Dislocation tri-material solution in the analysis of bridged crack in anisotropic bimaterial half-space
Source abstract
Abstract
The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (Ψ-integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.
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Research context
OpenAlex topics: Numerical methods in engineering · Fatigue and fracture mechanics · Composite Material Mechanics
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References (30)
Show source-provided references
1. Braun M (1997) Configurational forces induced by finite-element discretization. Proc Estonian Acad Sci Phys Math 46: 24–31
2. Budiansky B, Amazigo J (1989) Toughening by aligned, frictionally constrained fibers. J Mech Phys Solids 37: 93–10910.1016/0022-5096(87)90006-8 ↗
3. Budiansky B, Hutchinson JW, Evans AG (1986) Matrix fracture in fiber-reinforced ceramics. J Mech Phys Solids 34: 167–18910.1016/0022-5096(86)90035-9 ↗
4. Choi ST, Earmme YY (2002) Elastic study on singularities interacting with interfaces using alternating technique part. Part I. Anisotropic trimaterial. Int J Solid Struct 39: 943–95710.1016/S0020-7683(01)00230-X ↗
5. Curtin WA (2000) Stress-strain behaviour of brittle matrix composites. In: Kelly A, Zweben C (eds) Comprehensive composite materials, vol 4. Pergamon Press, pp 47–7610.1016/B0-08-042993-9/00088-7 ↗
6. Dewynne JN, Hills DA, Nowell D (1992) Calculation of the opening displacement of surface-breaking plane cracks. Comp Methods Appl Mech Eng 97: 321–33110.1016/0045-7825(92)90049-P ↗
7. Erdogan F, Gupta GD, Ratwani M (1974) Interaction between a circular inclusion and an arbitrary oriented crack. J Appl Mech 12: 1007–101310.1115/1.3423424 ↗
8. Eshelby JD (1970) Energy relations and the energy-momentum tensor in continuum mechanics. In: Kanninen M et al (eds) Inelastic behavior of solids. McGraw Hill, New York , pp 77–115
9. Fett T, Munz D (1997) Stress intensity factors and weight functions. Computational Mechanics, Inc.
10. Gurtin ME (2000) Configurational forces as basic concepts of continuum physics. Springer, New York
11. He MY, Hutchinson JW (1989) Crack deflection at an interface between dissimilar elastic materials. Int J Solids Struct 25: 1053–106710.1016/0020-7683(89)90021-8 ↗
12. Hills DA, Kelly PA, Dai DN, Korsunsky AM (1996) Solution of crack problems. Kluwer Academic Publishers, Dordrecht10.1007/978-94-015-8648-1 ↗
13. Kienzler R, Herrmann G (2000) Mechanics in material space. Springer, Berlin10.1007/978-3-642-57010-0 ↗
14. Lekhnitskii SG (1963) Theory of elasticity of an anisotropic body. Holden-Day, San Francisco
15. Marshall DB, Cox BN (1988) J-integral method for calculating steady-state matrix cracking in composites. Mech Mater 7: 127–13310.1016/0167-6636(88)90011-7 ↗
16. Martin E, Leguillon D, Lacroix C (2001) A revisited criterion for crack deflection at an interface in a brittle bimaterial. Compos Sci Technol 61: 1671–167910.1016/S0266-3538(01)00067-7 ↗
17. Martinez D, Gupta V (1994) Energy criterion for crack deflection at an interface between two orthotropic media. J Mech Phys Solids 42: 1247–127110.1016/0022-5096(94)90034-5 ↗
18. Maugin GA (1995) Material forces: concepts and applications. ASME Appl Mech Rev 48: 213–24510.1115/1.3005101 ↗
19. Mueller R, Kolling S, Gross D (2002) On configurational forces in the context of the finite element method. Int J Numer Meth Eng 53: 1557–157410.1002/nme.351 ↗
20. Muschelishvili NI (1953) Some basic problems in the mathematical theory of elasticity. Noordhoff, Holland
21. Papadakis PJ, Babuska I (1995) A numerical procedure for the determination of certain quantities related to the stress intensity factors in two-dimensional elasticity. Comp Methods Appl Mech Eng 122: 69–9210.1016/0045-7825(94)00748-C ↗
22. Profant T, Ševeček O, Kotoul M (2007) Calculation of K-factor and T-stress for cracks in anisotropic bimaterials. accepted in Eng Fract Mech10.1016/j.engfracmech.2007.08.003 ↗
23. Sarrafi-Nour GR, Coyle TW, Fett T (1998) A weight function for the crack surface tractions in chevron-notched specimens. Eng Fract Mech 59: 439–44510.1016/S0013-7944(97)00154-9 ↗
24. Simha NK (2000) Toughening by phase boundary propagation. J Elast 59: 195–21110.1023/A:1011017620002 ↗
25. Simha NK, Fischer FD, Kolednik O, Predan J, Shan GX (2005) Crack tip shielding or anti-shielding due to smooth and discontinuous material inhomogeneities. Int J Fract 135: 73–9310.1007/s10704-005-3944-5 ↗
26. Stern M, Soni ML (1976) On the computation of stress intensities at fixed-free corners. Int J Solid Struct 12: 331–33710.1016/0020-7683(76)90023-8 ↗
27. Suo Z (1990) Singularities, interfaces and cracks in dissimilar anisotr. media. Proc R Soc Lond A 427: 331–35810.1098/rspa.1990.0016 ↗
28. Thouless MD, Evans AG (1988) Effects of pull-out on the mechanical properties of ceramic matrix composites. Acta Metall 36: 517–52210.1016/0001-6160(88)90083-1 ↗
29. Ting TCT (1997) Stress singularities at the tip of interfaces in polycrystals. In: Rossmanith HP (ed) Proceedings of first international conference on damage and failure of interfaces. Balkema Publishers, Rotterdam, Netherlands, pp. 45–82
30. Tullock DL, Reimanis IE, Graham AL, Petrovic JJ (1994) Deflection and penetration of cracks at an interface between two dissimilar materials. Acta Metall Mater 42: 3245–325210.1016/0956-7151(94)90422-7 ↗