Abstract: A constitutive equation was established using finite element method (FEM) combined with neural network optimization and dimensionless model to uniformly describe the nanoindentation behavior of different crystal planes of sapphire crystal. The surface micromechanical behavior of four typical crystal planes (C, A, R, M) of the sapphire crystal was studied using nanoindentation method. The comparison between the calculated results of the constitutive equation and the measured results show that: the loading and unloading curves can be expressed by quadratic functions of the indentation depth h; the loading curve is a function of the elastic modulus E, yield stress Y, and work hardening index n of the intrusion surface, while the unloading curve is also related to the unloading position (the maximum depth) h_max in addition to these three factors; for the same crystal plane, the residual depth h_r is proportional to h_max, and the plastic work W_p is proportional to the third power of h_max. The results also indicate that, for super hard and brittle materials such as sapphire crystal, which are difficult to apply conventional mechanical performance testing methods, the combination of the constitutive equation and nanoindentation testing can effectively obtain their basic mechanical property.

Key words: sapphire crystal, crystal plane, nanoindentation, finite element method, constitutive equation