Abstract
Approximate weight functions are derived and validated numerically for isotropic and orthotropic double cantilever beams loaded in mode II. They define the stress intensity factor at the crack tip due to a pair of unit point forces acting tangentially to the crack surfaces and have been deduced using asymptotic matching through finite elements and an orthotropy rescaling technique. Along with the related mode I weight functions, which are recalled in the paper, the functions can be used to formulate mixed mode problems in beams and plates as integral equations so avoiding the limitations imposed on accuracy by approximations based on structural theories. An accurate method such as the weight function method becomes necessary when dealing with short cracks, crack initiation and large scale bridging delamination problems with crack wake mechanisms acting over several scales. The accuracy of modes I and II solutions based on beam theory approximations is shown to be strongly influenced by the length of Dugdale type cohesive regions, with short lengths giving rise to large errors in the fracture parameters. Stress intensity factors obtained using the proposed functions for special problems agree with solutions from the literature.
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References
Andrews, M.G. (2005). The Static and Dynamic Interaction of Multiple Delaminations in Plates Subject to Cylindrical Bending, Dissertation, Ph.D. Degree, Northwestern University, Evanston, IL, U.S.A.
M.G. Andrews R. Massabò B.N. Cox (2006) ArticleTitleElastic interaction of multiple delaminations in plates subject to cylindrical bending International Journal of Solids and Structures 43 855–886 Occurrence Handle10.1016/j.ijsolstr.2005.04.025
ANSYS, release 5.5.3, Ansys Inc., Canonsburg, PA, U.S.A.
R.S. Barsoum (1977) ArticleTitleTriangular quarter-point elements as elastic and perfectly-plastic crack tip elements International Journal of Numerical Methods in Engineering 11 85–98 Occurrence Handle0348.73030 Occurrence Handle10.1002/nme.1620110109
D. Bruno F. Greco P. Lonetti (2003) ArticleTitleA coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites International Journal of Solids Structures 40 7245–7268 Occurrence Handle1065.74064 Occurrence Handle10.1016/j.ijsolstr.2003.09.006
Bückner (1970) ArticleTitleA novel principal for the computation of stress intensity factors ZAMM 50 529–545 Occurrence Handle0213.26603
A. Carpinteri R. Massabò (1996) ArticleTitleBridged versus cohesive crack in the flexural behavior of brittle matrix composites International Journal of Fracture 81 125–145 Occurrence Handle10.1007/BF00033178
B.N. Cox D.B. Marshall (1991) ArticleTitleStable and unstable solutions for bridged cracks in various specimens Acta Metallic Mater 39 579–89 Occurrence Handle10.1016/0956-7151(91)90126-L
Entov, B.M. and Salganik, V.M. (1965). On the beam theory approximation in crack theory. Bulletin of USSR Academy of Sciences, Mechanics 5, 95–102 (in Russian).
Fett, T. and Munz, D. (1997). Stress intensity factors and weight functions. Computational Mechanics Publications, Southampton, UK.
R.M.L. Foote V.T. Buchwald (1985) ArticleTitleAn exact solution for the stress intensity factor for a double cantilever beam International Journal of Fracture 29 125–134
He M.-Y. and Evans A.G. (1992). Finite element analysis of beam specimens used to measure the delamination resistance of composites. Journal of Composite Technology and Research 235–240
M.F. Kanninen (1974) ArticleTitleA dynamic analysis of unstable crack propagation and arrest in the DCB test specimen International Journal of Fracture 10 IssueID3 415–430 Occurrence Handle10.1007/BF00035502
Massabò, R. and Andrews, M. (2005). Interaction Effects of Multiple Delaminations on the Survivability of Composite Structures, Proceedings of the ONR meeting of the Solid Mechanics Program, University of Maryland, May 2005, pp.1–9.
R. Massabò B.N. Cox (1999) ArticleTitleConcepts for bridged mode II delamination cracks Journal of the Mechanics and Physics of Solids 47 IssueID6 1265–1300 Occurrence Handle0962.74054 Occurrence Handle10.1016/S0022-5096(98)00107-0
R. Massabò B.N. Cox (2001) ArticleTitleUnusual characteristics of mixed mode delamination fracture in the presence of large scale bridging Mechanics of Composite Materials and Structures 8 IssueID1 61–80 Occurrence Handle10.1080/107594101459833
R Massabò D. Mumm B.N. Cox (1998) ArticleTitleCharacterizing mode II delamination cracks in stitched composites International Journal of Fracture 92 IssueID1 1–38 Occurrence Handle10.1023/A:1007520324207
R. Massabò L. Brandinelli B.N. Cox (2003) ArticleTitleMode I weight functions for an orthotropic double cantilever beam International Journal of Engineering Science 41 1497–1518 Occurrence Handle10.1016/S0020-7225(03)00029-6
J.R. Rice (1968) ArticleTitleA path independent integral and the approximate analysis of strain concentration by notches and cracks Journal of Applied Mechanics 35 379–386
C.F. Shih H.G. De Lorenzi M.D. German (1976) ArticleTitleCrack extension modelling with singular quadratic isoparametric elements International Journal of Fracture 12 647–651
G.C. Sih P.C. Paris G.R. Irwin (1965) ArticleTitleOn cracks in rectilinear anisotropic bodies International Journal of Fracture 1 189–203
Z. Suo (1990) ArticleTitleDelamination specimens for orthotropic materials Journal of Applied Mechanics 57 627–634
Tada, H., Paris, P.C. and Irwin, G.R. (1985). The Stress Analysis of Cracks Handbook. Paris Productions Inc., St. Louis, Missouri.
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Brandinelli, L., Massabò, R. Mode II weight functions for isotropic and orthotropic double cantilever beams. Int J Fract 139, 1–25 (2006). https://doi.org/10.1007/s10704-006-6358-0
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DOI: https://doi.org/10.1007/s10704-006-6358-0