Indentation Schmid factor and incipient plasticity by nanoindentation pop-in tests in hexagonal close-packed single crystals

Abstract

For hexagonal close-packed (HCP) Hf, Mg and Ti single crystals, indentation Schmid factors, defined as the ratio of maximum resolved shear stress to the maximum contact pressure, were calculated for three typical families of slip systems, including basal 〈a〉, prismatic 〈a〉, and second pyramidal 〈c+a〉 slip systems. The dependence of indentation Schmid factors on the crystallographic orientation shows the same hard/soft directions as in the uniaxial tests, but with much reduced variations of magnitudes. The axial ratio, c/a, leads to noticeable effects on the indentation Schmid factors only when the indentation direction deviates from the c-axis by more than about 30°, as shown by the comparison among these three crystals. These predictions are compared to nanoindentation pop-in tests on Mg single crystals in literature and Hf single crystals conducted in this work. The elastic-plastic transition under spherical nanoindentation can be quantitatively measured by a sudden displacement burst (or pop-in) in the load-displacement curve. For defect-free single crystals, the first pop-in results from homogeneous dislocation nucleation, and correspondingly the maximum resolved shear stress (as calculated from pop-in load and indentation Schmid factor) reaches the theoretical strength of the material. Pop-in loads were found to be low for 〈101¯2〉 indentation and high for orientations close to the c-axis. While previous experiments in NiAl showed excellent agreement between indentation Schmid factor and pop-in measurements, Mg and Hf works here do not have such an agreement. It is suggested that each of the three sets of slip systems may govern a different range of indentation directions, or stress components other than resolved shear stress dictate the incipient plasticity.