Skip to main content
SpringerLink
Log in

A New Venue Toward Predicting the Role of Hydrogen Embrittlement on Metallic Materials

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

This paper presents a new crystal plasticity formulation to predict the role of hydrogen embrittlement on the mechanical behavior of metallic materials. Specifically, a series of experiments were carried out to monitor the role of hydrogen interstitial content on the uniaxial tensile deformation response of iron alloyed with hydrogen, and the classical Voce hardening scheme was modified to account for the shear stresses imposed on arrested dislocations due to the surrounding hydrogen interstitials. The proposed set of physically grounded crystal plasticity formulations successfully predicted the deformation response of iron in the presence of different degrees of hydrogen embrittlement. Moreover, the combined experimental and modeling effort presented herein opens a new venue for predicting the alterations in the performance of metallic materials, where the hydrogen embrittlement is unavoidable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. S. Wang, N. Hashimoto, Y. Wang, and S. Ohnuki: Acta Mater., 2013, vol. 61, pp. 4734–42.

    Article  Google Scholar 

  2. H. Kotake, R. Matsumoto, S. Taketomi, and N. Miyazaki: Int. J. Press. Vessel. Pip., 2008, vol. 85, pp. 540–49.

    Article  Google Scholar 

  3. M. Stashchuk and M. Dorosh: Int. J. Hydrogen Energy, 2012, vol. 37, pp. 14687–96.

    Article  Google Scholar 

  4. R.A. Siddiqui and H.A. Abdullah: J. Mater. Process. Technol., 2005, vol. 170, pp. 430–35.

    Article  Google Scholar 

  5. T. Kanezaki, C. Narazaki, Y. Mine, S. Matsuoka, and Y. Murakami: Int. J. Hydrogen Energy, 2008, vol. 33, pp. 2604–19.

    Article  Google Scholar 

  6. S. Jothi, T.N. Croft, and S.G.R. Brown: Int. J. Hydrogen Energy, 2014, vol. 39, pp. 20671–88.

    Article  Google Scholar 

  7. M. B. Djukic, V. Sijacki Zeravcic, G. Bakic, A. Sedmak, and B. Rajicic: Procedia Mater. Sci., 2014, vol. 3, pp. 1167–72. DOI:10.1016/j.mspro.2014.06.190.

    Article  Google Scholar 

  8. W.H. Johnson: Proc R Soc L., 1875, vol. 23, pp. 168–79.

    Article  Google Scholar 

  9. G.P. Tiwari, A. Bose, J.K. Chakravartty, S. L. Wadekar, and M. K. Totlani: 2000, vol. 286, pp. 269–81.

    Google Scholar 

  10. H. Kimura, H. Matsui: Scr. Metall., 1987, vol. 21, pp. 319–24.

    Article  Google Scholar 

  11. W.Ko, J. Bae, J. Shim, and B. Lee: Int. J. Hydrogen Energy, 2012, vol. 37, pp. 13583–93.

    Article  Google Scholar 

  12. A. Toshimitsu Yokobori, T. Uesugi, M. Sendoh, and M. Shibata: Strength Fract. Complex. 1, 2003, vol. 1, pp. 187–204.

  13. I.M. Dmytrakh, O.D. Smiyan, A.M. Syrotyuk, and O.L. Bilyy: Int. J. Fatigue, 2013, vol. 50, pp. 26–32.

    Article  Google Scholar 

  14. Y. Mine, C. Narazaki, K. Murakami,S. Matsuokai, and Y. Murakami: Int. J. Hydrogen Energy, 2009, vol. 34, pp. 1097–1107.

    Article  Google Scholar 

  15. J.A. Clum: Scr. Metall., 1975, vol. 9, pp. 51–58.

    Article  Google Scholar 

  16. K.A. Nibur, D.F. Bahr, and B.P. Somerday: Acta Mater., 2006, vol. 54, pp. 2677–84.

    Article  Google Scholar 

  17. P.J. Ferreira, I.M. Robertson, and H.K. Birnbaum: Acta Mater., 1999, vol. 47, pp. 2991–98.

    Article  Google Scholar 

  18. J.R Rice: J. Mater. Sci., 1992, vol. 40, pp. 239–71.

  19. A. Turnbull: Corros. Sci., 1993, vol. 34, pp. 921–60.

    Article  Google Scholar 

  20. C.A. Zapffe: J Iron Steel Inst, 1946, vol. 154, pp. 123–31.

    Google Scholar 

  21. A.S. Tetelman and W.D. Robertson: Trans Met. Soc AIME, 1962, vol. 224, pp. 775–83.

    Google Scholar 

  22. N.J. Petch and P. Stables: Nature, 1952, vol. 169, pp. 842–43.

    Article  Google Scholar 

  23. R. Thompson: J. Mater. Sci., 1978, vol. 13, pp. 128–42.

    Article  Google Scholar 

  24. D. Shih, I.M. Robertson, and H.K. Birnbaum: Acta Metall., 1988, vol. 36, pp. 111–24.

    Article  Google Scholar 

  25. S. Gahr, M.L. Grossbeck, and H.K. Birnbaum: Acta Metall. Mater., 1977, vol. 25, pp. 125–34.

    Article  Google Scholar 

  26. A.R. Troiano: Trans. ASM, 1960, vol. 52, pp. 54–80.

    Google Scholar 

  27. R.A. Oriani and P.H. Josephic: Acta Metall., 1974, vol. 22, pp. 1065–74.

    Article  Google Scholar 

  28. H.K. Birnbaum: Scr. Metall., 1994, vol. 31, pp. 149–53.

    Article  Google Scholar 

  29. P. Sofronis and H.K. Birnbaum: J Mech Phys Solids, 1995, vol. 43, pp. 49–90.

    Article  Google Scholar 

  30. H.K. Birnbaum and P. Sofronis: Mater. Sci. Eng. A, 1994, vol. 176, pp. 191–202.

    Article  Google Scholar 

  31. T. Tabata and H.K. Birnbaum: Scr. Metall., 1983, vol. 17, pp. 947–50.

    Article  Google Scholar 

  32. J. Lufrano, P. Sofronis, and H.K. Birnbaum: J Mech Phys Solids, 1996, vol. 44, pp. 179–205.

    Article  Google Scholar 

  33. W. Qin, J. A. Szpunar, and J. Kozinski: Acta Mater., 2012, vol. 60, pp. 4845–55.

    Article  Google Scholar 

  34. D. Delafosse and T. Magnin: Eng. Fract. Mech., 2001, vol. 68, pp. 693–729.

    Article  Google Scholar 

  35. A.G. Varias and A.R. Massih: J. Mech. Phys. Solids, 2002, vol. 50, pp. 1469–1510.

    Article  Google Scholar 

  36. R.A. Oriani and P.H. Josephic: Acta Metall., 1977, vol. 25, pp. 979–88.

    Article  Google Scholar 

  37. E.A. Steigerwald, F.W. Schaller, and A.R. Troiano: Trans Met. Soc AIME, 1960, vol. 218, pp. 832–41.

    Google Scholar 

  38. A. Taha and P. Sofronis: Eng. Fract. Mech., 2001, vol. 68, pp. 803–37.

    Article  Google Scholar 

  39. P. Sofronis, Y. Liang, and N. Aravas: Eur. J. Mech. - A/Solids, 2001, vol. 20, pp. 857–72.

    Article  Google Scholar 

  40. I.M. Robertson and H.K. Birnbaum: Acta Mater., 1986, vol. 34, pp. 353–66.

    Article  Google Scholar 

  41. J. Toribio, V. Kharin, M. Lorenzo, and D. Vergara: Corros. Sci., 2011, vol. 53, pp. 3346–55.

    Article  Google Scholar 

  42. T. Doshida and K. Takai: Acta Mater., 2014, vol. 79, pp. 93–107.

    Article  Google Scholar 

  43. T. Michler and J. Naumann: Int. J. Hydrogen Energy, 2008, vol. 33, pp. 2111–22.

    Article  Google Scholar 

  44. T. Dieudonné, L. Marchetti, M. Wery, J. Chêne, C. Allely, P. Cugy, and C.P. Scott:5Corros. Sci., 2014, vol. 82, pp. 218–26.

  45. C. Borchers, T. Michler, and A. Pundt: Adv Eng Mater, 2008, vol. 10, pp. 11–23.

    Article  Google Scholar 

  46. A.R. Troiano: in Am. Soc. Met., 1973, pp. 3–15.

  47. F. Galliano, E. Andrieu, C. Blanc, J. Cloue, D. Connetable, and G. Odemer: Mater. Sci. Eng. A, 2014, vol. 611, pp. 370–82.

    Article  Google Scholar 

  48. D.F. Teter, I.M. Robertson, and H.K. Birnbaum: 2001, vol. 49, pp. 4313–23.

  49. W.W. Gerberich, D.D. Stauffer, and P. Sofronis: in Int. Hydrog. Conf. - Eff. Hydrog. Mater., 2009, pp. 38–45.

  50. Y. Chen, X. Wan, F. Li, Q. Wang, and Y. Liu: Mater. Sci. Eng. A, 2007, vol. 466, pp. 156–59.

    Article  Google Scholar 

  51. T. Boniszewski and G.C. Smith: Acta Metall. Mater., 1963, vol. 11, pp. 165–78.

    Article  Google Scholar 

  52. J.W. Watson, Y.Z. Shen, and M. Meshii: Metall. Mater. Trans. A, 1988, vol. 19, pp. 2299–2304.

    Article  Google Scholar 

  53. O. Takakuwa, Y. Mano, and H. Soyama: Int. J. Hydrogen Energy, 2014, vol. 39, pp. 6095–6103.

    Article  Google Scholar 

  54. R.A. Oriani: Acta Metall., 1970, vol. 18, pp. 147–57.

    Article  Google Scholar 

  55. D.C. Ahn, P. Sofronis, and R. Dodds: Int. J. Fract., 2007, vol. 145, pp. 135–57.

    Article  Google Scholar 

  56. A. Krom, A.H.M. Koers, R.W.J. Bakker: J. Mech. Phys. Solids, 1999, vol. 47, pp. 971–92.

    Article  Google Scholar 

  57. S. Taketomi, R. Matsumoto, and N. Miyazaki: Int. J. Mech. Sci., 2010, vol. 52, pp. 334–38.

    Article  Google Scholar 

  58. J. Lufrano and P. Sofronis: Acta Mater., 1998, vol. 46, pp. 1519–26.

    Article  Google Scholar 

  59. B. Strnadel: Eng. Fract. Mech., 1998, vol. 61, pp. 299–310.

    Article  Google Scholar 

  60. P. Sofronis and H.K. Birnbaum: J Mech Phys Solids, 1995, vol. 43, pp. 49–90.

    Article  Google Scholar 

  61. Y. Liang, P. Sofronis, and R.H. Dodds: Mater. Sci. Eng. A, 2004, vol. 366, pp. 397–411.

    Article  Google Scholar 

  62. J.C. Sobotka, R.H. Dodds, and P. Sofronis: Int. J. Solids Struct., 2009, vol. 46, pp. 4095–4106.

    Article  Google Scholar 

  63. R. Miresmaeili, M. Ogino, T. Nakagawa, and H. Kanayama: Int. J. Hydrogen Energy, 2010, vol. 35, pp. 1506–14.

    Article  Google Scholar 

  64. X. Yu, F. Gou, B. Li, and Ni Zhang: Fusion Eng. Des., 2014, vol. 89, pp. 1096–1100.

  65. C.V.D. Leo and L. Anand: Int. J. Plast., 2013, vol. 43, pp. 42–69.

    Article  Google Scholar 

  66. A. van den Beukel: Phys. Status Solidi., 1975, vol. 30, pp. 197–206.

    Article  Google Scholar 

  67. M.A. Soare and W.A. Curtin: Acta Mater., 2008, vol. 56, pp. 4091–4101.

    Article  Google Scholar 

  68. Y. Estrin and P.G. McCormick: Acta Metall. Mater., 1991, vol. 39, pp. 2977–83.

    Article  Google Scholar 

  69. N. Anjabin, A.K. Taheri, and H.S. Kim: Mater. Sci. Eng. A, 2013, vol. 585, pp. 165–73.

    Article  Google Scholar 

  70. P.G. McCormick: Acta Metall., 1988, vol. 36, pp. 3061–67.

    Article  Google Scholar 

  71. J.P. Hirth and B. Carnahan: Acta Metall., 1978, vol. 26, pp. 1795–1803.

    Article  Google Scholar 

  72. M.C. Uslu and D. Canadinc: J. Mater. Sci., 2010, vol. 45, pp. 1683–87.

    Article  Google Scholar 

  73. A.H. Cottrell and M.A. Jaswon: Proc. Phys. Cos. L. A, 1949, vol. 199, pp. 104–14.

    Google Scholar 

  74. J.D. Eshelby: Proc R Soc L. A, 1957, vol. 241, pp. 376–96.

    Article  Google Scholar 

  75. F.M. Mazzolai and H.K. Birnbaum: J. Phys. F Met. Phys, 1985, vol. 15, pp. 507–23.

    Article  Google Scholar 

  76. J. Lufrano and P. Sofronis: Int. J. Solids Struct., 1996, vol. 33, pp. 1709–23.

    Article  Google Scholar 

  77. F. Springer and C. Schwink: Scr. Metall., 1995, vol. 32, pp. 1771–76.

    Article  Google Scholar 

  78. C. Fressengeas, A. J. Beaudoin, M. Lebyodkin, L.P. Kubin, and Y. Estrin: Mater. Sci.Eng. A, 2005, vol. 400-401, pp. 226–30.

    Article  Google Scholar 

  79. J.L. Chaboche, A. Gaubert, P. Kanouté, A. Longuet, F. Azzouz, and M. Mazière: Int. J. Plast., 2013, vol. 46, pp. 1–22.

    Article  Google Scholar 

  80. M.A. Soare and W.A. Curtin: Acta Mater., 2008, vol. 56, pp. 4046–61.

    Article  Google Scholar 

  81. S. Narayanan, D.L. McDowell, and T. Zhu: J. Mech. Phys. Solids, 2014, vol. 65, pp. 54–68.

    Article  Google Scholar 

  82. H. Peter: Mater. Sci. Eng. A, 1996, vol. 207, pp. 208–15.

    Article  Google Scholar 

  83. C.J. Bayley, W.A.M. Brekelmans, and M.G.D. Geers: Int. J. Solids Struct., 2006,vol. 43, pp. 7268–86.

    Article  Google Scholar 

  84. B.Bal, B. Gumus and D. Canadinc: J. Eng. Mater. Technol., 2016, vol. 183(3), pp. 031012–031012-8

  85. N. Naveen Kumar, R. Tewari, P.V. Durgaprasad, B.K. Dutta, and G.K. Dey: Comput. Mater. Sci., 2013, vol. 77, pp. 260–63.

  86. A. Dilwar, M. Nasreen, and M.Z. Butt: J. Mater. Sci., 2011, vol. 46, pp. 3812–21.

    Article  Google Scholar 

  87. A. Argon: Strengthening Mechanisms in Crystal Plasticity. Oxford University Press, 2008.

  88. R. Gröger, V. Racherla, J. Basani, and V. Vitek: Acta Mater., 2008, vol. 56, pp. 5412–25.

    Article  Google Scholar 

  89. A. Latapie and D. Farkas: Model. Simul. Mater. Sci. Eng, 2003, vol. 11, pp. 745–53.

    Article  Google Scholar 

  90. V. Shastry and D. Farkas: Model. Simul. Mater. Sci. Eng, 1996, vol. 4, pp. 473–92.

    Article  Google Scholar 

  91. S. Naamane, G. Monnet, and B. Devincre: Int. J. Plast., 2010, vol. 26, pp. 84–92.

    Article  Google Scholar 

  92. F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, and D Raabe: Acta Mater., 2010, vol. 58, pp. 1152–1211.

    Article  Google Scholar 

  93. J. Friedel: Dislocations, 1964.

  94. K. Kang, J. Yin, and W. Cai: J. Mech. Phys. Solids, 2014, vol. 62, pp. 181–93.

    Article  Google Scholar 

  95. F. Springer, A. Nortmann, and C. Schwing: Phys Status Solidi A, 1998, vol. 170, pp. 63–81.

    Article  Google Scholar 

  96. U.F. Kocks, A.S. Argon, and M.F. Ashby: Prog.Mater.Sci, 1975, vol. 19, pp. 1–281.

    Article  Google Scholar 

  97. K. Aenne, M. Anxin, and H. Alexander: Acta Mater., 2012, vol. 60, pp. 3894–3901.

    Article  Google Scholar 

  98. C.R. Weinberger, C.C. Battaile, T.E. Buchheit, and E.A. Holm: Int. J. Plast., 2012, vol. 37, pp. 16–30.

    Article  Google Scholar 

  99. H.Jörn: Int. J. Plast., 1999, vol. 15, pp. 605–24.

    Article  Google Scholar 

  100. S.Y Yang and W. Tong: Mater. Sci. Eng. A, 2001, vol. 309-310, pp. 300–303.

    Article  Google Scholar 

  101. Z.Y. Huang, J. Chaboche, Q.Y. Wang, D. Wagner, and C. Bathias: Mater. Sci. Eng. A, 2014, vol. 589, pp. 34–40.

    Article  Google Scholar 

  102. J. Wang, I.J. Beyerlein, and C.N. Tomé: Int. J. Plast., 2014, vol. 56, pp. 156–72.

    Article  Google Scholar 

  103. L. Evers: J. Mech. Phys. Solids, 2004, vol. 52, pp. 2379–2401.

    Article  Google Scholar 

  104. L.P Evers, W.a.M Brekelmans, and M.G.D Geers: Int. J. Solids Struct., 2004, vol. 41, pp. 5209–30.

    Article  Google Scholar 

  105. B. Liu, P. Eisenlohr, F. Roters, and D. Raabe: Acta Mater., 2012, vol. 60, pp. 5380–90.

    Article  Google Scholar 

  106. H. Lim, M.G. Lee, J.H. Kim, B.L. Adams, and R.H. Wagoner: Int. J. Plast., 2011, vol. 27.

  107. E.Bayraktar, F.a. Khalid, and C. Levaillant: J. Mater. Process. Technol., 2004, vol. 147, pp. 145–54.

    Article  Google Scholar 

  108. I. J. Beyerlein, N. A. Mara, J. Wang, J. S. Carpenter, S. J. Zheng, W. Z. Han, R. F. Zhang, K. Kang, T. Nizolek and T. M. Pollock: JOM, 2012, vol. 64, pp. 1192-207.

    Article  Google Scholar 

  109. N.A. Fleck, G.M. Muller, M.F. Ashby, and J.W. Hutchinson: Acta Metall., 1994, vol. 42, pp. 475–487.

    Article  Google Scholar 

  110. D.M. Duan, N.Q. Wu, W.S. Slaughter, and S.X. Mao: Mater. Sci. Eng. A, 2001, vol. 303, p. 241.

    Article  Google Scholar 

  111. H. Mughrabi: Mater. Sci. Eng. A, 2004, vol. 387-389, pp. 209–13.

    Article  Google Scholar 

  112. S. Brinckmann, T. Siegmund, and Y. Huang: Int. J. Plast., 2006, vol. 22, pp. 1784–97.

    Article  Google Scholar 

  113. E. Voce: J. Inst. Met, 1948, vol. 74, pp. 537–62.

    Google Scholar 

  114. D. Canadinc, H. Sehitoglu, H.J. Maier, and Y.I. Chumlyakov: Acta Mater., 2005, vol. 53, pp. 1831–42.

    Article  Google Scholar 

  115. S.Chou and W.Tsai: Mater. Chem. Phys., 1999, vol. 60, pp. 137–42.

    Article  Google Scholar 

  116. I.M. Robertson: Eng. Fract. Mech., 2001, vol. 68, pp. 671–92.

    Article  Google Scholar 

  117. T.E. García, C. Rodríguez, F.J. Belzunce, I Peñuelas, and B Arroyo: Mater. Sci. Eng. A, 2015, vol. 626, pp. 342–51.

    Article  Google Scholar 

  118. H. Matsui, H. Kimura, and S. Moriya: Mater. Sci. Eng., 1979, vol. 49, pp. 207–16.

    Article  Google Scholar 

  119. J.S. Lee, A. Kimura, S. Ukai and M. Fujiwara: J. Nucl. Mater., 2004, vol. 333, pp. 1122–26.

    Article  Google Scholar 

  120. R.A. Oriani: Berichte Der Bunsengesellschaft, 1972, vol. 76, pp. 848–57.

    Google Scholar 

  121. D.C. Ahn, P. Sofronis and R.H. Dodds Jr.: Int. J. Hydrogen Energy., 2007, vol. 32, pp. 3734-42.

    Article  Google Scholar 

  122. Y. Liang, D.C. Ahn, P. Sofronis, R.H. Dodds Jr. and D. Bammann: Mech Mate, 2008, vol. 40, pp. 115-32.

    Article  Google Scholar 

  123. T. Tabata and H.K. Birnbaum: Scripta. Metall., 1984, vol. 18, pp. 231-36.

    Article  Google Scholar 

  124. D. Canadinc, E. Biyikli, T. Niendorf, and H.J. Maier: Adv. Eng. Mater., 2011, vol. 13, pp. 281–87.

    Article  Google Scholar 

  125. J.P. Chateau, D. Delafosse and T. Magnin: Acta Mater., 2002, vol. 50, pp. 1523–38.

    Article  Google Scholar 

  126. M. Ichiba, J. Sakai, T. Doshida, and K. Takai: Scr. Mater., 2015, vol. 102, pp. 59–62.

    Article  Google Scholar 

  127. Y. Qi, H. Luo, S. Zheng, C. Chen, and D. Wang: Corros. Sci., 2013, vol. 69, pp. 164–74.

    Article  Google Scholar 

  128. A. Koester, A. Ma and A. Hartmaier: Acta Mater., 2012, vol. 60, pp. 3894-3901.

    Article  Google Scholar 

  129. T. Yalcinkaya, W.A.M Brekelmans, and M.G.D Geers: Model. Simul. Mater. Sci. Eng2, 2008, vol. 16, p. 085007.

  130. M. Tang, L.P. Kubin and G.R. Canova: Acta Metall. Mater., 1998, vol. 46, pp. 3221-35.

    Article  Google Scholar 

  131. R.A. Lebensohn and C.N. Tomé: Acta Metall. Mater., 1993, vol. 41, p. 2611.

    Article  Google Scholar 

  132. D. Roylance: Mechanical Properties of Materials, MIT: 2008, pp. 1–128.

Download references

Acknowledgments

This study was supported by the Koç University TÜPRAŞ Energy Center (KÜTEM) seed funding program. XRD analyses were carried out at Koç University Surface Technology and Science Center (KUYTAM). A.U. acknowledges the BAGEP Award by the Science Academy of Turkey.

Author information

Authors and Affiliations

  1. Advanced Materials Group (AMG), Department of Mechanical Engineering, Koç University, Sariyer, 34450, Istanbul, Turkey

    Burak Bal (Graduate Student) & Demircan Canadinc (Associate Professor, Associate Director)

  2. Department of Chemical and Biological Engineering, Koç University, Sariyer, 34450, Istanbul, Turkey

    Ibrahim Sahin (Graduate Student) & Alper Uzun (Assistant Professor)

  3. Surface Science and Technology Center (KUYTAM), Koç University, Sariyer, 34450, Istanbul, Turkey

    Demircan Canadinc (Associate Professor, Associate Director)

Authors
  1. Burak Bal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ibrahim Sahin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alper Uzun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Demircan Canadinc
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Demircan Canadinc.

Additional information

Manuscript submitted December 27, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bal, B., Sahin, I., Uzun, A. et al. A New Venue Toward Predicting the Role of Hydrogen Embrittlement on Metallic Materials. Metall Mater Trans A 47, 5409–5422 (2016). https://doi.org/10.1007/s11661-016-3708-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-016-3708-z

Keywords

Search

Navigation