Tensile and compressive behavior of tungsten, molybdenum, tantalum and niobium at the nanoscale
Introduction
The mechanical behavior of metals with the body-centered cubic (bcc) structure has been widely studied as their high strengths and high melting temperatures make them attractive for structural applications [1], [2], [3], [4]. The stress–strain relationships in these metals generally have a strong temperature, strain-rate and orientation dependence, and also exhibit a tension–compression asymmetry due to their unusual slip behavior, i.e. a breakdown in Schmid’s law, where slip occurs on crystallographic planes other than the one with the maximum resolved shear stress [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. This atypical slip is due to the presence of non-planar screw dislocation cores, whose mobility can be significantly lower than that of edge dislocations, thereby governing plastic deformation in bcc metals. Ever since Vitek clearly showed that the 3-fold symmetry of screw dislocations in bcc metals is due to a core effect rather than to dislocation dissociation [4], many atomistic simulations have focused on studying the screw dislocation core structure in great detail [2], [7], [11], and it is now generally accepted that the lower mobility of the screw dislocation in bcc crystals is a direct consequence of its non-planar core structure [12].
A wealth of recent studies on the compression and tension of submicron cylindrical samples prepared by the focused ion beam (FIB) technique have made it possible to investigate the effect of sample size on the mechanical behavior of various metals and their alloys [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. It has been found that a variety of face-centered cubic (fcc) metals exhibit a pronounced increase in strength with decreasing pillar size due to the materials’ transition to dislocation nucleation and source-controlled plasticity at these small sizes [13], [14], [15], [25]. While FIB-fabricated bcc Mo nanopillars also show size effects in the flow stress [20], [21], [27], the underlying foundation for this size-dependent strength is quite the opposite: rather than annihilating at the free surfaces, dislocations in bcc metals have been found to form intricate networks as a result of mechanical deformation even in the smallest pillar size of ∼200 nm diameter [20], [21]. Molecular dynamics and dislocation dynamics simulations of Mo nanopillars under compression also clearly show dislocation self-multiplication, by which a single dislocation loop generates several additional dislocation segments and debris, moving in the opposite directions from one another towards the nanopillar surface [28]. Unlike FIB-fabricated nanopillars, Mo alloy nanopillars prepared by etching away the NiAl matrix in directionally solidified NiAl–Mo fibrous composites show near-theoretical strengths in compression, typical of the deformation of dislocation-free crystals [18]. When pre-strained, the same Mo alloy nanopillars weaken, suggesting that the initial microstructure, e.g. initial dislocation density and distribution, plays a critical role in the subsequent deformation [19].
Here we report the mechanical response during uniaxial compression and tension of four different 〈0 0 1〉-oriented single-crystalline bcc metals: W, Mo, Ta and Nb. We analyze yield strength, flow stress and strain-hardening, as well as strain-rate effects, and provide a transmission electron microscopy (TEM) analysis of microstructural evolution in the course of compression of the smallest Mo nanopillar.
Section snippets
Experiments
Nanopillars with circular cross-sections for compression and diameters between 200 and 900 nm and tension samples with rectangular cross-sections and effective diameters between 250 and 1000 nm were milled out of the well-annealed and electropolished (1 0 0) W, Mo, Ta, and Nb bulk crystals with a FIB [23]. The tension samples have effective diameters between 250 and 1000 nm, where , with d1 and d2 being the width and thickness of the rectangular cross-section measured from front and
Results
Fig. 1 shows typical compressive stress–strain curves of the studied metals and clearly demonstrates that plastic deformation regions are composed of discrete strain bursts (a nearly instantaneous drop in stress with increasing strain) followed by reloading segments. Most of the reloading segments appear to be elastic, however at least some of them are probably indicative of plastic strain-hardening associated with dislocation multiplication [21]. For example, Mo nanopillars with diameters of
Discussion
To investigate the specific aspects of Mo nanopillar deformation, we performed compression tests at different constant nominal displacement rates. When running the experiments under nominal displacement rate control, the linear relationship between displacement and time is maintained before an extended catastrophic strain burst, thereby allowing for direct conversion of the displacement rate into a constant strain rate. The yield strengths of Mo nanopillars at different sizes given as a
Conclusions
Uniaxial compression and tension tests on (0 0 1) single-crystalline bcc metals W, Mo, Ta and W at the nanoscale reveal the following results:
- 1.
The flow stress shows strong size effects in both compression and tension.
- 2.
The power-law slope for size-dependent flow stress in compression of Nb (−0.93) is much higher than those of other three metals: W (−0.44), Mo (−0.44) and Ta (−0.43). The power-law slopes for size-dependent flow stress in tension of the group VB metals Ta (−0.80) and Nb (−0.77) are
Acknowledgements
This work was supported by NSF CAREER Award (DMR-0748267) and by ONR under Grant No. N00014-09-1-0883. The authors acknowledge B. Van Leer from FEI Company for TEM sampling using FIB at 2 kV.
References (46)
- et al.
Acta Mater
(1998) - et al.
Acta Mater
(2008) - et al.
Acta Mater
(2008) - et al.
Acta Mater
(2008) Mater Sci Eng A
(2001)- et al.
Acta Mater
(2005) - et al.
Acta Mater
(2005) - et al.
Scr Mater
(2007) - et al.
Acta Mater
(2008) - et al.
Appl Phys Lett
(2008)
Scr Mater
Acta Mater
Acta Mater
J Mech Phys Solids
Mater Sci Eng – Struct Mater Prop Microstruct Process
MRS Bull
Acta Mater
Mater Sci Eng A – Struct Mater Prop Microstruct Process
Acta Metall Mater
Acta Mater
Acta Mater
Acta Mater
Mater Sci Eng A – Struct Mater Prop Microstruct Process
Cited by (316)
Thermal stabilizing and toughening of a dual-phase Nb alloy by tuning stabilizing element C in Nb-BCC
2024, Journal of Materials Science and TechnologyDeformation twinning in body-centered cubic metals and alloys
2023, Progress in Materials Science