Computational modeling of the forward and reverse problems in instrumented sharp indentation

Abstract

A comprehensive computational study was undertaken to identify the extent to which elasto-plastic properties of ductile materials could be determined from instrumented sharp indentation and to quantify the sensitivity of such extracted properties to variations in the measured indentation data. Large deformation finite element computations were carried out for 76 different combinations of elasto-plastic properties that encompass the wide range of parameters commonly found in pure and alloyed engineering metals; 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, and the Poisson's ratio, ν, was fixed at 0.3. Using dimensional analysis, a new set of dimensionless functions were constructed to characterize instrumented sharp indentation. From these functions and elasto-plastic finite element computations, analytical expressions were derived to relate indentation data to elasto-plastic properties. Forward and reverse analysis algorithms were thus established; the forward algorithms allow for the calculation of a unique indentation response for a given set of elasto-plastic properties, whereas the reverse algorithms enable the extraction of elasto-plastic properties from a given set of indentation data. A representative plastic strain ε r was identified as a strain level which allows for the construction of a dimensionless description of indentation loading response, independent of strain hardening exponent n. The proposed reverse analysis provides a unique solution of the reduced Young's modulus E*, a representative stress σ r, and the hardness p ave. These values are somewhat sensitive to the experimental scatter and/or error commonly seen in instrumented indentation. With this information, values of σ y and n can be determined for the majority of cases considered here provided that the assumption of power law hardening adequately represents the full uniaxial stress–strain response. These plastic properties, however, are very strongly influenced by even small variations in the parameters extracted from instrumented indentation experiments. Comprehensive sensitivity analyses were carried out for both forward and reverse algorithms, and the computational results were compared with experimental data for two materials.