| 講演要旨： |
The most valuable studies on the crystal lattice instability have been done in the field of phase transitions in solids. This problem is also very important in the Materials Science. A huge gap between theoretical strength estimated for defect-free crystals and measured yield stress for real materials stimulated development of the dislocation theory. First practical application of the theoretical strength was related to whiskers, nominally dislocation-free filamentary crystals. Nanoindentation experiments havea wakened fresh interest to the theoretical strength problem. In such experiments for single crystals the measured load-displacement response shows characteristic discontinuities attributed to the generation of crystal defects. Surprisingly, defects can be generated not only at the contact surface but also in the bulk of the defect-free single crystal. To explain these experiments, recently the theoretical strength of crystalline materials has been much studied numerically and theoretically, and some attempts to develop criteria for lattice instability under homogenous strain have been made. We will present the very essential ideas employed in the fascinating field of lattice instability. (i) We will start from the general theory of bifurcation and instability. There is a nice saying that “all stable systems are equally stable but every unstable system is unstable in its own way”. We will see that this can be applied to the lattice instability as well. The variety of faces of instability makes the development of a universal instability criterion a difficult task. (ii) Next point is the relation between discrete media and continuum. The lattice instability will be discussed at the atomistic level and also with the use of a phenomenological approach. (iii) We will touch some open problems in the theory of lattice instability such as the post-critical behavior, interaction of the sample with the loading device, “dependence on the path”, etc. (iv) Finally, some numerical results on the 2D nanoindentation problem will be presented. The ideas will be presented at an elementary level, without the use of complicated mathematics. |
