Boundary element analysis of stress state at the bridged zone of an interface crack
DOI:
https://doi.org/10.7242/1999-6691/2012.5.4.49Keywords:
boundary element method, cracks, bridged zone, material interface, stress intensity factorsAbstract
The direct boundary element method has been applied to analyze stresses in a fracture process zone (a crack bridged zone) and to calculate the modulus of stress intensity factors for structures with bridged interface cracks under mechanical loading. The bridged zones of interface cracks are considered as parts of these cracks and it is assumed that distributed spring-like bonds with given bond deformation law link crack surfaces. Numerical analysis of the bridged interface cracks is based on the multi-domain formulation of the boundary integral equation method. The results are compared with those obtained previously for a straight crack at the interface between two different materials using singular integral-differential equations. Parametric analysis of the influence of the bridged zone bond stiffness, the physical-mechanical properties of jointed materials and the bridged zone length on the stress intensity factor modulus is performed. In addition, the problem for a curvilinear bridged crack at the interface between a matrix and a cylindrical inclusion in a composite material is considered.
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Barenblatt G.I. O ravnovesnyh tresinah, obrazuusihsa pri hrupkom razrusenii // PMM. - 1959. - T. 23, Vyp. 3. - S. 434-444; Vyp. 4. - S. 706-721; Vyp. 5. - S. 893-900.
2. Dugdale D.S. Yielding of steel sheets containing slits // J. Mech. Phys. Solids. - 1960. - V. 8, N. 2. - P. 100-104. DOI
3. Leonov M.A., Panasuk V.V. Razvitie mel’cajsih tresin v tverdom tele // Prikladnaa mehanika. - 1959. - T. 5, No 4. - S. 391-401.
4. Nemat-Nasser S., Nori M. Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites // Mech. Mater. - 1987. - V. 6, N. 3. - P. 245-269. DOI
5. Bao G., Suo Z. Remarks on crack-bridging concepts // Appl. Mech. Rev. - 1992. - V. 45, N. 8. - P. 355-366. DOI
6. Cox B.N., Marshall D.B. Concepts for bridged cracks in fracture and fatigue // Acta Metall. Mater. - 1994. - V. 42, N. 2. -P. 341-363. DOI
7. Weitsman Y. Nonlinear analysis of crazes // J. Appl. Mech. - 1986. - V. 53, N. 1. - P. 97-102. DOI
8. Rose L.R.F. Crack reinforcement by distributed springs // J. Mech. Phys. Solids. - 1987. - V. 35, N. 4. - P. 383-405. DOI
9. Budiansky B., Cui Y.L. On the tensile strength of a fiber-reinforced ceramic composite containing a crack-like flaw // J. Mech. Phys. Solids. - 1994. - V. 42, N. 1. - P. 1-19. DOI
10. Grekov M.A., Morozov N.F. O ravnovesnyh tresinah v kompozitah, armirovannyh odnonapravlennymi voloknami // PMM. - 2006. - T. 70, No 6. - S. 1054-1066.
11. Goldstein R.V., Perelmuter M.N. Modeling of bonding at an interface crack // Int. J. Fracture. - 1999. - V. 99, N. 1-2. - P. 53-79. DOI
12. Gol’dstejn R.V. Perel’muter M.N. Tresina na granice soedinenia materialov so svazami mezdu beregami // MTT. - 2001.- No 1. - C. 94-112.
13. Gol’dstejn R.V., Perel’muter M.N., Modelirovanie tresinostojkosti kompozicionnyh materialov // Vycisl. meh. splos. sred. - 2009. - T. 2, No 2. - S. 22-39.
14. Perel’muter M.N. Tresina na granice razdela materialov c nelinejnymi svazami v koncevoj oblasti // PMM - 2011. - T. 75, No 1. - S. 152-173.
15. Bakirov V.F., Gol’dstejn R.V. Model’ Leonova-Panasuka-Dagdejla dla tresiny na granice soedinenia materialov // PMM. - 2004. - T. 68, No 1. - S. 170-179.
16. Lee K.Y., Choi H.J. Boundary element analysis of stress intensity factors for bimaterial interface cracks // Eng. Fract. Mech. - 1988. - V. 29, N. 4. - P. 461-472. DOI
17. Yuuki R., Cho S.-B. Efficient boundary element analysis of stress intensity factors for interface cracks in dissimilar materials // Eng. Fract. Mech. - 1989. - V. 34, N. 1. - P. 179-188. DOI
18. Tan C.L., Gao Y.L. Treatment of bimaterial interface crack problems using the boundary element method // Eng. Fract. Mech. - 1990. - V. 36, N. 6. - P. 919-932. DOI
19. Raveendra S.T., Banerjee P.K. Computation of stress intensity factors for interfacial cracks // Eng. Fract. Mech. - 1991. - V. 40, N. 1. - P. 89-103. DOI
20. Dong Y., Wang Z., Wang B. On the computation of stress intensity factors for interfacial cracks using quarter-point boundary elements // Eng. Fract. Mech. - 1997. - V. 57, N. 4. - P. 335-342. DOI
21. Ikeda T., Sun C.T. Stress intensity factor analysis for an interface crack between dissimilar isotropic materials under thermal stress // Int. J. Fracture. - 2001. - V. 111, N. 3. - P. 229-249. DOI
22. Hadjesfandiari A.R., Dargush G.F. Analysis of bi-material interface cracks with complex weighting functions and non-standard quadrature // Int. J. Solids Struct. - 2011. - V. 48, N. 10. - P. 1499-1512. DOI
23. Liu Y.-F., Masuda C., Yuuki R. An efficient BEM to calculate weight functions and its application to bridging analysis in an orthotropic medium // Comput. Mech. - 1998. - V. 22, N. 5. - P. 418-424. DOI
24. Rauchs G., Thomason P.F., Withers P.J. Finite element modeling of frictional bridging during fatigue crack growth in fibre-reinforced metal matrix composites // Comp. Mater. Sci. - 2002. - V. 25, N, 1-2. - P. 166-173. DOI
25. Cudzilo B.E., Tan C.L. Numerical fracture mechanics analysis of cracked fibre-metal laminates with cut-outs // Electronic Journal of Boundary Elements. - 2003. - V. 1, N. 3. - P. 336-403.
26. Selvadurai A.P.S. Crack-bridging in a unidirectionally fibre-reinforced plate // J. Eng. Math. - 2010. - V. 68, N. 1. - P. 5-14. DOI
27. Salganik R.L. O hrupkom razrusenii skleennyh tel // PMM. -1963. - T. 27, No 5. - C. 957-962.
28. Rice J.R. Elastic fracture mechanics concepts for interfacial cracks // J. Appl. Mech. - 1988. - V. 55. - P. 98-103. DOI
29. Benerdzi P., Batterfild R. Metod granicnyh elementov v prikladnyh naukah.- M.: Mir, 1984. - 494 s.
30. Balanford G.E., Ingraffea A.R., Liggett J.A. Two-dimensional stress intensity factor computations using the boundary element method // Int. J. Numer. Meth. Eng. - 1981. - V. 17, N. 3. - P. 387-404. DOI
31. Perel’muter M.N. Primenenie metoda granicnyh elementov pri issledovanii prostranstvennogo naprazennogo sostoania sostavnyh konstrukcij // Problemy procnosti i dinamiki v aviadvigatelestroenii: Sb. - 1989. - Vyp. 4. - Tr. CIAM No 1237. - S. 74-99.
32. Martinez J., Dominguez J. On the use of quarter-point boundary elements for stress intensity factor computations // Int. J. Numer. Meth. Eng. - 1984. - V. 20, N. 10. - P. 1941-1950. DOI
33. Rice J.R., Sih G.C. Plane problems of cracks in dissimilar media // J. Appl. Mech. - 1965. - V. 32, N. 2. - P. 418-423. DOI
34. Cerepanov G.P. O naprazennom sostoanii v neodnorodnoj plastinke s razrezami // Izvestia AN SSSR. OTN. Mehanika i masinostroenie. - 1962. - No 1. - C. 131-137.
35. England A.H. An arc crack around a circular elastic inclusion // J. Appl. Mech. - 1966. - V. 33, N. 3. - P. 637-640. DOI
36. Perlman A.B., Sih G.C. Elastostatic problems of curvilinear cracks in bonded dissimilar materials // Int. J. Eng Sci. - 1967. - V. 5, N. 11. - P. 845-867. DOI
37. Toya M. Crack along interface of a circular inclusion embedded in an infinite solid // J. Mech. Phys. Solids. - 1974. - V. 22, N. 5. - P. 325-348. DOI
38. Perelmuter M. Bridged interface cracks under transient thermal loading // PAMM. - 2007. - V. 7, N. 1. - P. 4030033-4030034. DOI
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