Modelling Small Deformations of Polycrystals by A. S. Argon, J. Zarka (auth.), John Gittus, Joseph Zarka

By A. S. Argon, J. Zarka (auth.), John Gittus, Joseph Zarka (eds.)

The clinical paintings of Jean Mandel has been really wealthy within the quarter of the mechanics of solids; the themes which he has handled were super diversified, from the speculation of plasticity, buckling, soil mechanics, visco-elasticity, the speculation of decreased versions, and thermo­ dynamics, to percolation in porous media. yet all through this com­ prehensive paintings Jean Mandel has consistently maintained his curiosity in forming connections among the houses of fabrics (strength, deformability, viscosity) and the houses in their easy components. what's occasionally said in fabrics technology because the transition from the microscopic to the macroscopic has for him been a truly consistent course of analysis, which he by no means ceased to motivate within the Laboratoire de Mecanique des Solides of which he used to be the director. it truly is identified that during the plasticity of metals everlasting deformations has to be sought in intercrystalline slip and extra in most cases in disloca­ tions and some of the microstructural defects. prior to deformation of polycrystals is tackled, it will be important to appreciate the mechanisms which happen in the crystal: different structures of slip that may be activated and likewise the undemanding mechanisms of twinning. Jean Mandel has proven find out how to make the transition from the behaviour of the only crystal to that of the polycrystal and has given the relation­ ships among the final everlasting deformation of the polycrystal and the plastic deformation of the one crystal.

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INTRODUCTION In practice, it is often convenient to regard engineering materials as continua, even though, in reality, most materials are highly heterogeneous at the micro-level, consisting of a variety of constituents. Polycrystals, composites, rocks, soils, and plain and reinforced concrete are typical examples. To apply the continuum theory to the analysis of boundary value problems associated with materials of this kind, a 'homogenisation' of one kind or another must be introduced, whereby an equivalent locally homogeneous (but not necessarily isotropic) continuum is 41 42 S.

B and we put (Ox, b ) = 8 (Fig. 13). (8 = 0, for an edge dislocation; 8 = lT /2, for a screw dislocation). z L b ~-----------------+y Fig. 13. Geometry for a straight dislocation. (iv) We define the self-energy of a dislocation by the stored energy of the elastic strain due to it. 2) where c lies between I and 5. (c) How Can We Interpret Plastic Strain With the Help o/the Dislocation? So have to be displaced, one in respect to the other by a translation, the vector of which is the Burgers vector.

PHYSICAL BASIS FOR PLASTICITY AND VISCOPLASTICITY + ~-. -I I I - I"-- + +b \ \ I \ \ \ I I \ \ \ I I I I U 33 \ -b \ \ Fig. 17. Annihilation of two opposite straight dislocations. (g) How Are the Dislocations Distributed? Several observations with the help of electron microscopes have shown that the dislocation lines are randomly distributed and generally split into small straight segments which stretch out in some particular directions. These segments are arrested in front of other segments or intersect them, forming tangles.

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