Computational Methods for Debonding in Composites

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72 B.N. Cox et al. mixed-mode crack are not enough.) A map of the vector displacement field around an initiating crack would in principle be a sufficient measurement, but the questions of how to make such a measurement and the accuracy required of it remain very much open. New experimental methods for measuring very small crack displacements, e.g., with high-resolution x-ray tomography, are very promising; however, data acquisition and analysis for such experiments are challenging and yet to be demonstrated. A simpler prospect may be to use the evolution of the macroscopic crack shape as the calibrating information, since Fig. 3.4 and similar figures in [13, 20, 38, 60] suggest that this is an information-rich experiment for determining p(u). Current research continues to seek a calibration method, validated by testing the accuracy to which ensuing predictions match fracture experiments. 3.7 Concluding Remarks A functioning virtual test is a system of theoretical models, specialized laboratory tests, and engineering field tests, linked by statistical and decision theory tools, which only when taken in its entirety can satisfy the goal of substituting simulations for a large fraction of real tests in a material design or material certification procedure. The virtual test is a rich and complex system, requiring Systems Engineering and Systems Science governance of activities in a number of disparate research and engineering disciplines. Prior efforts to develop virtual tests for composite materials (or other engineering or biological materials) appear not to have addressed the assembly of the complete structure. Advances in modeling, computation and experimental techniques over the past two decades make the development of a virtual test a realistic goal; the major new challenge is achieving the integration of the necessary disciplines. This challenge should not be mistaken as merely the need for more experiments or more modeling. The greatest gaps in the technology of virtual tests lie where models and experiments should be unified. In particular, theorists are challenged by (1) the need to participate in the design of new experiments that will yield the information they need to inform and calibrate models and (2) the need for model-based methods of inferring data from tests. Experimentalists are challenged by designing experiments that yield the correct type of information for extending the scope of models. Higher spatial and temporal resolution and three-dimensional imaging are of course very useful, but more specifically experiments must be devised that probe those aspects of materials damage that are critical to formulating and quantifying models. The skill sets needed to meet these challenges are not necessarily to be found among current modeling and experimental communities. Other disciplines, especially statistics, decision theory, and physics, must be brought into the effort. A virtual test should be a living, continually evolving system. Therefore a key challenge is to create a structure that can support its maintenance. Both systems engineering and systems science aspects exist in this challenge, with the whole integrated by the tools of information science.
3 Practical Challenges in Formulating Virtual Tests for Structural Composites 73 Acknowledgements Brian N. Cox supported by the Army Research Office, Agreement No. W911NF-05-C-0073. S. Mark Spearing partially funded by a Royal Society-Wolfson Research Merit Award and EPSRC grant EP/E003427/1. References 1. Abraham FF (2003) How fast can cracks move? A research adventure in materials failure using millions of atoms and big computers. Adv Phys 52:727–790 2. Abraham FF, Walkup R, Gao H et al. (2002) Simulating materials failure by using up to one billion atoms and the world’s fastest computer: brittle fracture. Proc Natl Acad Sci USA 99:5777–5782 3. Ashby MF (1992) Physical modelling or materials problems. Mat Sci Technol 8:102–111 4. Bao G, Suo Z (1992) Remarks on crack-bridging concepts. Appl Mech Rev 24:355–366 5. de Borst R (2003) Numerical aspects of cohesive-zone models. Eng Fract Mech 70:1743–1757 6. Buehler MJ (2006) Nature designs tough collagen: Explaining the nanostructure of collagen fibrils. Proc Natl Acad Sci USA 103:12285–12290 7. Buehler MJ (2006) Large-scale hierarchical modeling of nanoscale, natural and biological materials. J Comput Theor Nanosci 3:603–623 8. Buehler MJ, Gao H (2005) Ultra large scale atomistic simulations of dynamic fracture. In: Rieth M, Schommers W (eds) Handbook of Theoretical Computational Nanotechnology, Volume X, pp 1–41, American Scientific Publishers Ranch, CA 9. Cai W, Bulatov VV, Chang J et al. (2004) Dislocation core effects on mobility. In: Nabarro FNR, Hirth JP (eds) Dislocations in Solids, Volume 12, Chapter 64, Elsevier, Amsterdam 10. Camanho PP, Dávila CG, Pinho ST (2004) Fracture analysis of composite co-cured structural joints using decohesion elements. Fatigue Fract Eng Mat Struct 27:745–757 11. Carpinteri A (ed) (1999) Nonlinear Crack Models for Nonmetallic Materials. Kluwer, Dordrecht, The Netherlands 12. Carroll FE, Mendenhall MH, Traeger RH, Brau C et al. (2003) Pulsed tunable monochromatic X-ray beams from a compact source: New opportunities. Am J Roentgenol 181:1197–1202 13. Case SW, Reifsnider KL (1999) Mrlife12 theory manual – a strength and life prediction code for laminated composite materials. Technical report, Materials Response Group, Virginia Polytechnic Institute and State University 14. Corigliano A (1993) Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int J Solids Struct 30:2779–2811 15. Cox BN (1999) Constitutive model for a fiber tow bridging a delamination crack. Mech Compos Mat Struct 6:117–138 16. Cox BN (2005) Snubbing effects in the pullout of a fibrous rod from a laminate. Mech Adv Mat Struct 12:85–98 17. Cox BN, Marshall DB (1991) The determination of crack bridging forces. Int J Fract 49: 159–176 18. Cox BN, Marshall DB (1994) Concepts for bridged cracks in fracture and fatigue. Acta Metall Mater 42:341–363 19. Cox BN, Marshall DB (1996) Crack initiation in brittle fiber reinforced laminates. J Am Ceram Soc 79:1181–1188 20. Cox BN, Yang QD (2006) In quest of virtual tests for structural composites. Science 314:1102–1107 21. Dawood TA, Shenoi RA, Sahin M (2007) A procedure to embed fibre Bragg grating strain sensors into GFRP sandwich structures. Compos Part A 38:217–226 22. Dobashi K, Fukuasawa A, Uesaka M et al. (2005) Design of compact monochromatic tunable hard X-ray source based on X-band linac. Jpn J Appl Phys 44:1999–2005 23. Dvorak GJ, Laws N (1987) Analysis of progressive matrix cracking in composite laminates. II - First ply failure. J Compos Mat 21:309–329
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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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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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234 J.A. Oliveira et al. Fig. 11.7
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14 Development of DST for the Model
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