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Cohesive models for damage evolution in laminated composites. (English) Zbl 1196.74231
Summary: A trend in the last decade towards models in which nonlinear crack tip processes are represented explicitly, rather than being assigned to a point process at the crack tip (as in linear elastic fracture mechanics), is reviewed by a survey of the literature. A good compromise between computational efficiency and physical reality seems to be the cohesive zone formulation, which collapses the effect of the nonlinear crack process zone onto a surface of displacement discontinuity (generalized crack). Damage mechanisms that can be represented by cohesive models include delamination of plies, large splitting (shear) cracks within plies, multiple matrix cracking within plies, fiber rupture or microbuckling (kink band formation), friction acting between delaminated plies, process zones at crack tips representing crazing or other nonlinearity, and large scale bridging by through-thickness reinforcement or oblique crack-bridging fibers. The power of the technique is illustrated here for delamination and splitting cracks in laminates. A cohesive element is presented for simulating three-dimensional, mode-dependent process zones. An essential feature of the formulation is that the delamination crack shape can follow its natural evolution, according to the evolving mode conditions calculated within the simulation. But in numerical work, care must be taken that element sizes are defined consistently with the characteristic lengths of cohesive zones that are implied by the chosen cohesive laws. Qualitatively successful applications are reported to some practical problems in composite engineering, which cannot be adequately analyzed by conventional tools such as linear elastic fracture mechanics and the virtual crack closure technique. The simulations successfully reproduce experimentally measured crack shapes that have been reported in the literature over a decade ago, but have not been reproduced by prior models.

MSC:
74R10 Brittle fracture
74E30 Composite and mixture properties
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[1] Andrews, M., Massabò, R., and Cox, B.N. (2005). Crack stability during quasi-static multiple delamination, International Journal of Solids and Stuctures, in press.
[3] Barenblatt, G.I. (1962). The mathematical theory of equilibrium cracks in brittle fracture. In: Advances in Applied Mechanics (edited by H.L. Dryden and T. Von Karman) Academic Press, pp. 55–129.
[50] Rice, J.R. (1980). The mechanics of earthquake rupture. International School of Physics ”E. Fermi”, Course 78, 1979: Italian Physical Society/North Holland Publ. Co.
[51] Roberts S.J. (2000). Modelling of microcracking in composite materials (Ph. D.), The University of Newcastle upon Tyne.
[57] Shivakumar, K.N., Tan, P.W. and Newman, J.C. Jr. 1988. A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies. International Journal of Fracture R43–R50.
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