E4 Base Mechanical Properties

Topic

The elastic constants of this metal—which characterize its stiffness and elastic response under load—follow the same isotropic elastic formalism used by a model describing the fundamental mechanical properties of glass; because this metal is a polycrystal with sufficiently random grain orientation, its elastic constants are independent of the loading direction, allowing them to be described using this isotropic formalism rather than the anisotropic formalism required for an oriented single crystal. The fact that this metal is polycrystalline, with grains oriented randomly relative to one another, results in isotropic effective elastic constants, even though each individual grain is itself elastically anisotropic.

Beyond these elastic constants, the metal's mechanical strength—its intrinsic resistance to plastic deformation—is primarily determined by the grain size established by another model in this set, in accordance with the Hall-Petch relationship: the smaller the grain size, the greater the number of grain boundaries per unit volume acting as obstacles to dislocation movement, and consequently, the higher the metal's mechanical strength according to the Hall-Petch relationship.

This mechanical strength is also determined by the dislocation density established by yet another model in the set, based on the Taylor relationship: the higher the dislocation density, the more the dislocations impede one another as they move through each other's strain fields, resulting in greater mechanical strength according to the Taylor relationship. Since grain size and dislocation density influence mechanical strength in this way—albeit through distinct mechanisms—their respective contributions are approximately additive in determining the metal's total mechanical strength. Therefore, the mechanical strength associated with the onset of yielding in this model can also be estimated empirically—without the need for an actual tensile test—based on the metal's hardness, using Tabor's relationship; indeed, both quantities (hardness and this mechanical strength) are measured via the two tests described in other models within this set: the tensile test and the hardness test. Establishing this mechanical strength—and specifically the yield stress marking the elastic limit—as a static property of the metal allows it to serve as the static reference point against which another model in the set measures the metal's fatigue: the progressive failure occurring under cyclic loading at levels well below that same static yield stress.

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