Effective Yield Strength for Material Powder Consolidated at Stage II Compaction
ABSTRACT
This work is concerned with the estimation from the outside of effective yield strength for the stage II consolidated material package of axisymmetric solid particles. Once an appropriate simple representative axisymmetric unit cell is chosen, the kinematical approach of the yield design homogenization method is used in order to obtain external estimates which has been found depending on the loading history (isostatic and closed die compactions) as well as on the relative density of the material powder. For comparison purpose, finite element simulations that describe the behavior of spherical elastic plastic particles uniformly distributed inside the material powder are carried out.
This work is concerned with the estimation from the outside of effective yield strength for the stage II consolidated material package of axisymmetric solid particles. Once an appropriate simple representative axisymmetric unit cell is chosen, the kinematical approach of the yield design homogenization method is used in order to obtain external estimates which has been found depending on the loading history (isostatic and closed die compactions) as well as on the relative density of the material powder. For comparison purpose, finite element simulations that describe the behavior of spherical elastic plastic particles uniformly distributed inside the material powder are carried out.
KEYWORDS
Stage II Compaction, Kinematic Approach, Relevant Failure Mechanism, Unit Cell Model, Effective Yield Strength, Finite Element Analysis
Stage II Compaction, Kinematic Approach, Relevant Failure Mechanism, Unit Cell Model, Effective Yield Strength, Finite Element Analysis
Cite this paper
Siad, L. and Gangloff, S. (2014) Effective Yield Strength for Material Powder Consolidated at Stage II Compaction. World Journal of Mechanics, 4, 273-288. doi: 10.4236/wjm.2014.49028.
Siad, L. and Gangloff, S. (2014) Effective Yield Strength for Material Powder Consolidated at Stage II Compaction. World Journal of Mechanics, 4, 273-288. doi: 10.4236/wjm.2014.49028.
References
[1] M.F. Ashby Back Ground Reading: Hot Isostatic Pressing and Sintering. Internal Report, Cambridge University Engineering Department, Cambridge, 1990. [2] McMeeking, R.M. and Kuhn, L.T. (1992) A Diffusional Creep Law for Powder Compacts. Acta Metallurgica et Materialia, 40, 961-969.
http://dx.doi.org/10.1016/0956-7151(92)90073-N [3] Helle, H.S., Easterling, K.E. and Ashby, M.F. (1985) Hot-Isostatic Pressing Diagrams: New Developments. Acta Metallurgica, 33, 2163-2174.
http://dx.doi.org/10.1016/0001-6160(85)90177-4 [4] Brewin, P.R., Coube, O., Doremus, P. and Tweed, J.H. (2008) Modelling of Powder Die Compaction. Springer-Verlag, London. [5] Gu, C., Kim, M. and Anand, L. (2001) Constitutive Equations for Metal Powder: Application to Powder Forming Process. International Journal of Plasticity, 17, 147-209.
http://dx.doi.org/10.1016/S0749-6419(00)00029-2 [6] Fleck, N.A., Kuhn, L.T. and McMeeking, R.M. (1992) Yielding of Metal Powder Bonded by Isolated Contacts. Journal of the Mechanics and Physics of Solids, 40, 1139-1162.
http://dx.doi.org/10.1016/0022-5096(92)90064-9 [7] Fleck, N.A. (1995) On the Cold Compaction of Powders. Journal of the Mechanics and Physics of Solids, 43, 1409-1431.
http://dx.doi.org/10.1016/0022-5096(95)00039-L [8] Bishop, J.F.W. and Hill, R. (1951) A Theoretical Derivation of the Plastic Properties of a Polycrystalline Face-Centred Metal. Philosophical Magazine Series 6, 42, 1298-1307.
http://dx.doi.org/10.1080/14786444108561385 [9] Xin, X.J., Jayaraman, P., Daehn, G.S. and Wagoner, R.H. (2003) Investigation of Yield Surface of Monolithic and Composite Powders by Explicit Finite Element Simulation. International Journal of Mechanical Sciences, 45, 707-723.
http://dx.doi.org/10.1016/S0020-7403(03)00107-3 [10] Salencon, J. (2013) Yield Design. ISTE Ltd. and John Wiley & Sons, Inc., London, Hoboken.
http://dx.doi.org/10.1002/9781118648988 [11] Salencon, J. (1993) Yield Design: A Survey of the Theory. CISM Lectures Series, No. 332, Springer, Wien, New York, 1-44. [12] Suquet, P. (1983) Analyse limite et homogeneisation. Comptes Rendus de l’Academie des Sciences, 1355-1358. [13] de Buhan, P. (1986) A Fundamental Approach to the Yield Design of Reinforced Soil Structures. Chap. 2, Yield Design Homogenization Theory for Periodic Media. Doctorat d’Etat, Universite Pierre et Marie Curie, Paris (In French). [14] Benabbes, A., Siad, L., Dormieux, L. and Liu, W.K. (2010) Yield Design Homogenization Method for Compaction of Monosized Spherical Powders. International Journal of Applied Mechanics, 2, 457-4883.
http://dx.doi.org/10.1142/S1758825110000615 [15] Ogbonna, N. and Fleck, N.A. (1995) Compaction of an Array of Spherical Particles. Acta Metallurgica et Materialia, 43, 603-620.
http://dx.doi.org/10.1016/0956-7151(94)00286-Q [16] Mesarovic, S.D. and Padbidri, J. (2005) Minimal Kinematic Boundary Conditions for Simulations of Disordered Microstructures. Philosophical Magazine, 85, 65-78.
http://dx.doi.org/10.1080/14786430412331313321 [17] Trillat, M., Pastor, J. and Francescato, P. (2006) Yield Criterion for Porous Media with Spherical Voids. Mechanics Research Communications, 33, 320-328.
http://dx.doi.org/10.1016/j.mechrescom.2005.05.013 [18] Brown, S.B. and Weber, G.G.A. (1988) A Constitutive Model for the Compaction of Metal Powders. Proceedings of International Powder Metallurgical Conference, 18, 465-476. [19] Brown, S. and Abou-Chedid, G. (1994) Yield Behaviour of Metal Powder Bonded Assemblages. Journal of the Mechanics and Physics of Solids, 42, 383-399.
http://dx.doi.org/10.1016/0022-5096(94)90024-8
[1] M.F. Ashby Back Ground Reading: Hot Isostatic Pressing and Sintering. Internal Report, Cambridge University Engineering Department, Cambridge, 1990. [2] McMeeking, R.M. and Kuhn, L.T. (1992) A Diffusional Creep Law for Powder Compacts. Acta Metallurgica et Materialia, 40, 961-969.
http://dx.doi.org/10.1016/0956-7151(92)90073-N [3] Helle, H.S., Easterling, K.E. and Ashby, M.F. (1985) Hot-Isostatic Pressing Diagrams: New Developments. Acta Metallurgica, 33, 2163-2174.
http://dx.doi.org/10.1016/0001-6160(85)90177-4 [4] Brewin, P.R., Coube, O., Doremus, P. and Tweed, J.H. (2008) Modelling of Powder Die Compaction. Springer-Verlag, London. [5] Gu, C., Kim, M. and Anand, L. (2001) Constitutive Equations for Metal Powder: Application to Powder Forming Process. International Journal of Plasticity, 17, 147-209.
http://dx.doi.org/10.1016/S0749-6419(00)00029-2 [6] Fleck, N.A., Kuhn, L.T. and McMeeking, R.M. (1992) Yielding of Metal Powder Bonded by Isolated Contacts. Journal of the Mechanics and Physics of Solids, 40, 1139-1162.
http://dx.doi.org/10.1016/0022-5096(92)90064-9 [7] Fleck, N.A. (1995) On the Cold Compaction of Powders. Journal of the Mechanics and Physics of Solids, 43, 1409-1431.
http://dx.doi.org/10.1016/0022-5096(95)00039-L [8] Bishop, J.F.W. and Hill, R. (1951) A Theoretical Derivation of the Plastic Properties of a Polycrystalline Face-Centred Metal. Philosophical Magazine Series 6, 42, 1298-1307.
http://dx.doi.org/10.1080/14786444108561385 [9] Xin, X.J., Jayaraman, P., Daehn, G.S. and Wagoner, R.H. (2003) Investigation of Yield Surface of Monolithic and Composite Powders by Explicit Finite Element Simulation. International Journal of Mechanical Sciences, 45, 707-723.
http://dx.doi.org/10.1016/S0020-7403(03)00107-3 [10] Salencon, J. (2013) Yield Design. ISTE Ltd. and John Wiley & Sons, Inc., London, Hoboken.
http://dx.doi.org/10.1002/9781118648988 [11] Salencon, J. (1993) Yield Design: A Survey of the Theory. CISM Lectures Series, No. 332, Springer, Wien, New York, 1-44. [12] Suquet, P. (1983) Analyse limite et homogeneisation. Comptes Rendus de l’Academie des Sciences, 1355-1358. [13] de Buhan, P. (1986) A Fundamental Approach to the Yield Design of Reinforced Soil Structures. Chap. 2, Yield Design Homogenization Theory for Periodic Media. Doctorat d’Etat, Universite Pierre et Marie Curie, Paris (In French). [14] Benabbes, A., Siad, L., Dormieux, L. and Liu, W.K. (2010) Yield Design Homogenization Method for Compaction of Monosized Spherical Powders. International Journal of Applied Mechanics, 2, 457-4883.
http://dx.doi.org/10.1142/S1758825110000615 [15] Ogbonna, N. and Fleck, N.A. (1995) Compaction of an Array of Spherical Particles. Acta Metallurgica et Materialia, 43, 603-620.
http://dx.doi.org/10.1016/0956-7151(94)00286-Q [16] Mesarovic, S.D. and Padbidri, J. (2005) Minimal Kinematic Boundary Conditions for Simulations of Disordered Microstructures. Philosophical Magazine, 85, 65-78.
http://dx.doi.org/10.1080/14786430412331313321 [17] Trillat, M., Pastor, J. and Francescato, P. (2006) Yield Criterion for Porous Media with Spherical Voids. Mechanics Research Communications, 33, 320-328.
http://dx.doi.org/10.1016/j.mechrescom.2005.05.013 [18] Brown, S.B. and Weber, G.G.A. (1988) A Constitutive Model for the Compaction of Metal Powders. Proceedings of International Powder Metallurgical Conference, 18, 465-476. [19] Brown, S. and Abou-Chedid, G. (1994) Yield Behaviour of Metal Powder Bonded Assemblages. Journal of the Mechanics and Physics of Solids, 42, 383-399.
http://dx.doi.org/10.1016/0022-5096(94)90024-8