETC), theral diffusivities and voluetric heat capacity of particulate filled PU and SR coposites with Al and graphite particles for different aount of filling fractions as obtained through experientations at roo teperature (3 C) are illustrated in fig.. Fro the experiental results, it is quite evident that theral conductivities of particulate filled PU and SR are increasing (by around 1 ties) with increasing aount of filler and the increasing rate starts ore drastically at around 3% volue fraction of filler for soe coposites. This is due to the foration of theral.. Effective Theral Conductivity (W/-k) Effective Theral Diffusivity( /sec) (a) (b) 4. Voluetric heat 3 capacity (MJ/ -k) (c) PU+Graphite PU+Al SR+Graphite SR+Al Figure : Equivalent theral properties of PU and SR coposites with aluiniu and graphite particles: (a) theral conductivity; (b) theral diffusivity; (c) voluetric heat capacity. WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

9 Coposites: Advances in Manufacture and Characterisation 7 conductive chains in coposite whose tendency is high in elevated filler content. In fig., another point is noticed, naely that the increasing rate of theral conductivity is coparatively higher for any level of filler content when graphite filler is used in both ould aterials. The reason is that large particles which are equivalent to those coposed of aggregates of filler particles are uch ore capable of foring conductive chains than fine particles. Moreover, the aount of heat scattered around the contact points in case of coarse particles is saller than that for fine particles, since a saller nuber of contact points are required to for the sae length of conductive chain []. (a) (b) Figure 3: Morphological structure of PU and aluiniu coposites with volue fraction levels: (a) 39.9%; (b) %. On the other hand, it is worth entioning that the coposite anufacturing process is an iportant aspect in achieving a axiu value of ETC in flexible ould aterial coposites. This is because there is a high possibility of the presence of voids in the ould due to fault(s) in anufacturing, which will reduce the effective theral conductivity. This phenoenon is observed in the results of PU-Al coposites (fig. (a)). It is found that, though the coposite contains a higher aount of filler (48.66%), it exhibits a lower ETC than that of the coposite having less (39.9%) filler due to the presence of ore voids (as seen in fig. 3). There was an effort to explain the experiental results for ETC fro 4 kinds of coposites by several epirical/sei-epirical odels as shown in fig. 4. It is observed that the Lewis Nielsen odel provides closer estiations (average % error, 8.48) than other epirical odels for all four coposites. Moreover, a better fit is observed with the sei-epirical odel of Agari Uno whose controlling paraeters are deterined based on the experiental data. The average % errors of Agari Uno odel are found as.35, 1.1, 8.9 and 16.8 by individually fitting the coposite systes entioned in figs 4(a), 4(b), 4(c) and 4(d), respectively. However, it was found that the average % error of the Agari Uno odel by fitting all data fro the 4 coposite systes is considerably high (19.9%) though still lower than that of Lewis Nielsen odel. Therefore, it ay be argued that the developent of a generic odel for ETC is a difficult task and it ay be achieved by the use of a suitable data-driven odelling technique. WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

10 8 Coposites: Advances in Manufacture and Characterisation.. Effective Theral Effective Theral Conductivity (W/-k) Conductivity (W/-k) (a) Effective Theral Conductivity (W/-k) Effective Theral Conductivity (W/-k) (b) (c) (d) Experiental Maxwell-Eucken [1] Cheng-Vackon [13] Ziebland [14] Bruggean [15] Lewis-Nielsen [16] Torquato [17] Agari-Uno [18] Figure 4: Theral conductivities of coposites (a) PU-Al (b) PU-Graphite (c) SR-Al (d) SR-Graphite: experiental values and various odels. In looking at the Agari Uno odels [18], it was found that the values of C1 ( , 1., 1. and 1.) are nearer to 1. and the values of C are.65,.8595,.4944 and.6913 for the suspension systes, figs 4(a), 4(b), 4(c) and 4(d), respectively. A value of C1 close to 1. indicates that the effect of crystallinity and crystal size of polyer and changing theral conductivity of polyers is negligible due to the inclusion of both graphite and Al particles. A value of C close to 1 indicates ore ease in foring conductive chains of particles in a coposite. In the present coposites, it is observed that the value of C is greater for large particle size filler (graphite) than for the saller one (Al) which agrees well with the results of Boudenne et al. [19]. WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

11 Coposites: Advances in Manufacture and Characterisation 9 5 Conclusions In the present work, an experiental study is carried out to find the equivalent theral properties of particle reinforced flexible ould aterials using the hot disk technique. The easureents of theral properties using the hot disk technique are presented. A significant increase of theral conductivity of coposite ould aterials (PU and SR) was observed which will be helpful to reduce the cooling tie in an ST process. However, the presence of voids in the coposite due to anufacturing fault(s) reduces the effective theral conductivity considerably. It was observed that the data driven odel, Agari Uno and the nuerical odel Lewis Nielsen provide better TC estiations than other odels. Acknowledgeents The authors are thankful to DST (Departent of Science and Technology), New Delhi, India, for supporting this research work under the BOYSCAST fellowship prograe. References [1] Rosochowski, A. & Matuszak, A., Rapid tooling: the state of the art. Journal of Materials Processing Technology, 16(1-3), pp ,. [] Agari, Y. & Uno, T., Theral conductivity of polyer filled with carbon aterials: Effect of conductive particle chains on theral conductivity. Journal of Applied Polyer Science, 3, pp. 5-35, [3] Bigg, D.M., Conductive polyeric copositions. Polyer Engineering and Science, 17(1), pp , [4] Nagata, K., Iwabuki, H. & Nigo, H., Effect of particle size of graphites on electrical conductivity of graphite/polyer coposites. Coposite Interfaces, 6(5), pp , [5] Murthy, M.V., Peranent EMI shielding of plastics using copper fibers. Proc. of the Society of Plastics Engineers Annual Technical Conference, San Francisco, New York, pp , [6] Gustafsson, S.E., Transient plane source techniques for theral conductivity and theral diffusivity easures of solid aterials. Review of Scientific Instruents, 6(3), pp , [7] Gustavsson, M., Karawacki, E. & Gustafsson, S.E., Theral conductivity, theral diffusivity, and specific heat of thin saples fro transient easureents with hot disk sensors. Review of Scientific Instruents, 65(1), pp , [8] Log, T. & Gustafsson, S.E., Transient plane source (TPS) technique for easuring theral transport properties of building aterials. Fire and Materials, 19(1), pp , WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press

12 1 Coposites: Advances in Manufacture and Characterisation [9] Bohac, V., Gustavsson, M.K., Kubicar, L. & Gustafsson, S.E., Paraeter estiations for easureents of theral transport properties with the hot disk theral constants analyzer. Review of Scientific Instruents, 71(6), pp ,. [1] Carslaw, H.S. & Jaeger, J.C., Conduction of heats in solids, nd ed., Oxford Science Publications: New York,. [11] He, Y., Rapid theral conductivity easureent with a hot disk sensor Part 1. Theoretical considerations. Terochiica Acta, 436, pp. 1-19, 5. [1] Maxwell, J.C., A Treatise on Electricity and Magnetis, 3rd edition, Chapter 9, Dover Inc.: New York, NY, [13] Cheng, S.C. & Vachon, R.I., The prediction of the theral conductivity of two and three phase solid heterogeneous ixture. International Journal of Heat Mass Transfer, 1(3), pp , [14] Butta, E. & Migliaresi, C., Materiali copositi a atrice polierica, AIMAT Manuale dei Materiali per l Ingegneria, McGraw Hill, ISBN , [15] Bruggean, D.A.G., Berechnung Verschiedener physikalischer konstanten von heterogenen substanzen. Annals Physics (Leipzig), 4(5), pp , [16] Lewis, T. & Nielsen, L.E., Dynaic echanical properties of particulatefilled coposites. Journal of Applied Polyer Science, 14, pp , 197. [17] Torquato, S., Effective electrical conductivity of two-phase disordered coposite edia. Journal of Applied Physics, 58(1), pp , [18] Agari, Y. & Uno, T., Estiation on theral conductivities of filled polyers. Journal of Applied Polyer Science, 3(7), pp , [19] Boudenne, A., Ibos, L., Fois, M., Gehin, E. & Majeste, J.C., Therophysical properties of polypropylene/aluiniu coposites. Journal of Polyer Science: Part B: Polyer physics, 4(4), pp. 7-73, 4. WIT Transactions on State of the Art in Science and Engineering, Vol 88, 15 WIT Press