Depth-sensing instrumented indentation with dual sharp indenters

Abstract

A methodology for interpreting instrumented sharp indentation with dual sharp indenters with different tip apex angles is presented by recourse to computational modeling within the context of finite element analysis. The forward problem predicts an indentation response from a given set of elasto-plastic properties, whereas the reverse analysis seeks to extract elasto-plastic properties from depth-sensing indentation response by developing algorithms derived from computational simulations. The present study also focuses on the uniqueness of the reverse algorithm and its sensitivity to variations in the measured indentation data in comparison with the single indentation analysis on Vickers/Berkovich tip (Dao et al. Acta Mater 49 (2001) 3899). Finite element computations were carried out for 76 different combinations of elasto-plastic properties representing common engineering metals for each tip geometry. Young’s modulus, E, was varied from 10 to 210 GPa; yield strength, σ y, from 30 to 3000 MPa; and strain hardening exponent, n, from 0 to 0.5; while the Poisson’s ratio, ν, was fixed at 0.3. Using dimensional analysis, additional closed-form dimensionless functions were constructed to relate indentation response to elasto-plastic properties for different indenter tip geometries (i.e., 50°, 60° and 80° cones). The representative plastic strain ε r, as defined in Dao et al. (Acta Mater 49 (2001) 3899), was constructed as a function of tip geometry in the range of 50° and 80°. Incorporating the results from 60° tip to the single indenter algorithms, the improved forward and reverse algorithms for dual indentation can be established. This dual indenter reverse algorithm provides a unique solution of the reduced Young’s modulus E ∗, the hardness p ave and two representative stresses (measured at two corresponding representative strains), which establish the basis for constructing power-law plastic material response. Comprehensive sensitivity analyses showed much improvement of the dual indenter algorithms over the single indenter results. Experimental verifications of these dual indenter algorithms were carried out using a 60° half-angle cone tip (or a 60° cone equivalent 3-sided pyramid tip) and a standard Berkovich indenter tip for two materials: 6061-T6511 and 7075-T651 aluminum alloys. Possible extensions of the present results to studies involving multiple indenters are also suggested.