Skip to main content
Log in

A finite element analysis of fracture initiation in ductile/brittle periodically layered composites

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

A near-tip plane strain finite element analysis of a crack terminating at and normal to the interface in a laminate consisting of alternate brittle and ductile layers is conducted under mode-I loading. The studies are carried out for a system representing steel/alumina composite laminate. The Gurson constitutive model, which accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence, is employed within the framework of small deformation plasticity theory. Evolution of plastic zone and damage in the ductile layer is monitored with increasing load. High plastic strain localization and microvoid damage accumulation are found to occur along the brittle/ductile interface at the crack-tip. Fracture initiation in the ductile phase is predicted and the conditions for crack renucleation in the brittle layer ahead of the crack are established for the system under consideration. Ductile fracture initiation has been found to occur before plasticity spreads in multiple ductile layers. Effects of material mismatch and yield strength on the plastic zone evolution are briefly discussed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • ABAQUS. (1995). Version 5.5. Hibbit, Karlsson and Sorensen, Inc. Pawtucket, RI, U.S.A.

  • Anderson, H. (1977). Analysis of a model for void growth and coalescence ahead of a moving crack tip. Journal of Mechanical Physics and Solids 25, 217–233.

    Article  ADS  Google Scholar 

  • Aravas, N. and McMeeking, R.M. (1985). Microvoid growth and failure in the ligament between a hole and a blunt crack tip. International Journal of Fracture 29, 21–38.

    Article  Google Scholar 

  • Ashby, M.F., Blunt, F.J. and Bannister, M. (1989). Flow characteristics of highly constrained metal wires. Acta Metallurgica 37, 1847–1857.

    Article  Google Scholar 

  • Ballarini, R. and Luo, H.A. (1991). Green's functions for dislocations in bonded strips and related crack problems. International Journal of Fracture 50, 239–262.

    Google Scholar 

  • Ballarini, R., Charalambides, P.G. and Islam, S. (1995). Near–tip dual length scale mechanics of mode–I cracking in laminated brittle matrix composites. International Journal of Fracture 70, 275–304.

    Article  Google Scholar 

  • Berg, C.A. (1970). Inelastic Behavior of Solids(Edited by M.F. Kanninen, W.F. Adler, A.R. Rosenfield, and R.I. Jaffee), 171–209. McGraw–Hill.

  • Brown, L.M. and Embury, J.D. (1973). The microstructure and design of alloy. Proceedings of the 3rd International Conference on the Strength of Metals and Alloys. Cambridge, England.

    Google Scholar 

  • Cao, H.C. and Evans, A.G. (1991). On crack extension in ductile/brittle laminates. Acta Metallurgica 39, 2997– 3005.

    Article  Google Scholar 

  • Chao, Y.J., Sutton, M.A. and Wu, R. (1993). Determination of the asymptotic crack tip fields for a crack perpendicular to an interface between elastic–plastic materials. Acta Mechanica 100, 13–36.

    Article  MATH  Google Scholar 

  • Chu, C.C. and Needleman, A. (1980). Void nucleation effects in biaxially stretched sheets. Journal of Engineering and Material Technology 102, 249–256.

    Article  Google Scholar 

  • Cook, T.S. and Erdogan, F. (1972). Stresses in bonded materials with a crack perpendicular to the interface. International Journal of Engineering Science 10, 677.

    Article  MATH  Google Scholar 

  • Cormeau, I.C. (1975). Numerical stability in quasi–static elasto/visco–plasticity. International Journal of Numerical Methods and Engineering 9, 109–127.

    Article  MATH  MathSciNet  Google Scholar 

  • Cox, T.B. and Low, J.R. (1974). An investigation of the plastic fracture of AISI 4340 and 18Ni–200 grade maraging steels. Metallurgical Transactions 5, 1457–1470.

    ADS  Google Scholar 

  • Dalgleish, B.J., Trumble, K.P. and Evans. A.G. (1989). The strength and fracture of alumina bonded with aluminum alloys. Acta Metallurgica 37, 1923–1931.

    Article  Google Scholar 

  • Deve, H.E. and Meloney, M.J. (1991). On the toughening of intermetallics with ductile fibers: The role of interfaces. Acta Metallurgica 39, 2275–2284.

    Article  Google Scholar 

  • Erdogan, F. and Biricikoglu, V. (1973). Two bonded half planes with a crack going through an interface. International Journal of Solids Structures 11(4), 745–766.

    Google Scholar 

  • Fish, J., Fares, F. and Nath, A. (1993). Micromechanical elastic crack–tip stresses in a fibrous composite. International Journal of Fracture 60, 135–146.

    Article  ADS  Google Scholar 

  • Gurson, A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth: Part I – Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology 99, 2–15.

    Google Scholar 

  • He, M.Y. and Hutchinson, J.W. (1989). Crack deflection at an interface between dissimilar elastic materials. International Journal of Solids Structures 25(9), 1053–1067.

    Article  Google Scholar 

  • Huang, Y., Hutchinson, J.W. and Tvergaard, V. (1991). Cavitation instabilities in elastic–plastic solids. Journal of Mechanical Physics and Solids 39, 223–241.

    Article  ADS  Google Scholar 

  • Hutchinson, J.W. (1968). Singular behavior at the end of a tensile crack in a hardening material. Journal of Mechanical Physics and Solids 16, 337–347.

    Article  ADS  Google Scholar 

  • Hutchinson, J.W. and Suo, Z. (1992). Mixed mode cracking of layered material. Advances in Applied Mechanics 29, 63–191.

    Article  MATH  Google Scholar 

  • Jha, M. and Charalambides, P.G. (1997). Crack tip micro mechanical fields in layered elastic composites: crack perpendicular to the layers. International Journal of Solids and Structures.

  • Jha, M. and Charalambides, P.G. (1998). Crack tip micro mechanical fields in layered elastic composites: crack parallel to the interfaces. International Journal of Solids and Structures 35, 149–179.

    Article  MATH  Google Scholar 

  • Jha, M., Charalambides, P.G. and Ballarini, R. (1997). Crack tip location effects on the near–tip mechanics in bimaterial layered systems. Manuscript in preparation.

  • Lu, M.C. and Erdogan, F. (1983). Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface – I. Analysis, II. Solution and results. Engineering of Fracture Mechanics 18, Pt.I, 491–506; Pt. II, 507–528.

    Article  Google Scholar 

  • Martinez, D. and Gupta, V. (1993). Energy criterion for crack deflection at an interface between two orthotropic media II. Results and experimental verification. Journal of Mechanical Physics Solids 42(8), MPS81.

    Google Scholar 

  • McClintock, F.A. (1968). Journal of Applied Mechanics 35, 363–371.

    Google Scholar 

  • Nagtegaal, J.C., Parks, D.M. and Rice, J.R. (1974). Computational Methods in Applied Mechanics and Engineering 4, 153–177.

    Article  MATH  MathSciNet  Google Scholar 

  • Narasimhan, R., Rosakis, A.J. and Moran, B. (1989). A three dimensional numerical investigation of fracture initiation by ductile failure mechanisms in a 4340 steel. Technical Report SM 89–5, CALTECH.

  • Pan, J., Saje, M. and Needleman, A. (1983). Localisation of deformation in rate sensitive porous plastic solids. International Journal of Fracture 21, 261–278.

    Article  Google Scholar 

  • Pierce, D., Shih, C.F. and Needleman, A. (1984). A tangent modulus method for rate dependent solids. Computers and Structures 18, 875–887.

    Article  Google Scholar 

  • Rice, J.R. and Rosengren, G.F. (1968). Plane strain deformation near a crack tip in a power law hardening material. Journal of Mechanical Physics and Solids 16, 1–22.

    Article  MATH  ADS  Google Scholar 

  • Rice, J.R. and Tracey, D.M. (1969). On the ductile enlargement of voids in tri–axial stress fields. Journal of Mechanical Physics Solids 17, 201–217.

    Article  ADS  Google Scholar 

  • Rice, J.R. and Tracey, D.M. (1973). Numerical Methods in Structural Mechanics, Academic Press, New York, 585–623.

    Google Scholar 

  • Rogers, H.C. (1960). Transations of Metallurgical SocietyAIME 218, 498–506.

    Google Scholar 

  • Sih, G.C., Paris, P.C. and Irwin, H. (1965). On cracks in rectilinearly anisotropic bodies. International Journal of Fracture Mechanics 1, 189–203.

    Article  Google Scholar 

  • Sugimura, Y., Lim, P.G., Shih, C.F. and Suresh, S. (1995). Fracture normal to a bimaterial interface: effects of plasticity on crack–tip shielding and amplification. Acta Metallurgica Materialia 43(3), 1157.

    Article  Google Scholar 

  • Suresh, S., Sugimura, Y. and Tschegg, E.K. (1992). The growth of a fatigue crack approaching a perpendicularlyoriented, bimaterial interface. Scripta Metallurgica et Materialia 27, 1189.

    Article  Google Scholar 

  • Stahle, P. and Shih, C.F. (1992). In: Proceedings of Material Resorces Society Symposium. vol. 239, p. 567.

    Google Scholar 

  • Swenson, D.O. and Rau, Jr. C.A. (1970). The stress distribution around a crack perpendicular to an interface between materials. International Journal of Fracture Mechanics 6, 357–360.

    Article  Google Scholar 

  • Tullock, D.L., Reimanis, I.E. Graham, A.L. and Petrovic, J.J. (1994). Deflection and penetration of cracks at an interface between two dissimilar materials. Acta Metallurgica et Materia 42, 3245–3252.

    Article  Google Scholar 

  • Tvergaard, V. (1981). Influence of voids on shear band instabilities under plain strain conditions. International Journal of Fracture 17, 389–407.

    Article  Google Scholar 

  • Tvergaard, V. (1982). International Journal of Solids Structures 18, 659–672.

    Article  MATH  Google Scholar 

  • Tvergaard, V. and Needleman, A. (1984). Analysis of the cup–cone fracture in a round tensile bar. Acta Metallurgica 32, 157–169.

    Article  Google Scholar 

  • Wang. T.C. (1990). Elastic–plastic asymptotic fields for cracks on bimaterial interfaces. Engineeering Fracture Mechanics 37(3), 527–538.

    Article  Google Scholar 

  • Xia, L. and Shih, C.F. (1995). Ductile crack growth – I. A numerical study using computational cells with microstructurally–based length scales. Journal of Mechanical Physics and Solids 43(2) 233–259.

    Article  ADS  Google Scholar 

  • Zak, A.K. and Williams, M.L. (1963). Crack point singularities at a bi–material interface. Journal of Applied Mechanics 30, 142–143.

    Google Scholar 

  • Zienkiewicz, O.C. and Cormeau, I.C. (1974). Viscoplasticity–plasticity and creep in elastic solids–A unified numerical solution approach. International Journal of Numerical Methods and Engineering 8, 821–845.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jha, M., Charalambides, P. A finite element analysis of fracture initiation in ductile/brittle periodically layered composites. International Journal of Fracture 90, 299–323 (1998). https://doi.org/10.1023/A:1007488927130

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007488927130

Navigation