Materials Science and Engineering A 525 (2009) 68–77 Contents lists available at ScienceDirect Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea Inﬂuence of specimen dimensions and strain measurement methods on tensile stress–strain curves Y.H. Zhao a,∗ , Y.Z. Guo b,c , Q. Wei b,∗∗ , T.D. Topping a , A.M. Dangelewicz d , Y.T. Zhu e , T.G. Langdon f,g , E.J. Lavernia a a Department of Chemical Engineering and Materials Science, University of California at Davis, Davis, CA 95616, USA b Department of Mechanical Engineering, University of North Carolina at Charlotte, Charlotte, NC 28223, USA c NW Polytech University, Sch Aeronaut, Xian 710072, PR China d Los Alamos National Laboratory, Los Alamos, NM 87545, USA e Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695-7919, USA f Departments of Aerospace & Mechanical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089-1453, USA g Materials Research Group, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK article info Article history: Received 5 May 2009 Received in revised form 15 June 2009 Accepted 16 June 2009 Keywords: Strain measurements Tensile testing Finite element modeling (FEM) Miniature specimens Stress–strain curves abstract Miniature tensile specimens, having various sizes and geometries, are often used to measure the mechan- ical properties of bulk nanostructured materials. However, these samples are generally too small for use with conventional extensometers so that the strains are usually calculated from the crosshead displace- ments. This study uses experimental results and ﬁnite element modeling (FEM) to critically evaluate the inﬂuence of the specimen dimensions and strain measurement methods on the tensile curves obtained from miniature specimens. Using coarse-grained Cu as a model material, the results demonstrate that the values of strain obtained from the crosshead displacement are critically inﬂuenced by the speci- men dimensions such that the uniform elongation and the post-necking elongation both increase with decreasing gauge length and increasing specimen thickness. The results provide guidance on the opti- mum procedures for the tensile testing of miniature specimens of both coarse-grained and nanostructured materials. © 2009 Elsevier B.V. All rights reserved. 1. Introduction The numerous reports of super-high strength for various nanos- tructured (NS, structural features <100nm) metals and alloys continue to attract interest from the scientiﬁc and technical communities. It is evident, however, that a signiﬁcant obstacle obstructing the widespread engineering application of this class of materials lies in their generally poor ductility [1–4]. Inspec- tion of the scientiﬁc literature shows numerous recent efforts directed towards developing strategies for improving the ductil- ity of these materials and these strategies have met with varying degrees of success [5–15]. A review of the published experimental results reveals that the ductility is frequently measured using non- standardized mechanical testing incorporating miniature dog-bone tensile specimens having different sizes and geometries that are not in conformity with ASTM standards [16]. Thus, the thickness of some of these nanostructured tensile specimens vary from about ∗ Corresponding author. Tel.: +1 530 7529568; fax: +1 530 7529554. ∗∗ Corresponding author. Tel.: +1 704 6878213. E-mail addresses: yhzhao@ucdavis.edu (Y.H. Zhao), qwei@uncc.edu (Q. Wei). 100 m [10,11] or even about 10 m [17] to several millimeters [8,9,12–15] and the gauge lengths vary from 1 mm [18–21] to sev- eral millimeters [8–15,17] or even several centimeters [22] where these various dimensions depend primarily upon the availability of material. On the basis of ASTM standards, a subsize rectangular tensile specimen should have a gauge length of 25 mm, a width of 6 mm, a thickness smaller than 6 mm and a radius ﬁllet of 6 mm. An impor- tant requirement is that the ratio of gauge length to width should be maintained at 4. In the case of tensile specimens with circular cross-sections, the ratio of gauge length to gauge diameter should be 5 and the ﬁllet radius should equal the gauge diameter. In prac- tice, the ratio of gauge length to thickness/diameter used in NS materials is frequently smaller than 4. Moreover, because of the small dimensions of the gauge lengths, the strains of the minia- ture specimens are often derived from the crosshead displacements due to the difﬁculties in attaching strain gauges or applying exten- someters [18–21]. As a consequence of these variations, it is not surprising that published results for bulk NS materials are often dif- ﬁcult to interpret in terms of the underlying mechanisms (ductility, for example) and they invariably pose a challenge in any attempts to reproduce the data. 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.06.031