Effects of Alloying Elements on the Multiplication and Motion of Dislocations during High-Temperature Deformation in Solid-Solution Copper Alloys

Abstract

Pure copper and Cu-30 mass% Zn (Cu-Zn) alloy were subjected to tensile deformation at room temperature (approximately 298 K) and 573 K. Dislocation multiplication and motion during deformation were analyzed using neutron diffraction line-profile analysis. For the pure copper specimens, the dislocation density during deformation at 573 K was lower than that at room temperature. In contrast, the Cu-Zn alloys exhibited comparable levels of dislocation multiplication at both temperatures. Line-profile analysis revealed that the crystallites in the pure copper specimens became finer as the dislocation density increased, while the crystallite size of the Cu-Zn alloy specimens deformed at 573 K was considerably large and beyond the range that can be evaluated by the line-profile analysis. In the Cu-Zn alloys, although the dislocation density at 573 K was comparable to that at room temperature, the texture evolved by dislocation motion was weakened at 573 K, suggesting suppressed dislocation motion under these conditions. Transmission electron microscopy observations further demonstrated distinct dislocation substructures in the Cu-Zn alloys deformed at room temperature and 573 K. At room temperature, a Taylor lattice structure was observed, characterized by dislocations accumulating on planar slip planes. In contrast, at 573 K, dislocations were randomly distributed in a wavy form without forming tangles. This behavior suggests that the mobility of dislocations is reduced owing to interactions between solid solution elements and dislocations in the Cu-Zn alloys at 573 K.

 

This Paper was Originally Published in Japanese in J. Japan Inst. Copper 63 (2024) 1–7. Title and abstract were slightly modified.

Evolution of dislocation substructures of Cu-Zn alloy during tensile deformation at room temperature and 573 K.

1. Introduction

The work hardening properties of copper alloys during plastic deformation depend on both the alloying elements and the deformation temperature. Work hardening is governed by dislocation multiplication, and the relationship between flow stress (σ) and dislocation density (ρ) is expressed in eq. (1), where the flow stress increases proportionally with the square root of the dislocation density [1, 2].

  

\begin{equation} \sigma = \sigma_{0} + M_{T}\alpha Gb\sqrt{\rho}. \end{equation} (1)

Here, σ₀, M_T, α, G, and b represent the frictional stress, Taylor factor, dislocation strengthening coefficient, shear modulus, and the size of the Burgers vector, respectively. Additionally, dislocation density is related to plastic shear strain (γ), as expressed in terms of dislocation density and the mean travel distance of dislocations ($\bar{x}$) in eq. (2):

  

\begin{equation} \gamma = \rho b\bar{x}. \end{equation} (2)

Alloying elements resist dislocation glide, thereby reducing dislocation mobility. As $\bar{x}$ decreases in eq. (2), dislocation multiplication compensates for the reduced mobility. The behavior of dislocation multiplication during plastic deformation varies with the type and concentration of solid solution elements in solid-solution-type copper alloys. Stronger size effects and higher concentrations of alloying elements reduce dislocation mobility while promoting dislocation multiplication [3, 4]. However, at high deformation temperatures, dislocation mobility increases, leading to a larger $\bar{x}$, which makes dislocation multiplication less likely. Thus, alloying elements and deformation temperature collectively influence dislocation mobility, dislocation multiplication, and consequently, flow stress.

The stacking fault energy of copper alloys, which varies with ambient temperature, also impacts plastic deformation [5]. In alloys with low stacking fault energy, dislocations dissociate, and the slip plane becomes fixed, resulting in planar dislocation motion. At elevated temperatures, increased stacking fault energy causes dissociated dislocations to revert to perfect dislocations, enabling non-planar motion through cross-slip. Additionally, dislocation climb and diffusion of alloying elements occur at high temperatures. Therefore, when analyzing work hardening at room and elevated temperatures, it is crucial to account for the differing dislocation motions and multiplication behaviors under each condition.

Line profile analysis using diffraction methods is an effective approach for quantitatively evaluating dislocation parameters, including dislocation density, dislocation strain field, and crystallite size [6–10]. Such measurements should be conducted on bulk samples to observe deformation at high temperatures. Although laboratory X-ray diffraction methods are commonly employed, the influence of surface oxide films formed at elevated temperatures cannot be overlooked. Neutrons, with their high penetration depth into metals, provide an alternative light source well-suited for such analyses. The Materials and Life Science Experimental Facility (MLF) at the Japan Proton Acceleration Research Complex (J-PARC) offers time-of-flight neutron diffraction using 25 Hz pulsed neutrons. Diffraction patterns obtained at this frequency enable continuous monitoring of microstructural evolution during high-temperature deformation. At BL20 (iMATERIA) in the MLF, texture analysis can also be performed alongside line profile analysis [11–13]. As alloy textures are formed by dislocation glide, dislocation motion can be indirectly evaluated by texture analysis.

This study evaluates dislocation multiplication during deformation at room and elevated temperatures in pure copper and Cu-Zn alloys with low stacking fault energies. In situ neutron diffraction measurements were used to assess dislocation multiplication and motion through line profile analysis. Texture analysis was also conducted to examine the influence of solute atoms on dislocations and texture evolution during high-temperature deformation.

2. Experimental

Pure copper (>99.90 mass% Cu) and Cu-30 mass% Zn alloys, referred to as Cu-Zn alloys, were used to explore the effects of solid-solution elements. The grain morphologies of the samples are shown in Fig. 1, with average grain sizes of 40 µm for pure copper and 25 µm for the Cu-Zn alloy. Dumbbell-shaped tensile specimens had a deformation gauge diameter of 8 mm and a parallel length of 26 mm, which exceeded the incident neutron beam size (22 mm × 22 mm). In situ neutron diffraction measurements during tensile deformation were performed at BL20 (iMATERIA), MLF, J-PARC. Tensile deformation tests were conducted at room temperature (RT, approximately 298 K) and at 573 K. To facilitate high-temperature measurements, the chamber was filled with He gas, and specimens were heated using an infrared furnace [14] positioned to avoid the neutron beam path. Temperature control was achieved with an R-type thermocouple attached to the specimen. To ensure uniform heating, tensile testing began after maintaining the target temperature for 600 s. The initial strain rate was 1 × 10⁻⁴ s⁻¹.

Fig. 1

Grain maps of (a) pure copper and (b) Cu–Zn alloy specimens before tensile deformation.

Line profile analysis was conducted using the convolutional multiple whole profile (CMWP) method [15]. Variations in the shape and width of neutron diffraction peaks were analyzed to determine microstrain and crystallite refinement caused by dislocations. The CMWP method estimates dislocation parameters, such as dislocation density and crystallite size, by fitting a theoretical line profile (I_theoretical) to experimental diffraction profiles. The theoretical line profile was obtained by convolving the line profile due to microstrain dislocations (I_strain), crystallite size (I_size), and the instrumental system (I_inst).

  

\begin{equation} I_{\text{theoretical}} = I_{\text{strain}} \otimes I_{\text{size}} \otimes I_{\text{inst}} + B.G. \end{equation} (3)

Texture analysis was performed using Rietveld analysis of the neutron diffraction data. Diffraction patterns were collected at 132 observation orientations in iMATERIA utilizing detectors surrounding the specimen [14]. Rietveld analysis was applied to the diffraction patterns from each orientation, and orientation distribution function (ODF) analysis was simultaneously conducted to evaluate the texture. The MAUD program [16] and the E-WIMV method [17] were employed for Rietveld texture and ODF analyses, respectively.

Dislocation substructures were observed using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). EBSD samples were sectioned parallel to the direction of the tensile axis, polished with colloidal silica, and finished using argon-ion milling. TEM was performed at an acceleration voltage of 200 kV, with the electron beam incident oriented in the ⟨110⟩ direction. Specimens were prepared parallel to the tensile axis and thinned using electropolishing with the twin-jet method.

3. Results and Discussions

3.1 Characteristics of dislocation multiplication at room- and high-temperature deformations

Figure 2 presents the true stress-true strain curves for the pure copper and Cu-Zn specimens. The Cu-Zn specimen exhibited a higher flow stress than the pure copper specimen, with flow stress decreasing at 573 K compared to room temperature. These variations in flow stress with alloying elements and deformation temperature can be explained by changes in parameters such as dislocation density and shear modulus, as indicated in eq. (1). To examine how dislocation density varies with alloying elements and deformation temperature, kernel average misorientation (KAM) maps from EBSD observations are shown in Fig. 3. KAM values are primarily associated with geometrically necessary (GN) dislocations and are proportional to dislocation density [18]. Comparisons between the KAM maps of pure copper and Cu-Zn specimens indicate that the KAM values for the Cu-Zn alloy were consistently higher than those for pure copper, reflecting a higher GN dislocation density in the Cu-Zn specimen. This higher GN dislocation density corresponds to the higher flow stress observed in the Cu-Zn alloy. When comparing KAM values for room- and high-temperature deformation, no significant difference was observed for either the pure copper or Cu-Zn alloy specimens. This indicates that the number of GN dislocations generated during room-temperature deformation and high-temperature deformation was similar. Consequently, GN dislocations do not appear to account for the differences in flow stress between room- and high-temperature deformations.

Fig. 2

True stress–strain curves of pure copper and Cu–Zn alloy specimens at room temperature (RT) and 573 K.

Fig. 3

KAM maps at true strain of 0.14 of the pure copper specimens deformed at (a) RT, (b) 573 K, and the Cu–Zn alloy specimens deformed at (c) RT, (d) 573 K. θ_ave is the average KAM value.

Neutron diffraction line profile analysis provides the total dislocation density, which is the sum of GN and statistically stored (SS) dislocation densities. Variations in dislocation density with true strain, as determined from neutron diffraction line profile analysis, are shown in Fig. 4. The Cu-Zn specimen exhibited a higher dislocation density than the pure copper specimen, irrespective of deformation temperature. As flow stress is proportional to the square root of dislocation density, the higher dislocation density in the Cu-Zn specimen accounts for its higher flow stress.

Fig. 4

Changes in root square of dislocation density, $\sqrt{\rho } $ of (a) pure copper and (b) Cu–Zn alloy specimens as a function of true strain.

The dislocation density of the pure copper specimen during high-temperature deformation was lower than that during room-temperature deformation. This reduction is likely due to higher dynamic recovery at elevated temperatures. Additionally, increased dislocation mobility at high temperatures led to a greater mean travel distance for dislocations. Consequently, the rate of increase in dislocation density was reduced, as described by eq. (2), resulting in a lower flow stress for the pure copper specimen. In contrast, while the flow stress of the Cu-Zn specimen during high-temperature deformation was lower than that during room-temperature deformation, its dislocation density remained nearly unchanged between the two conditions. This suggests that factors other than dislocation density contribute to the reduced flow stress of the Cu-Zn specimen during high-temperature deformation.

To understand the relationship between flow stress and deformation temperature, variations in the shear modulus (G) and the dislocation strengthening coefficient (α) from eq. (1) must be considered. The shear modulus was measured using the torsional resonance method, and its values at room temperature and 573 K are presented in Table 1. At 573 K, the shear modulus decreased by approximately 10%, which contributed to the reduced flow stress. Table 2 summarizes the dislocation strengthening coefficients calculated from the flow stress and dislocation density using eq. (1). Both specimens exhibited significant reductions in the dislocation strengthening coefficient at 573 K. For the Cu-Zn specimen, the comparable dislocation densities at room temperature and 573 K indicate that the lower strengthening coefficient at 573 K was the primary factor behind the decreased flow stress. Since the dislocation strengthening coefficient depends on the frequency of forest dislocation cutting [19], differences in the spatial distribution of dislocations between room temperature and 573 K likely influenced this variation.

Table 1 Shear moduli (GPa) of pure copper and Cu–Zn alloy specimens at room temperature and 573 K.

Table 2 Dislocation strengthening factor of pure copper and Cu–Zn alloy specimens at room temperature and 573 K.

The spatial distribution of dislocations can be estimated from the crystallite size determined through line profile analysis. Crystallites are regions dominated by dislocation structures, such as arrays and cell walls. During plastic deformation, dislocations align through motion, and crystallites become refined as dislocation substructures evolve into features such as cell structures. Figure 5 illustrates the changes in crystallite size as a function of true strain. For both pure copper and Cu-Zn specimens under room-temperature deformation, crystallite sizes decreased with increasing true strain. However, for the pure copper specimen at 573 K, the crystallite size was larger than that at room temperature due to the lower dislocation density. In contrast, the crystallite sizes of the Cu-Zn specimen at 573 K were identified only as larger than 2000 nm due to the negligible diffraction broadening related to crystallite size. This large crystallite size suggests that dislocation motion in the Cu-Zn specimen was suppressed at 573 K.

Fig. 5

Changes in area–weighted crystallite size, ⟨x⟩_area with true strain of (a) pure copper and (b) Cu–Zn alloy specimens.

3.2 Effects of deformation temperature and alloying elements on texture evolution

Dislocation glide behaviors affect texture evolution during deformation. Consequently, dislocation mobility can be indirectly assessed through changes in texture during plastic deformation. Figure 6 presents inverse pole figures (IPFs) in the tensile direction, derived from neutron diffraction, for pure copper and Cu-Zn specimens before deformation and at a true strain of 0.14. The figures use polar density as a scale, where a random crystallographic orientation distribution corresponds to a density of one, with higher values indicating multiples of the random density. Both specimens initially exhibited nearly random crystallographic orientations. After tensile deformation, both developed a ⟨111⟩ + ⟨001⟩ texture, typical of FCC metals under tensile stress, irrespective of deformation temperature. However, the ⟨111⟩ texture evolution at 573 K was weaker than at room temperature. Thirathipviwat et al. observed that in solid solution aluminum alloys, dislocation multiplication increases with the solid solution element content, enhancing texture evolution [20]. Although the specific relationship between texture evolution and dislocation density remains unclear, this study showed that the pure copper specimen exhibited a lower dislocation density at 573 K than at room temperature, corresponding to a reduced ⟨111⟩ pole density. Thus, the decrease in the ⟨111⟩ pole density of the pure copper specimen at 573 K likely reflects a reduction in dislocation density.

Fig. 6

Inverse pole figures (IPF) for the tensile direction. (a) Pure copper and (b) Cu–Zn alloy specimens before deformation. (c) Pure copper and (d) Cu–Zn alloy specimens at the true strain of 0.14 deformed at RT. (e) Pure copper and (f) Cu–Zn alloy specimens at true strain of 0.14 deformed at 573 K. The numbers shown on the ⟨001⟩, ⟨101⟩, and ⟨111⟩ are the polar density values.

In contrast to the pure copper specimen, the Cu-Zn specimen showed no significant difference in dislocation density between deformation at room temperature and 573 K. Consequently, the reduction in the ⟨111⟩ pole density at 573 K for the Cu-Zn specimen was not directly associated with dislocation density. As discussed in Section 3.1, the absence of appreciable crystallite refinement in the Cu-Zn specimens at 573 K suggests that the dislocations were uniformly distributed. A comparable dislocation substructure has been observed in high-temperature creep deformation of Al-Mg alloys, attributed to solute drag of edge dislocations [21]. The solute drag mechanism enhances the strain rate sensitivity of the shear stress needed to move dislocations [22, 23], potentially activating more slip systems at moderate shear stress levels when viscous dislocation motion occurs. Changes in the activity balance of slip systems under such conditions influence texture evolution.

This effect can be qualitatively evaluated through plastic deformation simulations using a visco-plastic self-consistent model [24]. In this model, the shear strain (γ_s) introduced in the slip system (s) during micro deformation is related to the resolved shear stress (τ_s) of the slip system as follows:

  

\begin{equation} \gamma_{s} = \gamma_{0}\left(\frac{\tau_{s}}{\tau_{0}^{s}}\right)^{n}, \end{equation} (4)

where γ₀ is a constant, $\tau_{0}^{s}$ is the threshold stress, and n is the stress index (reciprocal of the strain rate sensitivity index). For room-temperature deformation, n was sufficiently large (n > 10), implying γ_s was negligible below the threshold stress but could vary above it, representing free-flying dislocation motion. Conversely, at lower n, γ_S exhibited viscous resistance behavior strongly dependent on τ_s.

Figure 7 illustrates IPFs in the tensile direction at a true strain of 0.14, calculated using the vpsc-7 code [25]. The initial texture was assumed random, and the simulation employed 500 discrete orientations. Figure 7(a) reflects conditions with n = 20, assuming free-flying dislocation motion, similar to the cold-rolled texture in a previous study [26]. No twinning deformation was assumed due to the low strain. Figure 7(b) represents conditions with n = 3, indicating viscous dislocation motion, with all other conditions unchanged. Comparing Figs. 7(a) and 7(b) reveals that texture evolution is suppressed in Fig. 7(b), where viscous dislocation motion is modeled. This suppression aligns with the smaller ⟨111⟩ pole density observed in the Cu-Zn specimen at 573 K, suggesting that viscous dislocation motion contributed to the reduced texture evolution under these conditions.

Fig. 7

IPFs for the tensile direction at true strain of 0.14 calculated by using vpsc–7 code with the stress exponent, n = (a) 20 and (b) 3. The numbers shown on the ⟨001⟩, ⟨101⟩, and ⟨111⟩ are the polar density values.

3.3 Dislocation substructure observed by TEM

Line-profile analysis and texture analysis suggested that the dislocation mobility of the Cu-Zn alloy was low during high-temperature deformation. The dislocation substructures in the pure copper and Cu-Zn specimens were observed via TEM to understand the effects of dislocation mobility during high-temperature deformation. Figure 8 illustrates the dislocation substructures of specimens deformed to a true strain of 0.14. For pure copper, room-temperature deformation resulted in a dislocation cell structure with well-developed cell walls. In contrast, the specimen deformed at 573 K exhibited a reduced dislocation density and a sparsely distributed cell wall structure. These dislocation substructure characteristics align with the dislocation density and crystallite size trends obtained from neutron diffraction analysis.

Fig. 8

TEM images at true strain of 0.14 of the pure copper specimens at (a) RT and (b) 573 K, and of the Cu–Zn alloy specimen at (c) RT and (d) 573 K. Arrows in (a) and (b) and dotted lines in (c) denote cell wall and Taylor lattice, respectively.

The Cu-Zn specimen displayed a markedly different dislocation substructure compared to pure copper during room-temperature deformation. Taylor lattices were formed, characterized by dislocation accumulation along planar slip planes. The Cu-30 mass% Zn alloy has a significantly lower stacking-fault energy (14 mJ/m²) compared to pure Cu (78 mJ/m²) [27]. This low stacking-fault energy likely caused dislocations to dissociate into partial dislocations, which restricted the motion of dislocations to fixed slip planes, forming a planar dislocation morphology. At 573 K, the dislocation substructure of the Cu-Zn specimen differed substantially from that at room temperature. The dislocations were randomly distributed in a wavy morphology, with no observed tangles or well-defined cell walls. These features are attributed to the increase in stacking-fault energy at elevated temperatures. The absence of a developed cell structure suggests viscous dislocation motion, consistent with the lack of crystallites detectable by line-profile analysis under high-temperature deformation (Section 3.1).

The solute drag effect on dislocations can reduce dislocation mobility and average travel distance. According to eq. (2), this effect could increase the dislocation density. On the other hand, at 573 K, dynamic recovery becomes more likely, leading to a decrease in the dislocation density. This balance between increased dislocation multiplication due to solute drag and recovery processes likely explains the similar dislocation densities of the Cu-Zn specimens observed at room temperature and 573 K.

4. Conclusion

In-situ neutron diffraction measurements were performed during tensile deformation to investigate the effects of solute elements on the multiplication and motion of dislocations during high-temperature deformation. The dislocation behavior was analyzed through neutron diffraction line profile and texture analyses, while transmission electron microscopy provided insights into the dislocation substructures. The following conclusions were drawn:

1. (1)    In pure Cu, the rate of increase in dislocation density during high-temperature deformation at 573 K was smaller than that during room-temperature deformation. This reduction is likely attributed to the increased mobility of dislocations at elevated temperatures.
2. (2)    In the Cu-Zn alloys, the rates of increase in dislocation density were comparable at room temperature and 573 K. The lower flow stress observed at 573 K, compared to room temperature, was explained by the reduced shear modulus and dislocation strengthening coefficient in the Bailey–Hirsch equation.
3. (3)    The dislocation substructure of the Cu-Zn alloys during room-temperature deformation exhibited a planar Taylor lattice. Conversely, at 573 K, the dislocations were randomly distributed with a wavy morphology. This distinct substructure at 573 K is believed to result from solute atom drag on the dislocations, driven by the interaction between dislocations and alloying elements.

Acknowledgment

This study was supported by research funding from the Japan Institute of Copper (2020).

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• This Paper was Originally Published in Japanese in J. Japan Inst. Copper 63 (2024) 1–7. Title and abstract were slightly modified.