The mechanical design of nacre
Tóm tắt
Mother-of-pearl (nacre) is a platelet-reinforced composite, highly filled with calcium carbonate (aragonite). The Young modulus, determined from beams of a span-to-depth ratio of no less than 15 (a necessary precaution), is of the order of 70 GPa (dry) and 60 GPa (wet), much higher than previously recorded values. These values can be derived from ‘shear-lag’ models developed for platey composites, suggesting that nacre is a near-ideal material. The tensile strength of nacre is of the order of 170 MPa (dry) and 140 MPa (wet), values which are best modelled assuming that pull-out of the platelets is the main mode of failure. In three-point bending, depending on the span-to-depth ratio and degree of hydration, the work to fracture across the platelets varies from 350 to 1240 J m -2 . In general, the effect of water is to increase the ductility of nacre and increase the toughness almost tenfold by the associated introduction of plastic work. The pull-out model is sufficient to account for the toughness of dry nacre, but accounts for only a third of the toughness of wet nacre. The additional contribution probably comes from debonding within the thin layer of matrix material. Electron microscopy reveals that the ductility of wet nacre is caused by cohesive fracture along platelet lamellae at right angles to the main crack. The matrix appears to be well bonded to the lamellae, enabling the matrix to be stretched across the delamination cracks without breaking, thereby sustaining a force across a wider crack. Such a mechanism also explains why toughness is dependent on the span-to-depth ratio of the test piece. With this last observation as a possible exception, nacre does not employ any really novel mechanisms to achieve its mechanical properties. It is simply ‘well made’. The importance of nacre to the mollusc depends both on the material and the size of the shell. Catastrophic failure will be very likely in whole, undamaged shells which behave like unnotched beams at large span-to-depth ratios. This tendency is increased by the fact that predators act as ‘soft’ machines and store strain energy which can be fed into the material very quickly once the fracture stress has been reached. It may therefore be advantageous to have a shell made of an intrinsically less tough material which is better at stopping cracks (e. g. crossed lamellar). However, nacre may still be preferred for the short, thick shells of young molluscs, as these have a low span-to-depth ratio and can make better use of ductility mechanisms.
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Tài liệu tham khảo
American Society for Testing and Materials 1976 Standard test method for apparent interlaminar shear strength of parallel fiber composites by short beam method. A8TM D2344.
Atkins A. G. & Mai Y.-W. 1985 Elastic and plastic fracture: metals polymers ceramics composites biological materials. Chichester: Ellis-Horwood.
Brown W. F. & Srawley J. E. 1966 Plane strain crack testing of high strength metallic materials. ASTM Special Technical Publication no. 410.
Cox H. L., 1952, The elasticity and strength of paper and other fibrous materials. Br. J . appl, Phys., 3, 72
Currey J. D. 1980 Mechanical properties of mollusc shell. In The mechanical properties of biological materials pp. 75-97. Cambridge University Press.
{Symp.Soc. exp. Biol. 34) (ed. J. F. V. Vincent & J. D. Currey)
Currey J. D. & Brear K. 1984 Fatigue fracture of mother-of-pearl and its significance for predatory techniques. J .Zool. 204. 541-548.
Harris B. 1980 The mechanical behaviour of composite materials. In The mechanical properties of biological materials {Symp. Soc. exp. pp. 37-74. Cambridge University Press.
Bio34) (ed. J. F. V. Vincent & J. D. Currey)
Hearmon R. F. S., 1946, The elastic constants of anisotropic materials. Rev. mod, Phys., 18, 409
Hull D. 1981 An introduction to composite materials. Cambridge University Press.
Jackson A. P. 1986 The mechanical design of nacre. Ph.D. thesis University of Reading.
Kitchener A. C. 1985 The functional design of horns. Ph.D. thesis University of Reading.
Knott J. F. 1973 Fundamentals of fracture mechanics. London: Butterworths.
Krampitz G. Drolshagen H. Hausle J. & Hof-Irmscher K. 1983 Organic matrices of mollusc shells. In Biomineralization and biological metal accumulation (ed. P. Westbroek & E. W. de Jong) pp. 231-247. Dordrecht: Reidel.
Lusis J., 1973, The effect of flake aspect ratio on the flexural properties of mica reinforced plastics, Polym. Sci., 13, 139
Outwater J., 1970, Fracture energy of unidirectional laminates, Mod. Plant., 47, 160
Piggott M. R. 1980 Load bearing fibre composites. Oxford: Pergamon Press.
Riley V. R., 1968, Fibre/fibre interaction. J.comp, Mater., 2, 436
Roark R. J. & Young W. C. 1975 Formulas for stress and strain 5th edn London: MacGraw-Hill International.
Sih G. C. Paris P. C. & Irwin G. R. 1965 On cracks in rectilinearly anisotropic bodies. Int. J.Fract. M ech.1 189-203.
Srinivasan P. S., 1941, The elastic properties of molluscan shells, Q. Jl Ind. Inst., 4, 189
Stephens R. C. 1970 Strength of materials: theory and examples. London: Edward Arnold.
Wainwright S. A. Biggs W. D. Currey J. D. & Gosline J. M. 1976 Mechanical design in organisms. London: Edward Arnold.
Weiner S. & Traub W. 1981 Organic matrix-mineral relationships in mollusk shell nacreous layers. In Structural aspects of recognition and assembly in biological macromolecules (ed. M. Balban J. L. Sussman W. Traub & A. Yonath) pp. 467-482. Philadelphia: Rehvot.
Williams J. G. 1984 Fracture mechanics of polymers. Chichester: Ellis Horwood.
Zweben C. Smith W. S. & Wardle M. W. 1979 Test methods for fiber tensile strength composite flexural modulus and properties of fabric-reinforced laminates. Tn Composite materials: testing and design ( publication 674.
5thconference) (ed. S. W. Tsai) pp. 244-262. ASTM special