- Email: [email protected]
Infiltration as post-processing of laser sintered metal parts
Powder Technology 145 (2004) 62 – 68 www.elsevier.com/locate/powtec
Infiltration as post-processing of laser sintered metal parts J. Du¨ck a,*, F. Niebling b, T. Neeße a, A. Otto b a
Department of Environmental Process Engineering and Recycling, University Erlangen-Nuremberg, Paul-Gordon-Street 3, Erlangen 91052, Germany b Chair of Manufacturing Technology, University Erlangen-Nuremberg, Germany Received 16 July 2003; accepted 13 May 2004 Available online 14 July 2004
Abstract Laser sintering of metal parts is an additive production method applied in the field of rapid prototyping and rapid tooling. Direct metal laser sintering (DMLS) is a variant of the laser sintering processes. Metal powder is locally molten in this process and parts are built from layers. A fast laser sintering process, which is economically favourable, results in porous metal parts. For a technical application as e.g. the production of injection moulds for plastic parts, the surface has to be dense at a defined quality. A post-processing via infiltration is a possible solution for creating such surfaces. This paper describes the results of a study of the infiltration process: A model for describing the infiltration behaviour has been developed and validated through experiments. D 2004 Elsevier B.V. All rights reserved. Keywords: Laser sintering; Rapid prototyping; Infiltration
1. Introduction As a result of the trend toward smaller product life cycles, it is necessary to shorten the product development cycle [1]. Presently, it is impossible to develop products only virtually [2], which requires tests with physical prototypes. The process of fast production of prototypes is called rapid prototyping [3]. The development of these processes originated from model making. Here illustrative models were manufactured with high manual effort, while functional models were produced with conventional machining. The resulting parts were typically over-dimensioned for lifetime and stability. The vision of a time- and cost-saving preproduction was the starting point for the development of the first rapid prototyping processes. This aim was achieved by using the computer model directly as a basic source of information for an automated manufacturing process, which uses an additive technology [4] to build the part without any specific tools. For the laser sintering process, a 3D computer model of the part is used and the part is virtually cut into 2D layers by a
* Corresponding author. Tel.: +49-9131-8523-189; fax: +49-91318523-178. E-mail address: [email protected] (J. Du¨ck). 0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2004.05.006
computer software. The resulting 2D layers are used by the laser sintering machine. It builds up a 3D part from iterative spreading powder on a building platform and locally melting the powder by a laser beam with respect to the shape information of the layer (Fig. 1). Processing fusible powders, the laser sintering process can be used to build plastic, ceramic and metallic components. Direct metal laser sintering (DMLS) is a variant of the usual laser sintering processes producing metal parts directly from metal powder mixtures. In this investigation, a modified EOS M250 sintering machine is used. For the laser sintering, the metal powder ‘Direct Metal 50-V1’ at a layer height of 100 Am was chosen. The metal powder has got an average grain size of about 30 Am and mainly consists of two fractions: A bronze binder component with a melting point of 850 jC and nickel powder as a structure component with a melting point of 1450 jC [5]. For the laser sintering process, the temperature is locally set by the energy input of the laser beam [6]. The binder component is locally molten and flows around the structure component. This fluid phase sintering takes place locally at time periods of less than 20 ms. The total time of the laser sintering production for complex parts can nevertheless exceed 24 h, depending mainly on the volume of the part. An example of a crosscut of the resulting microstructure of a typical laser sintered part is given in Fig. 2.
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
63
Fig. 1. Basic principle of laser sintering.
Especially for an economically fast laser sintering production, the resulting pieces are porous with a porosity of up to 50%. However, for an application as e.g. in the field of rapid tooling for injection moulds, the tools need a dense surface. This can be done by shot peening of the surface, as suggested by EOS, but especially for deep cuts within the mould accessibility can become a problem. Infiltration of the parts would be another method. This paper is focused on a study of the infiltration process aiming at acquiring parts with a dense surface at a defined infiltration depth. A very interesting approach is the filling of tin into the pores of the part. In the investigation, Sn60PbAg was used as an infiltration liquid.
2. Investigation of infiltration process: theoretical model Before we discuss the experimental investigation of the infiltration of tin into the manufactured part, a theoretical model is presented in the following. Basic assumptions for a scheme of the infiltration process are shown in Fig. 3. The model of the infiltration process must take into account all internal and external forces. Here, the internal force is proportional to the surface tension, while the
external force exists due to the difference in pressure outside and inside the pore [7]. The equation for the dynamics of infiltration can be written as: dh r2 2r ¼ P1 P0 þ dt r 8lh
ð2:1Þ
Here 2r/r corresponds to capillary force, r is the surface tension (N/m), P0 is the outside pressure (bar) and P1 is the pressure in a pore. Furthermore, h is the infiltration depth, t is the infiltration time and l is the viscosity. For the radius of the pore, we assume the mean radius of the particle in the stack r = dp/2. Assuming that the pore is tube-shaped (Fig. 3), the volume can be expressed as: V ¼ ð2L 2hÞpr2 ¼ V0 ð1 h=LÞ
ð2:2Þ
L is half of the part width. Using the gas law PV = P0V0, we arrive at the following from Eq. (2.2):
P1 P0 ¼ P0
h L 1
ð2:3Þ
h L
Substituting Eq. (2.3) into Eq. (2.1) results in: 2
3 h dh r 6 2r 7 ¼ 4 P0 L 5 h dt 8lh r 1 L 2
At the beginning of the process, therefore:
Fig. 2. Crosscut of a laser sintered piece.
rffiffiffiffiffiffiffiffi rr t h¼ 2l
ð2:4Þ
j
dh2 dt t¼0
rr ¼ 2l > 0 and
ð2:5Þ
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J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
Two limiting cases follow from Eq. (2.10). 1. For pffiffiffiffiffiffiffisffi ! 0 and y ! 0, the solution transforms into y ¼ 2As, which corresponds to Eq. (2.5). 3 2 ylim )ln(1 ( y/ylim)) 2. For y ! ylim follows As ! ( ylim and consequently Fig. 3. Scheme of the infiltration process.
y
When the infiltration time tends to infinite the infiltration depth moves towards rP0 1 ð2:6Þ hlim ¼ L 1 þ 2r It is possible to define tinf as a time during which h reaches hlim if the infiltration follows Eq. (2.5). rffiffiffiffiffiffi pffiffiffiffiffiffi 2l rP0 1 tinf ¼ L ð2:7Þ 1þ rr 2r It is favourable to make a transition to dimensionless variables and parameters: y = h/L; 2r A¼ : rP0 After that, Eq. (2.4) can be written as: dy r2 P0 1 y ¼ A dt 1y 8lL2 y
ð2:8Þ
The characteristic infiltration time t* = 8lL2/P0r2 can be introduced. It represents the time for filling a pore with a length L, the constant pressure difference equals to P0. After introducing the dimensionless variable s = t/t*, Eq. (2.8) can be transformed: dy 1 y ¼ A ; ð2:9Þ ds y 1y with the initial condition y(0) = 0 This is the mathematical formulation of the problem. The solution depends only on one parameter, A. The formal solution is: y y 2 3 As ¼ ylim F1 þ y1 F 2 ; ð2:10Þ ylim ylim
ylim
ð1 þ AÞ3 ¼ 1 exp s A
!
The law for the increasing penetration changes from a parabolic growth at the beginning to an exponential growth for longer durations. Fig. 4 shows the calculated infiltration depth for two different values of the parameter A. The arrows mark the infiltration times according to Eq. (2.7). The transition from parabolic behaviour to exponential behaviour proceeds faster with an increase of A. The Solution (2.10) can be written in physical variations as follow: (" # 4lL2 hlim 3 hlim 2 hlim t¼ ln 1 rr L L h 2 2 ) h hlim h hlim hlim þ þ L L2 2L3 L
A ; 1þA y y y F1 ln 1 ¼ ; ylim ylim ylim F2
y ylim
¼
y ylim
1 y 2 3 y þ þylim ln 1 ; 2 ylim ylim
ð2:15Þ
From the theoretical analysis, the following conclusions can be derived: 1. The limiting infiltration depth hlim is proportional to the thickness of the part L and also rises with the growth of the dimensionless parameter 2r/rP0. 2. The infiltration time tinf is proportional to the square of the thickness of the part L2 and also proportional to the dimensionless number 2l/rr. For very thin
with ylim ¼
ð2:14Þ
ð2:11Þ
ð2:12Þ
ð2:13Þ Fig. 4. Dynamics of infiltration after Eq. (2.10).
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
65
pores, the infiltration time tinf can therefore be quite long.
3. Experimental results of the infiltration process The variables of the infiltration process that were studied are ‘temperature’ and ‘infiltration time’. The surface tension value (for different temperatures) can be obtained by applying the experimentally limiting infiltration depth to Eq. (2.6). With Eq. (2.8) and the experimental values of the surface tension, the viscosity can be calculated. For a first series of infiltration experiments, 16 rectangular items (sizes approximately equal to 12 12 40 mm) were produced with the EOS M 250 machine, applying identical sintering process parameters (400 mm/s scan velocity, 160 W laser power and 0.1 mm hatch distance). These items were preheated for 5 min to the infiltration temperature and put into a heated chamber filled with tin, which infiltrated into the part. The experiments were carried out for five different infiltration temperatures (200, 220, 252, 342 and 432 jC). The infiltration duration was varied at four steps (30, 60, 120 and 240 s). All infiltrated pieces were cut in two parts and the crosscuts were examined. A typical enlarged picture of a crosscut is given in Fig. 5. The infiltration front was not always exactly parallel to the surface, so a picture processing helped to determine the infiltrated area of the crosscuts. This area was correlated with a mutual infiltration depth h. A square area can be defined with the same surface area. This procedure was carried out for both crosscut surfaces of the part and an mean value was calculated. The mean values and the corresponding standard deviation are illustrated in the next graphs. In Fig. 6, the experimental values for infiltration temperatures of 220 and 430 jC are represented together with the theoretical curves of infiltration depth as a
Fig. 6. Dynamics of tin infiltration for two infiltration temperatures.
function of infiltration time. For the theoretical curves, Eq. (2.15) has been applied. To be able to apply Eq. (2.15), the values of the surface tension and the viscosity must be known. Actually, information about the dependency of r and l on T for the chosen material is very rare, but these variables can be estimated by a comparison of the measured final infiltration depth and the theoretical equation (Eq. (2.6)): r¼
rP0 hlim =L 2 1 hlim =L
ð3:1Þ
The dependency of hlim on the infiltration temperature is shown in Fig. 7. It follows Eq. (3.2): hlim ¼ 4:44
T 200
0:63 ð3:2Þ
Herewith is hlim = 4.44 mm at T = 200 jC. Inserting the experimental limiting infiltration depth values into Eq. (3.1) reveals the corresponding surface tension r. The results (Fig. 8) are matched by an exponential function and can be compared to values found in Ref. [8].
Fig. 5. Crosscut of an infiltrated item. Part infiltrated at 342 jC.
66
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
temperatures. The resulting experimental data together with the reference value for T = 280 jC [8] are shown in Fig. 9. The experimental fit can be expressed as l = 0.102 exp ( 0.0065T). Usually, the temperature dependency of viscosity is represented in a formula such as [9]: l ¼ l0 exp
DG ; RðT þ 273:15Þ
ð3:5Þ
where l0 is a constant (consists of Avogadro’s and Planck’s numbers and the volume of a mole of liquids) and DG is the molar free energy of activation. Applying this, the following equation can be derived: Fig. 7. Limiting infiltration depth for different temperature of tin.
The experimental results follow the equation: T 1:4 r ¼ 0:84 200
ð3:3Þ
At T = 200 jC follows r = 0.84 N/m. The measurements show that an increase of infiltration temperature causes a decrease of the surface tension. Consequently, an increase of temperature leads to a decrease of infiltration depth (Fig. 7). This behaviour is in good agreement with the expectations. Finally, the viscosity derived from experimental data is represented as a function of temperature. The values of l have been obtained by combining Eq. (2.5) with Eq. (3.1): l ¼ t0:5
r2 P0 1 : 2 L hlim =Lð1 hlim =LÞ
ð3:4Þ
Hereby, t0.5 is the time during which h rises from 0 up to hlim/2. The measurements for T = 200 jC and T = 252 jC show strong deviations in comparison to the data for other
Fig. 8. Dependence of surface tension on temperature.
ln l ¼ 2102ðT þ 273:15Þ 10:25
ð3:6Þ
Accordingly, the molar activation energy is found to be equal to 4204 cal/mol. These results can be compared with the viscosity values obtained from literature [8]. The values from literature are around 0.00218 N s/m2 for 280 jC and correspond to the experimentally derived values. The good correlation of the temperature-dependent functions for surface tension and viscosity, in comparison to results from literature, underlines the applicability of the theoretical model. For a technical application of the infiltration of laser sintered parts, the quality of the infiltration has to be studied, too. Fig. 10 gives a detailed view of the infiltrated regions for different infiltration temperatures. At an infiltration temperature of 220 jC, the infiltrated regions are almost dense. This reveals that the laser sintered material must have an open pore system mainly. At higher infiltration temperatures, the residual porosity rises in the infiltrated regions. This is assumed to be due to the reduced capillar forces at elevated temperatures and the irregular laser sintered pore system. Caused by infiltration behaviour, the underdeveloped connections between the pores are
Fig. 9. Dependence of viscosity on temperature.
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
67
Fig. 10. Crosscuts of infiltrated regions of a laser sintered body at different infiltration temperatures.
increasingly ignored by the penetrating tin due to low surface tension.
4. Conclusion Porous metal parts produced by the DMLS process can be infiltrated with a lower melting metal component and a defined surface thickness can be achieved. For the description of the infiltration process, a theoretical model was developed and compared to experimental results. The developed theoretical infiltration model accounts for capillary forces and the pressure difference in the pore. The results are in good agreement to experimental results. Furthermore, the results show that surface tension and pressure difference in the pore are the most important forces driving the infiltration. Consequently, for a successful infiltration, the temperature in the infiltration chamber must be slightly above the melting point of the infiltrating liquid. For tin infiltration of laser sintered bronze –nickel parts with Sn60PbAg, the infiltration depth reaches around 4 –5 mm at a total wall thickness of 6 mm, which is sufficient for a technical application of the surface. This level of infiltration is reached at infiltration times at about 1 min.
List of symbols hlim [m] limit infiltration depth r [m] pore radius t [s] infiltration time t* [– ] characteristic infiltration time y [– ] dimensionless infiltration depth A [ –] dimensionless parameter L [m] thickness of the part P1 [bar] pressure within pore P0 [bar] atmosphere pressure T [jC] temperature l [N s/m2] viscosity r [N/m] surface tension s [– ] dimensionless infiltration time
Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft (DFG).
References [1] M. Macht, Vielfalt des Rapid Prototyping. Grundlagen, Verfahren und Einsatzbeispiele, Seminarberichte IWB 21: Rapid Prototyping, Rapid
68
[2]
[3] [4] [5]
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68 Tooling: Schnell zu funktionalen Prototypen, Herbert Utz Verlag Wissenschaft, Mu¨nchen, 1996. M. Schenk, A. Hintze, M. Schumann, S. Stu¨ring, Erweiterte «Digital Mockups» zur Modellierung und Simulation technischer Systeme im integrierten Entwicklungsprozess. Entwicklungsmethoden und Entwicklungs-prozesse im Maschinenbau, Magdeburg: 4. Magdeburger Maschinenbautage, 22. – 23. September 1999, Logos Verlag, Berlin 1999, pp. S.11 – S.18. A. Gebhardt, Rapid protoyping, Werkzeuge fu¨r die schnelle Produktentwicklung, Carl Hanser Verlag, Mu¨nchen, 2000. M. Burns, Automated Fabrication: improving productivity in manufacturing, Ennex, Los Angeles, 1993. A. Coremans, Direktes Laserstrahlsintern von Metallpulver - Prozeßmo-
[6]
[7]
[8] [9]
dellierung, Systemtechnik, Eigenschaften laserstrahlgesinterter metallischer Werkstu¨cke, Meisenbach Verlag, Bamberg, 1999. F. Niebling, A. Otto, FE-simulation of the selective laser sintering process of metallic powders, in: M. Geiger, A. Otto (Eds.), Lane, vol. 3, Meisenbach Verlag, Bamberg, 2001, pp. 371 – 382. V.G. Levich, Motion induced by capilarity (Chapter VII), Physicochemical Hydrodynamics, University of Minnesota, Englewood Cliffs, Prentice Hall 1962. Bruneel, P.O., Website Interflux USA, http://www.interfluxusa.com/ Technical/Sixsigma.htm. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York, 1960.
Infiltration as post-processing of laser sintered metal parts J. Du¨ck a,*, F. Niebling b, T. Neeße a, A. Otto b a
Department of Environmental Process Engineering and Recycling, University Erlangen-Nuremberg, Paul-Gordon-Street 3, Erlangen 91052, Germany b Chair of Manufacturing Technology, University Erlangen-Nuremberg, Germany Received 16 July 2003; accepted 13 May 2004 Available online 14 July 2004
Abstract Laser sintering of metal parts is an additive production method applied in the field of rapid prototyping and rapid tooling. Direct metal laser sintering (DMLS) is a variant of the laser sintering processes. Metal powder is locally molten in this process and parts are built from layers. A fast laser sintering process, which is economically favourable, results in porous metal parts. For a technical application as e.g. the production of injection moulds for plastic parts, the surface has to be dense at a defined quality. A post-processing via infiltration is a possible solution for creating such surfaces. This paper describes the results of a study of the infiltration process: A model for describing the infiltration behaviour has been developed and validated through experiments. D 2004 Elsevier B.V. All rights reserved. Keywords: Laser sintering; Rapid prototyping; Infiltration
1. Introduction As a result of the trend toward smaller product life cycles, it is necessary to shorten the product development cycle [1]. Presently, it is impossible to develop products only virtually [2], which requires tests with physical prototypes. The process of fast production of prototypes is called rapid prototyping [3]. The development of these processes originated from model making. Here illustrative models were manufactured with high manual effort, while functional models were produced with conventional machining. The resulting parts were typically over-dimensioned for lifetime and stability. The vision of a time- and cost-saving preproduction was the starting point for the development of the first rapid prototyping processes. This aim was achieved by using the computer model directly as a basic source of information for an automated manufacturing process, which uses an additive technology [4] to build the part without any specific tools. For the laser sintering process, a 3D computer model of the part is used and the part is virtually cut into 2D layers by a
* Corresponding author. Tel.: +49-9131-8523-189; fax: +49-91318523-178. E-mail address: [email protected] (J. Du¨ck). 0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2004.05.006
computer software. The resulting 2D layers are used by the laser sintering machine. It builds up a 3D part from iterative spreading powder on a building platform and locally melting the powder by a laser beam with respect to the shape information of the layer (Fig. 1). Processing fusible powders, the laser sintering process can be used to build plastic, ceramic and metallic components. Direct metal laser sintering (DMLS) is a variant of the usual laser sintering processes producing metal parts directly from metal powder mixtures. In this investigation, a modified EOS M250 sintering machine is used. For the laser sintering, the metal powder ‘Direct Metal 50-V1’ at a layer height of 100 Am was chosen. The metal powder has got an average grain size of about 30 Am and mainly consists of two fractions: A bronze binder component with a melting point of 850 jC and nickel powder as a structure component with a melting point of 1450 jC [5]. For the laser sintering process, the temperature is locally set by the energy input of the laser beam [6]. The binder component is locally molten and flows around the structure component. This fluid phase sintering takes place locally at time periods of less than 20 ms. The total time of the laser sintering production for complex parts can nevertheless exceed 24 h, depending mainly on the volume of the part. An example of a crosscut of the resulting microstructure of a typical laser sintered part is given in Fig. 2.
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
63
Fig. 1. Basic principle of laser sintering.
Especially for an economically fast laser sintering production, the resulting pieces are porous with a porosity of up to 50%. However, for an application as e.g. in the field of rapid tooling for injection moulds, the tools need a dense surface. This can be done by shot peening of the surface, as suggested by EOS, but especially for deep cuts within the mould accessibility can become a problem. Infiltration of the parts would be another method. This paper is focused on a study of the infiltration process aiming at acquiring parts with a dense surface at a defined infiltration depth. A very interesting approach is the filling of tin into the pores of the part. In the investigation, Sn60PbAg was used as an infiltration liquid.
2. Investigation of infiltration process: theoretical model Before we discuss the experimental investigation of the infiltration of tin into the manufactured part, a theoretical model is presented in the following. Basic assumptions for a scheme of the infiltration process are shown in Fig. 3. The model of the infiltration process must take into account all internal and external forces. Here, the internal force is proportional to the surface tension, while the
external force exists due to the difference in pressure outside and inside the pore [7]. The equation for the dynamics of infiltration can be written as: dh r2 2r ¼ P1 P0 þ dt r 8lh
ð2:1Þ
Here 2r/r corresponds to capillary force, r is the surface tension (N/m), P0 is the outside pressure (bar) and P1 is the pressure in a pore. Furthermore, h is the infiltration depth, t is the infiltration time and l is the viscosity. For the radius of the pore, we assume the mean radius of the particle in the stack r = dp/2. Assuming that the pore is tube-shaped (Fig. 3), the volume can be expressed as: V ¼ ð2L 2hÞpr2 ¼ V0 ð1 h=LÞ
ð2:2Þ
L is half of the part width. Using the gas law PV = P0V0, we arrive at the following from Eq. (2.2):
P1 P0 ¼ P0
h L 1
ð2:3Þ
h L
Substituting Eq. (2.3) into Eq. (2.1) results in: 2
3 h dh r 6 2r 7 ¼ 4 P0 L 5 h dt 8lh r 1 L 2
At the beginning of the process, therefore:
Fig. 2. Crosscut of a laser sintered piece.
rffiffiffiffiffiffiffiffi rr t h¼ 2l
ð2:4Þ
j
dh2 dt t¼0
rr ¼ 2l > 0 and
ð2:5Þ
64
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
Two limiting cases follow from Eq. (2.10). 1. For pffiffiffiffiffiffiffisffi ! 0 and y ! 0, the solution transforms into y ¼ 2As, which corresponds to Eq. (2.5). 3 2 ylim )ln(1 ( y/ylim)) 2. For y ! ylim follows As ! ( ylim and consequently Fig. 3. Scheme of the infiltration process.
y
When the infiltration time tends to infinite the infiltration depth moves towards rP0 1 ð2:6Þ hlim ¼ L 1 þ 2r It is possible to define tinf as a time during which h reaches hlim if the infiltration follows Eq. (2.5). rffiffiffiffiffiffi pffiffiffiffiffiffi 2l rP0 1 tinf ¼ L ð2:7Þ 1þ rr 2r It is favourable to make a transition to dimensionless variables and parameters: y = h/L; 2r A¼ : rP0 After that, Eq. (2.4) can be written as: dy r2 P0 1 y ¼ A dt 1y 8lL2 y
ð2:8Þ
The characteristic infiltration time t* = 8lL2/P0r2 can be introduced. It represents the time for filling a pore with a length L, the constant pressure difference equals to P0. After introducing the dimensionless variable s = t/t*, Eq. (2.8) can be transformed: dy 1 y ¼ A ; ð2:9Þ ds y 1y with the initial condition y(0) = 0 This is the mathematical formulation of the problem. The solution depends only on one parameter, A. The formal solution is: y y 2 3 As ¼ ylim F1 þ y1 F 2 ; ð2:10Þ ylim ylim
ylim
ð1 þ AÞ3 ¼ 1 exp s A
!
The law for the increasing penetration changes from a parabolic growth at the beginning to an exponential growth for longer durations. Fig. 4 shows the calculated infiltration depth for two different values of the parameter A. The arrows mark the infiltration times according to Eq. (2.7). The transition from parabolic behaviour to exponential behaviour proceeds faster with an increase of A. The Solution (2.10) can be written in physical variations as follow: (" # 4lL2 hlim 3 hlim 2 hlim t¼ ln 1 rr L L h 2 2 ) h hlim h hlim hlim þ þ L L2 2L3 L
A ; 1þA y y y F1 ln 1 ¼ ; ylim ylim ylim F2
y ylim
¼
y ylim
1 y 2 3 y þ þylim ln 1 ; 2 ylim ylim
ð2:15Þ
From the theoretical analysis, the following conclusions can be derived: 1. The limiting infiltration depth hlim is proportional to the thickness of the part L and also rises with the growth of the dimensionless parameter 2r/rP0. 2. The infiltration time tinf is proportional to the square of the thickness of the part L2 and also proportional to the dimensionless number 2l/rr. For very thin
with ylim ¼
ð2:14Þ
ð2:11Þ
ð2:12Þ
ð2:13Þ Fig. 4. Dynamics of infiltration after Eq. (2.10).
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
65
pores, the infiltration time tinf can therefore be quite long.
3. Experimental results of the infiltration process The variables of the infiltration process that were studied are ‘temperature’ and ‘infiltration time’. The surface tension value (for different temperatures) can be obtained by applying the experimentally limiting infiltration depth to Eq. (2.6). With Eq. (2.8) and the experimental values of the surface tension, the viscosity can be calculated. For a first series of infiltration experiments, 16 rectangular items (sizes approximately equal to 12 12 40 mm) were produced with the EOS M 250 machine, applying identical sintering process parameters (400 mm/s scan velocity, 160 W laser power and 0.1 mm hatch distance). These items were preheated for 5 min to the infiltration temperature and put into a heated chamber filled with tin, which infiltrated into the part. The experiments were carried out for five different infiltration temperatures (200, 220, 252, 342 and 432 jC). The infiltration duration was varied at four steps (30, 60, 120 and 240 s). All infiltrated pieces were cut in two parts and the crosscuts were examined. A typical enlarged picture of a crosscut is given in Fig. 5. The infiltration front was not always exactly parallel to the surface, so a picture processing helped to determine the infiltrated area of the crosscuts. This area was correlated with a mutual infiltration depth h. A square area can be defined with the same surface area. This procedure was carried out for both crosscut surfaces of the part and an mean value was calculated. The mean values and the corresponding standard deviation are illustrated in the next graphs. In Fig. 6, the experimental values for infiltration temperatures of 220 and 430 jC are represented together with the theoretical curves of infiltration depth as a
Fig. 6. Dynamics of tin infiltration for two infiltration temperatures.
function of infiltration time. For the theoretical curves, Eq. (2.15) has been applied. To be able to apply Eq. (2.15), the values of the surface tension and the viscosity must be known. Actually, information about the dependency of r and l on T for the chosen material is very rare, but these variables can be estimated by a comparison of the measured final infiltration depth and the theoretical equation (Eq. (2.6)): r¼
rP0 hlim =L 2 1 hlim =L
ð3:1Þ
The dependency of hlim on the infiltration temperature is shown in Fig. 7. It follows Eq. (3.2): hlim ¼ 4:44
T 200
0:63 ð3:2Þ
Herewith is hlim = 4.44 mm at T = 200 jC. Inserting the experimental limiting infiltration depth values into Eq. (3.1) reveals the corresponding surface tension r. The results (Fig. 8) are matched by an exponential function and can be compared to values found in Ref. [8].
Fig. 5. Crosscut of an infiltrated item. Part infiltrated at 342 jC.
66
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
temperatures. The resulting experimental data together with the reference value for T = 280 jC [8] are shown in Fig. 9. The experimental fit can be expressed as l = 0.102 exp ( 0.0065T). Usually, the temperature dependency of viscosity is represented in a formula such as [9]: l ¼ l0 exp
DG ; RðT þ 273:15Þ
ð3:5Þ
where l0 is a constant (consists of Avogadro’s and Planck’s numbers and the volume of a mole of liquids) and DG is the molar free energy of activation. Applying this, the following equation can be derived: Fig. 7. Limiting infiltration depth for different temperature of tin.
The experimental results follow the equation: T 1:4 r ¼ 0:84 200
ð3:3Þ
At T = 200 jC follows r = 0.84 N/m. The measurements show that an increase of infiltration temperature causes a decrease of the surface tension. Consequently, an increase of temperature leads to a decrease of infiltration depth (Fig. 7). This behaviour is in good agreement with the expectations. Finally, the viscosity derived from experimental data is represented as a function of temperature. The values of l have been obtained by combining Eq. (2.5) with Eq. (3.1): l ¼ t0:5
r2 P0 1 : 2 L hlim =Lð1 hlim =LÞ
ð3:4Þ
Hereby, t0.5 is the time during which h rises from 0 up to hlim/2. The measurements for T = 200 jC and T = 252 jC show strong deviations in comparison to the data for other
Fig. 8. Dependence of surface tension on temperature.
ln l ¼ 2102ðT þ 273:15Þ 10:25
ð3:6Þ
Accordingly, the molar activation energy is found to be equal to 4204 cal/mol. These results can be compared with the viscosity values obtained from literature [8]. The values from literature are around 0.00218 N s/m2 for 280 jC and correspond to the experimentally derived values. The good correlation of the temperature-dependent functions for surface tension and viscosity, in comparison to results from literature, underlines the applicability of the theoretical model. For a technical application of the infiltration of laser sintered parts, the quality of the infiltration has to be studied, too. Fig. 10 gives a detailed view of the infiltrated regions for different infiltration temperatures. At an infiltration temperature of 220 jC, the infiltrated regions are almost dense. This reveals that the laser sintered material must have an open pore system mainly. At higher infiltration temperatures, the residual porosity rises in the infiltrated regions. This is assumed to be due to the reduced capillar forces at elevated temperatures and the irregular laser sintered pore system. Caused by infiltration behaviour, the underdeveloped connections between the pores are
Fig. 9. Dependence of viscosity on temperature.
J. Du¨ck et al. / Powder Technology 145 (2004) 62–68
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Fig. 10. Crosscuts of infiltrated regions of a laser sintered body at different infiltration temperatures.
increasingly ignored by the penetrating tin due to low surface tension.
4. Conclusion Porous metal parts produced by the DMLS process can be infiltrated with a lower melting metal component and a defined surface thickness can be achieved. For the description of the infiltration process, a theoretical model was developed and compared to experimental results. The developed theoretical infiltration model accounts for capillary forces and the pressure difference in the pore. The results are in good agreement to experimental results. Furthermore, the results show that surface tension and pressure difference in the pore are the most important forces driving the infiltration. Consequently, for a successful infiltration, the temperature in the infiltration chamber must be slightly above the melting point of the infiltrating liquid. For tin infiltration of laser sintered bronze –nickel parts with Sn60PbAg, the infiltration depth reaches around 4 –5 mm at a total wall thickness of 6 mm, which is sufficient for a technical application of the surface. This level of infiltration is reached at infiltration times at about 1 min.
List of symbols hlim [m] limit infiltration depth r [m] pore radius t [s] infiltration time t* [– ] characteristic infiltration time y [– ] dimensionless infiltration depth A [ –] dimensionless parameter L [m] thickness of the part P1 [bar] pressure within pore P0 [bar] atmosphere pressure T [jC] temperature l [N s/m2] viscosity r [N/m] surface tension s [– ] dimensionless infiltration time
Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft (DFG).
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