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R9.5.1

A critical examination of the Berkovich vs. conical indentation based on 3D finite element calculation Sanghoon Shim1, Warren C. Oliver2, and George M. Pharr1,3 1 The University of Tennessee, Dept. of Materials Science & Eng., Knoxville, TN 37996 2 MTS Systems Corporation, Nanoinstruments Innovation Center, Oak Ridge, TN 37830 3 Oak Ridge National Laboratory, Metals & Ceramics Division, Oak Ridge, TN 37831 ABSTRACT Much of our understanding of the elastic-plastic contact mechanics needed to interpret nanoindentation data comes from two-dimensional, axisymmetric finite element simulations of conical indentation. In many instances, conical results adequately describe real experimental results obtained with the Berkovich triangular pyramidal indenter, particularly if the angle of the cone is chosen to give the same area-to-depth ratio as the pyramid. For example, conical finite element simulations with a cone angle of 70.3° have been found to accurately simulate experimental load-displacement curves obtained with the Berkovich indenter. There are instances, however, where conical simulations fail to capture important behavior. Here, 3D finite element simulations of Berkovich indentation of fused silica are compared to similar simulations with a 70.3° cone. It is shown that a potentially significant difference between the two indenters exists for the contact areas and contact stiffnesses. Implications for the interpretation of nanoindentation data are discussed. INTRODUCTION One of the more popular methods for evaluating hardness, H, and elastic modulus, E, from nanoindentation load-displacement data is that of Oliver and Pharr [1]. This method is based on two important relations: S=β and

2

π

E eff

A

P hc = hmax − ε max , S

(1)

(2)

where S is the contact stiffness, Eeff the effective elastic modulus, A the contact area, hc the contact depth, hmax the maximum indentation depth, Pmax the maximum indenter load, and β and ε are constants that depend on the indenter geometry. In order to implement the method, the contact stiffness is measured either from unloading data or by continuous stiffness measurement techniques, the contact depth is determined from directly measured quantities by means of Eq. 2, and the projected contact area is derived by evaluating an empirically determined area function at the contact depth, that is A=f(hc). For indentation with the Berkovich triangular pyramidal indenter used commonly in nanoindentation experiments, the constants β and ε used for data evaluation are derived largely by assuming that the Berkovich indenter can be adequately modeled by a conical indenter with a half-included tip angle of 70.3°, which gives the same area-to-depth ratio as the Berkovich. The conical geometry has the advantage that it is analytically more tractable, as well as being easier to implement in finite element simulation. However, the sharp edges on a Berkovich indenter can

R9.5.2

clearly have an important bearing on how elastic and plastic deformations proceed. Here, we conduct elastic and