A NECESSARY AND SUFFICIENT FORMULATION FOR TORSION PROBLEMS OF ANISOTROPIC BODIES

Non-dimensionalized equations and boundary conditions are presented for the torsion problem of an anisotropic body. The error of the fundamental solution cited in some boundary element books Is pointed out after an examination of the fundamental solution. Furthermore,a necessary and sufficient boundary integral equation is given for the problem and compared with the conventional boundary integral equation. Numerical results show that great errors of the boundary shear stresses obtained by the conventional boundary integral equation appear with a small error of torsion stiffness. Meanwhile,the necessary and sufficient;boundary integral equation always gives accurate results.

Microstructure and strength of a tantalum-tungsten alloy after cold rolling from small to large strains

Microstructural evolution of a refractory tantalum-tungsten alloy(Ta-4%W)after cold rolling from small to large von-Mises strains(0.12-2.7)was quantitatively studied using transmission electron microscopy.Grain subdivision was observed to take place at two levels.Geometrically necessary boundaries nearly paralleling to slip planes enclosed volumes further divided by diffuse cells and by remnants of Taylor lattices.With increasing strain,the diffuse cells evolved into clear incidental dislocation boundaries enclosing cells,while the Taylor lattices disappeared.Grain subdivision was thus intermediate between those observed in cell forming and in non-cell forming alloys.Meanwhile,the average misorientation angle across all boundaries increased while the average boundary spacing decreased.Distributions of the microstructural parameters at each strain level were found to exhibit universal scaling laws.The microstructural evolution was found closely linking to the observed high strength and strain hardening of this alloy.Based on measured microstructural parameters,the flow stress was calculated utilizing linearly addition of the strengthening by solutes,incidental dislocation boundaries(Taylor strengthening)and geometrically necessary boundaries(Hall-Petch equation).The relative contribution of each strength mechanism evolved with increasing strain and with microstructural evolution:solutes and friction stress dominated at small strains while boundaries dominated at larger strains.Calculated strengths were in close agreement with experimental tension tests and demonstrated an unexpectedly high and continuous parabolic hardening without transition across this large strain range.