Geometrically necessary dislocation density distributions in Ti–6Al–4V deformed in tension
Introduction
Ti alloys offer good strength-to-weight ratios, corrosion resistance and fatigue performance, and consequently have found extensive use in both static and rotating components within the aerospace industry. Ti–6Al–4V is the most widely used Ti alloy and is one of the near-α alloys. Within the predominant α-phase plastic deformation primarily occurs through slip of dislocations with either 〈a〉 or 〈c + a〉 Burgers vectors [1]. The 〈a〉 Burgers vector is considerably shorter and so is energetically favoured and easier to move through the lattice. For the 〈a〉 dislocations, slip is generally easiest on prism planes, but basal slip is also possible and often only requires slightly more stress [1], [2], [3], [4], [5], [6]. The 〈c + a〉 dislocations slip on the pyramidal planes and have a considerably higher critical resolved shear stress [1], [2]. However 〈c + a〉 dislocations may be important in maintaining compatibility during deformation of Ti polycrystals. Grains close to having the c-axis aligned to the direction of uniaxial tensile deformation are both elastically stiffer [7], [8] and plastically hard, and as there is little resolved shear stress on the easy 〈a〉 prism or basal slip systems, slip on the harder 〈c + a〉 pyramidal slip systems may be required.
The existence of grains with hard and soft orientations in Ti and other hexagonal metals should lead to considerable heterogeneity in the distribution of stress and strain. Externally imposed strain gradients are known to cause increased strength in, for example, torsion or bending of thin structures [9], [10]. Strain gradients at the microstructural level are to be expected and will contribute to microstructure length scale effects on strength (e.g. the Hall–Petch effect). Physically based strain gradient plasticity has long been linked to the role of geometrically necessary dislocations (GNDs) in raising the total dislocation density and thus causing some hardening through a Taylor model for the flow stress. Nye [11] has shown that the density of GNDs may be represented by a second-rank tensor, called the dislocation tensor, which can be fully evaluated using geometry if the strain gradients are known. However, there are ambiguities in describing the dislocation tensor in terms of densities of different types of dislocations that may be present in the crystal lattice. Such analysis has been incorporated into finite-element-based crystal plasticity simulations of polycrystals [12], [13], [14] mostly in face-centred cubic materials. Dunne and co-workers [15], [16], [17] have used such simulations to study the deformation of near α-Ti, including examination of the grain size and orientation dependence of the technologically important cold-dwell effect in fatigue.
The scanning electron microscopy (SEM)-based electron backscatter diffraction (EBSD) method is well placed to bridge between X-ray and transmission electron microscopy (TEM) methods by revealing spatial patterning in deformation structures over regions that span several contiguous grains. The grain–grain interactions may become more apparent as any particular grain and the stress–strain distribution within it is seen in the context of its neighbourhood. Early work with EBSD used pattern blurring as a measure of the dislocation content [18], [19], but the advent of automated mapping has allowed the misorientations within the grains to be measured and used to assess the effects of plastic strain [20], [21], [22]. This has led to attempts to estimate the density of GNDs from the gradients in the lattice orientation distribution [23], [24] including recent extension of the method to 3-D focused ion beam SEM-generated datasets [25]. However, the Hough transform-based analysis of EBSD has an angular resolution limit in the range 1–0.5° [26], which limits analysis to the higher end of probable dislocation densities and so removes much of the detail from maps of the deformed metals.
In this paper we aim (i) to describe the application of the relatively new high-resolution EBSD technique to polycrystals, and (ii) to examine experimentally the nature of GND distributions within Ti deformed to a moderate tensile strain.
Section snippets
Material, microstructure and texture
The experiment was conducted on rolled bar stock of Ti–6Al–4V supplied by Rolls-Royce. This had first been pre-strained in the α–β temperature range, recrystallized in the β range, α–β forged and then rolled from a 125 mm square cross-section to a 75 mm diameter bar. Finally, it was annealed for 2 h at 700 °C to relieve residual stresses, and air cooled. This results in a microstructure composed primarily of globular α grains with small amounts of β primarily at the grain boundaries; the overall α
Results
Fig. 4a and b shows example maps of the total GND density measured within the undeformed Ti–6Al–4V alloy. Two further maps were also obtained and all showed similar patterns of low overall densities with a few regions with considerably higher densities. There is also some evidence of GND storage near grain boundaries. Errors in the cross-correlation analysis brought about by pattern overlap as the grain boundary is approached are one possible concern. However, analysis of patterns taken from
Discussion
The scatterplot in Fig. 11, and in the Supplementary material, shows higher GND density for smaller grains areas, but there is no strong trend with orientation or Schmid factor. The small grain areas seen in the two-dimensional maps could correspond to genuinely lower volume grains, or they could be sections through grains of average volume far from the equator. The mean equivalent circle diameter measured in the large-area EBSD maps (Fig. 2) was 11 μm but this includes grains sectioned near to
Conclusions
We have used the cross-correlation-based high-resolution analysis of EBSD patterns to assess the GND content in Ti–6Al–4V processed so as to be predominantly globular primary α-phase with some β-phase present mainly at grain boundaries and triple junctions. We make the following conclusions from the study:
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The average GND density within the undeformed material is well above the noise floor of the measurement and we observe elevated GND densities in a number of apparently small grains. These
Acknowledgements
This work was in part funded by EPSRC through grant EP/E044778/1, and P.D.L. is grateful for receipt of a Clarendon Scholarship. We thank Rolls-Royce for materials and some financial support for P.D.L.
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Present address: Technical University of Denmark, Kongens Lyngby, Denmark.