Finite element analysis and experimental investigation of the Hertzian assumption on the characterization of initial pla
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Dylan J. Morrisa) National Institute of Standards and Technology, Materials Science and Engineering Laboratory, Gaithersburg, Maryland 20899-8520
Stefhanni L. Jennerjohn and David F. Bahr Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99164
Lyle Levine National Institute of Standards and Technology, Materials Science and Engineering Laboratory, Gaithersburg, Maryland 20899-8520 (Received 31 July 2008; accepted 12 November 2008)
Sudden displacement excursions during load-controlled nanoindentation of relatively dislocation-free surfaces of metals are frequently associated with dislocation nucleation, multiplication, and propagation. Insight into the nanomechanical origins of plasticity in metallic crystals may be gained through estimation of the stresses that nucleate dislocations. An assessment of the potential errors in the experimental measurement of nucleation stresses, especially in materials that exhibit the elastic–plastic transition at small indentation depths, is critical. In this work, the near-apex shape of a Berkovich probe was measured by scanning probe microscopy. This shape was then used as a “virtual” indentation probe in a 3-dimensional finite element analysis (FEA) of indentation on h100i-oriented single-crystal tungsten. Simultaneously, experiments were carried out with the real indenter, also on h100i-oriented single-crystal tungsten. There is good agreement between the FEA and experimental load–displacement curves. The Hertzian estimate of the radius of curvature was significantly larger than that directly measured from the scanning probe experiments. This effect was replicated in FEA simulation of indentation by a sphere. These results suggest that Hertzian estimates of the maximum shear stresses in the target material at the point of dislocation nucleation are a conservative lower bound. Stress estimates obtained from the experimental data using the Hertzian approximation were over 30% smaller than those determined from FEA.
I. INTRODUCTION
Instrumented indentation, widely used in the measurement of mechanical properties such as elastic modulus and hardness, is also frequently used to probe interesting mechanical phenomena. Many of the phenomena sensed through nanoindentation are a combination of defect nucleation and propagation events. Examples of combined nucleation and propagation events include the initiation of plastic yield and fracture, and phase transformations. The advantage of very small-scale instrumented indentation (nanoindentation) is its potential to probe nucleation phenomena at length scales a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0134 J. Mater. Res., Vol. 24, No. 3, Mar 2009
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representative of the nucleating defect. The nucleation and propagation events are detected by discontinuous events in the load–displacement data. Typically, the discontinuities are of the “pop-in” type, which is a sudden displacement excursion i
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