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Materials Science and Engineering A282 (2000) 29–37 Effect of ceramic ball inclusion on densification of metal powder compact K.T. Kim *, H. Park Department of Mechanical Engineering, Pohang Uni6ersity of Science and Technology, San 31 Hyoja-dong, Nam-ku, Pohang 790-784, South Korea Received 4 August 1999; received in revised form 22 November 1999 Abstract The effect of a ceramic ball inclusion on densification behavior of a metal powder compact w
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  Materials Science and Engineering A282 (2000) 29–37 Effect of ceramic ball inclusion on densification of metalpowder compact K.T. Kim *, H. Park Department of Mechanical Engineering  ,  Pohang Uni   ersity of Science and Technology ,  San  31  Hyoja - dong  ,  Nam - ku , Pohang   790  - 784  ,  South Korea Received 4 August 1999; received in revised form 22 November 1999 Abstract The effect of a ceramic ball inclusion on densification behavior of a metal powder compact was investigated under cold isostaticpressing, pressureless sintering and hot isostatic pressing. Several constitutive models in the literature were implemented into afinite element program (ABAQUS) to analyse densification behaviors of metal powder with a ceramic ball inclusion under coldisostatic pressing, pressureless sintering and hot isostatic pressing. Densification and deformation of powder compacts withvarious sizes of ceramic balls were also studied to investigate the size effect of a ceramic ball inclusion during hot isostaticpressing. Finite element calculations for residual stress distributions were obtained to study the effect of ceramic ball inclusionswith different thermal expansion coefficients. Measured density distributions of metal powder compacts were compared with finiteelement results. © 2000 Elsevier Science S.A. All rights reserved. Keywords :   Cold isostatic pressing; Hot isostatic pressing; Power-law creep; Pressureless sintering; Residual stresswww.elsevier.com / locate / msea 1. Introduction As a method of improving mechanical properties of metal parts, structural ceramics may be added into ametal part because of their good thermomechanical andchemical properties [1]. Due to the difference in ther-momechanical properties between metal and ceramic,however, the stress concentration and residual stressmay also be induced at the interface between metal andceramic. Thus, it is important to investigate residualstress distribution in a metal and ceramic composite topredict mechanical characteristics of metal–ceramicparts.To examine the strengthening effect of inclusionsunder macroscopic loads, Hom and McMeeking [2]obtained finite element calculations for a cubic array of rigid spherical inclusions embedded in the matrix of elastic–perfectly plastic material. Recently, Turner andAshby [3] investigated densification behavior for mix-ture of spherical plasticene powder and rigid inclusionswith various shapes, sizes and volume fractions duringcold isostatic pressing. Bonnenfant et al. [4] also studiedthe effect of spherical inclusions with different sizes andvolume fractions in powder during hot compaction.Among various forming processes, P / M forming pro-cess may be appropriate to produce metal–ceramiccomponents because of its capability for near-net-shapeforming [5–7]. P / M forming process generally producesparts by sintering after cold compaction or by hotisostatic pressing. Cold isostatic pressing has been usedin many applications to produce high-quality compo-nents with homogenous microstructure [8]. After coldisostatic pressing, a sample requires sintering to en-hance its mechanical property [9,10]. Hot isostaticpressing has also been widely used to produce highquality components. Highly densified components canbe produced under hot isostatic pressing, because asample is subjected to hydrostatic pressure under hightemperature [11].Recently, Kwon et al. [12] investigated densificationbehavior of 316L stainless steel powder during cold diecompaction. By employing the yield function of Shimaand Oyane [13] in a finite element analysis, they com-pared experimental data with finite element calcula- * Corresponding author. Tel.:  + 82-562-2792164; fax:  + 82-562-2795569. E  - mail address :   korean@postech.edu (K.T. Kim)0921-5093 / 00 / $ - see front matter © 2000 Elsevier Science S.A. All rights reserved.PII: S0921-5093(99)00785-6  K  . T  .  Kim ,  H  .  Park   /   Materials Science and Engineering A 282 (2000) 29–37  K  . T  .  Kim ,  H  .  Park   /   Materials Science and Engineering A 282 (2000) 29–37  30 tions. They also showed that experimental data of stainless steel powder agreed better with the yield func-tion of Shima and Oyane [13] than that of Fleck et al.[14] and Gurson [15].To analyse densification behaviors of powder com-pacts with a ceramic ball inclusion under cold isostaticpressing, sintering and hot isostatic pressing, severalconstitutive models in the literature were implementedinto a finite element program ( ABAQUS ). Densificationbehavior of a powder compact under cold isostaticpressing was studied by using the yield function of Shima and Oyane [13]. To study densification behaviorof a powder compact under sintering, the constitutiveequations proposed by Besson and Abouaf [16] underdiffusional creep was employed [17]. To analyse densifi-cation behavior of a powder compact under hot iso-static pressing, the constitutive model of Abouaf et al.[18] under power-law creep was used.Finite element results were compared with experi-mental data for densification of metal powder compactswith a ceramic ball inclusion. To investigate the effectof ceramic ball inclusions with different thermal expan-sion coefficients, densification behaviors of metal pow-der compacts with an alumina ball and a tungstencarbide ball were investigated. The size effect of aceramic ball inclusion was also studied during hotisostatic pressing. Finally, measured density distribu-tions of metal powder compacts were compared withfinite element results. 2. Experimental Mixed powder of iron, nickel, and carbon powderwas used in this work. Mixtures of iron, nickel, andcarbon powder were produced by using a gravity mixerfor 1 h to obtain uniform mixing. In mixed powder,iron powder (Acros Organics, NJ, USA) with an aver-age particle size of 45   m, nickel powder (High PurityChemicals, Japan) with an average particle size of 50  m, and carbon powder (Aldrich Chemical Co., WI,USA) with an average particle size of 45   m weremixed in the weight ratio of 96.5:3: 0.5. Chemicalcomposition of iron powder is Fe–0.0005As–0.001Cu– 0.1Mn–0.05Ni–0.002Pb–0.005Zn–0.01S. That of nickel powder is Ni–0.002Al–0.08Co–0.001Cu– 0.004Fe. Metal powder compacts with a ceramic ballinclusion were produced either by sintering after coldisostatic pressing or by hot isostatic pressing in thiswork. Table 1 shows mechanical and physical proper-ties of metal powder [19]. Two types of ceramic ballswere used in this work, e.g. alumina ball (POSCORefractories Co., South Korea) and tungsten carbideball (Asia Metallurgical Co., South Korea). Table 2shows material properties of alumina and tungstencarbide [20]. 2  . 1 .  Cold isostatic pressing and sintering  To produce a sample under cold isostatic pressing, arubber mould with 78 mm in inner diameter, 80 mm ininner height, and 6 mm in thickness was used. Onethousand one hundred and twelve grams of mixedmetal powder was poured into the rubber mould and aceramic ball with 30 mm in diameter was placed in thecenter of metal powder. The air in the rubber mouldwas evacuated after powder was filled. The sample wascompacted in a cold isostatic press (wet type CIP, ABBAutoclave Systems, USA) under hydrostatic pressure of 300 MPa. The compacting pressure was unloadedslowly after the pressure was held constantly for 2 min.The relative density of the compact was 0.772 excludingthe ceramic ball. The relative density of the compactwas measured by Archimedes’ method.Then the compact was sintered for 2 h at 1150°C invacuum. The average dimension of the sintered samplesis 61.7 mm in diameter and 63.8 mm in height withrelative density of 0.775 excluding the ceramic ball. 2  . 2  .  Hot isostatic pressing  To produce a sample under hot isostatic pressing(HIPing), a 304 stainless steel tube with 82 mm indiameter, 95 mm in height, and 1 mm in thickness wasused as a container. As a ventilation tube for degassing,a 304 stainless steel tube with 8 mm in diameter and 1mm in thickness was also welded on the top cap of thecontainer. The container was washed by dilute hy-drochloric acid before powder was filled.Mixed powder (1365 g) was filled in the containerand a ceramic ball was also placed in the middle of the Table 1Mechanical and physical properties of metal powder [19]Young’s modulus, GPa 217Poisson’s ratio 0.2875Thermal conductivity, J ms − 1 K − 1 13.8Thermal expansion coefficient, K − 1 18.2 × 10 − 6 Specific heat, J kg − 1 K − 1 1223Table 2Material properties of alumina and tungsten carbide [20]Material property Al 2 O 3  WCYoung’s modulus, GPa 403 696Poisson’s ratio 0.220.263940Theoretical density, kg m − 3 14 4006.0 71.4Thermal conductivity, J ms − 1 K − 1 5.2 × 10 − 6 9.3 × 10 − 6 Thermal expansion coefficient K − 1 237.7Specific heat, J kg − 1 K − 1 131.3  K  . T  .  Kim ,  H  .  Park   /   Materials Science and Engineering A 282 (2000) 29–37  K  . T  .  Kim ,  H  .  Park   /   Materials Science and Engineering A 282 (2000) 29–37   31 powder. The sample was vibrated to obtain a tapdensity of 0.44. The powder in the container was de-gassed for 6 h at 400°C.HIPing was done under hydrostatic pressure of 50MPa at 1100°C. The HIPing schedule was as follows:argon gas was supplied to the chamber to attain aninternal pressure of 7.84 MPa and the temperature wasraised at a rate of 10°C min − 1 up to the test condition.The pressure holding time during HIPing was 120 minafter the test condition was attained. 2  . 3  .  Uniaxial compression of the matrix material  Uniaxial stress–strain response of the matrix mate-rial at room temperature was obtained from uniaxialcompression of a fully dense sample by using an MTSservohydraulic testing machine at a constant load rateof 200 Ns − 1 . The solid sample was produced by HIP-ing the mixed powder in this work. The sample has 10mm in diameter and 12 mm in height after machiningfrom the HIPed sample. To reduce the friction, Teflonsheets were inserted between the sample and the com-pression platens during the test. The flow stress of thematrix material was obtained by measuring the diame-ter and height of the sample by interrupting the test.Teflon sheets were changed at each interruption. 3. Analysis To investigate densification behavior of metal pow-der with a ceramic ball inclusion under cold isostaticpressing, sintering and hot isostatic pressing, severalconstitutive models in the literature were used. Toanalyse densification of metal powder during cold iso-static pressing, the yield function for porous metalsproposed by Shima and Oyane [13] was used. Toanalyse densification during sintering, the model byBesson and Abouaf [16] under diffusional creep wasused. For densification of metal powder during HIPing,the model proposed by Abouaf et al. [18] under power-law creep was used. The details of constitutive modelsused in this paper can also be found in a recent paperby Kim and Jeon [17] for densification behavior of toolsteel powder under high temperature. 3  . 1 .  Cold isostatic pressing  A yield function    for a porous material can bewritten as  (  ,    ¯  m  p ,  D ) =   q  m  2 +   p  m F   2 − D 2 N  = 0 (1)where  D ,  p ,  q ,   m ,  N   and    ¯  m  p , respectively, denote therelative density, hydrostatic pressure, the equivalentstress, the flow stress of the matrix material, a materialconstant and the equivalent plastic stress of the matrixmaterial. The function F can be determined from exper-imental data and represented by a function of relativedensity. Shima and Oyane [13] obtained  F  = 1 / [2.49(1 − D ) 0.514 ] and  N  = 2.5 from uniaxial compres-sion of porous copper. 3  . 2  .  Sintering  Abouaf et al. [18] proposed the equivalent Misesstress for a porous material  eq2 =  f I  12 + 3  c J  2  (2)where  I  1 =  ii  ,  J  2 = 1 / 2(  s ij  s ij  ) and  s ij  =  ij  −  kk  / 3. Theparameters  c  and  f   in Eq. (2) can be determined fromexperiments as functions of relative density  D . When c = 1 and  f  = 0,   eq  in Eq. (2) reduces to the usualMises stress.To analyse densification of powder compacts duringsintering, Besson and Abouaf [16] proposed a creepstrain rate      ij   under diffusional creep by considering thesintering potential. Thus,     ij  = DA diff   exp( − Q    / RT  ) TG  3   f  (  kk  − 3  s )  ij  + 32  cs ij    (3)where   s ,  A diff  ,  T  ,  G  ,  R ,  Q     and   ij   are the sinteringpotential, the diffusional creep constant, absolute tem-perature, grain size, diffusional activation energy, andthe Kronecker delta, respectively. 3  . 3  .  Hot isostatic pressing  Assuming that the viscoplastic work of the matrixmaterial is the same as that of a porous material [21],Abouaf and co-workers [16,18] proposed a creep strainrate      ij   under power-law creep. Thus,     ij  = D     0  eq n − 1  0 n   fI  1  ij  + 32  cs ij   = DA  eq n − 1   fI  1  ij  + 32 cs ij    (4)where      0  and   0  are creep parameters and  D  denotesrelative density. For a solid exhibiting power-law creep,i.e.      =     0 (  /  0 ) n ,  A  and  n  in Eq. (4) denote Dorn’sconstant and the creep exponent, respectively. 3  . 4  .  Finite element analysis To investigate densification and residual stress distri-bution in a powder compact with a ceramic ball inclu-sion under cold isostatic pressing, sintering and HIPing,the interface between the surface of the ceramic balland metal powder was assumed to have a perfect-bond-ing boundary condition in the finite element analysis.We also assumed that the ceramic ball has only ther-moelastic deformation.  K  . T  .  Kim ,  H  .  Park   /   Materials Science and Engineering A 282 (2000) 29–37  K  . T  .  Kim ,  H  .  Park   /   Materials Science and Engineering A 282 (2000) 29–37  32Fig. 1. Finite element meshes and boundary conditions for (a) cold isostatic pressing and sintering and (b) hot isostatic pressing of a metal powdercompact with a ceramic ball inclusion. Fig. 1 shows finite element meshes and boundaryconditions for (a) cold isostatic pressing and sinteringand (b) hot isostatic pressing of a metal powder com-pact with a ceramic ball inclusion. Three hundred four-node axisymmetric thermally coupled quadrilateral,bilinear displacement and temperature elements(CAX4T) were used in both cases. Due to the symmetrycondition in the  x -axis and the axisymmetry conditionin the  y -axis only the first quadrant of the sample isconsidered in Fig. 1(a) and (b). 4. Results and discussion To analyse densification of metal powder with aceramic ball inclusion under cold isostatic pressing, themodel by Shima and Oyane [13] was implemented intothe user subroutine  UMAT  of   ABAQUS  [22]. For densifi-cation of metal powder with a ceramic ball inclusionunder sintering and HIPing, the models by Abouaf andco-workers [16,18] were implemented into the user sub-routine CREEP of ABAQUS. Experimental data ob-tained for densification of powder compacts with aceramic ball inclusion under cold isostatic pressing,sintering and hot isostatic pressing were compared withfinite element calculations. Finite element results werealso obtained for residual stress distribution at theceramic–metal interface.Fig. 2 shows uniaxial stress–plastic strain relation forthe matrix of metal powder obtained under uniaxialcompression at room temperature. The solid curve wasobtained from Ludwik’s equation to represent experi-mental data. Thus,  m = 209 + 354.8(   ¯  m  p ) 0.4737 MPa (5)Table 3 shows temperature-dependent elastic modulusfor the matrix of metal powder [23]. Table 4 showsdiffusional creep properties of metal powder [19]. Ta-bles 5 and 6, respectively, show creep properties of metal powder and 304 stainless steel for the container Fig. 2. Uniaxial stress–plastic strain relation for the matrix of metalpowder.Table 3Variation of elastic modulus with temperature for the matrix material[23]1100100060040020Temperature, °C 119192217 E  , GPa 2525Table 4Diffusional creep properties for the matrix of metal powder [19]Volume diffusion constant,  D v  6.15 × 10 − 9 m 2 s − 1 419 kJ mol − 1 Volume diffusion activation energy14.1   mGrain size8.3 kJ kg − 1 K − 1 Gas constant
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