《金属材料强韧化与组织调控》教学资源（参考文献）Quantifying the Microstructures of Pure Cu Subjected to Dynamic Plastic Deformation at Cryogenic Temperature

Available online at www.sciencedirect.com ScienceDirect JMST ELSEVIER J.Mater..Sci.Technol..,2011,27(8).673-679. www.JMST.org Quantifying the Microstructures of Pure Cu Subjected to Dynamic Plastic Deformation at Cryogenic Temperature F.Yan,H.W.Zhang',N.R.Tao and K.Lu Shenyang National Laboratory for Materials Science,Institute of Metal Research,Chinese Academy of Sciences,Shenyang 110016.China Manuscript received April 12,2011,in revised form May 30,2011] A pure Cu(99.995 wt%)has been subjected to dynamic plastic deformation at cryogenic temperature to a strain of 2.1.Three types of microstructures that are related to dislocation slip,twinning and shear banding have been quantitatively characterized by transmission electron microscopy (TEM)assisted by convergent beam electron diffraction (CBED)analysis.Microstructures originated from dislocation slip inside or outside the shear bands are characterized by low angle boundaries(<15)that are spaced in the nanometer scale,whereas most deformation twins are deviated from the perfect >3 coincidence(60/<111>)up to the maximum angle of 9.The quantitative structural characteristics are compared with those in conventionally deformed Cu at low strain rates,and allowed a quantitative analysis of the flow stress-structural parameter relationship. KEY WORDS:Quantitative structural characterization;Cu;Dynamic plastic deformation;Trans- mission electron microscopy;Convergent beam electron diffraction 1.Introduction parameters and to set up the relationship between flow stress and these parameters. There is a current interest in the microstructural The material chosen for investigation was high- refinement by plastic deformation at high strain rates purity Cu (99.995 wt%)processed by dynamic plas- and low temperature-4.Generally,three types of tic deformation (DPD)at cryogenic temperature to deformation mechanisms are activated in metals with a strain of 2.1.TEM (transmission electron mi- low stacking fault energy(SFE)such as Cu and Cu- croscopy)based CBED (convergent beam electron alloy,i.e.dislocation slip,twinning and shear banding diffraction)technique was used to quantify the mi- (SB)12).The microstructural refinement induced by crostructural parameters.The structural characteris- these three mechanisms is different,with the smallest tic as well as the strengthening mechanism has been value(47 nm)by twinning,followed by SB(75 nm) discussed and dislocation slip (121 nm)1.However,detailed 2.Experimental microstructural characters including the structural parameters such as boundary misorientation angles. fraction of high or low angle boundaries and the dis- High-purity polycrystalline Cu (99.995 wt%)in location density between and in the boundaries are the form of cylinder (9 mm in diameter and 12 mm in lacking,whereas these parameters play a crucial role thickness)was subjected to DPD at cryogenic temper- ature (liquid nitrogen),which is denoted as LN-DPD in understanding the deformation mechanism and the structure-strength relationship.It is thus the objec- Cu.Prior to DPD,the sample was annealed at 973 K for 2 h in order to remove the residual stress and to tive of the present study to quantify the structural obtain the fully-recrystallized structures.The start- ing material is composed of equiaxed recrystallized Corresponding author.Tel.:+86 24 23971890;E-mail ad- grains with an average size of 200 um and a fraction dress:hwzhang@imr.ac.cn (H.W.Zhang)

J. Mater. Sci. Technol., 2011, 27(8), 673-679. Quantifying the Microstructures of Pure Cu Subjected to Dynamic Plastic Deformation at Cryogenic Temperature F. Yan, H.W. Zhang† , N.R. Tao and K. Lu Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China [Manuscript received April 12, 2011, in revised form May 30, 2011] A pure Cu (99.995 wt%) has been subjected to dynamic plastic deformation at cryogenic temperature to a strain of 2.1. Three types of microstructures that are related to dislocation slip, twinning and shear banding have been quantitatively characterized by transmission electron microscopy (TEM) assisted by convergent beam electron diffraction (CBED) analysis. Microstructures originated from dislocation slip inside or outside the shear bands are characterized by low angle boundaries (<15◦) that are spaced in the nanometer scale, whereas most deformation twins are deviated from the perfect Σ3 coincidence (60◦/<111>) up to the maximum angle of 9◦. The quantitative structural characteristics are compared with those in conventionally deformed Cu at low strain rates, and allowed a quantitative analysis of the flow stress-structural parameter relationship. KEY WORDS: Quantitative structural characterization; Cu; Dynamic plastic deformation; Trans￾mission electron microscopy; Convergent beam electron diffraction 1. Introduction There is a current interest in the microstructural refinement by plastic deformation at high strain rates and low temperature[1–4]. Generally, three types of deformation mechanisms are activated in metals with low stacking fault energy (SFE) such as Cu and Cu￾alloy, i.e. dislocation slip, twinning and shear banding (SB)[1,2]. The microstructural refinement induced by these three mechanisms is different, with the smallest value (47 nm) by twinning, followed by SB (75 nm) and dislocation slip (121 nm)[1]. However, detailed microstructural characters including the structural parameters such as boundary misorientation angles, fraction of high or low angle boundaries and the dis￾location density between and in the boundaries are lacking, whereas these parameters play a crucial role in understanding the deformation mechanism and the structure-strength relationship. It is thus the objec￾tive of the present study to quantify the structural † Corresponding author. Tel.: +86 24 23971890; E-mail ad￾dress: hwzhang@imr.ac.cn (H.W. Zhang). parameters and to set up the relationship between flow stress and these parameters. The material chosen for investigation was high￾purity Cu (99.995 wt%) processed by dynamic plas￾tic deformation (DPD) at cryogenic temperature to a strain of 2.1. TEM (transmission electron mi￾croscopy) based CBED (convergent beam electron diffraction) technique was used to quantify the mi￾crostructural parameters. The structural characteris￾tic as well as the strengthening mechanism has been discussed. 2. Experimental High-purity polycrystalline Cu (99.995 wt%) in the form of cylinder (9 mm in diameter and 12 mm in thickness) was subjected to DPD at cryogenic temper￾ature (liquid nitrogen), which is denoted as LN-DPD Cu. Prior to DPD, the sample was annealed at 973 K for 2 h in order to remove the residual stress and to obtain the fully-recrystallized structures. The start￾ing material is composed of equiaxed recrystallized grains with an average size of 200 μm and a fraction

674 F.Yan et al.:J.Mater.Sci.Technol.,2011,27(8),673-679 20 161 15 d=91 nm 10 d =473 nm h 200 400 600 800 10001200 Boundary spacing /nm 20 8=3.8° 40 5 10 15 Misorientation angle deg. Fig.1 A representative TEM image of dislocation structure in LN-DPD Cu (a),the corresponding statistic distribution of boundary spacing (b)and the boundary misorientation angles (c).The arrow shows the loading direction of high angle boundaries >99%.Details of the DPD been observed in the LN-DPD Culll.The quantita- treatment can be found elsewherell.In the present tive characterizations of these microstructures will be investigation,the pure Cu was subjected to DPD at followed by an analysis of the strengthening mecha- cryogenic temperature to a strain of 2.1. nisms. The deformed microstructures of LN-DPD Cu were observed by JEOL 2010 TEM in the plane that is 3.1 DS-region parallel to the loading direction,i.e.longitudinal sec- tion.The boundary spacing was measured directly The DS-region is composed of extended disloca- from the micrographs and the boundary misorienta- tion boundaries that are nearly perpendicular to the tion angles were determined by CBED in the following loading direction,interconnecting dislocation bound- ways:(1)obtaining the Kikuchi diffraction patterns of aries and isolated dislocations presented in the vol- crystallites adjacent to a boundary,(2)calculating the umes between the boundaries,Fig.1(a).Such mi- orientation matrix of each crystallite,(3)calculating crostructural features resemble those observed in Cu the rotation matrix or angle/axis pair by considering deformed at low strain rates at room temperatures(71. the crystallographic symmetry of cubic structure(to- However,they are less recovered as reflected by the tally 576 rotation matrixes or angle/axis pairs),(4)se- higher interior dislocation density and poorly-defined lecting the minimum rotation angle as the misorienta- interconnecting dislocation boundaries.The bound- tion angle across the boundary and(5)repeating these ary spacing was determined by measuring the inter- operations,allowing large number of boundaries to be ception length along a line perpendicular (dr)and analyzed.Detailed information of this technique can parallel(dL)to the extended dislocation boundaries. be found elsewherel5,61. dr gives a narrow distribution from 30 to 300 nm, whereas dL shows a wide one from 150 to 1200 nm. 3.Results and Discussion Fig.1(b).The average value of dr and dL is 91 and 473 nm,respectively,which pins an one-dimensional Three types of microstructures relevant to dislo- nanostructure with an aspect ratio,i.e.dL/dr=5.2. cation slip (denoted as DS-region),nano-scale twin- The misorientation angles across these boundaries, ning (NT-region)and shear banding (SB-region)have Fig.1(c),are in the range from 0.1 to 12 with an

674 F. Yan et al.: J. Mater. Sci. Technol., 2011, 27(8), 673–679 Fig. 1 A representative TEM image of dislocation structure in LN-DPD Cu (a), the corresponding statistic distribution of boundary spacing (b) and the boundary misorientation angles (c). The arrow shows the loading direction of high angle boundaries >99%. Details of the DPD treatment can be found elsewhere[1]. In the present investigation, the pure Cu was subjected to DPD at cryogenic temperature to a strain of 2.1. The deformed microstructures of LN-DPD Cu were observed by JEOL 2010 TEM in the plane that is parallel to the loading direction, i.e. longitudinal sec￾tion. The boundary spacing was measured directly from the micrographs and the boundary misorienta￾tion angles were determined by CBED in the following ways: (1) obtaining the Kikuchi diffraction patterns of crystallites adjacent to a boundary, (2) calculating the orientation matrix of each crystallite, (3) calculating the rotation matrix or angle/axis pair by considering the crystallographic symmetry of cubic structure (to￾tally 576 rotation matrixes or angle/axis pairs), (4) se￾lecting the minimum rotation angle as the misorienta￾tion angle across the boundary and (5) repeating these operations, allowing large number of boundaries to be analyzed. Detailed information of this technique can be found elsewhere[5,6]. 3. Results and Discussion Three types of microstructures relevant to dislo￾cation slip (denoted as DS-region), nano-scale twin￾ning (NT-region) and shear banding (SB-region) have been observed in the LN-DPD Cu[1]. The quantita￾tive characterizations of these microstructures will be followed by an analysis of the strengthening mecha￾nisms. 3.1 DS-region The DS-region is composed of extended disloca￾tion boundaries that are nearly perpendicular to the loading direction, interconnecting dislocation bound￾aries and isolated dislocations presented in the vol￾umes between the boundaries, Fig. 1(a). Such mi￾crostructural features resemble those observed in Cu deformed at low strain rates at room temperatures[7]. However, they are less recovered as reflected by the higher interior dislocation density and poorly-defined interconnecting dislocation boundaries. The bound￾ary spacing was determined by measuring the inter￾ception length along a line perpendicular (dT) and parallel (dL) to the extended dislocation boundaries. dT gives a narrow distribution from 30 to 300 nm, whereas dL shows a wide one from 150 to 1200 nm, Fig. 1(b). The average value of dT and dL is 91 and 473 nm, respectively, which pins an one-dimensional nanostructure with an aspect ratio, i.e. dL/dT=5.2. The misorientation angles across these boundaries, Fig. 1(c), are in the range from 0.1◦ to 12◦ with an

F.Yan et al.:J.Mater.Sci.Technol.,2011,27(8),673-679 675 Table 1 Structural parameters of three types of microstructures in the LN-DPD Cu Structure dr/nm dr/nm 0av/deg. JHAB/% p/105m-2 DS-region 91 473 3.8 0 5.6 NT-region 26 60 100 17 SB-region 46 149 7.4 7 16 average of 3.80 (0av),implying that all the newly- formed boundaries are low angle dislocation bound- 6 (a) -CRI☒ aries.This is highly different from the nanostructures ECAPIS ECAP formed by traditional severe plastic deformation at ←RT-DPDI19 large strains,where the density of high angle bound- ◆LN-DPD湖 ★RT-DPD [Present data] aries can be ~70%16.8.91. 2 These boundary parameters allow the dislocation density to be roughly estimated,based on the assump- (b) ·-ECAP1 tion that dislocations are mainly presented in the low ECAPI1 angle dislocation boundaries,whereas the dislocation ARBI20 -Compressionl22 density in the volumes between boundaries is rela- Con tively low (1014 m-2)[i0]: 200 LN-DPD Present data] p≥ 1.5SLABOLAB (c) b (1) 40 where SLAB and LAB are the surface area per unit volume and the average misorientation angle of low 20 ◆CR2 angle dislocation boundaries,that are misoriented AP -ARBI2iT <l5o(SLAB=f九AB(h+孟))，andbis Burgers ★ LNDPD (Prescm t vector of Cu(0.256 nm).By inserting the structural (d) parameters given in Table 1,the dislocation density is approximated as 5.6x1015 m-2.Although this calcu- lation underestimates the dislocation density due to neglecting the abundant dislocations that do not con- tribute to the misorientation rise,the value is higher *LN-DPD [Present data] by a factor of 5-6 compared with the counterparts 6 10 deformed via cold rolling(CR)12],equal channel an- gular pressing (ECAP)[13.14]and RT-DPD(DPD at room temperature)(15],Fig.2(a).The relative low Fig.2 Comparison of characteristic parameters of dis- dislocation density of LN-DPD Cu in literature 15 location structures in Cu processed by different may be due to the lower strain(1.8)than the present approaches:(a)the dislocation density;(b)the investigation (2.1). average boundary spacing;(c)the average bound- ary misorientation angle;and (d)the fraction of The significantly high dislocation density of LN- high angle boundaries.Data obtained by EBSD DPD Cu can be partially attributed to the high strain and CBED are marked by and **respectively rate,which facilitates the accumulation of disloca- tions,because the strain rate (is proportional to the velocity (v)and the density (pm)of mobile disloca- is the significantly low fraction of high angle bound- tions:Additionally,low temperature in- aries (fHAB)and the smaller average misorientation hibits the annihilation of dislocations by cross-slip and angle (0),Fig.2(c)and (d).This is partially as- climbl171.Consequently,LN-DPD Cu shows higher cribed to the quantitative characterization techniques dislocation density.This may explain the smaller being used.When electron backscatter diffraction spacing between the dislocation boundaries,as com- (EBSD)was used to quantify the microstructures. pared with ECAP,accumulative rolled bonding the boundaries with the misorientation angle <2 (ARB)120.21]and compressionl1.22]deformed counter- are excluded for statistics due to the uncertaintyl231 parts,Fig.2(b).As the boundary spacing was deter- On the contrary,these boundaries are included dur- mined by the moving distance of dislocations before ing CBED analysis due to its high angular resolu- being captured to form dislocation boundaries,i.e.the tion >0.15.61.Consequently,EBSD analysis gener- free path of mobile dislocations.Given the strain am- ally results in higher fHAB and eav than CBED.The plitude(s),the free path(A)of mobile dislocations is large values for the ARB Cul211,CR Cul24]and ECAP inversely proportional to the density:=/pmb6. Cul9l in Fig.2 are obtained by EBSD,whereas the Another important characteristic of LN-DPD Cu smaller data for compression[22 are obtained from

F. Yan et al.: J. Mater. Sci. Technol., 2011, 27(8), 673–679 675 Table 1 Structural parameters of three types of microstructures in the LN-DPD Cu Structure dT/nm dL/nm θav/deg. fHAB/% ρ/ 1015m−2 DS-region 91 473 3.8 0 5.6 NT-region 26 – ∼60 100 17 SB-region 46 149 7.4 7 16 average of 3.8◦ (θav), implying that all the newly￾formed boundaries are low angle dislocation bound￾aries. This is highly different from the nanostructures formed by traditional severe plastic deformation at large strains, where the density of high angle bound￾aries can be ∼70%[6,8,9]. These boundary parameters allow the dislocation density to be roughly estimated, based on the assump￾tion that dislocations are mainly presented in the low angle dislocation boundaries, whereas the dislocation density in the volumes between boundaries is rela￾tively low (1014 m−2)[10]: ρ = 1.5SLABθLAB b (1) where SLAB and θLAB are the surface area per unit volume and the average misorientation angle of low angle dislocation boundaries, that are misoriented <15◦ (SLAB = fLAB( 1 dT + π 2dL )[11]), and b is Burgers vector of Cu (0.256 nm). By inserting the structural parameters given in Table 1, the dislocation density is approximated as 5.6×1015 m−2. Although this calcu￾lation underestimates the dislocation density due to neglecting the abundant dislocations that do not con￾tribute to the misorientation rise, the value is higher by a factor of 5–6 compared with the counterparts deformed via cold rolling (CR)[12], equal channel an￾gular pressing (ECAP)[13,14] and RT-DPD (DPD at room temperature)[15], Fig. 2(a). The relative low dislocation density of LN-DPD Cu in literature [15] may be due to the lower strain (1.8) than the present investigation (2.1). The significantly high dislocation density of LN￾DPD Cu can be partially attributed to the high strain rate, which facilitates the accumulation of disloca￾tions, because the strain rate ( ˙ε) is proportional to the velocity (v) and the density (ρm) of mobile disloca￾tions: ˙ε=ρmbν[16]. Additionally, low temperature in￾hibits the annihilation of dislocations by cross-slip and climb[17]. Consequently, LN-DPD Cu shows higher dislocation density. This may explain the smaller spacing between the dislocation boundaries, as com￾pared with ECAP[18,19], accumulative rolled bonding (ARB)[20,21] and compression[1,22] deformed counter￾parts, Fig. 2(b). As the boundary spacing was deter￾mined by the moving distance of dislocations before being captured to form dislocation boundaries, i.e. the free path of mobile dislocations. Given the strain am￾plitude (ε), the free path (λ) of mobile dislocations is inversely proportional to the density: λ = ε/ρmb[16]. Another important characteristic of LN-DPD Cu Fig. 2 Comparison of characteristic parameters of dis￾location structures in Cu processed by different approaches: (a) the dislocation density; (b) the average boundary spacing; (c) the average bound￾ary misorientation angle; and (d) the fraction of high angle boundaries. Data obtained by EBSD and CBED are marked by ∗ and ∗∗, respectively is the significantly low fraction of high angle bound￾aries (fHAB) and the smaller average misorientation angle (θ), Fig. 2(c) and (d). This is partially as￾cribed to the quantitative characterization techniques being used. When electron backscatter diffraction (EBSD) was used to quantify the microstructures, the boundaries with the misorientation angle <2◦ are excluded for statistics due to the uncertainty[23]. On the contrary, these boundaries are included dur￾ing CBED analysis due to its high angular resolu￾tion >0.1◦[5,6]. Consequently, EBSD analysis gener￾ally results in higher fHAB and θav than CBED. The large values for the ARB Cu[21], CR Cu[24] and ECAP Cu[19] in Fig. 2 are obtained by EBSD, whereas the smaller data for compression[22] are obtained from

676 F.Yan et al.:J.Mater.Sci.Technol.,2011,27(8),673-679 25 (b) d.=26 nm Hma- 50 100 150 200 250 Boundary spacing/nm 40 d 30 20 500m 54 56 58 60 Misorientation angle/deg. Fig.3 (a)A typical TEM image of twin/matrix lamellae in the LN-DPD Cu.Statistic distribution of spacing between twin boundaries (b)and the misorientation angles (c)across the neighboring twin boundaries The arrow shows the loading direction CBED.Even such effect was considered,both the fect >3 coincidence,i.e.60<111>128].This toler- fHAB (0)and 0av(38)of LN-DPD Cu are signifi- ance can be determined by the misorientation angle cantly lower than those of ECAP,CR,ARB and com- across deformation twin boundaries,Fig.3(c),where pression deformed counterparts to the same strain the boundaries are misoriented from51°to61°，giv- where a typical fHAB is about 15%-40%and 0av ing the maximum tolerant angle of 9 from the perfect is around 10-209.19,21.22.24.25].The cause is not 33. clear at present but might be related to the fact According to the deviation angle and the bound- that high strain rate and low temperature inhibit ary spacing,the dislocation density in the twin bound- crystallographic spin26],decrease the mobility of aries can be roughly estimated:p=A0/(db)1291,where dislocations(27 and inhibit the dynamic recrystalliza- d (26 nm)is the twin boundary spacing and A tion as observed in literature [22. is the deviation angle that was induced by excess 3.2 NT-region dislocations.In order to obtain the value of A0. the following matrix operation is required:assum- Twinning is an additional strain accommoda- ing the rotation matrix G3 corresponding to perfect tion mode in plastic deformation of low SFE met- X3 boundary and the rotation matrix Gl for the de- als in particular at high strain rates and low formed twin boundary (the experimental data),the temperatures1.2.17.Deformation twins in the LN- extra rotation matrix (G2)that results in the de- DPD Cu are formed nearly perpendicular to the load- viation angle can be determined:G2G3=G1.The ing direction (indicated by the arrow),Fig.3(a).The angle/axis pair corresponding to G2 can thus be twin boundaries are spaced from several nanometers calculated by considering crystallographic symmetry, to 250 nm with an average of 26 nm,Fig.3(b).This which gives an average deviation angle of 5.2.Con- average value is an arithmetic mean value,which is cerning dislocations in the twin boundaries are com- smaller than that(47 nm)obtained in literature [1], posed of Frank dislocations(1/3[111])and Shockley where the average was weighted by volume fraction. dislocations(1/6[121]),with the former contributing High densities of dislocations are present in the twin to the coherency deviation and the later leading to boundaries as indicated by the contrast difference twin boundary stepped and curvedl301.By inserting The interaction between these dislocations and twin 6=1/3111,the density of Frank dislocations can be boundaries will lead to the deviation from the per- approximated:1.7x1016 m-2.It should be noted that

676 F. Yan et al.: J. Mater. Sci. Technol., 2011, 27(8), 673–679 Fig. 3 (a) A typical TEM image of twin/matrix lamellae in the LN-DPD Cu. Statistic distribution of spacing between twin boundaries (b) and the misorientation angles (c) across the neighboring twin boundaries. The arrow shows the loading direction CBED. Even such effect was considered, both the fHAB (∼0) and θav (38◦) of LN-DPD Cu are signifi- cantly lower than those of ECAP, CR, ARB and com￾pression deformed counterparts to the same strain, where a typical fHAB is about 15%–40% and θav is around 10–20◦[9,19,21,22,24,25]. The cause is not clear at present but might be related to the fact that high strain rate and low temperature inhibit crystallographic spin[26], decrease the mobility of dislocations[27] and inhibit the dynamic recrystalliza￾tion as observed in literature [22]. 3.2 NT-region Twinning is an additional strain accommoda￾tion mode in plastic deformation of low SFE met￾als in particular at high strain rates and low temperatures[1,2,17]. Deformation twins in the LN￾DPD Cu are formed nearly perpendicular to the load￾ing direction (indicated by the arrow), Fig. 3(a). The twin boundaries are spaced from several nanometers to 250 nm with an average of 26 nm, Fig. 3(b). This average value is an arithmetic mean value, which is smaller than that (47 nm) obtained in literature [1], where the average was weighted by volume fraction. High densities of dislocations are present in the twin boundaries as indicated by the contrast difference. The interaction between these dislocations and twin boundaries will lead to the deviation from the per￾fect Σ3 coincidence, i.e. 60◦ <111>[28]. This toler￾ance can be determined by the misorientation angle across deformation twin boundaries, Fig. 3(c), where the boundaries are misoriented from 51◦ to 61◦, giv￾ing the maximum tolerant angle of 9◦ from the perfect Σ3. According to the deviation angle and the bound￾ary spacing, the dislocation density in the twin bound￾aries can be roughly estimated: ρ=Δθ/(db)[29], where d (26 nm) is the twin boundary spacing and Δθ is the deviation angle that was induced by excess dislocations. In order to obtain the value of Δθ, the following matrix operation is required: assum￾ing the rotation matrix G3 corresponding to perfect Σ3 boundary and the rotation matrix G1 for the de￾formed twin boundary (the experimental data), the extra rotation matrix (G2) that results in the de￾viation angle can be determined: G2G3=G1. The angle/axis pair corresponding to G2 can thus be calculated by considering crystallographic symmetry, which gives an average deviation angle of 5.2◦. Con￾cerning dislocations in the twin boundaries are com￾posed of Frank dislocations (1/3[111]) and Shockley dislocations (1/6[1¯21]), with the former contributing to the coherency deviation and the later leading to twin boundary stepped and curved[30]. By inserting b=1/3[111], the density of Frank dislocations can be approximated: 1.7×1016 m−2. It should be noted that

F.Yan et al.:J.Mater.Sci.Technol.,2011,27(8),673-679 677 (b) d,=46 nm anb 20406080100120140160180 Boundary spacing/nm 30 (c AB=7% 25 0=7.4° 20 15 10 500nm 0 10 20 30 50 60 MIsorientation angles /deg. Fig.4 (a)A typical TEM image of the microstructure of a well-developed shear band in the LN-DPD Cu.Statistic distribution of transverse spacing between (b)and the misorientation angle across (c)the dislocation boundaries inside the shear band.The arrow shows the loading direction,and the dashed lines mark the interface between shear band and the nano-twinned bundles this calculation underestimates the dislocation den- scale.The spacing between the extended dislocation sity in the twin boundaries due to the omitting Shock- boundaries ranges from 10 to 140 nm,giving an av- ley partials.If assuming the same amount of Shockley erage value of 46 nm,Fig.4(b),which is significantly partial is present,the total number can be approxi- smaller than that in the DS-regions.The distribu- mated:3.4x1016 m-2,which is close to the value tion of misorientation angles across these boundaries (5x1016 m-2)determined by high resolution trans- shows one peak at the low angle with the fraction mission electron microscopy(HRTEM)31).Compared of high angle boundaries around 7%.This implies with the dislocation density in the DS-region region that the microstructures inside the SBs are mainly (5.6x1015 m-2),this value is higher by a factor of 7, composed of low angle boundaries that are spaced which pins the significant storage of dislocations by <50nm. twin boundaries31l. The significantly smaller spacing between these boundaries in SBs is surprising,since the boundary 3.3 SB-region spacing for Cu subjected to severe plastic deforma- tion is generally larger than 200 nm7.22]and for the SBs are generally present in the twin-matrix lamel- DS-region of LN-DPD Cu it is about 120 nm.The lae (T/M lamellae)in low SFE metals subjected to cause might be related to the deformation condition plastic deformation at high strain rates and/or low of shear band.where high strain gradient has been temperatures[1.21.One of the well-developed SBs is produced,since strain gradient has been one of the shown in Fig.4(a),where the interfaces between SBs beneficial effect on the accumulation and storage of and NT-regions are delineated by the white dashed dislocation and in turn the grain refinement.It has lines,marking the width of the SB (~1 um).The been argued that the superior grain refinement by structures inside the SBs are typical dislocation mi- high pressure torsion (HPT)in relative to other se- crostructures,characterized by extended dislocation vere plastic deformations is attributed to the higher boundaries that are nearly perpendicular to the load- strain gradient 32).The strain gradient of HPT can be ing direction,interconnecting dislocation boundaries roughly estimated by:r=2mN/t,where N is the rev- and loose dislocations between the extended disloca olution and t is the sample thickness.By taking the tion boundaries.These structural features resemble typical HPT parameters,i.e.N=5 and t=0.5 mm,the those of DS-region,but with a higher density of loose strain gradient can be estimated to be r0.06 um-1. dislocations,poorly-defined boundaries and smaller Generally,the high strain gradient requires storage

F. Yan et al.: J. Mater. Sci. Technol., 2011, 27(8), 673–679 677 Fig. 4 (a) A typical TEM image of the microstructure of a well-developed shear band in the LN-DPD Cu. Statistic distribution of transverse spacing between (b) and the misorientation angle across (c) the dislocation boundaries inside the shear band. The arrow shows the loading direction, and the dashed lines mark the interface between shear band and the nano-twinned bundles this calculation underestimates the dislocation den￾sity in the twin boundaries due to the omitting Shock￾ley partials. If assuming the same amount of Shockley partial is present, the total number can be approxi￾mated: 3.4×1016 m−2, which is close to the value (5×1016 m−2) determined by high resolution trans￾mission electron microscopy (HRTEM)[31]. Compared with the dislocation density in the DS-region region (5.6×1015 m−2), this value is higher by a factor of 7, which pins the significant storage of dislocations by twin boundaries[31]. 3.3 SB-region SBs are generally present in the twin-matrix lamel￾lae (T/M lamellae) in low SFE metals subjected to plastic deformation at high strain rates and/or low temperatures[1,2]. One of the well-developed SBs is shown in Fig. 4(a), where the interfaces between SBs and NT-regions are delineated by the white dashed lines, marking the width of the SB (∼1 μm). The structures inside the SBs are typical dislocation mi￾crostructures, characterized by extended dislocation boundaries that are nearly perpendicular to the load￾ing direction, interconnecting dislocation boundaries and loose dislocations between the extended disloca￾tion boundaries. These structural features resemble those of DS-region, but with a higher density of loose dislocations, poorly-defined boundaries and smaller scale. The spacing between the extended dislocation boundaries ranges from 10 to 140 nm, giving an av￾erage value of 46 nm, Fig. 4(b), which is significantly smaller than that in the DS-regions. The distribu￾tion of misorientation angles across these boundaries shows one peak at the low angle with the fraction of high angle boundaries around 7%. This implies that the microstructures inside the SBs are mainly composed of low angle boundaries that are spaced <50 nm. The significantly smaller spacing between these boundaries in SBs is surprising, since the boundary spacing for Cu subjected to severe plastic deforma￾tion is generally larger than 200 nm[7,22] and for the DS-region of LN-DPD Cu it is about 120 nm. The cause might be related to the deformation condition of shear band, where high strain gradient has been produced, since strain gradient has been one of the beneficial effect on the accumulation and storage of dislocation and in turn the grain refinement. It has been argued that the superior grain refinement by high pressure torsion (HPT) in relative to other se￾vere plastic deformations is attributed to the higher strain gradient[32]. The strain gradient of HPT can be roughly estimated by: x=2πN/t, where N is the rev￾olution and t is the sample thickness. By taking the typical HPT parameters, i.e. N=5 and t=0.5 mm, the strain gradient can be estimated to be x ≈0.06 μm−1. Generally, the high strain gradient requires storage