Anisotropy in the hardness of single crystals

Abstract The results of this work, and those published by other researchers who have used Knoop indentation measurements, confirm that the nature of anisotropy in hardness is essentially determined by the crystal structure and the primary slip systems which accommodate dislocation motion during indentation. Materials belonging to the same class of crystal structure and having common slip systems possess similar anisotropic properties. The varying extent of work-hardening or fracture, associated with indentations, does not appear to influence the anisotropy— although twinning on the basal planes of hexagonal closepacked metals may have a significant effect. An analysis of the indentation process is presented which establishes a clear relationship between the ‘effective resolved shear stress’ (t0'), in the bulk of the crystal beneath the indenter, and the observed hardness. Directions which correspond to the minimum values of t'e, on specific crystallographic surfaces, are those of maximum hardness and conversely. The analysis is shown to be equally applicable to a wide range of crystalline solids including nonmetallic materials, of various crystal structure, and typical f.c.c., b.c.c. and c.p.h. metals. Finally, anisotropy in hardness can be used to identify active slip systems in those crystals where it is possible for dislocations to move on more than one system.