True Hardness Evaluation of Bulk Metallic Materials in the Presence of Pile Up: Analytical and Enhanced Lobes Method App
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THE mechanical properties, such as yield stress, of bulk metallic materials can be derived from their hardness measurements.[1,2] In this regard, in the last few decades, a variety of low-scale load indentation techniques have been developed to measure mechanical properties.[3] To measure the contact area, classic microhardness requires indent imaging after tip unloading. On the other hand, in the submicron range, nanoindentation is an instrumented indentation method widely used to determine the mechanical properties of both bulk solids and thin films, which in principle does not need any indent imaging[4–7] (to cite but a few). Nanoindentation equipment was first introduced in the early 1980s (e.g., Reference 8). Since then, owing to the particularly high load resolution, the accuracy of positioning, and displacement, continuous recording indentation techniques, such as nanoindentation, have become to be rapidly established as a means of determining material hardness.[9–14] Nanoindentation provides accurate measurements of the continuous variation in indentation M. CABIBBO, Associate Professor, and P. RICCI, PhD, are with Dipartimento di Ingegneria Industriale e Scienze Matematiche, Faculty of Engineering, Universita` Politecnica delle Marche, 60131 Ancona, Italy. Contact e-mail: [email protected] Manuscript submitted December 7, 2011. Article published online September 11, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A
load, P, down to lN, as a function of the indentation depth, h, down to tens of nanometers. The continuous load and displacement readings provide a material response to deformation from which the Young’s modulus, E, and the hardness, H, can be determined. Material hardness is generally obtained by dividing the maximum applied load by the residual contact area.[5,7,11–14] For the measurements of the Young’s modulus and hardness of materials, Doerner and Nix[7] were the first to propose the use of the unloading curve slope at the initial stage of unloading. Their method was later modified by Oliver and Pharr,[11,15] to extend to a larger scale the elastic recovery range during unloading. Thereafter, assumptions and limitations inherent to these methods were reviewed by Fisher-Cripps.[16] The indenter contact area is the key measurement feature in the Oliver and Pharr’s approach, which is directly evaluated from the load-displacement curves, thus making the imaging of the indent impression unnecessary. From the load-displacement curve, it is possible to determine the peak load, Pmax, the displacement at peak load, hmax, and the initial unloading contact stiffness, S = dP/dh, i.e., the slope of the initial portion of the unloading curve.[7,15–20] To date, a large number of nanoindentation investigations to determine hardness and other mechanical properties of different materials using the classical Oliver and Pharr’s method have been reported in the literature (e.g., References 7, 11–14, 16, 21–23). VOLUME 44A, JANUARY 2013—531
In general, sharp, geometrically similar indenters, such as the Ber
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