Cristian Teodosiu 教授 特別講演会

Over the last century, the research on the plastic behavior of materials has experienced a rather intriguing scenario. On one side, the solid-state physicists have gradually clarified the mechanisms of plastic deformations, recognizing the role played by dislocations and other crystal defects in the plastic deformation and the work-hardening of crystalline materials. On the other side, the engineering structural analysis has been essentially based on the use of phenomenological relationships, the so-called constitutive equations, which represent thermodynamic averages over space and time scales that are many orders of magnitude higher than the underlying elementary events of plastic deformation

In the last two decades, however, the attempts to overcome this gap by a multiscale approach have become more frequent and successful, being mainly motivated by (i) the necessity to clarify the damaging processes that take place within the grains and at the grain boundaries, (ii) the recognition of the fact that the design of new-generation materials, e.g. the very high-strength steels, requires the mastering of their microstructural properties, and (iii) the increasing interest in small-scale engineering systems.

While statistical approaches have considerably evolved in this area, the most effective way of incorporating in the continuum mechanics the knowledge acquired at the micro- and mesoscales remains the introduction of the so-called internal state variables. The current values of the latter are supposed to fully characterize the response of the material to further thermomechanical loadings, thus summarizing at the macroscopic scale the history of the microstructural events.

Within a multiscale modeling, the choice of the internal state variables and of their evolution equations should follow, at least in a heuristic way, the information obtained from the lower space and time scales and to eventually provide, in turn, the information to be used at larger scales. This information-passing approach is less rigorous than a statistical one, but proves to be more flexible and effective.

The aim of this lecture is to review some significant aspects of the dislocation modeling of the large deformation plasticity of single crystals and crystalline aggregates, by making use of such a multiscale internal-variable approach.

For single-crystal plasticity, the most important internal variables are the scalar dislocation densities on various glide planes. Their evolution is governed by balance equations involving dislocation production and annihilation rates. On the other hand, dislocation interactions determine the slip rates and the evolution of the critical shear stresses. The parameters of the flow and hardening rules involved in the model have been identified by mechanical tests and recently confirmed by simulations using 3-D lattice dislocation dynamics.

The dislocation-based models of single-crystal plasticity have been successfully validated by finite-element simulation of inhomogeneously deformed multicrystals. In particular, such simulations have helped understanding the influence of the crystallographic mismatch across grain boundaries and of the difference in size between neighboring grains on the heterogeneity of plastic deformation and on the strain localization and damage.

One of the most striking features of the microstructural organization inside the grains is that dislocations evolve towards some steady-state microstructures, e.g. dislocation walls, provided that a sufficient amount of monotonic deformation takes place along the same strain path. Reversed deformation and changes in strain path generally tend to the modification or dissolution of preformed microstructures and the formation of new ones that correspond to the last deformation mode. The last part of the lecture will focus on the modeling of such processes by means of tensor-valued internal variables associated with the directional strength and polarity of dislocation structures and will point out the relevance of this type of modeling for some classes of advanced materials.