Selective Laser Sintering of Calcium Polyphosphate: Finite Element Modeling and Experiments

Transcription

1 JLMN-Journl of Lser Micro/Nnoengineering Vol. 4, No. 1, 9 Selective Lser Sintering of Clcium Polyphosphte: Finite Element Modeling nd Experiments Yser Shnjni, Ehsn Toyserni Rpid Prototyping Lbortory, Deprtment of Mechnicl nd Mechtronics Engineering, University of Wterloo, Wterloo, Ontrio, Cnd E-mil: yshnjn@uwterloo.c In this pper, the selective lser sintering (SLS) process of bio-composite blend comprising of biodegrdble clcium polyphosphte (CPP) nd polyvinyl lcohol (PVA), s ic binder, is investigted. A multi-physics finite element model including both therml nd viscous sintering phenomen ws developed nd simulted in different process conditions. The model ws used to predict temperture nd porosity distribution of sintered regions throughout the process domin nd period. It is observed tht the porosity of the sintered region is logistic function of the lser scnning speed nd negtive logistic function of the lser power. The thicness of the fbricted CPP lyers, using n experimentl setup, firly demonstrtes n greement with the simultion. Keywords: selective lser sintering, liquid phse sintering, clcium polyphosphte, porosity, het ffected zone 1. Introduction Selective lser sintering (SLS) enbles the mnufcturing of prts from powdered mteril by selectively heting nd fusing of powder prticles using lser bem [1]. To relize the fbriction of complexshped implnts/scffolds composed of clcium polyphosphte (CPP), which is bio-degrdble with ic chins [], by the SLS technique, n dmixture of CPP nd ic binder or ic coted CPP powder is used. The powder is spred s sequentil lyers on the former ones. Then, the lser bem rsters the powder bed nd cts s incoming concentrted therml energy. The low melting-temperture flows nd merges when it is heted by the lser bem nd reifies when the lser bem psses. Consequently, the cts s binder nd binds the CPP prticles together. In other words, primry binding is conducted in the selected segments of the powder bed vi viscous sintering of the ic component. The prticles within the het ffected zone (HAZ) re bonded to the beneth lyers s well. The process repets until the desired green object completes. In the finl step, in order to increse the strength of the model, the green prt is het treted in furnce to decompose the binder followed by sintering process. Fig. 1 nd Fig. show the schemtic of liquid phse selective lser sintering process nd its mechnism. The strength nd the density of prototyped objects s well s their geometricl fetures re very dependent on the prticle binding during the lser sintering stge. Therefore, for the optimiztion of the prototyping process, the prediction of therml behviour of the powder bed under the moving lser het source through numericl modeling is of importnce. Fig. 1 Schemtic of selective lser sintering of powder () (b) Fig. Schemtic of CPP liquid phse sintering; () before nd (b) fter lser sintering Severl studies on the modeling of the SLS process hve been performed. Therml models of SLS in onedimensionl [3, 4], two-dimensionl [5, 6], nd threedimensionl forms [7] hve been reported. Nelson et l. constructed therml model of the SLS process for predicting the lyer-to-lyer fusion of polycrbonte powder [3]. This model cn predict, to within % ccurcy, the effects of the primry process vribles such s the scn speed, scn overlp, nd lser power on the fusion depths of the polycrbonte (PC) powder. Moreover, Nelson s finite difference model estimtes the sintering depths in poly(methyl methcrylte) (PMMA) nd coted silicon crbide (SiC) powders [4]. The SLS of n morphous, s well s crystlline nd glss-filled ws simulted by Childs et l. [6], using 8

2 JLMN-Journl of Lser Micro/Nnoengineering Vol. 4, No. 1, 9 sequentil therml finite element method. A numericl simultion of two-dimensionl melting nd reifiction of two-component metl powder lyer in the SLS process ws developed by Chen et l. [8]. The numericl prediction of the temperture nd density distribution in SLS process, bsed on Mcenzie nd Shuttelworth s model of the sintering rte ws published by Cerver et l. [7]. He hs eliminted the time prmeter by using locl coordinte system, locted t the centre of the moving lser bem. Recently, Dong et l. [9] developed model in ABAQUS with bi-level structure integrtion procedure. In his model, the density nd the het eqution re integrted t the outer nd inner levels, respectively. This wor ddresses the nlysis of selective lser sintering of CPP, which is highly receiving ttentions s suitble cndidte for osteochondrl implnts [1-11], through multi-physics finite element model. Since the porosity of n osteochondrl scffold hs gret effect on the bio-mechnicl properties, the chrcteriztion of SLS process my provide control on the mcro-porosity of the CPP scffolds. where r is the rdil component in polr coordintion system, nd I is the intensity scle fctor tht is defined by the lser power nd the chrcteristic rdius of the lser intensity profile,, s [13] I β P r π 1 exp( r bem bem ) where β is the bsoptivity nd P is the lser power. In Crtesin coordinte system, the lser incident rdius is s follows: r ( x x y (6) ) + ( y ) Consequently, the moving lser is defined s (5). Het trnsfer nlysis in the SLS process In the binding stge of the SLS process, the het trnsfer behviour in the substrte is described by the clssicl het conduction eqution: Q Lser I e ( x vx t x ) + ( y v y t y ) ( ) [(( x v t x ) + ( y v t y ) ) < r ] x y bem (7) T ρ Cp ( T ) + Q gen (1) t where ρ is the density, Cp is the specific het, T is the temperture, t is the time, is the therml conductivity, nd Q gen represents the het generted in the physicl body. On the boundries, Eqution () is pplicble: 4 4 n q QLser hconv ( T T ) ε ems σ ( T Tsurr ) () where n is the norml vector of the het flux pln, q is the het flux, is the therml convection coefficient, h conv ε ems is the emissivity, σ is the Stefn-Boltzmnn constnt (5.67E-8 W/m. K 4 ). It is obvious tht Q Lser is pplied only on the top surfce of the powder bed. If h conv is considered for combined rdition nd convection het trnsfer [1], the boundry condition is simplified s n q Q Lser h conv ( T T ).1 Lser irrdition submodel To determine the concentrted het flux of the lser bem on the top surfce of the substrte, chrcteriztion of the bem nd energy profile is required. By ssuming Gussin lser bem with TEM mode, the lser bem intensity profile is (3) r I( r) I exp( ) (4) where v nd v re the lser moving velocity components x y in x nd y directions, respectively. The lst term of (7) identifies the moving of the het flux.. Powder bed mteril properties submodel The density ( ) of the composite powder, ρ composite consisting CPP nd the ic binder, is clculted from the densities of the components s follows: ρcomposite φ ρ + ( 1 φ ) ρ (8) where φ is the volume frction of the components. The specific het of the composite powder Cp is estimted from the mss frction ( ω ) verge of the specific hets of the nd the by the clcultion of Cp ω Cp+ ( 1 ω) Cp (9) φ ρ ω φ ρ + ( 1 φ ) ρ Ygi et l. [14] lso formulted more ccurte model for the effective conductivity of pced bed, in which the conduction, convection nd rdition effects within the powder bed re considered. The model hs been developed for low-temperture nd high-temperture conditions. At low-tempertures, only convection cuses the het conductivity, wheres rdition evidently enhnces the het trnsfer by [9] Low Temperture: 9

3 JLMN-Journl of Lser Micro/Nnoengineering Vol. 4, No. 1, 9 (1 ε ) ( T ) (1) ( T ) 1+ ψ gs High Temperture: β (1 ε ) + ε β D γ 1 + ( T ) gs + D p hrs ψ p (11) For this study, polyvinyl lcohol (PVA) ws selected s the ic binder which ws used to be either mixed with the CPP powder or coted on the CPP prticles. Since the viscous flow occurs in the ic constituent, the sintering rte dt only for PVA is required. The correltion of PVA s porosity over different tempertures nd sintering time is plotted in Fig. 3, by using (15) nd (16). The initil porosity is ssumed to be 54%, bsed on the reported dt of commercil SLS systems [4]. ε ( ρ ρ ) / ρ (1) composite where is the conductivity of the powder mteril, gs is the conductivity of ir, ε is the void frction (porosity) of the bed, nd ψ is n empiricl coefficient normlly considered s [9] ψ ε (13) is derived for composite prticle which includes core with the overll rdius,, nd ic coting with the thicness,, by [] t th R c 1 B ( B ) ln( B t t B )) tth tth ( ) 1 ( ) ) + + ( ) tth ( ) R th th ( ) + (1 ( (14).3 Sintering submodel The modelling of SLS requires simultneous solution of equtions for the rte of the porosity collpse nd the chnges in locl therml properties. The chnge in the porosity occurs due to the viscous sintering nd merging of the ic constituent which cuses the CPP prticles to rerrnge nd be closer to ech other. The rte of porosity collpse is described s [] d ε dt ( ε ε ) (15) / where ε is the porosity of powder bed nd ε is the plteu porosity t sintering temperture, T, which is ssumed to be zero. Since sintering is rte process, it is resonble to ssume tht the rte constnt ( ) follows n Arrhenius form: A exp( E / R T) (16) Gs where E is the ctivtion energy, is the universl RGs Gs constnt, nd A is constnt. The ctivtion energy of the viscous flow cn lso be used for sintering [1, ]. c Fig. 3 PVA porosity vrition versus time nd temperture For the nlysis, D multi-physics finite element (FE) model of the coupled het trnsfer nd viscous sintering physics ws developed. The model is for sintering of single lyer of powder. The COMSOL Multiphysics pcge ws used for this purpose. The simultion prmeters re lists in Tble 1. The governing eqution of sintering ws modeled s time dependent prtil differentil eqution (PDE). The therml nd sintering equtions re lined by n expression which reltes the therml conductivity t ech point to the powder bed density ccording to (1) nd (11). The strtegy for the solution of this set of coupled equtions is to solve the PDE nd the therml eqution instntneously for every time step. The conductivity of ech node is clculted bsed on the updted porosity. It mens tht both physics re updting the required dt for ech other during the solution. The mesh independency nlysis ws conducted nd the optimum results were obtined with 3 qudrilterl elements. Tble 1 Simultion prmeters Prmeter Vlue PVA vol% % Initil porosity 54% Lser power 1.8W Lser scnning speed 5mm/s Preheting temperture 55 C 3. Modeling results nd discussion 3

4 JLMN-Journl of Lser Micro/Nnoengineering Vol. 4, No. 1, 9 Since the het ffected zone (HAZ) is drmticlly smll compring to the whole powder bed, the powder bed ws modeled s rectngulr of 4mm. In order to hve relible nd precise solution the mesh t the top surfce is finer thn the mesh within the other regions. Thus, the Gussin pttern of the energy is distributed over number of nodes. Furthermore, since the temperture grdient is quite lrge in this region, finer mesh will result in more precise clcultion of the temperture distribution. The simultion ws performed for severl conditions to investigte the effects of the process prmeters such s lser power nd lser scnning speed on the porosity of sintered portion of the powder. The temperture distributions on the top surfce of powder bed re plotted for ny. seconds in Fig. 4. The digrm represents n overview of the temperture history on the top surfce which is trveled by the lser bem. It is shown tht the temperture of the top surfce remins bout 4 ºK in verge, fter 1 second. Fig. 5 Porosity on top surfce for every. sec The sintering depth of the powder bed cn be determined using the dt presented in Fig. 6. It is observed tht bout 3μm of powder is sintered in the simultion condition. This sintering depth is desired considering tht the thicness of the spred powder lyer in lyer mnufcturing is bout 15μm. It mens tht the lyer sintering condition is pproprite for fbriction of multilyered prts with lyers of such thicness. The figure lso represents tht the porosity of the sintered region decresed bout 7% on the top surfce. Fig. 4 Temperture on top surfce for every. sec The history of the porosity (void frction) on the top surfce of the powder bed is presented in Fig. 5 for every.sec. A decrese in the porosity, which mens n increse in the ifiction, even fter the lser bem hs pssed, is obvious. This phenomenon indictes the significnt effect of the time in the physics of sintering. It mens tht the densifiction of the sintered region continues, with rte of, even fter the lser bem is fr from the trgeted re. Fig. 6 Porosity vrition in powder bed depth Fig. 7 nd Fig. 8, respectively, illustrte the mximum temperture nd porosity in the powder bed with different lser power for lser scnning speed of 5mm/s. A lrge decrese in porosity is observed when the power is higher thn 1.5W. Also, it is observed tht the porosity does not chnge remrbly with the lser powers less thn.5w. A typicl logistic function, s shown in the figure, is fitted on the dt. 31

5 JLMN-Journl of Lser Micro/Nnoengineering Vol. 4, No. 1, 9 Temperture (K) Porosity (%) ε v e Lser power (W) Fig. 7 Mximum temperture versus lser power Lser speed (mm/s) Fig. 1 Minimum porosity versus lser scnning speed Porosity (%) P e Lser power (W) Fig. 8 Minimum porosity versus lser power ε 4. Experiments For the fesibility study of the lser sintering of CPP, mixtures of CPP nd PVA powders with different volumertios were prepred. The CPP powder mesh size ws 45-75μm, wheres the prticle size of the PVA powder ws less thn 63μm. The mteril specifictions of the used PVA re listed in Tble. A CW fibre Erbium lser (IPG Photonics, MA, USA) with trnsverse mode of TEM nd wvelength of 155nm ws utilized for the process. The experimentl setup, developed t the University of Wterloo, is shown in Fig. 11. Fig. 1 shows fbricted lyer with the process prmeters of 1.8W lser power nd 5mm/s scnning speed. vol% PVA ws used. Tble Specifictions of the used PVA Chnging the lser scnning speed lso influences on the porosity of the smple, s shown in Fig. 9, fixing the lser power to 1.W. It is evident tht the higher the lser speed, the less the densifiction. It is noteworthy tht the porosity does not chnge remrbly with the lser scnning speed higher thn 7mm/s. PVA Hydrolyzed Moleculr Weight # % Medium # 86-89% Low 64 6 Temperture (K) Lser speed (mm/s) Fig. 9 Mximum temperture versus lser scnning speed Fig. 11 Experimentl setup for lser sintering of CPP 3

6 JLMN-Journl of Lser Micro/Nnoengineering Vol. 4, No. 1, 9 The section view of the fbricted lyer is shown in Fig. 13. To crete this smple, the fbricted CPP lyer ws mounted in n epoxy holder. The thicness of the smple ws mesured to be pproximtely 4μm s shown in the figure, wheres the counterprt modeling result ws obtined to be 3μm. The observed difference between the experimentl nd modeling results in terms of the lyer thicness my be resulted from the trnsmission of the lser bem through the surfce pores nd lso uncertin lser bem scttering due to non-uniform surfce prticle distribution (i.e., diffuse reflection explined by Drude reflectivity principle). This phenomenon ws not considered in the finite element modeling of the process tht my be the source of the discrepncies between the experimentl nd modeling results. () 1mm Fig. 1 A thin lyer of lser sintered CPP Fig. 13 A microscopic view of the section of sintered lyer Fig. 14 displys the SEM pictures of two smples which re fbricted with the sme process prmeters (16W nd 45mm/s) but different vlues of ic binder (3vol% nd 5vol%). Stronger ic bonds re obvious for the smples with 5vol% PVA. The wettbility of PVA, in contct with the CPP prticles, is criticl fctor which hs gret influence on the prt s green strength. The wettbility of liquid is defined s the contct ngle between the droplets on horizontl surfce. A liquid is deemed to be wetting, when the ngle vries between 9 nd 18 degrees. To chieve n improved performnce in the SLS process, the surfce tension of the liquid phse must be lower thn tht of the phse. It might be possible by choosing suitble binry mteril system. (b) Fig. 14 SEM of lser sintered smples with () 5vol% PVA#1 nd (b) 3vol% PVA#1 Noticing the forementioned phenomen, s viewed in Fig. 14, PVA my not be proper choice for liquid phse sintering of CPP, becuse it does not demonstrte ny wellwetted connections. However, the smple in Fig. 15 expresses n inverse behviour of PVA nd CPP, even though it ws fbricted with the sme lser power nd scnning speed (16W nd 45mm/s). Cermic prticles re suitbly wetted nd covered with PVA, lthough only vol% PVA ws used. The rrows evident the PVA bridges between CPP prticles. The difference between the smples of Fig. 14 nd Fig. 15 is the PVA s moleculr weight (MW) nd the degree of hydrolystion s listed in Tble. It is concluded tht these two properties of PVA might influence the wettbility with CPP nd should be studied more in future wor. Fig. 15 SEM of lser sintered smple with vol% PVA # PVA bridges 33

7 JLMN-Journl of Lser Micro/Nnoengineering Vol. 4, No. 1, 9 5. Conclusion The therml nlysis of the selective lser sintering of CPP ws conducted through multi-physics finite element model. Temperture nd porosity distributions of the sintered region were investigted versus process prmeters. The modeling results suggest tht the porosity of the sintered region is logistic function of the lser scnning speed nd negtive logistic function of the lser power. These results cn be used in the modifiction of the process prmeters in order to djust the porosity of the fbricted green prts. In ddition, the fesibility study on the SLS of CPP ws experimentlly performed. Thin single lyers of sintered CPP were studied in terms of thicness nd microstructure. Acnowledgments The CPP mteril ws produced nd provided by the Institute of Biomterils nd Biomedicl Engineering t the University of Toronto, under the supervision of Professor Robert M. Pillir. Their contribution is pprecited by the uthors. We re lso grteful to Dr. Andrew Pinerton for his technicl dvice nd the CIHR for providing finncil support. References [1] C.K. Chu nd K.F. Leong: Rpid Prototyping: Principles & Applictions in Mnufcturing ed. by C.S. Lim, (World Scientific, 3) p.173. [] R.M. Pillir, M.J. Filiggi, J.D. Wells, M.D. Grynps nd R.A. Kndel: Biomterils,, (1) 963. [3] J.N. Nelson, N.K. Vil, J.W. Brlow, J.J. Bemn, D.L. Bourel nd H.L. Mrcus: Ind. Eng. Chem. Res., 34, (1995) [4] J.C. Nelson, S. Xue, J.W. Brlow, J.J. Bemn, H.L. Mrcus nd D.L. Bourel: Ind. Eng. Chem. Res., 3, (1993) 35. [5] T.H. Childs, M. Berzins, G.R. Ryder nd A. Tontowi: Proceedings of the Institution of Mechnicl Engineers, Prt B: Journl of Engineering Mnufcture, 13(4), (1999) 333. [6] T.H. Childs nd A. Tontowi: Proceedings of the Institution of Mechnicl Engineers, Prt B: Journl of Engineering Mnufcture, 15(4), (1) [7] G.B.M. Cerver nd G. Lomber: Rpid Prototyping Journl, 5(1), (1999) 1. [8] T. Chen nd Y. Zhng: Numericl Het Trnsfer Prt A: Applictions, 46(7), (4) 633. [9] L. Dong, A. Mrdi, S. Ahzi nd Y. Remond: Mterils Science Forum, 553, (7) 75. [1] M.D. Grynps, R.M. Pillir, R.A. Kndel, R. Renlund nd M. Filiggi: Biomterils, 3(9), (3) 63. [11] S.D. Wldmn, M.D. Grynps, R.M. Pillir nd R.A. Kndel: Journl of Biomedicl Mterils Reserch, 6(3), () 33. [1] E. Toyserni, A. Khjepour nd S. Corbin: Optics nd Lsers in Engineering, 41(6), (4) 849. [13] A. Fthi, E. Toyserni, A. Khjepour nd M. Durli: Journl of Physics D: Applied Physics, 39(1), (6) 613. [14] S. Ygi nd D. Kunii: AIChE Journl, 3, (1957) 373. (Received: June 16, 8, Accepted: Februry, 9) 34