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Research on MIM achieved by cooperation between Femto-ST institute in France and SWJTU in China
Metal Powder Report Volume 00, Number 00 June 2016
metal-powder.net
SPECIAL FEATURE
Research on MIM achieved by cooperation between Femto-ST institute in France and SWJTU in China J. Shi1, T. Barriere2, Z. Cheng3, B. Liu3 and J. Gelin2 1
Southwest University of Science and Technology, School of Civil Engineering and Architecture, 621010 Mianyang, China Femto-ST Institute, Department of Applied Mechanics, ENSMM Besanc¸on, 26 Rue de l’Epitaphe, 25030 Besanc¸on, France 3 Southwest Jiaotong University, School of Mechanics and Engineering, 610031 Chengdu, China 2
Metal injection molding process consists of four main stages: feedstock preparation, injection molding, debinding and sintering. The Co-researches from FEMTO-ST institute in France and Southwest Jiaotong University in China covers all the four aspects in their activities. The co-tutorial Ph.D. thesis of Jianjun SHI made some improvement to the in-house developed vectorial explicit algorithm for simulation of injection molding and extended its function into the scope of micro-injection. For sintering stage, some new and interesting results were obtained in the microwave sintering experiments. Now the full cycle simulation on multi-physics coupling process of microwave sintering is realized. Although MIM theory has been developed for decades, the physical modeling and numerical simulation are far behind the practices. There remain some persistent problems in the previous developing algorithm, which results in the untrue injection filling patterns. There is still much work to do in physical experiment for the calibration of sintering behaviors of powder materials, especially for the case of microwave sintering. The authors dedicate to promote the application, experiment and numerical simulation for micro-injection molding and microwave sintering. The research background and achievements are briefly introduced as follows.
A similar upwind method proposed for improvement of wrongly adverted filling profile in MIM flow With the development of injection molding process, shape of the components is increasingly complex. Due to the constraints in physical experiments and the availability of measurements for micro-scale factors, the accurate numerical simulation becomes more and more important in designing and manufacturing. In general, Eulerian description is used for simulation of the filling flow problems. The governing equation for evolution of the filling state takes the form of an advection equation. The evolution of filling state is governed by the velocity field in whole mold cavity. E-mail address: [email protected].
In most cases it results often in an accurate and realistic simulation. However for some special cases when the opposite joining and bi-pass are involved, such as runners in shapes of ? and L, it is observed that the filling patterns predicted by simulation are not the realistic ones, as the previous result shown in Fig. 1. In these cases the flow directions subject to the sudden changes in the filling runners. A modified algorithm, which is similar to upwind method, was proposed to settle this problem. This proposed method makes the advection of filling state be mainly affected by the filling flow behind the filling front. Based on finite element method and the efficient vectorial explicit algorithm developed in research team, a systematic operation was proposed for modifying the velocity field ahead filling front. It makes advance of the flow front be guided more by the flow of the polymer instead of the fictive air flow. The simulation results in shapes of ? and L, see the modified result in Fig. 1, show that the proposed algorithm can improve effectively the untrue filling patterns in simulation.
Evaluation and implementation of surface tension effect in micro MIM flow Due to the micro-scale factors, filling flow in micro die cavity exhibits the rheological phenomena different from the conventional ones. The factors such as surface tension, wall slip, viscous
0026-0657/ß 2016 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mprp.2016.05.006
1 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006
MPRP-680; No of Pages 4 SPECIAL FEATURE
Metal Powder Report Volume 00, Number 00 June 2016
SPECIAL FEATURE FIGURE 1
The problems in previous filling simulation and the improved filling patterns of front joining for specific cavities in shape ? and L.
dissipation and convective heat transfer, will play the important roles in solution of the problems in micro-scaled sizes. These factors are not taken into account in simulation of macro-injection molding process. For extending the in-house FEM software into the scope of micro injection, surface tension effect is implemented in the injection molding simulation. The work takes the mathematical model of surface tension force as explained by Tong and Wang [1]. Implementation is realized in an explicit finite element solver with the easy method proposed by authors. The explicit finite element solver, developed by research team, appears to be an efficient tool for simulation of the viscous filling flow [2]. However, there exist some problems for evaluation of the filling front curvature. It involves the computation of Laplacian operation that requires the integration of a scalar function (filling function) in second derivative, but the effect is associated with the vector functions of velocity fields. The curvature of filling front is prerequisite for the implementation of surface tension. Due to the lack of appropriated FEM method for curvature calculation, a simpler and easier way to solve this problem is proposed. To avoid the complication in evaluation of the Laplacian operation on filling function, a specific method is proposed to evaluate curvature of the filling front by the simple and systematical procedures. Then the force of surface tension can be introduced directly in solution of the Navier-Stokes equation. Fig. 2 shows the surface tension force in the filling process of an
FIGURE 2
Distribution of surface tension force: (a) component in x direction; and (b) component in y direction (W – width of the mold; L – length of the mold; Fst – surface tension force).
injected polymer flow. By comparison between the magnitudes of surface tension force with the viscous force for a filling example in micro channels, the effects of surface tension in micro-injection molding were studied. It shows the importance of surface tension in micro-injection molding of sub-millimeter sizes, though this effect does not represent the significance in ordinary injection molding process. These numerical results are in close agreement with the data reported in physical experiments.
Microwave sintering of 17-4PH stainless steel powder and the resulting gradient in mechanical properties 17-4PH is a type of martensitic precipitation hardening stainless steel with high mechanical properties. Nowadays, most researches on sintering of 17-4PH stainless-steel focus on the ways by conventional resistive heating. For microwave sintering, many researches focused on other powder materials, such as ceramics, lead, tin, aluminum, copper, nickel, titanium, austenitic (316L) and ferritic (434L) stainless steels, etc. Only one investigation on the microwave processing of 17-4PH stainless-steel powder was found by the retrieves of literatures in the currently available resources. It was a preliminary study done by Bose et al. [3]. They found that Microwave sintering had not improved the mechanical properties compared to conventional sintering for 17-4PH stainless steel. To understand better the sintering properties of 17-4PH stainless steel, our work examined the densification and microstructure evolution of 17-4PH stainless steel powder processed by microwave sintering. The injected specimens subjected to 2.45 GHz microwaves in a multi-mode furnace. The influence factors in microwave sintering process were investigated, including the peak sintering temperature, holding time, heating rate and pre-sintering stages. After such a solid state sintering route, the evolutions of micro-structure, densification and mechanical response of the sintered specimens were studied. Comparison of the results between microwave sintering and conventional process was also studied. In this work, the authors confirmed that microwave sintering takes one tenth of the conventional sintering time to get the better
2 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006
MPRP-680; No of Pages 4
FIGURE 3
Vickers hardness values for each detected area (x1–x5) along the horizontal direction. (Small figure in the top right corner shows distribution of the detected areas on the polished section of a sintered specimen.)
results. The optimal peak temperature is 150–2008C lower. It results in the better densification, more homogeneous microstructure, higher mechanical properties, and more size shrinkage. The experiments proved also a remarkable fact for microwave sintering of the 17-4PH stainless steel powder. The heating rate must be set to an order of 30 8C/min. Lower heating rate leads to the poor results. The fast processing by microwave results in the gradient of mechanic properties in sintered bodies, as shown in Fig. 3. The prediction, evaluation and purposes of the gradient properties induced by microwave leads the studies to the more precise and profound insights. It is valuable to continue the studies on this nature for the application of functionally gradient materials produced by microwave sintering.
Mathematical modeling and full cycle simulation on multi-physics coupling process of microwave sintering Microwave sintering represents the coupling phenomena of multi-physical fields. It includes the coupling of electro-magnetic fields, thermal conduction and the densification process of sintered powders. The process involves three types of the physics. One is the transmission of microwave energy in the heating cavity. A part of the microwave energy is converted into heat energy, because of its dissipation during the transmission. The second one is the process of heat transfer. Because of
SPECIAL FEATURE
inhomogeneous distribution of the electric field in the heating cavity, it generates the heat in-homogeneously in the sintered material. Then there exists the process of heat transfer. The third one is the process of densification during sintering. The particles and grains of PIM material connect and fuse together. The pores among the particles reduce and disappear gradually. Macroscopically it appears to be the shrinkage of sintered products. The volume is reduced while the density increases. The evolution of density and temperature during sintering results in the variation of different parameters in physical equations. It results then the complicated coupling of different physics. In order to establish the mathematical model for microwave sintering, there exist five main aspects to be solved: 1. Solve Maxwell equation to get electromagnetic fields in cavity of the furnace; 2. Solve for distribution of the heat generation in process of microwave sintering; 3. Solution of heat transfer equation to get temperature field in the sintered body; 4. Solve the governing equations of sintering densification to get the structural response of sintered body; 5. Coupling of the Maxwell equation, heat transfer equation and mechanic equations. This coupling phenomenon can be shown clearly in Fig. 4. The true process of microwave sintering must be simulated under the condition that these complicated coupling are taken into account. Most of the actual literatures focus on the analysis of microwave heating and heat transfer, which couples with the evaluation of electromagnetic field. But none of them includes the densification behaviors of powder material. By analysis on the principles of microwave sintering, the mathematic model is established. The present work focuses on how to integrate such a sintering behavior in simulation to form a complete coupling cycle of the microwave sintering, from distribution of the electromagnetic field to the densification of sintered compacts. Based on a thermo-elasto-viscoplastic model, the work improves the previous work by Quinard, Song et al. in research team. The sintering behaviors of compacts formed by 316L stainless steel powders [4] and alumina powders [5] had been studied by means of the dilatometer and conventional sintering furnace. A macro model was established on the results to describe the shrinkage phenomena of thermal sintering process. Such a constitutive law is then employed into the model of microwave sintering process.
FIGURE 4
The coupling of multi-physics in simulation of the microwave sintering. 3 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006
SPECIAL FEATURE
Metal Powder Report Volume 00, Number 00 June 2016
MPRP-680; No of Pages 4 SPECIAL FEATURE
Metal Powder Report Volume 00, Number 00 June 2016
SPECIAL FEATURE
FIGURE 8
Evolution of temperature and relative density during the whole microwave sintering process.
FIGURE 5
Distribution of the electric field in empty cavity.
FIGURE 6
Temperature field in a cross section when the sintering undergoing 1500 s.
The numerical simulation has also been realized using the finite element solver COMSOL Multiphysics(C) platform. The RF module, heat transfer module, structure analysis module in COMSOL package is employed. The constitutive law, which describes sintering densification of CIM materials under high temperature, is implemented into the structure analysis. The coupling of multiphysics in microwave sintering is realized in simulation. It results in the 3D simulation for an example of microwave sintering in a multi-mode cavity. Fig. 5 investigates the distribution of the electric field in cavity of the microwave furnace. The temperature field on a cross section inside the PIM material, after heating 1500seconds, is shown in Fig. 6. At the same instant, the magnitude of resultant displacement is shown in Fig. 7. The evolution of temperature and relative density during the whole microwave sintering process can be seen in Fig. 8. The coupling in simulation of microwave electric field, thermal conduction and sintering densification of the powder material is achieved. This work provides a reliable way for the further investigations on microwave sintering. But it should be mentioned that the present work is still far from complete. It focuses on the modeling of the microwave sintering process and the methods for its simulation. It provides just an effective way for the further analysis and the achievement of knowledge on microwave sintering. For more accurate simulations, the true parameters and constitutive law of the MIM materials are required. Besides that, the external effect, such as boundary conditions, gravitation and friction, should be taken into account. It represents the great importance to study and achieve theses parameters and relationships by experiments.
Acknowledgments This work is financially supported by the National Natural Science Foundation of China (Grant No. 11502219) and Doctoral Research Foundation of Southwest University of Science and Technology (Grant No. 14zx7139). The authors also wish to thank Femto-ST Institute on experiment and simulation support. References
FIGURE 7
Resultant displacement on the cross section when the sintering undergoing 1500 s.
[1] A. Tong, Z. Wang, J. Comput. Phys. 221 (2) (2007) 506–523. [2] Z. Cheng, T. Barriere, B. Liu, et al. Polym. Eng. Sci. 49 (6) (2009) 1243–1252. [3] A. Bose, D. Agrawal, R. Dowding, International Conference on Powder Metallurgy and Particulate Materials, 2004, p. 53. [4] C. Quinard, J. Song, T. Barriere, et al. Powder Technol. 208 (2) (2011) 383–389. [5] J. Song, T. Barriere, J. Gelin, et al. Int. J. Powder Metal. 45 (3) (2009) 25–34.
4 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006
metal-powder.net
SPECIAL FEATURE
Research on MIM achieved by cooperation between Femto-ST institute in France and SWJTU in China J. Shi1, T. Barriere2, Z. Cheng3, B. Liu3 and J. Gelin2 1
Southwest University of Science and Technology, School of Civil Engineering and Architecture, 621010 Mianyang, China Femto-ST Institute, Department of Applied Mechanics, ENSMM Besanc¸on, 26 Rue de l’Epitaphe, 25030 Besanc¸on, France 3 Southwest Jiaotong University, School of Mechanics and Engineering, 610031 Chengdu, China 2
Metal injection molding process consists of four main stages: feedstock preparation, injection molding, debinding and sintering. The Co-researches from FEMTO-ST institute in France and Southwest Jiaotong University in China covers all the four aspects in their activities. The co-tutorial Ph.D. thesis of Jianjun SHI made some improvement to the in-house developed vectorial explicit algorithm for simulation of injection molding and extended its function into the scope of micro-injection. For sintering stage, some new and interesting results were obtained in the microwave sintering experiments. Now the full cycle simulation on multi-physics coupling process of microwave sintering is realized. Although MIM theory has been developed for decades, the physical modeling and numerical simulation are far behind the practices. There remain some persistent problems in the previous developing algorithm, which results in the untrue injection filling patterns. There is still much work to do in physical experiment for the calibration of sintering behaviors of powder materials, especially for the case of microwave sintering. The authors dedicate to promote the application, experiment and numerical simulation for micro-injection molding and microwave sintering. The research background and achievements are briefly introduced as follows.
A similar upwind method proposed for improvement of wrongly adverted filling profile in MIM flow With the development of injection molding process, shape of the components is increasingly complex. Due to the constraints in physical experiments and the availability of measurements for micro-scale factors, the accurate numerical simulation becomes more and more important in designing and manufacturing. In general, Eulerian description is used for simulation of the filling flow problems. The governing equation for evolution of the filling state takes the form of an advection equation. The evolution of filling state is governed by the velocity field in whole mold cavity. E-mail address: [email protected].
In most cases it results often in an accurate and realistic simulation. However for some special cases when the opposite joining and bi-pass are involved, such as runners in shapes of ? and L, it is observed that the filling patterns predicted by simulation are not the realistic ones, as the previous result shown in Fig. 1. In these cases the flow directions subject to the sudden changes in the filling runners. A modified algorithm, which is similar to upwind method, was proposed to settle this problem. This proposed method makes the advection of filling state be mainly affected by the filling flow behind the filling front. Based on finite element method and the efficient vectorial explicit algorithm developed in research team, a systematic operation was proposed for modifying the velocity field ahead filling front. It makes advance of the flow front be guided more by the flow of the polymer instead of the fictive air flow. The simulation results in shapes of ? and L, see the modified result in Fig. 1, show that the proposed algorithm can improve effectively the untrue filling patterns in simulation.
Evaluation and implementation of surface tension effect in micro MIM flow Due to the micro-scale factors, filling flow in micro die cavity exhibits the rheological phenomena different from the conventional ones. The factors such as surface tension, wall slip, viscous
0026-0657/ß 2016 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mprp.2016.05.006
1 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006
MPRP-680; No of Pages 4 SPECIAL FEATURE
Metal Powder Report Volume 00, Number 00 June 2016
SPECIAL FEATURE FIGURE 1
The problems in previous filling simulation and the improved filling patterns of front joining for specific cavities in shape ? and L.
dissipation and convective heat transfer, will play the important roles in solution of the problems in micro-scaled sizes. These factors are not taken into account in simulation of macro-injection molding process. For extending the in-house FEM software into the scope of micro injection, surface tension effect is implemented in the injection molding simulation. The work takes the mathematical model of surface tension force as explained by Tong and Wang [1]. Implementation is realized in an explicit finite element solver with the easy method proposed by authors. The explicit finite element solver, developed by research team, appears to be an efficient tool for simulation of the viscous filling flow [2]. However, there exist some problems for evaluation of the filling front curvature. It involves the computation of Laplacian operation that requires the integration of a scalar function (filling function) in second derivative, but the effect is associated with the vector functions of velocity fields. The curvature of filling front is prerequisite for the implementation of surface tension. Due to the lack of appropriated FEM method for curvature calculation, a simpler and easier way to solve this problem is proposed. To avoid the complication in evaluation of the Laplacian operation on filling function, a specific method is proposed to evaluate curvature of the filling front by the simple and systematical procedures. Then the force of surface tension can be introduced directly in solution of the Navier-Stokes equation. Fig. 2 shows the surface tension force in the filling process of an
FIGURE 2
Distribution of surface tension force: (a) component in x direction; and (b) component in y direction (W – width of the mold; L – length of the mold; Fst – surface tension force).
injected polymer flow. By comparison between the magnitudes of surface tension force with the viscous force for a filling example in micro channels, the effects of surface tension in micro-injection molding were studied. It shows the importance of surface tension in micro-injection molding of sub-millimeter sizes, though this effect does not represent the significance in ordinary injection molding process. These numerical results are in close agreement with the data reported in physical experiments.
Microwave sintering of 17-4PH stainless steel powder and the resulting gradient in mechanical properties 17-4PH is a type of martensitic precipitation hardening stainless steel with high mechanical properties. Nowadays, most researches on sintering of 17-4PH stainless-steel focus on the ways by conventional resistive heating. For microwave sintering, many researches focused on other powder materials, such as ceramics, lead, tin, aluminum, copper, nickel, titanium, austenitic (316L) and ferritic (434L) stainless steels, etc. Only one investigation on the microwave processing of 17-4PH stainless-steel powder was found by the retrieves of literatures in the currently available resources. It was a preliminary study done by Bose et al. [3]. They found that Microwave sintering had not improved the mechanical properties compared to conventional sintering for 17-4PH stainless steel. To understand better the sintering properties of 17-4PH stainless steel, our work examined the densification and microstructure evolution of 17-4PH stainless steel powder processed by microwave sintering. The injected specimens subjected to 2.45 GHz microwaves in a multi-mode furnace. The influence factors in microwave sintering process were investigated, including the peak sintering temperature, holding time, heating rate and pre-sintering stages. After such a solid state sintering route, the evolutions of micro-structure, densification and mechanical response of the sintered specimens were studied. Comparison of the results between microwave sintering and conventional process was also studied. In this work, the authors confirmed that microwave sintering takes one tenth of the conventional sintering time to get the better
2 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006
MPRP-680; No of Pages 4
FIGURE 3
Vickers hardness values for each detected area (x1–x5) along the horizontal direction. (Small figure in the top right corner shows distribution of the detected areas on the polished section of a sintered specimen.)
results. The optimal peak temperature is 150–2008C lower. It results in the better densification, more homogeneous microstructure, higher mechanical properties, and more size shrinkage. The experiments proved also a remarkable fact for microwave sintering of the 17-4PH stainless steel powder. The heating rate must be set to an order of 30 8C/min. Lower heating rate leads to the poor results. The fast processing by microwave results in the gradient of mechanic properties in sintered bodies, as shown in Fig. 3. The prediction, evaluation and purposes of the gradient properties induced by microwave leads the studies to the more precise and profound insights. It is valuable to continue the studies on this nature for the application of functionally gradient materials produced by microwave sintering.
Mathematical modeling and full cycle simulation on multi-physics coupling process of microwave sintering Microwave sintering represents the coupling phenomena of multi-physical fields. It includes the coupling of electro-magnetic fields, thermal conduction and the densification process of sintered powders. The process involves three types of the physics. One is the transmission of microwave energy in the heating cavity. A part of the microwave energy is converted into heat energy, because of its dissipation during the transmission. The second one is the process of heat transfer. Because of
SPECIAL FEATURE
inhomogeneous distribution of the electric field in the heating cavity, it generates the heat in-homogeneously in the sintered material. Then there exists the process of heat transfer. The third one is the process of densification during sintering. The particles and grains of PIM material connect and fuse together. The pores among the particles reduce and disappear gradually. Macroscopically it appears to be the shrinkage of sintered products. The volume is reduced while the density increases. The evolution of density and temperature during sintering results in the variation of different parameters in physical equations. It results then the complicated coupling of different physics. In order to establish the mathematical model for microwave sintering, there exist five main aspects to be solved: 1. Solve Maxwell equation to get electromagnetic fields in cavity of the furnace; 2. Solve for distribution of the heat generation in process of microwave sintering; 3. Solution of heat transfer equation to get temperature field in the sintered body; 4. Solve the governing equations of sintering densification to get the structural response of sintered body; 5. Coupling of the Maxwell equation, heat transfer equation and mechanic equations. This coupling phenomenon can be shown clearly in Fig. 4. The true process of microwave sintering must be simulated under the condition that these complicated coupling are taken into account. Most of the actual literatures focus on the analysis of microwave heating and heat transfer, which couples with the evaluation of electromagnetic field. But none of them includes the densification behaviors of powder material. By analysis on the principles of microwave sintering, the mathematic model is established. The present work focuses on how to integrate such a sintering behavior in simulation to form a complete coupling cycle of the microwave sintering, from distribution of the electromagnetic field to the densification of sintered compacts. Based on a thermo-elasto-viscoplastic model, the work improves the previous work by Quinard, Song et al. in research team. The sintering behaviors of compacts formed by 316L stainless steel powders [4] and alumina powders [5] had been studied by means of the dilatometer and conventional sintering furnace. A macro model was established on the results to describe the shrinkage phenomena of thermal sintering process. Such a constitutive law is then employed into the model of microwave sintering process.
FIGURE 4
The coupling of multi-physics in simulation of the microwave sintering. 3 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006
SPECIAL FEATURE
Metal Powder Report Volume 00, Number 00 June 2016
MPRP-680; No of Pages 4 SPECIAL FEATURE
Metal Powder Report Volume 00, Number 00 June 2016
SPECIAL FEATURE
FIGURE 8
Evolution of temperature and relative density during the whole microwave sintering process.
FIGURE 5
Distribution of the electric field in empty cavity.
FIGURE 6
Temperature field in a cross section when the sintering undergoing 1500 s.
The numerical simulation has also been realized using the finite element solver COMSOL Multiphysics(C) platform. The RF module, heat transfer module, structure analysis module in COMSOL package is employed. The constitutive law, which describes sintering densification of CIM materials under high temperature, is implemented into the structure analysis. The coupling of multiphysics in microwave sintering is realized in simulation. It results in the 3D simulation for an example of microwave sintering in a multi-mode cavity. Fig. 5 investigates the distribution of the electric field in cavity of the microwave furnace. The temperature field on a cross section inside the PIM material, after heating 1500seconds, is shown in Fig. 6. At the same instant, the magnitude of resultant displacement is shown in Fig. 7. The evolution of temperature and relative density during the whole microwave sintering process can be seen in Fig. 8. The coupling in simulation of microwave electric field, thermal conduction and sintering densification of the powder material is achieved. This work provides a reliable way for the further investigations on microwave sintering. But it should be mentioned that the present work is still far from complete. It focuses on the modeling of the microwave sintering process and the methods for its simulation. It provides just an effective way for the further analysis and the achievement of knowledge on microwave sintering. For more accurate simulations, the true parameters and constitutive law of the MIM materials are required. Besides that, the external effect, such as boundary conditions, gravitation and friction, should be taken into account. It represents the great importance to study and achieve theses parameters and relationships by experiments.
Acknowledgments This work is financially supported by the National Natural Science Foundation of China (Grant No. 11502219) and Doctoral Research Foundation of Southwest University of Science and Technology (Grant No. 14zx7139). The authors also wish to thank Femto-ST Institute on experiment and simulation support. References
FIGURE 7
Resultant displacement on the cross section when the sintering undergoing 1500 s.
[1] A. Tong, Z. Wang, J. Comput. Phys. 221 (2) (2007) 506–523. [2] Z. Cheng, T. Barriere, B. Liu, et al. Polym. Eng. Sci. 49 (6) (2009) 1243–1252. [3] A. Bose, D. Agrawal, R. Dowding, International Conference on Powder Metallurgy and Particulate Materials, 2004, p. 53. [4] C. Quinard, J. Song, T. Barriere, et al. Powder Technol. 208 (2) (2011) 383–389. [5] J. Song, T. Barriere, J. Gelin, et al. Int. J. Powder Metal. 45 (3) (2009) 25–34.
4 Please cite this article in press as: J. Shi, et al., Met. Powder Rep. (2016), http://dx.doi.org/10.1016/j.mprp.2016.05.006