Inverse scaling functions in nanoindentation with sharp indenters: Determination of material properties

Abstract

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 Λ=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 Λ 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.

Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach

“…1,2 Subsequently, several methods using multiple sharp-tipped indenters have been developed to extract plastic properties, [3][4][5][6][7][8] although these methods still present a degree of inconvenience when operating with these indenters. In changing to spherical indentation, various authors have demonstrated that, by analyzing the force-depth curves, it is possible to determine material plastic properties.…”

Micromechanics of pyramidal indentation in fcc metals: Single crystal plasticity finite element analysis

“…Such isotropic continuum simulations have provided an insight into the contact mechanics of strain hardening solids and constitute a robust, yet flexible tool to the development of methodologies for mechanical property extractions from indentation experiments (for sharp indentation, see, e.g., Bucaille et al, 2003;Chollacoop et al, 2003;Alcalá , 2003, Cao andLu, 2004;Casals and Alcalá , 2005;Wang et al, 2005;Tho et Alkorta et al, 2005;Ogasawara et al, 2006;Kim et al, 2006;Chollacoop and Ramamurty, 2006;. In the other spectrum of material length scales, atomistic and discrete dislocation dynamics simulations are shedding light into the mechanics of dislocation emission, the individual interactions between dislocations, and on the interplay between grain boundaries and dislocations in ultra low-load nano-indentation experiments (e.g., Kelchner et al, 1998;Fivel et al, 1998;Lilleodden et al, 2003;Feichtinger et al, 2003;Ma and Yang, 2003;Zhu et al, 2004, Shen andLeger, 2004;Yoon et al, 2004;Lee et al, 2005;Shiari et al, 2005;Saraev and Miller, 2006;Minor et al, 2006;Tsuru and Shibutani, 2007).…”

On the uniqueness and sensitivity issues in determining the elastic and plastic properties of power-law hardening materials through sharp and spherical indentation

“…As it is generally difficult to derive accurate analytical expressions for the indentation response of materials, numerical finite element simulations have been developed to address two classes of problems: (i) the 'forward problem' -where the characteristics of the indentation response are predicted from known material elasto-plastic properties, and (ii) the 'reverse problem' -where the material elasto-plastic properties are estimated from the measured indentation responses (e.g. [40][41][42][43][44][45]). By combining numerical simulations with dimensional analysis, the corresponding 'forward' and 'reverse' algorithms have been developed to characterize the indentation response of select classes of materials, such as the powerlaw hardening metallic materials.…”