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1 Journal of the Korean Ceramic Society Vol. 43, No. 1, pp. 859~864, 006. FE Analysis of Alumina Green Body Density for Pressure Compaction Process Jong-In Im and Young-Jin Yook Simulation Center for Fine Ceramics/Electronic Device Team, KICET, Seoul , Korea (Received October 16, 006; Accepted November 9, 006) xœ w ù x s FE Á ( )» l/ tq ( ; ) ABSTRACT For the pressure compaction process of the ceramic powder, the green density is very different with both the ceramic body shape and the processing conditions. The density difference cause non-uniform shrinkages and deformations, and make cracks in the sintered ceramics. In this paper, Material properties of the alumina powder mixed with binder and the friction coefficient between the powder and the tool set were determined through the simple compaction experiments. Also the powder flow characteristics were simulated and the green density was analyzed during the powder compaction process with Finite Element Method (FEM). The results show that the density distributions of the green body were improved at the optimized processing condition and both the possibility of the forming crack generation and the deformation of the sintered Alumina body were reduced. Key words : Alumina powder, Pressure compaction process, FEM, Green body density 1. w t w» w x, (Hot Press), e q (slip casting) w x t xœ xœ. xœ w x t w» ƒœ w w. x t ƒ j» w t š t» j» w w š. 1,) x w x w, w t w., x x w ³ w xw š, x ü ƒ ³ w x j w»». w x ³ w s z œ ³ w k x wš, t w j w. ù x ü Corresponding author : Jong-In Im Tel : Fax : s x d w»ƒ w x wš. x x w w xœ t x ü ³ j yw ƒ j» w w š. xœ x ü w p wš x x, x t re, w re, g œ w w» w œ w. 3,4), x v w yw ƒ ƒ w w x t xw» w x ƒ û x œ w w œ ƒ ƒw š, 3 x, œ w w x ù w œ w». -4) ù xœ w x ü s w w w wš, xœ y g x ü s e w w ³ w s x ƒ w š w. 859

2 860 Á. xœ w ew w x e y x dw x w w Shima Oyane 5) w w xk w. σ Φ α 1 D σ m ( ) p γ = + σ D m m», σ p ƒƒ z wš, D, σ m w. š α, γ, m x mw w w. x e y x e(associate flow rule) w - x w. σ ij σ = ε ij ε kkδ ij ε AD ( ) 33 ( AD ( )) ' 1 9», A = š, z σ z x 3 + α( 1 D) γ ε. AD σ ( ) 3 A( D) ' = σ ij' σ ij σ kk 3 ' ε = ε ij ε AD ( ) ' 1 ij ε kk 33 ( AD ( )) 1 -- (1) () (3) (4) d w» w x x v w y ) w. š m, a, b n» w x z ƒ w., x w ù š w ƒw w l. x l f vq(curve fitting)w ƒ ew m, a, b n w. š, x œ wš x z ƒ ùkù w. w l ƒ µ w w mw w. ù x w x re(p1), w re(p), g š, e x x Fig. 1 ùkü. x re w re w š, g š. Fig. x w w mw y k x ùkü. ù x w ƒ x w Table š 4.1. ù wwš w ù ƒœ y ƒ w, ùký. n σ m = a+ bε m», m, a, b, n p ùkü. 3. x ù xœ w x e y s w w» w y w v w. xœ w ew w ù ƒ yw x w (1) α, γ, m (5) a, b, n, š x x w w. (5) Fig. 1. Configuration of the forming mold and the alumina body shape. w wz

3 xœ w ù x s FE 861 Fig. 3. Variation of relative green density of the alumina powder with the forming pressure during die compaction. Fig.. Loading schedule of the compaction tool set for the alumina green body. Table 1. Displacement of the Compaction Tool Set for the Alumina Ceramic Powder at the end of Loading Schedule Upper Lower Tool Part punch 1) punch ) Core Outer die Condition 1.45 mm.45 mm 0 0 Condition.78 mm 1.9 mm 0 0 1) Downward directional displacement ) Upward directional displacement xœ w x ü s w» w ù w d wš, x yw s w w v w. w ù w 15 mm mx x w x mw d w ƒ y d wš, Fig. 3 ùkü.», w (ù) xe x y z g w xw w. w, œ ƒ x y š 10 g w w x (ø). Shima Oyaneƒ w w ƒ w x œ w yw 6,7) j w α γ ù w w š ƒ w. α = 6.0, γ = 1.08 š w ù x y d w ù w. Fig. 3 w (ù) d l ù m, a, b n w. š œ w x y š xw (ø) l µ w. d w ù. m = 3.6, σ m = εm 0.0, µ = x ù x s ù Fig. ùkü x w w xœ ù p x y wš, Figs. 4 l 6¾ ùkü. Fig. 4 x (6) (7) 43«1y(006)

4 임종인 육영진 86 Fig. 4. Fig. 5. Fig. 6. Flow velocity distributions of the alumina powder with the loading schedule during the compaction process. Relative density variations of the alumina green body with the loading conditions during the compaction process. Density deviations of the alumina green body with the loading conditions during the compaction process. 한국세라믹학회지 나는 알루미나 분말의 유동속도 분포를 나타낸 결과이고, Fig. 5의 결과는 압축성형 과정 중 알루미나 분말 성형체 의 평균 상대밀도 변화를 나타낸 결과이다. 그리고 Fig. 6 의 결과는 압축 성형공정 과정 중 성형체의 밀도편차를 시간에 따라 나타낸 결과이다. Fig. 4(a)의 결과에서 알 수 있듯이, Fig. (a)의 성형조 건과 같이 금형의 상부 및 하부 펀치가 동일하게 이동한 경우, 압축성형 과정에서 전체적인 알루미나 분말의 유동 이 불균일하고, 분말 유동이 일어나지 않는 부분이 외쪽 하단 모서리부분에서 우측 측면부분으로 사선방향으로 존 재하는 것으로 분석되었다. 그러나 Fig. (b)와 같이 상부 및 하부 펀치 이동거리를 다르게 하여 성형한 경우, 분말 유동이 일어나지 않는 부분이 거의 수평으로 나타나는 것 으로 분석되었다. 이 결과로부터 압축 성형조건의 변경에 의하여 분말 유동특성이 아주 많이 변경됨을 확인할 수 있었고, 지금까지 추측만 하고 있었던 사항을 가시화하여 보여준 결과라 할 수 있다. 알루미나 분말의 압축 성형공정 중 평균 밀도변화를 나 타낸 Fig. 5의 결과에서 알 수 있듯이, 성형조건을 변화 시킴에 따라 성형체의 상대 평균밀도는 동일하게 변화됨 을 알 수 있고, 성형종료 후 이론밀도의 약 75%에 도달 하는 것으로 분석되었다. 이 결과로부터 성형조건 변화에 시켜 전체 성형체의 밀도를 측정하는 경우, 성형조건이 변화하여도 밀도가 변화하지 않는 것으로 잘못 판단할 수 있는 것으로 분석된다. 그러나 성형공정 중 성형체의 밀도 분포를 근거로 최대 및 최소의 밀도편차를 분석한 Fig. 6 의 결과에서 알 수 있듯이, 동일한 평균밀도를 보이더라 도 내부의 밀도편차는 성형조건에 따라 아주 많이 차이가 나는 것으로 분석되었다. 즉, 성형조건 1의 경우, 성형체 내부의 밀도편차가 0.09 정도의 최대치에 이르다가 종료 시점에 0.05 정도로 감소한다. 반면 성형조건 의 경우, 성 형체 내부의 밀도편차는 0.01 미만의 아주 적은 밀도편차 를 보이고 있는 것으로 분석되었다. 이상의 결과로부터 성형조건의 변화가 압축 성형공정 중 알루미나 분말의 유동특성에 많은 영향을 주고, 이러 한 분말 유동특성변화로부터 성형체 내부의 밀도편차를 발생시킨다고 판단된다. Fig. 7의 결과는 알루미나 분말의 압축성형 종료 후, 성 형체의 상대 밀도분포를 나타낸 결과이다. 이 결과에서 알 수 있듯이, 성형체의 우측 하부 밀도가 상부 보다 다 소 높고, 우측 하단부에서 좌측 하단부로 휘어지는 모서 리 곡면부분이 가장 밀도가 낮은 것으로 나타났다. 또한 성형조건이 변화됨에 따라 성형체 내부의 밀도변화가 판 이하게 달라지고, 밀도분포 차이도 크게 변화하는 알 수 있다. 즉, 성형조건 1의 경우, 성형체 내부의 상대밀도는 약 0%정도 차이가 나고, 성형조건 로 변경할 경우, 성 형체 내부의 상대밀도는 약 10% 이내의 분포를 보이고

5 xœ w ù x s FE 863 Fig. 7. Comparison of the relative density distribution of the alumina green body at the end of compaction process. Fig. 8. Crack generation possibility analysis results of the alumina green body with the loading schedule of the compaction process ù x w x ƒ t w x w x x y z q w»ƒ š, z t w q w. ù t w w» ¾ š, w x w w q w» j w. w w w w ù ¾ w w x w ƒ z x dw w wš w. Fig. 8 xœ x y k ƒ z l x ü w ƒ w w ùkü. x z Drucker-Prager wt l w ƒ w. Fig. 8, x w ƒ ƒ x ü yƒ ƒ j ùkù d w d w { š. š x 1, x w ƒ x w, x w ƒ 0.05 j w. x w ƒ ùkü e x yƒ k w š. x w Fig. 9. Deformed shape analysis results of the sintered alumina body with the loading schedule of the compaction process., x w ƒ 1/10 w š q š, x ü s ew š q. Fig. 9 s³ l ³ w w x ü s l x ü ƒ 100% ƒ w ƒ w w x x w. l x 1 x, z x x w d t ƒœ yw q. 43«1y(006)

6 864 Á 5. ù xœ w x ü s w w w wš, xœ y g x ü s e w w ³ w s x ƒ w w., x x mw ù w w mw ù x w. š ù xœ w xk x ü s w š, x w y w x ü ³ y w. w w x s l x w ƒ z x dwš, ³ w ü s x yw x w x x. REFERENCES 1. R. M. German, Powder Metallurgy Science, Second Edition, Metal Powder Industries Federation, Princeton, NJS Y. S. Kwon, S. H. Chung, H. I. Sanderow, K. T. Kim, and R. M. German, Numerical Analysis and Optimization of Die Compaction Process, PMTECH, (003). 3. J. Kergadallan, G. Puente, P. Doremus, and E. Pavier, Compression of an Axisymmetric Part with an Instrumented Press, Grenoble, (1997). 4. P. M. Modnet Computer Modeling Group, State of the Art Review : Comparison of Computer Models Representing Powder Compaction Process, Powder Metallurgy, 4 [4] (1999). 5. S. Shima and M. Oyane, Plasticity Theory for Porous Metals, Int. J. Mech. Sci., 18 [6] (1976). 6. Y. S. Kwon, H. T. Lee, and K. T. Kim, Analysis for Cold Die Compaction of Stainless-Steel Powder, ASME J. Eng. Mater. Tech., 119 [4] (1997). 7. S. C. Lee and K. T. Kim, Densification Behavior of Metal Power Under Cold Compaction, KSM(A), (00). w wz

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