Inverse scaling functions in nanoindentation with sharp indenters: Determination of material properties
- PDF / 2,890,484 Bytes
- 15 Pages / 612 x 792 pts (letter) Page_size
- 47 Downloads / 207 Views
This paper, based on extensive finite element simulations and scaling analysis, presents scaling functions for the inverse problem in nanoindentation with sharp indenters to determine material properties from nanoindentation response. All the inverse scaling functions were directly compared with results calculated using the large deformation finite element method and are valid from the elastic to the full plastic regimes. To relate the material properties to measurable indentation parameters a new nondimensional experimental parameter ⌳⳱P/(DS) was introduced, where P is load, D is indentation depth, and S is contact stiffness. This parameter is monotonically related to the ratio of yield stress to modulus. The modulus, hardness and yield stress are presented as explicit functions of ⌳ and the strain hardening exponent. The error in the inverse modulus, hardness, and yield stress due to uncertainty of the strain hardening exponent was studied and is compared with that of the traditional Oliver–Pharr method. The method of determining the strain hardening exponent from measurement with an additional indenter with a different cone apex angle is described. For this, a scaling function with the strain hardening exponent as the only unknown was obtained. In this way, the modulus, hardness, yield stress and strain hardening exponent may be determined. Experimental results show the inversion method permits the modulus and hardness to be accurately determined irrespective of the effects of pileup or sink-in.
I. INTRODUCTION
Instrumented micro- and nanoindentation have become important tools for measuring mechanical properties on a small scale.1–5 Measurements are performed with very small diamond indenter tips and high force and displacement resolution by well-controlled nanoindentation instruments, allowing measurement of very small samples and localized phases of materials. Due to the very complex nature of the indentation process, numerical methods are essential to relate material properties to measurable indentation parameters. Simulations of load– displacement indentation response during loading and unloading have been performed in several comprehensive studies using finite element analysis (FEA).6–11 To reduce the number of governing parameters and formulate general relations between measuring parameters— load P, indentation depth D, and the initial slope of unloading S [N/m] [Fig. 1(a)]—and the material parameters, dimensional analysis has been applied to obtain
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0124 J. Mater. Res., Vol. 20, No. 4, Apr 2005
scaling relations for conical indentation in elasto-plastic solids.7,12–16 The scaling analysis has been extended to include the cone angle using similarity analysis.17 Young’s modulus and indentation hardness1,2 are traditionally determined by inverse analysis of the indentation loading and unloading responses based on Sneddon’s elastic solution.18 However since Sneddon’s solution is based on linear elastic theory, t
Data Loading...
