International Journal of Fracture

, Volume 183, Issue 2, pp 241–258 | Cite as

An analysis of competing toughening mechanisms in layered and particulate solids

  • Giovanni Noselli
  • Vikram S. Deshpande
  • Norman A. Fleck
Original Paper


The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus \(90^{\circ }\) symmetric kinking is considered for an isotropic, homogeneous solid with weak interfaces. Each interface is treated as a cohesive zone of finite strength and toughness. Third, the degree of toughening associated with crack multiplication is assessed for a particulate solid comprising isotropic elastic grains of hexagonal shape, bonded by cohesive zones of finite strength and toughness. The study concludes with the prediction of R-curves for a mode I crack in a multi-layer stack of elastic and elastic–plastic solids. A detailed comparison of the potency of the above mechanisms and their practical application are given. In broad terms, crack tip kinking can be highly potent, whereas multiple cracking is difficult to activate under quasi-static conditions. Plastic dissipation can give a significant toughening in multi-layers especially at the nanoscale.


Toughening mechanisms Multi-layered composites Particulate solids Crack resistance curves 



The authors are grateful to DARPA for their financial support through Grant W91CRB-10-1-005 titled “A micro-cellular solids approach to thermo-structural materials with controlled architecture”.


  1. Bertoldi K, Bigoni D, Drugan WJ (2008) Nacre: an orthotropic and bimodular elastic material. Compos Sci Technol 68:1363–1375CrossRefGoogle Scholar
  2. Cao HC, Evans AG (1991) On crack extension in ductile/brittle laminates. Acta Metall Mater 39:2997–3005CrossRefGoogle Scholar
  3. Chan KS, He M-Y, Hutchinson JW (1993) Cracking and stress redistribution in ceramic layered composites. Mater Sci Eng A 167:57–64CrossRefGoogle Scholar
  4. Cocks ACF, Ashby MF (1980) Intergranular fracture during power-law creep under multiaxial stresses. Metal Sci 14:395–402CrossRefGoogle Scholar
  5. Cocks ACF, Ashby MF (1982) Creep fracture by coupled power-law creep and diffusion under multiaxial stress. Metal Sci 16:465–474CrossRefGoogle Scholar
  6. Cocks ACF, Pan J (1993) Void growth ahead of a dominant crack in a material which deforms by Coble creep. Int J Fract 60:249–265CrossRefGoogle Scholar
  7. Currey JD (1977) Mechanical properties of mother of pearl in tension. Proc R Soc Lond B 196:443–463CrossRefGoogle Scholar
  8. Dean RH, Hutchinson JW (1980) Quasi-static crack growth in small-scale yielding. In: Fracture mechanichs. Proceedings of the twelfth national symposium of fracture mechanics, ASTM STP 700, American Society for Testing and Materials, pp 383–405Google Scholar
  9. de la Osa R, Estevez R, Olagnon C, Chevalier J, Vignoud L, Tallaron C (2009) Cohesive zone model and slow crack growth in ceramic polycrystals. Int J Fract 158:157–167CrossRefGoogle Scholar
  10. Evans AG, Faber KT (1984) Crack-growth resistance of microcracking brittle materials. J Am Ceram Soc 67:255–260CrossRefGoogle Scholar
  11. Espinosa HD, Juster AL, Latourte FJ, Loh OY, Gregoire D, Zavattieri PD (2011) Tablet-level origin of toughening in abalone shells and translation to synthetic composite materials. Nat Commun 2:1–9CrossRefGoogle Scholar
  12. Freund LB (1998) Dynamic fracture mechanics. Cambridge University Press, CambridgeGoogle Scholar
  13. Frost HJ, Ashby MF (1982) Deformation mechanism maps. The plasticity and creep of metals and ceramics. Pergamon Press, New YorkGoogle Scholar
  14. Gao H, Ji B, Jäger IL, Arzt E, Fratzl P (2003) Materials become insensitive to flaws at the nanoscale: lesson from nature. Proc Natl Acad Sci USA 100:5597–5600CrossRefGoogle Scholar
  15. Gao H (2006) Application of fracture mechanics concepts to hierarchical biomechanics of bone and bone-like materials. Int J Fract 138:101–137CrossRefGoogle Scholar
  16. Gordon JE (1968) The new science of strong materials: or why you don’t fall through the floor. Penguin Books, LondonGoogle Scholar
  17. He M-Y, Hutchinson JW (1989a) Crack deflection at an interface between dissimilar elastic materials. Int J Solid Struct 25:1053–1067CrossRefGoogle Scholar
  18. He M-Y, Hutchinson JW (1989b) Kinking of a crack out of an interface. J Appl Mech 56:270–278CrossRefGoogle Scholar
  19. He M-Y, Heredia FE, Wissuchek DJ, Shaw MC, Evans AG (1993) The mechanics of crack growth in layered materials. Acta Metall Mater 41:1223–1228CrossRefGoogle Scholar
  20. He M-Y, Wu B, Suo Z (1994) Notch-sensitivity and shear bands in brittle matrix composites. Acta Metall Mater 42:3065–3070CrossRefGoogle Scholar
  21. Hull D, Clyne TW (1996) An introduction to composite materials. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  22. Hutchinson JW (1987) Crack tip shielding by micro-cracking in brittle solids. Acta Metall Mater 35:1605–1619CrossRefGoogle Scholar
  23. Jackson AP, Vincent JFV, Turner RM (1988) The mechanical design of nacre. Proc R Soc Lond B 234:415–440CrossRefGoogle Scholar
  24. Jackson AP, Vincent JFV, Turner RM (1990) Comparison of nacre with other ceramic composites. J Mater Sci 25:3173–3178CrossRefGoogle Scholar
  25. Jang D, Li X, Gao H, Greer JR (2012) Deformation mechanisms in nanotwinned metal nano pillars. Nat Nanotechnol 7:594–601CrossRefGoogle Scholar
  26. Kaim Y, Onck PR, van der Giessen E (2004) Simulations of crack meandering and crack branching in intergranular creep fracture. In: Advanced fracture mechanics for life and safety assessments. Proceedings of the 15th European Conference on Fracture, ECF15Google Scholar
  27. Kaim Y, Onck PR, van der Giessen E (2005) The topology of fracture surfaces in intergranular creep fracture. In: Proceedings of the 11th international conference on fracture 2005, ICF11, pp 3090–3095Google Scholar
  28. Kelly A (1973) Strong solids. Clarendon Press, OxfordGoogle Scholar
  29. Kreher W, Pompe W (1981) Increased fracture toughness of ceramics by energy-dissipative mechanisms. J Mater Sci 16:694–706CrossRefGoogle Scholar
  30. Lawn BR, Wilshaw TR (1975) Fracture of brittle solids. Cambridge University Press, CambridgeGoogle Scholar
  31. Lin A, Meyers MA (2005) Growth and structure in abalone shell. Mater Sci Eng A 390:27–41CrossRefGoogle Scholar
  32. Lo KK (1978) Analysis of branched cracks. J Appl Mech 45:797–802CrossRefGoogle Scholar
  33. Lubliner J (1990) Plasticity theory. Pearson Education, Upper Saddle River, NJ Google Scholar
  34. Needleman A, Rice JR (1980) Plastic creep flow effects in the diffusive cavitation of grain boundaries. Acta Metall Mater 28:1315–1332CrossRefGoogle Scholar
  35. Pan J, Cocks ACF (1993) The effect of grain-size on the stress and velocity fields ahead of a crack in a material which deforms by Coble creep. Int J Fract 60:121–134CrossRefGoogle Scholar
  36. Rice JR (1979) Plastic creep flow processes in fracture at elevated temperature. In: Time dependent fracture of materials at elevated temperature. U.S. Department of Energy Report CONF 790236 UC-25, pp 130–145Google Scholar
  37. Rose LRF (1986) Microcrack interaction with a main crack. Int J Fract 31:233–242CrossRefGoogle Scholar
  38. Rühle M, Evans AG, McMeeking RM, Charalambides PG, Hutchinson JW (1987) Microcrack toughening in aluminia/zirconia. Acta Metall Mater 35:2701–2710CrossRefGoogle Scholar
  39. Shabir Z, Van der Giessen E, Duarte CA, Simone A (2011) The role of cohesive properties on intergranular crack propagation in brittle polycrystals. Model Simul Mater Sci Eng 19:1–21CrossRefGoogle Scholar
  40. Shao Y, Zhao H-P, Feng X-Q, Gao H (2012) Discontinuous crack-bridging model for fracture toughness analysis of nacre. J Mech Phys Solids 60:1400–1419CrossRefGoogle Scholar
  41. Shaw MC, Clyne TW, Cocks ACF, Fleck NA, Pateras SK (1996) Cracking patterns in metal-ceramic laminates: effects of plasticity. J Mech Phys Solids 44:801–821CrossRefGoogle Scholar
  42. Shum DKM, Hutchinson JW (1990) On toughening by microcracks. Mech Mater 9:83–91CrossRefGoogle Scholar
  43. Suo Z, Shih C, Varias AG (1993) A theory for cleavage cracking in the presence of plastic flow. Acta Metall Mater 41:1551–1557CrossRefGoogle Scholar
  44. Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40:1377–1397CrossRefGoogle Scholar
  45. Tvergaard V (1997) Cleavage crack growth resistance due to plastic flow around a near-tip dislocation-free region. J Mech Phys Solids 45:1007–1023CrossRefGoogle Scholar
  46. Wang RZ, Suo Z, Evans AG, Yao N, Aksay IA (2001) Deformation mechanisms in nacre. J Mater Res 16:2485–2493CrossRefGoogle Scholar
  47. Xu X-P, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42:1397–1434CrossRefGoogle Scholar
  48. Youa Z, Lib X, Guic L, Lua Q, Zhuc T, Gao H, Lua L (2013) Plastic anisotropy and associated deformation mechanisms in nanotwinned metals. Acta Mater 61:217–227CrossRefGoogle Scholar
  49. Zhang Z, Zhang Y-W, Gao H (2011) On optimal hierarchy of load-bearing biological materials. Proc R Soc Lond B 278:519–525CrossRefGoogle Scholar
  50. Zhu T, Gao H (2012) Plastic deformation mechanism in nanotwinned metals: an insight from molecular dynamics and mechanistic modeling. Scr Mater 66:843–848CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Giovanni Noselli
    • 1
  • Vikram S. Deshpande
    • 1
  • Norman A. Fleck
    • 1
  1. 1.Cambridge University Engineering DepartmentCambridgeUK

Personalised recommendations