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We consider the method of Poincaré to investigate thelocal index of vector fields in the plane. If m is the degreeof the first non-zero jet, Xm, of the vector field X at an isolatedzero, we explore the geometry of the pencil generated by thecoordinate functions of Xm when the absolute value of the indexof X, |ind (X)|, is m. We also find necessary and sufficientconditions for |ind (X)| to be m. 相似文献
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The theory of the work-hardening curve of a pure single crystal is discussed. An outline is given of the experimental methods available for the study of the mechanism of plastic deformation and work hardening. An attempt is made to correlate existing theories of work hardening. The theory is illustrated by discussions of copper, of other face-centred cubic metals, of the diamond and sphalerite structures, of hexagonal close-packed metals, of ionic face-centred cubic crystals and of body-centred cubic metals. 相似文献
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F. R. M. Nabarro 《Physics of the Solid State》2000,42(8):1456-1459
If a stress σ is applied to a polycrystal of grain size L, the mode of creep deformation depends on the answers to the following questions: (I) Does σ exceed the Peierls stress σp; (II) Does L exceed the dislocation spacing in a Taylor lattice stabilized by σp; (III) Does Lσ exceed the value required for a Frank-Read or Bardeen-Herring source to operate within the grain? (IV) Does L 1/2σ exceed the Hall-Petch value required for slip to propagate across a grain boundary? The (L, σ) plane is thus partitioned into regions in which different creep modes predominate. 相似文献
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F. R. N. Nabarro 《哲学杂志》2013,93(26):3047-3054
The analysis of thermal activation under shear stress in three- and even two-dimensional models presents unresolved problems. The analysis of one-dimensional models presented here may illuminate the study of more realistic models. For the model in which as many dislocations are poised for backward jumps as for forward jumps, the experimental activation volume V ?e(σa) under applied stresses close to σa is different from the true activation volume V(σ) evaluated at σ = σa. The relations between the two are developed. A model is then discussed in which fewer dislocations are available for backward than for forward jumps. Finally, the appropriateness of the hyperbolic sine approximation for moderately low stresses is defined and shown to be very limited. 相似文献
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