Computational modeling of the forward and reverse problems in instrumentedsharp indentation

A comprehensive computational study was undertaken to identify the extent t o which elastoplastic properties of ductile materials could be determined f rom 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 c ombinations of elasto-plastic properties that encompass the wide range of p arameters commonly found in pure and alloyed engineering metals: Young's mo dulus, E, was varied from 10 to 210 GPa, yield strength, sigma (y), from 30 to 3000 MPa, and strain hardening exponent, n, from 0 to 0.5, and the Pois son's ratio, v, 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 comput ations, analytical expressions were derived to relate indentation data to e lasto-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 epsil on (r) was identified as a strain level which allows for the construction o f a dimensionless description of indentation loading response, independent of strain hardening exponent n. The proposed reverse analysis provides a un ique solution of the reduced Young's modulus E*, a representative stress si gma (r), and the hardness p(ave). These values are somewhat sensitive to th e experimental scatter and/or error commonly seen in instrumented indentati on. With this information, values of sigma (y) and n can be determined for the majority of cases considered here, provided that the assumption of powe r law hardening adequately represents the full uniaxial stress-strain respo nse. These plastic properties, however, are very strongly influenced by eve n small variations in the parameters extracted from instrumented indentatio n experiments. Comprehensive sensitivity analyses were carried out for both forward and reverse algorithms, and the computational results were compare d with experimental data for two materials. (C) 2001 Acta Materialia Inc. p ublished by Elsevier Science Ltd. All rights reserved.