Huiyang Fei Amit Abraham Mechanical and Aerospace Engineering, School for Engineering of Matter, Transport and Energy, Fulton Schools of Engineering, Arizona State University, Tempe, AZ, 85287-8706 Nikhilesh Chawla Mechanical and Aerospace Engineering, Materials Science and Engineering, School for Engineering of Matter, Transport and Energy, Fulton Schools of Engineering, Arizona State University, Tempe, AZ, 85287-8706 Hanqing Jiang 1 Mechanical and Aerospace Engineering, School for Engineering of Matter, Transport and Energy, Fulton Schools of Engineering, Arizona State University, Tempe, AZ, 85287-8706 e-mail: hanqing.jiang@asu.edu Evaluation of Micro-Pillar Compression Tests for Accurate Determination of Elastic-Plastic Constitutive Relations The micro-pillar compression test is emerging as a novel way to measure the mechanical properties of materials. In this paper, we systematically conducted finite element analysis to evaluate the capability of using a micro-compression test to probe the mechanical properties of both elastic and plastic materials. We found that this test can provide an al- ternative way to accurately and robustly measure strain, and to some extent, stress. Therefore, this test can be used to measure some strain related quantities, such as strain to failure, or the stress-strain relations for plastic materials. [DOI: 10.1115/1.4006767] Keywords: micro-pillar compression, finite element analysis, elastic, plastic 1 Introduction Understanding deformation behavior of materials requires knowledge of the local stress-strain behavior of individual micro- structural phases and constituents. For example, the deformation behavior of dual phase steels is controlled by the martensite con- stituent and ferrite. In Sn-rich alloys used in electronic packaging, the mechanical properties of Cu 6 Sn 5 intermetallic, Sn-Ag 3 Sn eutectic, and pure Sn dendrites need to be measured. Such meas- urements cannot be made by making these materials in bulk form, because the microstructure, texture, and density of defects may change. Quantifying the stress-strain behavior of small volumes is a challenge. Indentation techniques have been developed that ena- ble the measurement of Young’s modulus and hardness. Cur- rently, the nanoindentation technique can achieve subnanometer displacement resolution and 1 nano-Newton force resolution, which makes the technique widely used to determine mechanical properties of small volumes [1]. Despite the popularity of the in- dentation test, it still has some intrinsic shortcomings. The main problem is that indentation involves a complex stress/strain field underneath the indenter depending on the specific tip geometry. Furthermore, extraction of uniaxial stress-strain constitutive rela- tions, while possible, require complex iterative methods [1]. Recently, a variant on nanoindentation, called micropillar com- pression, has been developed. The technique uses a nanoindenter with a flat punch to compress a small cylindrical volume (1 lm di- ameter by 2 lm length cylinders) to obtain a uniaxial stress-strain behavior (Fig. 1(a)). Micropillars are machined by milling materi- als of interest using focused ion beam (FIB) (Fig. 1(b)) with diam- eters ranging from 200 nm to a few lm[2] within a single phase of the constituent. Figure 1(c) shows a pillar of Cu 6 Sn 5 intermetal- lic milled by FIB [3]. Various materials have been tested by this technique, including Mg, Ta, and Cu 6 Sn 5 [3–6]; other studies have focused on simulations based on crystal plasticity [7] and dislocation dynamics [8]. Compared with the micro-indentation test, micro-compression has the obvious advantage of a relatively uniform stress/strain field. However, since micro-compression test is a new technology to measure the strain-strain relation, there is no standard yet. Moreover, there are several experimental variables, however, that may affect accurate measurements of strain and stress. These vari- ables include the aspect ratio a (the ratio of height h and diameter d of the pillar), size of substrate below the pillar, taper angle h (>0) (the angle between the tangent of wall and axis of the pillar), fillet angle, misalignment between the pillar axis and the compres- sion direction, and stiffness of the substrate. It also must be real- ized that the presence of the substrate leads this problem to become complicated and many straightforward analytical analyses cannot be simply applied. The effect of some of these variables can be intuitively under- stood. For example, for a compliant substrate, the pillar will sink upon compression and the majority of the deformation will be car- ried by the substrate instead of the pillar, which will lead to inac- curate measurement of the pillar deformation. This sink-in effect may be magnified for pillars with a large aspect ratio and sup- pressed for pillars with a large taper angle. A larger aspect ratio may also lead to premature buckling of the pillars upon compres- sion. This intuitive argument indicates that these factors may be coupled together to influence the accuracy of the experimental measurement. Zhang et al. [4] used the finite element method to study some of these effects, including aspect ratio, fillet angle, taper angle and misalignment for a pillar on a very thin substrate sitting on a rigid base. In this paper, we have conducted systematic and parametric fi- nite element analysis to evaluate the micro-compression test from several aspects, and propose methods to accurately calculate stress and strain with good correlation with experimentally measureable 1 Corresponding author. Manuscript received July 31, 2011; final manuscript received February 16, 2012; accepted manuscript posted May 3, 2012; published online September 17, 2012. Assoc. Editor: Daining Fang. Journal of Applied Mechanics NOVEMBER 2012, Vol. 79 / 061011-1 Copyright V C 2012 by ASME Downloaded 26 Dec 2012 to 129.219.247.33. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm