Indentation Schmid factor and orientation dependence of nanoindentation pop-in behavior of NiAl single crystals

Instrumented nanoindentation techniques have been widely used to characterize the small-scale mechanical behavior of materials. The elastic-plastic transition during nanoindentation is often indicated by a sudden displacement burst (pop-in) in the measured load-displacement curve. In defect-free single crystals, the pop-in is believed to be the result of homogeneous dislocation nucleation because the maximum shear stress corresponding to the pop-in load approaches the theoretical strength of the materials and because the statistical distribution of pop-in stresses is consistent with what is expected for a thermally activated process of homogeneous dislocation nucleation. This paper investigates whether this process is affected by crystallography and stress components other than the resolved shear stress. A Stroh formalism coupled with the two-dimensional Fourier transformation is used to derive the analytical stress fields in elastically anisotropic solids under Hertzian contact, which allows the determination of an indentation Schmid factor, namely, the ratio of maximum resolved shear stress to the maximum contact pressure. Nanoindentation tests were conducted on B2-structured NiAl single crystals with different surface normal directions. This material was chosen because it deforms at room temperature by {1 1 0}〈0 0 1〉 slip and thus avoids the complexity of partial dislocation nucleation. Good agreement is obtained between the experimental data and the theoretically predicted orientation dependence of pop-in loads based on the indentation Schmid factor. Pop-in load is lowest for indentation directions close to 〈1 1 1〉 and highest for those close to 〈0 0 1〉. In nanoindentation, since the stress component normal to the slip plane is typically comparable in magnitude to the resolved shear stress, we find that the pressure sensitivity of homogeneous dislocation nucleation cannot be determined from pop-in tests. Our statistical measurements generally confirm the thermal activation model of homogeneous dislocation nucleation. That is, the extracted dependence of activation energy on resolved shear stress is almost the same for all the indentation directions considered in this study, except for those close to 〈0 0 1〉. Because very high pop-in loads are measured for orientations close to 〈0 0 1〉, which implies a large contact area at pop-in, there is a higher probability of activating pre-existing dislocations in these orientations, which may explain the discrepancy near 〈0 0 1〉.