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Influences of stress on the measurement of mechanical properties using nanoindentation: Part II. Finite element simulations A. Bolshakov Department of Materials Science, Rice University, 6100 Main Street, Houston, Texas 77005

W. C. Oliver Nano Instruments, Inc., 1001 Larson Drive, Oak Ridge, Tennessee 37830

G. M. Pharr Department of Materials Science, Rice University, 6100 Main Street, Houston, Texas 77005 (Received 5 September 1995; accepted 10 November 1995)

The finite element method has been used to study the behavior of aluminum alloy 8009 during elastic-plastic indentation to establish how the indentation process is influenced by applied or residual stress. The study was motivated by the experiments of the preceding paper which show that nanoindentation data analysis procedures underestimate indentation contact areas and therefore overestimate hardness and elastic modulus in stressed specimens. The NIKE2D finite element code was used to simulate indentation contact by a rigid, conical indenter in a cylindrical specimen to which biaxial stresses were applied as boundary conditions. Indentation load-displacement curves were generated and analyzed according to standard methods for determining hardness and elastic modulus. The simulations show that the properties measured in this way are inaccurate because pileup is not accounted for in the contact area determination. When the proper contact area is used, the hardness and elastic modulus are not significantly affected by the applied stress.

I. INTRODUCTION

The experimental results presented in the preceding companion paper demonstrate that applied or residual stresses in materials tested by nanoindentation methods can influence the measurement of their hardness, H, and elastic modulus, E, in ways that can lead to important errors.1 The experiments, which were conducted using special specimens of aluminum alloy 8009 to which stresses could be applied in a controlled manner, showed that the errors have their origin in the contact areas, A, determined from analysis of the nanoindentation loaddisplacement data. The magnitude of the error depends on the magnitude and sign of the applied stress and is largest when the specimen is stressed in compression; when compressive stresses approaching the elastic limit are applied to alloy 8009, the contact areas are underestimated by as much as 15%. Furthermore, since both the hardness and elastic modulus are computed in a manner that directly depends on A, the error in the contact area produces errors in H and E which manifest themselves as apparent decreases in these parameters with increasing stress. Optical measurement of the actual indentation contact areas revealed that the apparent stress dependences of H and E are in fact not real; rather, when H and E are computed using the optically meas760

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J. Mater. Res., Vol. 11, No. 3, Mar 1996

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ured contact areas, both the hardness and the elastic modulus of alloy 8009 are ess