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A combined dislocation–cohesive zone model for fracture in nanocrystalline materials

Published online by Cambridge University Press:  25 January 2012

Yingguang Liu ,
Jianqiu Zhou  and
Tongde Shen
Yingguang Liu
Affiliation:
Department of Mechanical Engineering, Nanjing University of Technology, Nanjing 210009, Jiangsu, People’s Republic of China
Jianqiu Zhou*
Affiliation:
Department of Mechanical Engineering, Nanjing University of Technology, Nanjing 210009, Jiangsu, People’s Republic of China; and Department of Mechanical Engineering, Wuhan Institute of Technology, Wuhan 430070, Hubei, People’s Republic of China
Tongde Shen
Affiliation:
High-Tech Research Institute & State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing University of Technology, Nanjing 210009, Jiangsu, People’s Republic of China
*
a)Address all correspondence to this author. e-mail: zhouj@njut.edu.cn
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Abstract

A combined dislocation–cohesive zone model was proposed to describe the fracture toughness of nanocrystalline (nc) materials. In the framework of the model, cohesive stress near crack tip initiates edge dislocations, which move to the opposite grain boundaries. The emitted dislocations provide a shielding effect of the crack. The dependence of both the maximum number of dislocations, emitted by a crack, and the critical stress intensity factor on grain size d (ranging from 20 to100 nm) for Cu was calculated. The calculated results show that (i) nc materials have low fracture toughness, (ii) the critical stress intensity factor decreases with decreased grain size, and (iii) the grain size effect is not high; for instance, increasing the grain size from 20 to 100 nm increases the value of critical stress intensity factor only by 0.035 MPa/m1/2.

Keywords

NanostructureGrain sizeFracture
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 4 , 28 February 2012 , pp. 694 - 700
Copyright
Copyright © Materials Research Society 2012

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References

REFERENCES

1.Meyers, M.A., Mishra, A., and Benson, D.J.: Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 51, 427 (2006).Google Scholar
2.Shen, T.D., Koch, C.C., Tsui, T.Y., and Pharr, G.M.: On the elastic moduli of nanocrystalline Fe, Cu, Ni, and Cu–Ni alloys prepared by mechanical milling/alloying. J. Mater. Res. 10, 2892 (1995).Google Scholar
3.Kumar, K.S., Suresh, S., and Van Swygenhoven, H.: Mechanical behavior of nanocrystalline metals and alloys. Acta Mater. 51, 5743 (2003).CrossRefGoogle Scholar
4.Koch, C.C.: Structural nanocrystalline materials: An overview. J. Mater. Sci. 42, 1403 (2007).CrossRefGoogle Scholar
5.Lu, L., Wang, L.B., Ding, B.Z., and Lu, K.: High-tensile ductility in nanocrystalline copper. J. Mater. Res. 15, 270 (2000).Google Scholar
6.Dao, M., Lu, L., Asaro, R.J., De Hosson, J.T.M., and Ma, E.: Toward a quantitative understanding of mechanical behavior of nanocrystalline metals. Acta Mater. 55, 4041 (2007).Google Scholar
7.Liu, Y.G., Zhou, J.Q., Shen, T.D., and Hui, D.: Effects of ultrafine nanograins on the fracture toughness of nanocrystalline materials. J. Mater. Res. 26, 1734 (2011).CrossRefGoogle Scholar
8.Liu, Y.G., Zhou, J.Q., and Ling, X.: Impact of grain size distribution on the multiscale mechanical behavior of nanocrystalline materials. Mater. Sci. Eng., A 527, 1719 (2010).Google Scholar
9.Jiang, B. and Weng, G.J.: A generalized self-consistent polycrystal model for the yield strength of nanocrystalline materials. J. Mech. Phys. Solids 52, 1125 (2004).Google Scholar
10.Ovid’ko, I.A.: Review on the fracture processes in nanocrystalline materials. J. Mater. Sci. 42, 1694 (2007).Google Scholar
11.Kuntz, J.D., Zhan, G.D., and Mukherjee, A.K.: Nanocrystalline-matrix ceramic composite for improved fracture toughness. MRS Bull. 29, 22 (2004).CrossRefGoogle Scholar
12.Zhao, Y., Qian, J., Daemen, L.L., Pantea, C., Zhang, J., Voronin, G.A., and Zerda, T.W.: Enhancement of fracture toughness in nanostructured diamond–SiC composites. Appl. Phys. Lett. 84, 1356 (2004).CrossRefGoogle Scholar
13.Pei, Y.T., Galvan, D., and De Hosson, J.T.M.: Nanostructure and properties of TiC/a-C: H composite coatings. Acta Mater. 53, 4505 (2005).CrossRefGoogle Scholar
14.Singh, A., Tang, L., Dao, M., Lu, L., and Suresh, S.: Fracture toughness and fatigue crack growth characteristics of nanotwinned copper. Acta Mater. 59, 2437 (2011).CrossRefGoogle Scholar
15.Singh, A., Tang, L., Dao, M., Lu, L., and Suresh, S.: Enhanced fracture toughness and strength in bulk nanocrystalline Cu with nanoscale twin bundles. Acta Mater. 57, 6215 (2009).Google Scholar
16.Mirshams, R., Whang, S.H., Xiao, C.H., and Yin, W.M.: R-curve characterization of the fracture toughness of nanocrystalline nickel thin sheets. Mater. Sci. Eng., A 315, 21 (2001).CrossRefGoogle Scholar
17.Gutkin, M.Y. and Ovid’ko, I.A.: Homogeneous nucleation of dislocation loops in nanocrystalline metals and ceramics. Acta Mater. 56, 1642 (2008).Google Scholar
18.Bobylev, S.V., Mukherjee, A.K., Ovid’ko, I.A., and Sheinerman, A.G.: Effects of intergrain sliding on crack growth in nanocrystalline materials. Int. J. Plast. 26, 1629 (2010).CrossRefGoogle Scholar
19.Ovid’ko, I.A. and Sheinerman, A.G.: Ductile vs. brittle behavior of pre-cracked nanocrystalline and ultrafine-grained materials. Acta Mater. 58, 5286 (2010).Google Scholar
20.Liu, Y.G., Zhou, J.Q., Wang, L., Zhang, S., and Wang, Y.: Grain size dependent fracture toughness of nanocrystalline materials. Mater. Sci. Eng., A 528, 4615 (2011).Google Scholar
21.Bobylev, S.V., Morozov, N.F., and Ovid’ko, I.A.: Cooperative grain boundary sliding and migration process in nanocrystalline solids. Phys. Rev. Lett. 105, 055504 (2010).CrossRefGoogle ScholarPubMed
22.Morozov, N.F., Ovid’ko, I.A., Sheinerman, A.G., and Aifantis, E.C.: Special rotational deformation as a toughening mechanism in nanocrystalline solids. J. Mech. Phys. Solids 58, 1088 (2010).CrossRefGoogle Scholar
23.Yang, W. and Wang, H.T.: Brittle versus ductile transition of nanocrystalline metals. Int. J. Solids Struct. 45, 3897 (2008).Google Scholar
24.Yang, F. and Yang, W.: Crack growth versus blunting in nanocrystalline metals with extremely small grain size. J. Mech. Phys. Solids 57, 305 (2009).CrossRefGoogle Scholar
25.Needleman, A.: A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54, 525 (1987).CrossRefGoogle Scholar
26.Tvergaard, V. and Hutchinson, J.W.: The relation between crack growth resistance and fracture process parameters in elastic–plastic solids. J. Mech. Phys. Solids 40, 1377 (1992).CrossRefGoogle Scholar
27.Tvergaard, V. and Hutchinson, J.W.: The influence of plasticity on mixed mode interface toughness. J. Mech. Phys. Solids 41, 1119 (1993).CrossRefGoogle Scholar
28.Tvergaard, V. and Hutchinson, J.W.: On the toughness of ductile adhesive joints. J. Mech. Phys. Solids 44, 789 (1996).CrossRefGoogle Scholar
29.Cleveringa, H.H.M., van der Giessen, E., and Needleman, A.: A discrete dislocation analysis of mode-I crack growth. J. Mech. Phys. Solids 48, 1133 (2000).Google Scholar
30.O’Day, M.P. and Curtin, W.A.: Bimaterial interface fracture: A discrete dislocation model. J. Mech. Phys. Solids 53, 359 (2005).Google Scholar
31.Chng, A.G., O’Day, M.P., Curtin, W.A., Tay, A.A.O., and Lim, K.M.: Fracture in confined thin films: A discrete dislocation study. Acta Mater. 54, 1017 (2006).CrossRefGoogle Scholar
32.Broedling, N.G., Hartmaier, A., and Gao, H.J.: A combined dislocation–cohesive zone model for fracture in a confined ductile layer. Int. J. Fract. 140, 169 (2006).CrossRefGoogle Scholar
33.Broedling, N.G., Hartmaier, A., and Gao, H.J.: Fracture toughness of layered structures: Embrittlement due to confinement of plasticity. Eng. Fract. Mech. 75, 3743 (2008).CrossRefGoogle Scholar
34.Bhandakkar, T.K., Chng, A.C., Curtin, W.A., and Gao, H.J.: Dislocation shielding of a cohesive crack. J. Mech. Phys. Solids 58, 530 (2010).Google Scholar
35.Deshpande, V.S., Needleman, A., and van der Giessen, E.: A discrete dislocation analysis of near-threshold fatigue crack growth. Acta Mater. 49, 3189 (2001).CrossRefGoogle Scholar
36.Deshpande, V.S., Needleman, A., and van der Giessen, E.: Discrete dislocation modeling of fatigue-crack propagation. Acta Mater. 50, 831 (2002).CrossRefGoogle Scholar
37.Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100 (1960).Google Scholar
38.Chandra, N., Li, H., Shet, C., and Ghonem, H.: Some issues in the application of cohesive zone models for metal–ceramic interfaces. Int. J. Solids Struct. 39, 2827 (2002).Google Scholar
39.Scheider, I., Rajendran, M., and Banerjee, A.: Comparison of different stress-state dependent cohesive zone models applied to thin-walled structures. Eng. Fract. Mech. 78, 534 (2011).Google Scholar
40.Chokshi, A.H., Rosen, A., Karch, J., and Gleiter, H.: On the validity of the Hall–Petch relationship in nanocrystalline materials. Scr. Metall. Mater. 23, 1679 (1989).CrossRefGoogle Scholar
41.Kim, D.K. and Okazaki, K.: Processing of superconducting composite materials by electro-discharge compaction. Mater. Sci. Forum 88–90, 553 (1992).CrossRefGoogle Scholar
42.Shen, T.D., Schwarz, R.B., Feng, S., Swadener, J.G., Huang, J.Y., Tang, M., Zhang, J.Z., Vogel, S.C., and Zhao, Y.S.: Effect of solute segregation on the strength of nanocrystalline alloys: Inverse Hall–Petch relation. Acta Mater. 55, 5007 (2007).Google Scholar
43.Palumbo, G., Erb, U., and Aust, K.T.: Triple line disclination effects on the mechanical behaviour of materials. Scr. Metall. Mater. 24, 2347 (1990).Google Scholar
44.Zhang, T.Y. and Li, J.C.M.: Image forces and shielding effects of an edge dislocation near a finite length crack. Acta Metall. Mater. 39, 2739 (1991).Google Scholar
45.Lin, I.H. and Thomson, R.: Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Metall. 34, 187 (1986).CrossRefGoogle Scholar
46.Ovid’ko, I.A.: Deformation and diffusion modes in nanocrystalline materials. Int. Mater. Rev. 50, 65 (2005).Google Scholar
47.Liu, Y.G., Zhou, J.Q., Shen, T.D., and Hui, D.: Grain rotation dependent fracture toughness of nanocrystalline materials. Mater. Sci. Eng., A 528, 7684 (2011).Google Scholar
48.Li, H. and Ebrahimi, F.: Transition of deformation and fracture behaviors in nanostructured face-centered-cubic metals. Appl. Phys. Lett. 84, 4307 (2004).Google Scholar
49.Li, H. and Ebrahimi, F.: Ductile-to-brittle transition in nanocrystalline metals. Adv. Mater. 17, 1969 (2005).Google Scholar
50.Ebrahimi, F., Liscano, A.J., Kong, D., Zhai, Q., and Li, H.: Fracture of bulk face centered cubic metallic nanostructures. Rev. Adv. Mater. Sci. 13, 33 (2006).Google Scholar