The design of accurate micro-compression experiments
Introduction
Current commercial nano-indenters have sub-nanometer displacement resolution under ideal conditions (perhaps reduced to ∼0.1 nm due to thermal drift and noise), and a load resolution better than 1 nano-newton. This high precision makes the technique popular in many applications such as the measurement of mechanical properties of very thin films and tribological measurements of coatings. In a conventional nano-indentation experiment, a Berkovich tip is used to probe the nano-scale mechanical behavior (such as hardness and elastic modulus) as a function of indentation depth. For example, it was found that the indentation size has a strong effect on the hardness of single crystal silver [2]. Recently, a modified tip geometry has been utilized to probe the nano-scale mechanical behavior of micro-scale or even sub-micro pillars [1], [3], [4]. In this modification, the sharp Berkovich tip is truncated, resulting in a flat ended tip and converting the indentation system into a compression system. This technique is commonly called “micro-compression” or μ-compression, and has been used for the investigation of specimen size effects on the mechanical properties of single crystals of metals and alloys [1], [3], [4]. Although these previous works are for single crystals or large crystals where crystal anisotropy is significant, we are interested also in the application of this technique to isotropic materials, e.g., nano-structured materials and metallic glasses. This approach may be effective for many advanced materials which are difficult to obtain in bulk form, and whose tensile ductility is limited (so that micro-tension tests are difficult). For example, it is currently extremely difficult to produce bulk forms of many metals and ceramics with nano-crystalline micro-structure [5], [6]. Nevertheless, they can be readily produced in thin foils and small cubes or cylinders with dimensions less than 1 mm [7]. Further, advanced technologies such as micro-electromechanical and/or nano-electromechanical systems (MEMS, NEMS) require knowledge of the mechanical properties of the materials used to fabricate such systems [8]. Conventional mechanical testing techniques are not useful due to the small size of specimens.
Micro-compression makes use of a conventional nano-indenter and a flat-end tip, to measure the stress–strain curves of materials using posts as small as 200–300 nm in diameter [4]). Technologies such as focused ion beams (FIB) enable researchers to fabricate such posts with ease. However, these posts usually have one end (the bottom) fixed on the matrix (or the base material), while the top end is pressed by the flat-end tip during a μ-compression experiment. To what extent can the data from such micro-scale measurements be used to represent the macro-scale materials behavior? In this work, we present a parametric study of the design of accurate μ-compression experiments using two-dimensional (2D) and three-dimensional (3D) finite element modeling. We consider geometric factors such as the fillet radius (or the curvature at the bottom of the post connecting to the base), and the aspect ratio of the post (defined as the height/diameter ratio), as well as materials properties such as strain hardening and strain rate sensitivity. The 3D model is used to examine plastic buckling phenomena, and the effect of post taper and misalignment of the system on the accuracy of measurement. The numerical results presented here can serve as guidelines for the implementation of μ-compression experiments on various materials. We find that μ-compression can be used to measure the mechanical properties of mechanically isotropic materials (such as nano-structured materials and metallic glasses) to very good accuracy, as well as to explore size effects in such materials.
Section snippets
Modeling and results
In this section, we first use axisymmetric 2D simulations to study the effects of specimen geometry on the output. Next, we examine the effects of friction, post taper, and system misalignment on the buckling of the post using 3D simulations.
Conclusions
We have found that micro-compression tests can be used to faithfully measure the mechanical properties of certain materials. Our parametric study shows that:
- 1.
Fillet radius/post radius ratios of 0.2–0.5 are recommended to provide sufficient test accuracy.
- 2.
Strain hardening of the material significantly affects the μ-compression test accuracy, particularly when the fillet radius is large (close to the post radius).
- 3.
From our 3D μ-compression simulations, for aspect ratios ⩽5, first-mode plastic
Acknowledgements
The authors are grateful to Dr. Michael Uchic at the Air Force Research Laboratory for illuminating discussions. This work is supported by the US Army Research Laboratory through Grant No. DAAL01-96-2-0047 and ARMAC-RTP Cooperative Agreement Number DAAD19-01-2-0003. The authors wish to express appreciation for valuable discussions with F.H. Zhou and B.W. Schafer of Johns Hopkins University.
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