Does the stacking fault energy affect dislocation multiplication?
Introduction
Dislocation based plasticity requires the presence of mobile dislocations, which are either from pre-existing dislocation sources or homogenously nucleated. The stress required to activate a dislocation source depends inversely on its size, which results in various size effects in materials [[1], [2], [3], [4], [5]]. The likelihood of finding a dislocation source of a certain activation stress depends on the size of the strained volume. While large strained volumes potentially contain large dislocation sources (requiring low source activation stresses), the maximum dislocation source size in small volumes will be smaller. In the extreme case the strained volume is free of dislocation sources and new sources need to be nucleated homogenously [5,6].
This size effect has been experimentally investigated by nanoindentation in crystalline materials using spherical indenters. Upon loading, the spherical indenter creates a highly stressed region in the sample beneath the contact surface which can be described by Hertz contact mechanics. As soon as a dislocation source is activated or homogenously nucleated, a sudden displacement burst – called a pop-in – occurs [5]. The pop-in represents the transition from pure elasticity to plasticity, and the related maximum shear stress in the material at the pop-in can reach stresses of the order of the theoretical stress, ranging from G/2π to G/30 [[5], [6], [7]].
The most basic assumption of the theoretical shear strength τth required to cause plasticity in a perfect crystalline material is based on the shear stress required to displace perfectly stacked atoms by a Burgers vector b. The theoretical strength τth can then be estimated using the lattice spacing d, Hooke's law [8] with the shear modulus G according to Eq. (1).
Using this assumption one would expect that the theoretical strength should be similar for materials with the same crystal structure. However dislocation nucleation is a process involving the displacement of atoms, and therefore the chemical bonding characteristics will also impact τth. This is found by density functional theory (DFT) calculations [[9], [10], [11]]. If one compares Cu and Al – which both possess the same crystal structure – their theoretical strength is remarkably different (compare τth, Cu ≈ GCu/14, τth, Al ≈ GAl/9). It was shown that Al has a high theoretical shear strength because its strong directional bonds can sustain a long-range distortion before “breaking” [9].
Of course the bond characteristics influence many more physical properties than the theoretical strength. Take for instance the ability of creating stacking faults in a material. Atoms with strong directional bonds tend to have a higher SFE [9,10]. This is also reflected in the previous example of Cu and Al. Hence, one could hypothesize that the stress required for dislocation nucleation should systematically depend on the SFE. While the important role of the SFE on the plastic-deformation properties (microstructure evolution, mechanical performances [12,13]) is well understood, the impact of the SFE on dislocation nucleation and multiplication at stress close to the theoretical strength is to the best of our knowledge not investigated experimentally. Molecular dynamics (MD) simulations addressed the important role of the unstable stacking fault energy. For instance, Bitzek showed that the stress required for dislocation nucleation in Au nanowires strongly depends on the semi-empirical potential used [14]. If the potential shows a high unstable stacking fault energy, the stress required for dislocation nucleation is high. However, according to Bitzek's data the SFE is of minor importance.
The matter of interest to this study is therefore the mutual dependence of the SFE and the stress required to cause dislocation multiplication.
Section snippets
Materials and method
A diffusion couple with a pair of Cu-20 at.% Al alloy and pure Cu was employed to fabricate copper alloys with continuous change of Al content [12,15,16]. After being heated to 950 °C the sample was held at temperature for 48 h to bond the sample by interdiffusion. Subsequently, the diffusion couple was ground and mechanically polished by oxide polishing suspension (OPS). The local chemical composition was measurement by electron probe micro-analyzer (EPMA, JEOL JXA-8100). Then, the grain
Result
The EBSD micrograph of the diffusion couple (see Fig. 1a) shows a large area of {110}-oriented grains. In addition, the locations of site specific indents to probe different Al concentrations are indicated by a “P”. The local chemical composition as analyzed by EPMA shows, that the diffusion zone is ~1800 μm wide with a continuous change of Al (see Fig. 1b). Because the initial contact surface of the diffusion couple can well be identified in the SEM and EBSD image (marked by a black arrow in
Possible origin of the change in τmax
In all of our samples τmax are close to the theoretical strength of Cu which was reported to be ranging from 1.2 to 4 GPa [8,10]. However, due to the dispersion of the statistical distribution presented in Fig. 3b, we likely did not nucleate dislocations from an initially dislocation free area but rather activated pre-existing dislocation sources.
Our results clearly document a systematic variation of the stress required to activate a dislocation source with Al content. Possible sources of this
Conclusion
We investigated the impact of the stacking fault energy on the dislocation nucleation behaviour in face entered cubic metals by analysing the statistical pop-in behaviour. For this purpose we used various Cu-Al alloys with different Al content – thus different SFE – showing pop-in stresses close to the theoretical strength value. We found that the stress required to activate or nucleate dislocations scales with the SFE. The higher the SFE, the higher the pop-in stress. Our experimental data
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
Juan Li would like to thank the China Scholarship Council (CSC) for the scholarship granted to support this work. We thank Gerhard Dehm (MPIE) and George M. Pharr (Texas A&M) for comments regarding our work. The support from Angelika Bobrowski, Jürgen Wichert and Tristan Wickfeld for their help in sample preparation, Irina Wossack for EPMA measurement, and Stephan Spöllmann from the Ruhr University Bochum for AES measurements is acknowledged.
Data availability statement
The raw data required to reproduce these findings are available upon request.
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