Journal of Materials Science

, Volume 48, Issue 12, pp 4191–4204 | Cite as

Prediction models for the yield strength of particle-reinforced unimodal pure magnesium (Mg) metal matrix nanocomposites (MMNCs)

  • Chang-Soo KimEmail author
  • Il Sohn
  • Marjan Nezafati
  • J. B. Ferguson
  • Benjamin F. Schultz
  • Zahra Bajestani-Gohari
  • Pradeep K. Rohatgi
  • Kyu Cho


Particle-reinforced metal matrix nanocomposites (MMNCs) have been lauded for their potentially superior mechanical properties such as modulus, yield strength, and ultimate tensile strength. Though these materials have been synthesized using several modern solid- or liquid-phase processes, the relationships between material types, contents, processing conditions, and the resultant mechanical properties are not well understood. In this paper, we examine the yield strength of particle-reinforced MMNCs by considering individual strengthening mechanism candidates and yield strength prediction models. We first introduce several strengthening mechanisms that can account for increase in the yield strength in MMNC materials, and address the features of currently available yield strength superposition methods. We then apply these prediction models to the existing dataset of magnesium MMNCs. Through a series of quantitative analyses, it is demonstrated that grain refinement plays a significant role in determining the overall yield strength of most of the MMNCs developed to date. Also, it is found that the incorporation of the coefficient of thermal expansion mismatch and modulus mismatch strengthening mechanisms will considerably overestimate the experimental yield strength. Finally, it is shown that work-hardening during post-processing of MMNCs employed by many researchers is in part responsible for improvement to the yield strength of these materials.


Strengthening Mechanism Orowan Strengthen Orowan Mechanism Modulus Mismatch Geometrically Necessary Dislocation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is primarily supported by the Research Growth Initiative (RGI) Award from University of Wisconsin-Milwaukee (UWM). Partial support from the U.S. Army Research Laboratory (US ARL) under Cooperative Agreement No. W911NF-08-2-0014 is also acknowledged. The views, opinions, and conclusions made in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.


  1. 1.
    Ye J, Han BQ, Lee Z, Ahn B, Nutt SR, Schoenung JM (2005) Scr Mater 53:481. doi: 10.1016/j.scriptamat.2005.05.004 CrossRefGoogle Scholar
  2. 2.
    Tang F, Hagiwara M, Schoenung JM (2005) Scr Mater 53:619. doi: 10.1016/j.scriptamat.2005.05.034 CrossRefGoogle Scholar
  3. 3.
    Li Y, Zhao YH, Ortalan V, Liu W, Zhang ZH, Vogt RG, Browning ND, Lavernia EJ, Schoenung JM (2009) Mater Sci Eng A 527:305. doi: 10.1016/j.msea.2009.07.067 CrossRefGoogle Scholar
  4. 4.
    Li Y, Lin YJ, Xiong YH, Schoenung JM, Lavernia EJ (2011) Scr Mater 64:133. doi: 10.1016/j.scriptamat.2010.09.027 CrossRefGoogle Scholar
  5. 5.
    Hassan SF, Gupta M (2004) Mater Sci Technol 20:1383. doi: 10.1179/026708304X3980 CrossRefGoogle Scholar
  6. 6.
    Tun KS, Gupta M (2008) J Mater Sci 43:4503. doi: 10.1007/s10853-008-2649-3 CrossRefGoogle Scholar
  7. 7.
    Hassan SF, Tan MJ, Gupta M (2008) Mater Sci Eng A 486:56. doi: 10.1016/j.msea.2007.08.045 CrossRefGoogle Scholar
  8. 8.
    Paramsothy M, Hassan SF, Srikanth N, Gupta M (2009) Mater Sci Eng A 527:162. doi: 10.1016/j.msea.2009.07.054 CrossRefGoogle Scholar
  9. 9.
    Yang Y, Lan J, Li X (2004) Mater Sci Eng A 380(2004):378. doi: 10.1016/j.msea.2004.03.073 Google Scholar
  10. 10.
    Cao G, Kobliska J, Konishi H, Li X (2008) Metall Mater Trans A 39A:880. doi: 10.1007/s11661-007-9453-6 CrossRefGoogle Scholar
  11. 11.
    Dutkiewicz J, Litynska L, Maziarz W, Haberko K, Pyda W, Kanciruk A (2009) Cryst Res Technol 44:1163. doi: 10.1002/crat.200900455 CrossRefGoogle Scholar
  12. 12.
    Ahn JH, Kim YJ, Chung H (2008) Rev Adv Mater Sci 18:329Google Scholar
  13. 13.
    Mohammad Sharifi E, Karimzadeh F, Enayati MH (2011) Mater Des 32:3263. doi: 10.1016/j.matdes.2011.02.033 CrossRefGoogle Scholar
  14. 14.
    Mazahery A, Abdizadeh H, Baharvandi HR (2009) Mater Sci Eng A 518:61. doi: 10.1016/j.msea.2009.04.014 CrossRefGoogle Scholar
  15. 15.
    Yao B, Hofmeister C, Patterson T, Sohn YH, Van den Bergh M, Delahanty T, Cho K (2010) Compos A 41:933. doi: 10.1016/j.compositesa.2010.02.013 CrossRefGoogle Scholar
  16. 16.
    Schultz BF, Ferguson JB, Rohatgi PK (2011) Mater Sci Eng A 530:87. doi: 10.1016/j.msea.2011.09.042 CrossRefGoogle Scholar
  17. 17.
    Ferguson JB, Sheykh-Jaberi F, Kim CS, Rohatgi PK, Cho K (2012) Mater Sci Eng 558:193. doi: 10.1016/j.msea.2012.07.111 CrossRefGoogle Scholar
  18. 18.
    Mallick A, Vedantam S, Lu L (2009) Mater Sci Eng A 515:14. doi: 10.1016/j.msea.2009.03.002 CrossRefGoogle Scholar
  19. 19.
    Wang YN, Huang JC (2007) Mater Trans 48:184. doi: 10.2320/matertrans.48.184 CrossRefGoogle Scholar
  20. 20.
    Mann G, Griffiths JR, Caceres CH (2004) J Alloys Compd 378:188. doi: 10.1016/j.jallcom.2003.12.052 CrossRefGoogle Scholar
  21. 21.
    Ono N, Nowak R, Miura S (2003) Mater Lett 58:39. doi: 10.1016/S0167-577X(03)00410-5 CrossRefGoogle Scholar
  22. 22.
    Wang HY, Xue ES, Xiao W, Liu Z, Li JB, Jiang QC (2011) Mater Sci Eng A 528:8790. doi: 10.1016/j.msea.2011.07.052 CrossRefGoogle Scholar
  23. 23.
    Andersson P, Caceres CH, Koike J (2003) Mater Sci Forum 419–422:123. doi: 10.4028/ CrossRefGoogle Scholar
  24. 24.
    Yuan W, Panigrahi SK, Su JQ, Mishra RS (2011) Scr Mater 65:994. doi: 10.1016/j.scriptamat.2011.08.028 CrossRefGoogle Scholar
  25. 25.
    Kim HK (2009) Mater Sci Eng 515:66. doi: 10.1016/j.msea.2009.02.039 CrossRefGoogle Scholar
  26. 26.
    Afrin N, Chen DL, Cao X, Jahazi M (2008) Mater Sci Eng A 472:179. doi: 10.1016/j.msea.2007.03.018 CrossRefGoogle Scholar
  27. 27.
    Han BQ, Dunand DC (2000) Mater Sci Eng A 227:297. doi: 10.1016/S0921-5093(99)00074-X Google Scholar
  28. 28.
    Bohlen J, Dobron P, Meza Garcia E, Chmelik F, Lukac P, Letzig D, Kainer KU (2005) Adv Eng Mater 8:422. doi: 10.1016/j.msea.2006.02.469 CrossRefGoogle Scholar
  29. 29.
    Elsayed A, Kondoh K, Imai H, Umeda J (2010) Mater Des 31:2444. doi: 10.1016/j.matdes.2009.11.054 CrossRefGoogle Scholar
  30. 30.
    Hagihara K, Kinoshita A, Sugino Y, Yamasaki M, Kawamura Y, Yasuda HY, Umakoshi Y (2010) Acta Mater 58:6282. doi: 10.1016/j.actamat.2010.07.050 CrossRefGoogle Scholar
  31. 31.
    Zener C, quoted by Smith CS (1948) Trans AIME 175:15Google Scholar
  32. 32.
    Szaraz Z, Trojanova Z, Cabbibo M, Evangelista E (2007) Mater Sci Eng A 462:225. doi: 10.1016/j.msea.2006.01.182 CrossRefGoogle Scholar
  33. 33.
    Habibnejad-Korayem M, Mahmudi R, Poole WJ (2009) Mater Sci Eng A 519:198. doi: 10.1016/j.msea.2009.05.001 CrossRefGoogle Scholar
  34. 34.
    Zhang Z, Yu H, Wang S, Wang H, Min G (2010) J Mater Sci Technol 26:151. doi: 10.1016/S1005-0302(10)60025-4 CrossRefGoogle Scholar
  35. 35.
    Nguyen QB, Gupta M (2008) Compos Sci Technol 68:2185. doi: 10.1016/j.compscitech.2008.04.020 CrossRefGoogle Scholar
  36. 36.
    Miller WS, Humphreys FJ (1991) Scr Metall 25:33. doi: 10.1016/0956-716X(91)90349-6 CrossRefGoogle Scholar
  37. 37.
    Ashby MF (1968) The theory of the critical shear stress and work hardening of dispersion-hardened crystals. In: Proceeding of second Bolton landing conference on oxide dispersion strengthening. Gordon and Breach, Science Publishers, Inc., New York, p 143Google Scholar
  38. 38.
    Sun Y, Choi H, Konishi H, Pikhovich V, Hathaway R, Chen L, Li X (2012) Mater Sci Eng A 546:284. doi: 10.1016/j.msea.2012.03.070 CrossRefGoogle Scholar
  39. 39.
    Goh CS, Wei J, Lee LC, Gupta M (2007) Acta Mater 55:5115. doi: 10.1016/j.actamat.2007.05.032032 CrossRefGoogle Scholar
  40. 40.
    Robson JD, Stanford N, Barnett MR (2010) Scr Mater 63:23. doi: 10.1016/j.scriptamat.2010.06.026 CrossRefGoogle Scholar
  41. 41.
    Rosalie JM, Somekawa H, Singh A, Mukai T (2012) Mater Sci Eng A 539:230. doi: 10.1016/j.msea.2012.01.087 CrossRefGoogle Scholar
  42. 42.
    Zeng X, Zou H, Zhai C, Ding W (2006) Mater Sci Eng A 424:40. doi: 10.1016/j.msea.2006.02.021 CrossRefGoogle Scholar
  43. 43.
    Ferguson JB, Lopez H, Kongshaug D, Schultz B, Rohatgi P (2012) Metall Mater Trans A 43:2110. doi: 10.1007/s11661-011-1029-9 CrossRefGoogle Scholar
  44. 44.
    Dai LH, Ling Z, Bai YL (2001) Compos Sci Technol 61:1057. doi: 10.1016/S0266-3538(00)00235-9 CrossRefGoogle Scholar
  45. 45.
    Vogt R, Zhang Z, Li Y, Bonds M, Browning ND, Lavernia EJ, Schoenung JM (2009) Scr Mater 61:1052. doi: 10.1016/j.scriptamat.2009.08.025 CrossRefGoogle Scholar
  46. 46.
    Redsten AM, Klier EM, Brown AM, Dunand DC (1995) Mater Sci Eng A 201:88. doi: 10.1016/0921-5093(94)09741-0 CrossRefGoogle Scholar
  47. 47.
    Nardone VC (1987) Scr Metall 21:1313. doi: 10.1016/0036-9748(87)90105-0 CrossRefGoogle Scholar
  48. 48.
    Nardone VC, Prewo KM (1986) Scr Metall 20:43. doi: 10.1016/0036-9748(86)90210-3 CrossRefGoogle Scholar
  49. 49.
    Ramakrishnan N (1996) Acta Metall 44:69. doi: 10.1016/1359-6454(95)00150-9 Google Scholar
  50. 50.
    Kocks UF, Argon AS, Ashby MF (1975) Prog Mater Sci 19:224Google Scholar
  51. 51.
    Ebeling R, Ashby MF (1966) Phil Mag 13:805CrossRefGoogle Scholar
  52. 52.
    Lagerpusch U, Mohles V, Baither D, Anczykowski B, Nembach E (2000) Acta Mater 48:3647. doi: 10.1016/S1359-6454(00)00172-5 CrossRefGoogle Scholar
  53. 53.
    Chawla N, Andres C, Jones JW, Allison JE (1998) Metall Mater Trans A29:2843. doi: 10.1007/s11661-998-0325-5 CrossRefGoogle Scholar
  54. 54.
    Chawla N, Habel U, Shen YL et al (2000) Metall Mater Trans A31:531. doi: 10.1007/s11661-000-0288-7 CrossRefGoogle Scholar
  55. 55.
    Chawla N, Shen YL (2001) Adv Eng Mater 3:357. doi: 10.1002/1527-2648(200106)3:6<357:AID-ADEM357>3.3.CO;2-9 CrossRefGoogle Scholar
  56. 56.
    Arsenault RJ (1984) Mater Sci Eng 64:171. doi: 10.1016/0025-5416(84)90101-0 CrossRefGoogle Scholar
  57. 57.
    Clyne TW, Withers PJ (1995) An Introduction to Metal Matrix Composites. Cambridge University Press, CambridgeGoogle Scholar
  58. 58.
    Hull D, Clyne TW (1996) An introduction to composite materials. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  59. 59.
    Lilholt H (1985) Deformation of multi-phase and particle containing materials. In: Proceedings of the 4th rise international symposium on metallurgy and materials science, Roskilde, DenmarkGoogle Scholar
  60. 60.
    Sanaty-Zadeh A (2012) Mater Sci Eng A 531:112. doi: 10.1016/j.msea.2011.10.043 CrossRefGoogle Scholar
  61. 61.
    Zhang Z, Chen DL (2006) Scr Mater 54:1321. doi: 10.1016/j.scriptamat.2005.12.017 CrossRefGoogle Scholar
  62. 62.
    Hassan SF, Gupta M (2006) Compos Struct 72:19. doi: 10.1016/j.compstruct.2004.10.008 CrossRefGoogle Scholar
  63. 63.
    Hassan SF, Gupta M (2008) J Alloy Compd 457:244. doi: 10.1016/j.jallcom.2007.03.058 CrossRefGoogle Scholar
  64. 64.
    Wong WLE, Karthik S, Gupta M (2005) J Mater Sci 40:3395. doi: 10.1007/s10853-005-0419-z CrossRefGoogle Scholar
  65. 65.
    Hassan SF, Gupta M (2005) Mater Sci Eng A 392:163. doi: 10.1007/s11661-005-0344-4 CrossRefGoogle Scholar
  66. 66.
    Hassan SF, Gupta M (2007) J Alloy Compd 429:176. doi: 10.1016/j.jallcom.2006.04.033 CrossRefGoogle Scholar
  67. 67.
    Hassan SF (2011) Mater Sci Eng A 528:5484. doi: 10.1016/j.msea.2011.03.063 CrossRefGoogle Scholar
  68. 68.
    Hassan SF (2006) Creation of new magnesium-based material using different types of reinforcements. Dissertation, National University of SingaporeGoogle Scholar
  69. 69.
    Hassan SF, Gupta M (2006) Mater Sci Eng A 425:22. doi: 10.1016/j.msea.2006.03.029 CrossRefGoogle Scholar
  70. 70.
    Tun KS, Gupta M (2007) Compos Sci Technol 67:2657. doi: 10.1016/j.compscitech.2007.03.006 CrossRefGoogle Scholar
  71. 71.
    Misra A, Hirth JP, Hoagland RG (2005) Acta Mater 53:4817. doi: 10.1016/j.actamat.2005.06.025 CrossRefGoogle Scholar
  72. 72.
    Wong WLE, Gupta M (2007) Compos Sci Technol 67:1541. doi: 10.1016/j.compscitech.2006.07.015 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Chang-Soo Kim
    • 1
    Email author
  • Il Sohn
    • 2
  • Marjan Nezafati
    • 1
  • J. B. Ferguson
    • 1
  • Benjamin F. Schultz
    • 1
  • Zahra Bajestani-Gohari
    • 1
  • Pradeep K. Rohatgi
    • 1
  • Kyu Cho
    • 3
  1. 1.Materials Science and Engineering DepartmentUniversity of Wisconsin-MilwaukeeMilwaukeeUSA
  2. 2.Materials Science and Engineering DepartmentYonsei UniversitySeoulSouth Korea
  3. 3.U.S. Army Research LaboratoryWeapons and Materials Research DirectorateAberdeen Proving GroundUSA

Personalised recommendations