Résumé
The flow under stress of a layered compound (SmA, lyotropic lamellar phase) is usually a highly complex phenomenon involving several scales of deformations. At high shear-rate, the stress/strain-rate relations are frequently non-linear[1] because of the presence of dislocations and macroscopic structures such as focal conic domains and onions (« smectic hedgehog defects »). These defects are easily observed under optical microscope but the connection between their individual motion and the macroscopic behavior is still a challenging problem.
At lower strains, in small displacements experiments, the situation seems simpler because the geometry of the layers is initially well-defined[2]. However, the theoretical establishment of the stress-strain relationships remains often speculative because of a lack of in-situ observations. The authors frequently evoke some complex behaviors of microscopic defects such as edge and screw dislocations present in the sample in order to explain the experimental results. For example, the helical instability of screw dislocations[3] into edge dislocation loops could explain some compression experiments of smectics[4] or even time-resolved Surface Force Apparatus experiments[5].
We have developed a simple experiment of microplasticity in which we can observe by optical methods the dynamics of single microscopic defects (edge and screw dislocations) under microscope in a smectic slab while measuring the macroscopic deformation of the sample. Several important mechanisms at the origin of the plasticity of smectics have been elucidated or confirmed by our direct observations[6]:
a)The relation between the existence of a macroscopic yield stress and the individual depinning of mobile edge dislocations from anchored screw dislocations.
b)The role of the heterogeneous/homogeneous nucleation of edge dislocations under strain.
c)The validity domain of the Orowan relation ruling the motion of dislocations in a smectic.
d)Different regimes (change of shapes and interactions with other dislocations) for climbing edge dislocations.
[1] See for exemple, C. Meyer, S. Asnacios, and M. Kleman, Eur. Phys. J. E, 6, 245 (2001).
[2] R. Bartolino and G. Durand, Phys.Rev.Lett., 39, 1346 (1977).
[3] L. Bourdon, M. Kléman, L. Lejcek and D. Taupin, J. de Phys. 1981, 42, 261 (1981).
[4] P. Oswald and M. Kléman, J. de Phys. Lettres, 45, L319 (1984).
[5] R. A. Herke, N. A. Clark, and M. Handshy, Phys.Rev. E, 56, 3028 (1997).
[6] C. Blanc, N. Zuodar, I. Lelidis, M. Kleman, J.-L. Martin, Phys. Rev. E, 69, 011705 (2004).