On the measurement of stress–strain curves by spherical indentation
Introduction
The primary objective of this work was to compare the stress–strain curve of the aluminum alloy 6061-T6 as determined by spherical indentation and uniaxial tension. To accomplish that goal, existing indentation models were used to develop what we felt to be the most appropriate indentation test method. Developing the most appropriate load–time algorithm and the most accurate and meaningful way to establish the point of contact and the instrument load frame stiffness were among the most critical aspects of building the test method. Each of these issues plays a critical role in obtaining the most precise and accurate mechanical property measurements possible.
Developing the test method was an iterative process. The final verification of the models and our test method was based on their ability to determine the elastic modulus of the standard reference material, which in this case was fused silica. Young's modulus was chosen to benchmark the models and test method performance because it is an intrinsic material property and, as indicated by , , , , , it is a direct verification of whether or not the models and test method are calculating the correct contact area.
Once the models and test method demonstrated the ability to correctly measure the elastic modulus of the standard reference material, they were applied to the aluminum alloy 6061-T6. The primary questions were, can the models and test method accurately and precisely determine Young's modulus, E, and the yield strength, σy?
Section snippets
Theory
The models chosen to reduce the indentation data were that of Hertz [1], Oliver and Pharr [2] and Tabor [3]. Hertz's analysis, despite being based on the assumption of paraboloids in elastic contact, was chosen over Sneddon's [4] specific solution of spheres in elastic contact for two reasons: in the limit of small displacements (2hcR≫hc2), Hertz's solution is very similar to Sneddon's and Hertz's solution is algebraically much more simple. Hertz's analysis provides three expressions that are
Experimental methods
The indentation experiments were performed using a Nano Indenter® XP with MTS’ continuous stiffness measurement (CSM) technique. With this technique, each indent gives the load, displacement, and contact stiffness as a continuous function of the indenter's displacement into the sample [2]. Loading was controlled such that the loading rate divided by the load was held constant at 0.05/s. Experiments were terminated at the maximum load of the standard XP head, approximately 70 g. The four
Results and discussion
Fig. 1 represents the elastic modulus as a continuous function of the indenter's displacement into the sample for the standard reference material, fused silica. The literature value for fused silica is 72 GPa. Clearly, the models and method are doing a reasonably good job of evaluating the correct contact area using just the contact depth and the nominal radius of the tip. It is worth noting that all of the data in Fig. 1 are representative of an elastic contact, indicating that the
Conclusions
With the correct models and careful attention to experimental detail, spherical indentation can be successfully used to determine the elastic modulus of 6061-T6.
With sphere diameters of 120, 200, 260 and 300 μm, a good engineering estimate of the yield strength of 6061-T6 can be made.
Applying Hertz's elastic models to spherical indentation data can be successfully accomplished in the limit of small displacements and truly spherical tip geometry.
With respect to 6061-T6 and fused silica, the
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