2. Experimental Procedure
2 mm thick aluminum single crystals were grown by a Bridgman method from 99.999% purity raw materials. From the grown crystals, 10 mm width and 50 mm length sheet-shaped tensile specimens were cut by wire-spark sawing. Since tensile axes of the specimens were located at almost center of the crystallographic stereo triangle of which vertices were [0 0 1], [0 1 1] and $[\bar{1} \ 1\ 1]$ spots each, primary slip plane was (1 1 1) and Burgers vector of the primary slip system was parallel to $\text{[}\bar{1}\ 0\ 1\text{]}$. Table 1 shows the all 12 slip systems of the specimen for the present experiments. The notation of the slip systems corresponds to the Boas-Schmid notation adopted by Tiba et al.28)
Those specimens were heated to 893 K and kept for 3.6 ks and vertically dropped to salt water of which temperature was 253 K. Some of the specimens were not rapid cooled but air-cooled after the heating. After electro-polishing for removing oxidized films of surfaces, those specimens were uniaxially tensile deformed with a speed of 0.1 mm/min at room temperature. The deformed specimens were chemically polished with NaOH solution (NaOH: 20 g and H2O: 100 cm3) to 0.2 mm thickness. From the thinned specimens, disc-shaped foils of 3 mm diameter were carefully cut out by wire-spark sawing and jet-polished to produce wedge-shaped foils which have a small hole at their center for TEM observations with 200 kV acceleration voltage. For the present observation, the electron beam direction (z direction) and the diffraction vector (g vector) were controlled in order to characterize the dislocation structures. Our characterization procedures were as follows.
At the early deformation stage, in order to observe the dislocations belonging to the primary slip system, i.e., “B4” ((1 1 1)$[\bar{1}\ 0\ 1]$), we applied the combinations of z ≅ 0 1 1 and $\boldsymbol{g} = \bar{1}\ \bar{1}\ 1$ or $\boldsymbol{g} = 1\ 1\ \bar{1}$. And, for the clarification of dense dislocation structures, foil specimens were tilted by 2° to 4° pitch between −40° to +40° range by keeping the g vector active and obtained images were converted to three dimensionally reconstructed ones.
At the middle deformation stage, in order to check the activations of the dislocations belonging to the secondary slip systems, we applied the combinations of $\boldsymbol{z} \cong \bar{1}\ \bar{1}\ 2$ and g = 1 1 1. For this observation, the primary slip plane, i.e., (1 1 1), was perpendicular to the photo surface. This observation condition is called “edge-on”. In this case, clearly visible dislocations would be the secondary ones. On the other hand, because of the condition of the edge-on and the diffraction, i.e., g · b = 0, contrasts of dislocations on the primary slip planes were very weak or disappeared. Besides, due to the edge-on view, the primary dislocation channels can be clearly distinguished in matrices. After the edge-on observation, in order to observe the dislocations on the primary slip plane inside the channels, we inclined the foil and applied the combinations of z ≅ 0 1 1 and $\boldsymbol{g} = \bar{1}\ \bar{1}\ 1$ or $\boldsymbol{g} = 1\ 1\ \bar{1}$.
3. Results and Discussion
3.1 Rapid-cooled-in dislocation loops
Figure 2 shows rapid-cooled-in dislocation loops in an aluminum single crystal. Figure 2(a) was a bright field image taken under the condition of $\boldsymbol{z} \cong 0\ 1\ 1$ and $\boldsymbol{g} = \bar{1}\ \bar{1}\ 1$ and Fig. 2(b) was a weak-beam image of the same area. Since these dislocation loops were on {1 1 1} planes and had fringe-images inside the loops, these were identified as Frank-sessile dislocation loops. Average diagonal length of the dislocation loops was 43 nm and density of the loops about 0.5 × 1021/m3.
3.2 Stress-strain curves
Figure 3 shows examples of the nominal early stage tensile stress-tensile strain curves of a rapid-cooled specimen and an air cooled one. The 0.2% proof tensile stress, i.e., yield stress, was 9.0 MPa for a rapid-cooled specimen and 5.4 MPa for an air-cooled one. Due to the dislocation loop distribution, yield stresses of the rapid-cooled specimens were increased. On the other hand, macroscopic work hardening rate after the yielding of the rapid-cooled specimens were very low compared to the air-cooled ones.
3.3 Arrays of prismatic dislocation loops: Early stage of the work hardening process
Figure 4 shows a part of three dimensionally reconstructed TEM images of dislocation structures inside a cleared dislocation channel of the primary slip system in a foil taken from the specimen elongated to 1.0% macroscopic tensile strain. These images were taken by tilting the foils between −40° to +40° around $\boldsymbol{g} = 1\ 1\ \bar{1}$. Although we took 41 shots and reconstructed quasi-continuous moving images in order to clarify the detailed dislocation structures, the actual images cannot be posted on this literature. Instead, Fig. 4 shows representative discrete 9 shots taken by 10° pitch. Due to the whole images, dislocation bundles elongating along the almost same direction were found to be distributed inside the channel. And, based on the diffraction condition (g · b ≠ 0), these dislocations were considered to be belonging to the primary slip system.
Figure 5(a) shows an enlarged image of “0°” of Fig. 4 which was taken under the condition of z ≅ 0 1 1 and $\boldsymbol{g} = 1\ 1\ \bar{1}$. Arrows with dotted lines are indicating the projected traces of $[\bar{1}\ 2\ \bar{1}]$ (edge-dislocation-line direction of the primary slip system) and $[\bar{1}\ 0\ 1]$ (Burgers vector direction of the primary slip system) on the photo surface, respectively. In Fig. 5(a), we essentially see dislocation bundles elongating along the primary edge-dislocation-line (“D”). In order to clarify the structures of the bundles, we took magnified images of the enclosed area “A” and “B” of Fig. 5(a). Figure 5(b) and 5(c) show the magnified images of “A” and “B”, respectively. From these images, we can recognize that dislocations composing the bundles indicated as “D” in Fig. 5(a) were not simple edge dislocation bundles but arrays of elongated prismatic loops which have “closed ends” at the both sides which were indicated as “E”. In the arrays, each loop was stacking to $[\bar{1}\ 0\ 1]$ direction. Kroeger et al.5) and Tokuno et al.8) observed the similar edge dislocation structures inside the channels and called them as “dipole” or “dipole cluster”. However, since the both ends of their observed edge dislocations were cut by the foil surfaces, they could not identify the detailed structures.
In Fig. 5, other than the arrays of elongated prismatic loops, we see many isolated prismatic loops (“P”). On the other hand, screw dislocations parallel to the Burgers vector (“S”) were rarely observed inside the channels. Observed screw dislocations have cusps where they may have jogs or super-jogs. The isolated dislocation loops were considered to be formed through the glides of screw dislocations which had super-jogs as parts of them. As shown in Fig. 6, since the super-jogs of screw dislocations are unable to glide with screw dislocations, those were left behind as the isolated elongated-prismatic-loops (“P”). And, during the deformation, majority of the screw dislocations of opposite signs were considered to meet on the cross slip planes, mutually recombine, and disappear.
Regarding the formation process of the arrays of prismatic dislocation loops in face-centered-cubic metals during plastic deformation, Erel et al.29) proposed computational models based on “Discrete Dislocation Dynamics (DDD)”. Figure 7 and Fig. 8 show brief schematics based on their calculation results.29) In Fig. 7,
-
(a)
During deformation, two opposite signs’ screw dislocations on different but sufficient close primary slip planes meet.
-
(b)
These dislocations are attracted one another, resulting in cross-slipped configurations at multiple locations.
-
(c)
The two segments pinch-off at cross-slipped locations and make a loop, leaving two pinched-off hair-pin dislocations which have super jogs.
-
(d)
The self energy of the loop is reduced by being straighten-up to the $[\bar{1}\ 2\ \bar{1}]$ direction. Consequently, the first prismatic loop is created.
And
Fig. 8 shows that one of the hair-pin dislocations in
Fig. 7 creates the arrays of the prismatic loops. In
Fig. 8,
-
(a)
Two arms of one of the created hair-pin dislocation meet and make another pinch-off.
-
(b)
The pinch-off makes another loop.
-
(c)
The pinched-off loop is straighten-up to the $[\bar{1}\ 2\ \bar{1}]$ direction.
-
(d)
By the sequence of above process, arrays of the prismatic loops could be created.
Erel
et al. proposed that the events of
Fig. 7 would be the precursor to those of
Fig. 8. We consider, although the perfect mechanism which can explain the total behaviors of the screw dislocations is not still made clear, the calculation result by Erel
et al.29) is one of the most likely events for the creation of the arrays of prismatic dislocation loops observed in the present investigation.
3.4 Tangled structures of primary and primary coplanar dislocations: Middle stage of the work hardening process
Figure 9 shows dislocation structures inside a cleared dislocation channel of the primary slip system in a thick area of a foil taken from the specimen elongated to 12.1% macroscopic tensile strain. Figure 9(a) was taken under the condition of $\boldsymbol{z} \cong \bar{1}\ \bar{1}\ 2$ and $\boldsymbol{g} = 1\ 1\ 1$, the primary slip plane, i.e., (1 1 1), was perpendicular to the photo surface. Because of the condition of the edge-on and the diffraction, i.e., g · b = 0, contrasts of dislocations of the primary slip system were very weak. On the other hand, clearly visible dislocations were not observed inside the channel. In this channel, “band-shaped” weak contrasts parallel to the dislocation channel were observed (“D1”, “D2” and “D3”). Figure 9(b) was a TEM image which shows a magnified image of Fig. 9(a) under the condition of z ≅ 0 1 1 and $\boldsymbol{g} = \bar{1}\ \bar{1}\ 1$. Arrows with dotted lines show the projected traces of $[\bar{1}\ 0\ 1]$ and $[\bar{1}\ 2\ \bar{1}]$ on the photo surface, respectively. As described in the previous section, $[\bar{1}\ 0\ 1]$ is the primary Burgers vector and $[\bar{1}\ 2\ \bar{1}]$ is the primary edge dislocation direction. According to the Table 1, the primary slip system is quoted as “B4” ((1 1 1)$[\bar{1}\ 0\ 1]$). The band-shaped contrasts (“D1”, “D2” and “D3”) in Fig. 9(a) were considered to be arrays of prismatic dislocation loops in Fig. 9(b). Prismatic loops elongating $[\bar{1}\ 2\ \bar{1}]$ direction were densely packed along $[\bar{1}\ 0\ 1]$ direction in the arrays and the numbers of the loops composing the arrays increased, compared to the arrays in Fig. 4 and Fig. 5. In this channel, many isolated prismatic loops belonging to the primary slip system (“P”) were also observed. Screw dislocations parallel to the Burgers vector direction (“S”) were rarely remained inside the channels.
Since the dislocation channels are heterogeneously formed in deformed specimens, we can observe different stage channels, i.e., old and fresh channels, in one TEM foil. Figure 10 shows dislocation structures inside a different dislocation channel in a foil taken from the same specimen of Fig. 9. The observation condition of Fig. 10(a) was same with Fig. 9(a), i.e., $\boldsymbol{z} \cong \bar{1}\ \bar{1}\ 2$ and g = 1 1 1. Again, clearly visible dislocations were not observed inside the channel. In this channel, band-shaped contrasts which were similar with those of Fig. 9 were observed (“D”). Besides the contrasts (“D”), much thicker “band-shaped” contrasts were observed (“T1” and “T2”). Although thicknesses of “T1” and “T2” were much larger than “D”, contrasts of “T1” and “T2” were still weak. It means that the Burgers vectors of the structures’ dislocations were on the primary slip plane. Figure 10(b) shows a magnified image of Fig. 10(a) taken by the same procedure of Fig. 9(b). Arrows with dotted lines show the projected traces of $[\bar{1}\ 0\ 1]$, $[\bar{1}\ 2\ \bar{1}]$, $[0\ 1\ \bar{1}]$ and $[\bar{2}\ 1\ 1]$ on the photo surface, respectively. Here, $[0\ 1\ \bar{1}]$ and $[\bar{2}\ 1\ 1]$ are the Burgers vector and the edge dislocation direction of the primary coplanar system quoted as “B2” ((1 1 1)$[0\ 1\ \bar{1}]$) in Table 1. Based on the crystal coordination, the thicker band-shaped contrasts “T1” and “T2” in Fig. 10(a) were found to be tangled structures consisting of the two types of prismatic dislocation loops elongated along ⟨1 1 2⟩ directions which were belonging to the primary slip system, i.e., “B4” ((1 1 1)$[\bar{1}\ 0\ 1]$) and the primary coplanar one, i.e., “B2” ((1 1 1)$[0\ 1\ \bar{1}]$), respectively. Contrasts of these dislocations belonging to the two slip systems were not disappeared because of their diffraction conditions, i.e., g · b ≠ 0. Although detailed knitting-structure of the tangled dislocations could not be clarified, these tangled arrays are considered to be energetically stabilized and act as strong obstacles against multiplications and motions of following dislocations.
Mitchell30) proposed calculation results showing the stress-fields on 11 slip systems created by pile-ups of the primary dislocations. In their calculation,
| \begin{equation}
\boldsymbol{\tau}_{\boldsymbol{y}\boldsymbol{z}}
\end{equation}
| (1) |
means the created shear stress on the primary slip plane’s normal (
y plane) and the primary dislocation’s slip direction (
z direction). This shear stress was resolved on other 11 slip systems and described as,
| \begin{equation}
\boldsymbol{\tau}_{\boldsymbol{y}'\boldsymbol{z}'}
\end{equation}
| (2) |
where
y′ and
z′ were the slip plane normal direction and the slip direction of each slip system. According to their calculation, the resolved shear stress on the dislocations belonging to
“B2” ((1 1 1)
$[0\ 1\ \bar{1}]$) was obtained as follows.
| \begin{equation}
\boldsymbol{\tau}_{\boldsymbol{y}'\boldsymbol{z}'} = \frac{1}{2}\boldsymbol{\tau}_{\boldsymbol{y}\boldsymbol{z}}
\end{equation}
| (3) |
Since
$\boldsymbol{\tau}_{\boldsymbol{yz}}$ is increased with the number of the pile-up primary dislocations,
$\boldsymbol{\tau}_{\boldsymbol{y}'\boldsymbol{z}'}$ may reach a threshold magnitude for the activation of the dislocation sources belonging to
“B2” ((1 1 1)
$[0\ 1\ \bar{1}]$) with the progress of the deformation. In the channel of
Fig. 10(b), many isolated prismatic loops,
“P” and
“PB2”, which were belonging to
“B4” ((1 1 1)
$[\bar{1}\ 0\ 1]$) and
“B2” ((1 1 1)
$[0\ 1\ \bar{1}]$) and screw dislocations with cusps (
“SB2”) belonging to
“B2” ((1 1 1)
$[0\ 1\ \bar{1}]$) were observed. These results indicated that many dislocation sources belonging to
“B4” ((1 1 1)
$[\bar{1}\ 0\ 1]$) and
“B2” ((1 1 1)
$[0\ 1\ \bar{1}]$) in the channels were activated.
Basinski et al.31) rearranged the calculation of Mitchell30) and proposed that dislocations belonging to “C1” ($(1\ 1\ \bar{1})[0\ \bar{1}\ \bar{1}]$/conjugate slip system) and “A6” ($(1\ \bar{1}\ \bar{1})$[1 1 0])/critical slip system) in Table 1 would be activated due to pile-ups of the primary dislocations which are inclined by 60° to their Burgers vectors. If the secondary dislocations are activated inside the primary channels and react with the tangled dislocations like “T1” and “T2” of Fig. 10, much more complicated tangled structures would be created. We thought that the tangled structures indicated by “T” in Fig. 1(c)8) were the developed stage of “T1” and “T2” of Fig. 10. In Fig. 1, the layered structures “L” parallel to the primary slip plane were also formed attaching the tangled structures “T”. This means that the tangled structures “T” may be a triggering factor for the creation of the layered structure “L”. Tokuno et al.8) revealed that the layered structures “L” were the network-shaped dislocation structures consisting of dislocations of which Burgers vectors were parallel to $[\bar{1}\ 0\ 1]$, $[0\ \bar{1}\ \bar{1}]$ and [1 1 0]. $[\bar{1}\ 0\ 1]$, $[0\ \bar{1}\ \bar{1}]$ and [1 1 0] are matching with the Burgers vectors belonging to “B4” ((1 1 1)$[\bar{1}\ 0\ 1]$), “C1” ($(1\ 1\ \bar{1})[0\ \bar{1}\ \bar{1}]$) and “A6” ($(1\ \bar{1}\ \bar{1})$[1 1 0]) in Table 1, respectively. They also mentioned that the layered structures “L” were compatible ones with the “tilted bands” proposed by Sharp3) in the neutron irradiated copper single crystals and other layer-like ones reported in the well-annealed copper single crystals.21,22) We believe that the layered structures “L” are the part of the cell structure in work hardened face-centered-cubic metals and the tangled structures “T” have a strong correlation with the formation of the cell structure. Therefore, our present result showing the creation of the tangled structures consisting of the primary and the primary coplanar dislocations could be an “embryo” of the final cell structure.
