Continuum Plasticity Theory in Relation to Solid Solution, Dispersion, and Precipitation Hardening

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Abstract
Small volume fractions of very small particles in a pure metal eliminate easy glide in a single crystal and produce very high yield strength in a polycrystal. The validity of a partial explanation provided by the application of ordinary continuum mechanics on the microscale is explored here. Size effect associated with inhomogeneity of the metal matrix is seen to play a major role because a small volume fraction of rigid spheroidal particles in any homogeneous elastic-plastic matrix can contribute little to engineering yield strength and to subsequent work-hardening. However, particle strength in itself cannot provide the yield strength and flow level of a structural metal. The increased resistance to additional slip must be due mainly to the expanding network of intersecting slip triggered by many particles of very small size. This and the elastic distortion in the immediate vicinity of solute atoms and extremely small particles represent significant large local changes in geometry. Consequently, such predictions of the general theorems of conventional plasticity as the lack of influence of initial stress on flow level need not be valid.

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