Materials Science and Engineering A 528 (2011) 5036–5043 Contents lists available at ScienceDirect Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea Interpreting strain bursts and size effects in micropillars using gradient plasticity X. Zhang a,b , K.E. Aifantis b,c,∗ a School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China b Lab of Mechanics and Materials, Aristotle University of Thessaloniki, Greece c Physics, Michigan Technological University, USA article info Article history: Received 10 December 2010 Received in revised form 15 February 2011 Accepted 16 February 2011 Available online 22 February 2011 Keywords: Micropillar compression Strain gradient Size effects Strain bursts abstract Size effects and strain bursts that are observed in compression experiments of single crystalline micropil- lars are interpreted using a gradient plasticity model that can capture the process of sequential slip and heterogeneous yielding of thin material layers. According to in situ experiments during compression sub- grains and significant strain gradients develop, while deformation occurs through slip layers in the gauge region. In the multilayer strain gradient model, the higher order stress is discontinuous across the inter- face between a plastic layer and an elastic layer, but it becomes continuous across the interface between two plastic layers. Strain bursts occur when two neighboring layers yield. Based on this hypothesis the experimental stress–strain curves with strain bursts observed in micropillars can be fitted by properly selecting the number of layers that yield and the ratio of the internal length over the specimen size; the modulus and the yield stress are obtained from the experimental curves while the hardening modulus evolves during deformation based on the dislocation mechanisms. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Numerous studies have shown that the plastic deformation at the micron and sub-micron scales is dramatically different from that of the bulk material. Corresponding size effects that have been observed in torsion [1], indentation [2], and bending [3] are attributed to the presence of strain gradients developed dur- ing microscopically heterogeneous plastic deformation. In [4–6] it has been shown how this original gradient plasticity model [7] can conveniently describe such effects through the extra, internal length and specimen size dependent terms entering the relevant “load-deformation” relations. Conventional theories are incapable to explain size effects due to the lack of a length scale in the consti- tutive relations and the absence of spatial gradients and/or volume integrals accounting for non-local interactions. Size effects were not originally expected in tension/compression experiments as no macroscopic strain gradients were present, they have been experimentally observed, however, and gradient plas- ticity [4–6] was successfully used to interpret them by introducing “microscopic” rather than “macroscopic” strain gradients, which are obviously absent from tension/compression configurations. Recently, strong and rather peculiar size effects have also been observed in compression experiments of micro- and nano-pillars ∗ Corresponding author at: Aristotle University of Thessaloniki, Lab of Mechanics and Materials, Box 468, GR 54124 Thessaloniki, Greece. Fax: +30 2310 995921. E-mail address: k.aifantis@mom.gen.auth.gr (K.E. Aifantis). fabricated by the focused ion beam (FIB) method, where the flow stress increases when the diameter decreases [8–16]. Several researchers attributed the size effect to the FIB-induced precipitate strengthening and surface amorphization [15,16], however, pillars fabricated without the FIB method [17] also give the same size effect as the FIB-fabricated FCC micropillars, demonstrating that the size effects are not related to the fabrication method but to the underlying microstructure. In contrast to the smooth macroscopic stress–strain curve obtained during bulk compression, the stress–strain curves of micropillars contain several discrete slip bursts where the stress remains almost constant, while the strain “jumps” discontinuously to increasing values. The situation is reminiscent to “displacement bursts” observed during nanoindentation tests near grain bound- aries; a phenomenon which was also interpreted by using gradient plasticity with an interfacial energy [18]. In [8] it is argued that such kind of micropillar related deformation phenomena occur in the stochastic multiplication-limited exhaustion regime, and both size effects and strain bursts were attributed to the trunca- tion of dislocation sources and varying dislocation mechanisms at small volumes; for example it was argued that dislocations at such volumes are induced at large stresses and hence the disloca- tion velocity is very high and they accumulate at the pillar surface. But experimental evidence documenting these interpretations for micropillars is lacking. Some researchers have argued that the uniaxial compression behavior of micropillars can be attributed to the damage layer during the FIB method, but the experiments of [9] and the TEM 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.02.049