Abstract

The microstructural length scale of metals changes by orders of magnitude under extreme processing conditions producing a concurrent wide range of mechanical strength and plasticity behaviors. A unified stress-strain σε model is formulated that’s based on superposing the components of asymptotic-curvilinear work hardening Θσ to qualify and quantify these mechanical behaviors. This approach accounts for the rapid strengthening of metals beyond the initial yield point, through extended steady-state deformation, to the structural instability. The relationship between the softening coefficients cbi of the work hardening formulation Θσ and strength are found to reveal the microstructural scale in the material. Specifically, the rapid decrease in the slope of the Θσ curve provides a measure for microstructural size consistent with a functional Hall-Petch relationship of strength. A successful application is shown for the tensile behavior of pure aluminum microstructures that result from extreme plastic deformation by equal-channel angle pressing.

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