Model for the robust mechanical behavior of nacre
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R.Z. Wang and I.A. Aksay Department of Chemical Engineering and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544
M.Y. He Materials Department, University of California, Santa Barbara, California 93106
J.W. Hutchinson Division of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138 (Received 24 November 2000; accepted 15 May 2001)
The inelastic deformation of nacre that leads to its structural robustness has been characterized in a recent experimental study. This article develops a model for the inelastic behavior, measured in tension, along the axis of the aragonite plates. The model is based on observations for abalone nacre that the inelasticity is associated with periodic dilatation bands. These bands contain coordinated separations at the periphery of the plates. The separations open as the material strains. The response is attributed to nanoscale asperities on the surfaces of the plates. The model calculates the stresses needed to displace the plates, resisted by elastic contacts at the asperities. The results are compared with the measured stress/strain curves.
I. INTRODUCTION
Various naturally occurring materials have inherent mechanical robustness, despite the brittle nature of their predominant constituent: CaCO3, often present as aragonite.1–7 This robustness is manifest in inelastic strains prior to rupture.1,8 An example is presented on Fig. 1, for nacre, which consists of high aspect ratio aragonite plates separated by a very thin polymer interlayer.9,10 Its inelastic response is anisotropic, being dependent upon the loading and its orientation relative to the coordinates of the aragonite plates.8 Upon loading in tension parallel to the plates, the material “yields” after an initial elastic response (Young’s modulus, E ⳱ 70 GPa), exhibits rapid strain hardening, and, thereafter, deforms subject to a steady-state stress, ss ≈ 110 MPa (minimal strain hardening) up to a strain of about 1% [Fig. 1(a)].8 Unloading and reloading indicates a permanent strain and hysteresis [Fig. 1(b)].1 In compression, the material remains elastic and fails at a strain exceeding 0.5% [Fig. 1(a)].8 Loading at /4 to the plates, to induce a uniform shear across the interfaces, elicits another inelastic response, exhibiting strains in excess of 8%,8 subject to a shear resistance, ss ≈ 40 MPa [Fig. 1(c)]. The consequence of inelasticity, particularly that in tension, is an insensitivity to severe strain concentration sites, because the inelastic deformation reduces (and in some cases, eliminates) stress concentrations.11–14 Such J. Mater. Res., Vol. 16, No. 9, Sep 2001
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an inelastic zone has been observed for nacre.8 While there are precedents for mechanically robust materials made from predominantly brittle, oxide, constituents,12,14 the enabling topologies found in nacre are unique. Namely, robustness is realized in a brittle, tabular phase (CaCO3) by dispersing a minimal amount (
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