Computational Methods for Debonding in Composites

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4 Analytical and Numerical Investigation of the Length of Cohesive Zone 95 Table 4.3 Values of the parameter M MI M50% M80% MII 0.66 0.51 0.66 1.03 Fig. 4.9 Load-displacement curve of the lever point for different lengths of the elements ahead of the crack tip, reducing interface strengths Another simulation was done to demonstrate that the reduction factor fr needs to be computed for a unique mode-ratio, and that the mode I and mode II strengths must be reduced by the same factor fr. The mode I and mode II strengths were lowered independently, computing a reduction factor for mode I, frI = 0.22, and another for mode II, frII = 0.51, using in both cases the pure mode loading values and Ne = 5. The resulting load-displacement curve was added to Fig. 4.9 (with the label asymmetric reduction). It can be observed that the load-displacement curve obtained with the asymmetrical reduction of the interface strengths does not converge to the correct solution. If the pure mode interface strengths are lowered by a different factor, the shape of the initiation surface changes and, therefore, the results of the simulation become inaccurate, specially if the mode ratio changes during the simulation. Usually, the length of the cohesive zone is smaller for mode I than for other loading modes. Therefore, in problems where the mixed-mode ratio is not known or may change during the propagation of delamination, the reduction factor fr can be computed using the pure mode I properties.
96 A. Turon et al. 4.7 Conclusions An investigation of the length of the cohesive zone in delaminated composite materials was presented. It was shown that the length of the cohesive zone depends on the material properties, the geometry/size of the structure, and on the loading mode. New expressions to estimate the length of the cohesive zone of finite-sized specimens under general loading conditions were derived. The accuracy of the model was assessed by comparing its predictions with numerical results obtained in simulations of test specimens loaded in pure mode I, pure mode II, and mixed-mode I and II. The numerical simulations were performed using a cohesive zone model previously developed by the authors and implemented in ABAQUS as a user-written subroutine. A good agreement between predictions and experiments was obtained for all loading situations and sizes of the test specimens. Finally, the model presented was used to simulate delamination propagation in composites using coarse meshes. A methodology previously developed by the authors to simulate delamination using coarse meshes has been updated to be used under any general loading situation and specimen geometry. The results obtained using this methodology yield converged solutions even for elements that are ten time larger than the nominal length of the cohesive zone. References 1. Barenblatt G (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129 2. Baˇzant ZP, Planas J (1998) Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press, West Palm Beach, FL 3. Benzeggagh ML, Kenane M (1996) Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos Sci Technol 49:439–49 4. Camanho PP, Dávila CG, de Moura MF (2003) Numerical simulation of mixed-mode progressive delamination in composite materials. J Compos Mater 37:1415–1438 5. Cox BN, Marshall DB (1994) Concepts for bridged cracks in fracture and fatigue. Acta Metall Mater 42:341–363 6. Dávila CG, Camanho PP, Turon A (2008) Effective simulation of delamination in aeronautical structures using shells and cohesive elements. J Aircraft 45:663–672 7. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104 8. Falk ML, Needleman A, Rice JR (2001) A critical evaluation of cohesive zone models of dynamic fracture. J Phys IV, Proc:543–550 9. Gdoutos EE (1990) Fracture Mechanis Criteria and Applications. Kluwer, Dordrecht, The Netherlands 10. Hibbitt D, Karlsson B, Sorensen P (2005) ABAQUS 6.5 Users’s Manuals, Pawtucket, RI 11. Hillerborg A, Modéer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773–782 12. Hui CY, Jagota A, Bennison SJ, Londono JD (2003) Crack blunting and the strength of soft elastic solids. Proc Royal Soc Lond A 459:1489–1516
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Mechanical Response of Composites
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Pedro P. Camanho • C.G. Dávila S
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Preface The methodology for designi
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Acknowledgements The Editors of thi
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x Contents 3 Practical Challenges i
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xii Contents 8.2.4 Modelling Effect
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xiv Contents 13.1.2 EffectiveProper
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xvi List of Contributors Clara Schu
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Chapter 1 Computational Methods for
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1 Computational Methods for Debondi
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180 N. Zobeiry et al. There are sev
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186 N. Zobeiry et al. c = 38.7 mm h
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Chapter 10 Elastoplastic Modeling o
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10 Elastoplastic Modeling of Multi-
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