Eur. Phys. J. E 7, 303-310 (2002)
DOI: 10.1140/epje/i2001-10096-4
Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheets
K. OkumuraPhysique de la Matière Condensée, Collège de France, 11, place Marcelin-Berthelot, 75231 Paris cedex 05, France Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1, Otsuka, Bunkyo-ku, 112-8610, Japan
(Received 16 November 2001)
Abstract
In our previous paper (Eur. Phys. J. E 4, 121 (2001)) we proposed a
coarse-grained elastic energy for nacre, or stratified structure of hard and
soft layers found in certain seashells . We then analyzed a crack running
perpendicular to the layers
and suggested one possible reason for the enhanced toughness of this
substance. In the present paper, we consider a crack running parallel to the
layers. We propose a new term added to the previous elastic energy, which is
associated with the bending of layers. We show that there are two regimes
for the parallel-fracture solution of this elastic energy; near the fracture
tip the deformation field is governed by a parabolic differential equation
while the field away from the tip follows the usual elliptic equation.
Analytical results show that the fracture tip is lenticular, as suggested in
a paper on a smectic liquid crystal (P.G. de Gennes, Europhys. Lett. 13,
709 (1990)). On the contrary, away from the tip, the stress and
deformation distribution recover the usual singular behaviors (
and
, respectively, where
x is the distance from the tip).
This indicates there is no enhancement in toughness in the case of parallel
fracture.
87.68.+z - Biomaterials and biological interfaces.
46.50.+a - Fracture mechanics, fatigue and cracks.
81.07.-b - Nanoscale materials and structures: fabrication and characterization.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002
