Hall–Petch Relationship in Aluminum and Aluminum Alloys

The mechanical properties of aluminum are shown to be of special importance beginning from the early 20th-century production of the material in single crystal and polycrystalline form. Experimental and theoretical researches of the time were concerned with particular influence of polycrystalline microstructure and the presence of crystal (grain) boundaries on both the material strength properties and on relation of those same properties to those for the full range of metal and alloy structures. Now it is well established that a relatively low value of the microstructural stress intensity, k_ε , is obtained for aluminum in the generalized Hall–Petch relation for its stress–strain, σ_ε − ε, behavior depending on the average grain diameter, l, with intercept (friction) stress, σ _0ε , which relation is given as: https://www.w3.org/1998/Math/MathML"> σ ε = σ 0 ε + k ε l − 1 / 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351045636/7e78a12c-3835-43b7-8655-9d9a7815bf87/content/unequ63_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>

With hindsight, taking σ _ε = σ _0ε provided the first connection between single crystal and polycrystalline strength measurements in the pioneering Taylor theory of plasticity proposed for aluminum and other face-centered cubic metals. Later, conventional and ultrafine grain size measurements are shown to verify the fuller H–P dependence. The present account builds onto the early history. A description is given for temperature, strain rate, and alloy-dependent mechanical property measurements. An understanding of the total measurements is described in terms of a dislocation pile-up model description for the relation. Emphasis is given to k_ε for pure aluminum and related metals being determined by cross-slip forced at grain boundaries. Particular attention is given to two characteristics of the metal mechanical behavior: (1) very high rate loading deformations leading to shock and shock-less isentropic compression experiments and (2) important grain size influences on nanopolycrystalline material behaviors. Additional results are presented on H–P aspects of the material strain ageing, shear banding, ductile fracturing, and fatigue behaviors.