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(3 coincidence(60/)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 () 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; Transmission 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 Cualloy, 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 dislocation 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 objective of the present study to quantify the structural † Corresponding author. Tel.: +86 24 23971890; E-mail address: 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 highpurity Cu (99.995 wt%) processed by dynamic plastic deformation (DPD) at cryogenic temperature to a strain of 2.1. TEM (transmission electron microscopy) based CBED (convergent beam electron diffraction) technique was used to quantify the microstructural parameters. The structural characteristic 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 temperature (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 starting 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 section. The boundary spacing was measured directly from the micrographs and the boundary misorientation 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 (totally 576 rotation matrixes or angle/axis pairs), (4) selecting the minimum rotation angle as the misorientation 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 dislocation slip (denoted as DS-region), nano-scale twinning (NT-region) and shear banding (SB-region) have been observed in the LN-DPD Cu[1]. The quantitative characterizations of these microstructures will be followed by an analysis of the strengthening mechanisms. 3.1 DS-region The DS-region is composed of extended dislocation boundaries that are nearly perpendicular to the loading direction, interconnecting dislocation boundaries and isolated dislocations presented in the volumes between the boundaries, Fig. 1(a). Such microstructural 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 boundary spacing was determined by measuring the interception 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 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 newlyformed boundaries are low angle dislocation boundaries. This is highly different from the nanostructures formed by traditional severe plastic deformation at large strains, where the density of high angle boundaries can be ∼70%[6,8,9]. These boundary parameters allow the dislocation density to be roughly estimated, based on the assumption that dislocations are mainly presented in the low angle dislocation boundaries, whereas the dislocation density in the volumes between boundaries is relatively 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 0.1◦[5,6]. Consequently, EBSD analysis generally 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.60128].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 compression 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 recrystallization as observed in literature [22]. 3.2 NT-region Twinning is an additional strain accommodation mode in plastic deformation of low SFE metals in particular at high strain rates and low temperatures[1,2,17]. Deformation twins in the LNDPD Cu are formed nearly perpendicular to the loading 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 perfect Σ3 coincidence, i.e. 60◦ [28]. This tolerance can be determined by the misorientation angle across deformation twin boundaries, Fig. 3(c), where the boundaries are misoriented from 51◦ to 61◦, giving the maximum tolerant angle of 9◦ from the perfect Σ3. According to the deviation angle and the boundary spacing, the dislocation density in the twin boundaries 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: assuming the rotation matrix G3 corresponding to perfect Σ3 boundary and the rotation matrix G1 for the deformed twin boundary (the experimental data), the extra rotation matrix (G2) that results in the deviation 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◦. Concerning dislocations in the twin boundaries are composed 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 density in the twin boundaries due to the omitting Shockley partials. If assuming the same amount of Shockley partial is present, the total number can be approximated: 3.4×1016 m−2, which is close to the value (5×1016 m−2) determined by high resolution transmission 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 lamellae (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 microstructures, characterized by extended dislocation boundaries that are nearly perpendicular to the loading direction, interconnecting dislocation boundaries and loose dislocations between the extended dislocation 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 average value of 46 nm, Fig. 4(b), which is significantly smaller than that in the DS-regions. The distribution 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 deformation 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 severe 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 revolution 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
678 F.Yan et al.:J.Mater.Sci.Technol.,2011,27(8),673-679 Table 2 Parameters used for flow stress calculation for the three types of mi- crostructures Structure dr/nm Sv/nm-I 0LAB/deg·fLAB/% fvol/%ccal/MPa DS-region 140 0.014 1.3 21 22 518 NT-region 47 0.043 63 666 SB-region 62 0.032 1.3 8 15 713 of high amount of geometrically necessary dislocations be assumed to be a linear additivity of disloca- (GNDs).The localized shear strain that results in the tion strengthening (o(p))from low angle dislocation formation of SBs in the T/M lamellae has been de- boundaries and isolated dislocations and boundary termined to be 2-412).This strain amplitude present strengthening(o(b))from high angle boundariesliol. in a width of 1 um gives a strain gradient around 2- For the NT-region,only boundary strengthening will 4 um-1,which is two orders of magnitude higher than be involved.Here the high angle boundaries refer to that of HPT.The low bound for the GND density to the boundaries larger than the critical angle that de- accommodate such strain gradient (z)can be esti- termines the transition of strengthening from disloca- matod=.By inserting x=2-4 um tion strengthening to boundary strengthening.Such and b0.256 nm,the GND density is approximated critical angle is generally very small,being 2-3341. as (1.8-3.6)x1016 m-2,which is close to the estimate In the present investigation,the critical angle was set according to Eq.(1):1.6x1016 m-2.This value is to be 2.By taking o(p)is proportional to square root higher than the value of DS-region by a factor of 2-3 of dislocation density and (o(b))is inversely propor- However,further investigation is required to clarify tional to the square root of boundary spacing(Hall- such point. Petch),the flow stress can be related to the structural It is seen that the well-developed shear bands are parameters: mainly composed of low angle dislocation boundaries =00+aMGbyp+K/Vd (4) This seems contrary to the previous investigations where shear bands in LN-DPD Cu have been be- =0o +aMGV1.5Sb0LAB fLAB+ lieved to be composed of randomly-oriented grains, implying the formation of high density of high angle KV(I-f九AB)Sv2 (5) boundaries.However.Fig.9 in literature1 revealed where oo is the flow stress (20 MPa),a is a con- that only thin SBs gives continuous diffraction circles, stant (0.24),M is the Taylor factor (3.0),G is whereas for the well-developed SBs the diffraction cir- the shear modulus (45 GPa),b is the Burgers vec- cles are discontinuous,which implies that high angle tor (0.256 nm),K is the Hall-Petch slope of coarse- boundaries are present in thin SBs but disappear in grained Cu(140 MPa-um1/2),S is the surface area wide ones.Concerning the development of SBs in- per unit volume ()0LAB and fLAB are the volves bending and necking of deformation twins,de- average misorientation angle and the fraction of low twinning and the evolution of dislocation structures in angle dislocation boundaries that are misoriented less the detwinned bands21,the thin SBs should consist of than critical angle,respectively.Equation (2)can twin boundaries and high angle boundaries due to the thus be rewritten: incomplete detwinning.This is consistent with the present observation,as high angle boundaries around 50 were detected.Accompanied by the complete de- Gtotal fais(0o +aMGV/1.5SdisbodaB fuB+ twinning,dislocation boundaries are formed,which is mainly composed of low angle dislocation boundaries. KV(1-fuiB)Stis/2)+ftwin(o+K/vd+fsb(co+ This means the evolution of dislocation boundaries after the detwinning as in literature [2]. aMG√/1.5Sb9兜BfB+KV/(1-fB)S-/2) 3.4 Strengthening mechanism (6) By inserting the parameters of the three different The above quantitative characterizations of the microstructures given in Table 2,Eq.(6)gives a flow three types of microstructures in LN-DPD Cu allow stress of 640 MPa,which is very close to the measured a quantitative analysis of the strengthening mecha- tensile yield strength of 620 MPal3). nisms in the LN-DPD Cu.Assuming a linear additiv- ity of strengthening from DS-(odis),NT-(otwin)and 4.Conclusions SB-(osb)regions weighted by their respective volume fraction fdis,ftwin and fsb,the flow stress(ototal)can A pure Cu (99.995 wt%)has been subjected to dy- be expressed: namic plastic deformation at cryogenic temperature to a strain of 2.1.Three types of microstructures(DS- Ototal =fdisOdis ftwinOtwin fsbOsb (2) region,NT-region,and SB-region)have been quanti- fied and the strengthening mechanism has been dis- For the DS-and SB-regions,strengthening can cussed.The following conclusions are drawn:
678 F. Yan et al.: J. Mater. Sci. Technol., 2011, 27(8), 673–679 Table 2 Parameters used for flow stress calculation for the three types of microstructures Structure dr/nm Sv/nm−1 θLAB/deg. fLAB/% fvol/% σcal/MPa DS-region 140 0.014 1.3 21 22 518 NT-region 47 0.043 – – 63 666 SB-region 62 0.032 1.3 8 15 713 of high amount of geometrically necessary dislocations (GNDs). The localized shear strain that results in the formation of SBs in the T/M lamellae has been determined to be 2–4[2]. This strain amplitude present in a width of 1 μm gives a strain gradient around 2– 4 μm−1, which is two orders of magnitude higher than that of HPT. The low bound for the GND density to accommodate such strain gradient (x) can be estimated by: ρGND= √ 4x 3b [33]. By inserting x=2–4 μm−1 and b≈0.256 nm, the GND density is approximated as (1.8–3.6)×1016 m−2, which is close to the estimate according to Eq. (1): 1.6×1016 m−2. This value is higher than the value of DS-region by a factor of 2–3. However, further investigation is required to clarify such point. It is seen that the well-developed shear bands are mainly composed of low angle dislocation boundaries. This seems contrary to the previous investigations[2,4], where shear bands in LN-DPD Cu have been believed to be composed of randomly-oriented grains, implying the formation of high density of high angle boundaries. However, Fig. 9 in literature [1] revealed that only thin SBs gives continuous diffraction circles, whereas for the well-developed SBs the diffraction circles are discontinuous, which implies that high angle boundaries are present in thin SBs but disappear in wide ones. Concerning the development of SBs involves bending and necking of deformation twins, detwinning and the evolution of dislocation structures in the detwinned bands[2], the thin SBs should consist of twin boundaries and high angle boundaries due to the incomplete detwinning. This is consistent with the present observation, as high angle boundaries around 50◦ were detected. Accompanied by the complete detwinning, dislocation boundaries are formed, which is mainly composed of low angle dislocation boundaries. This means the evolution of dislocation boundaries after the detwinning as in literature [2]. 3.4 Strengthening mechanism The above quantitative characterizations of the three types of microstructures in LN-DPD Cu allow a quantitative analysis of the strengthening mechanisms in the LN-DPD Cu. Assuming a linear additivity of strengthening from DS-(σdis), NT-(σtwin) and SB-(σsb) regions weighted by their respective volume fraction fdis, ftwin and fsb , the flow stress (σtotal) can be expressed: σtotal = fdisσdis + ftwinσtwin + fsbσsb (2) For the DS- and SB-regions, strengthening can be assumed to be a linear additivity of dislocation strengthening (σ(ρ)) from low angle dislocation boundaries and isolated dislocations and boundary strengthening (σ(b)) from high angle boundaries[10]. For the NT-region, only boundary strengthening will be involved. Here the high angle boundaries refer to the boundaries larger than the critical angle that determines the transition of strengthening from dislocation strengthening to boundary strengthening. Such critical angle is generally very small, being 2◦–3◦[34]. In the present investigation, the critical angle was set to be 2◦. By taking σ(ρ) is proportional to square root of dislocation density and (σ(b)) is inversely proportional to the square root of boundary spacing (HallPetch), the flow stress can be related to the structural parameters: σ = σ0 + αMGb√ρ + K/√ d (4) σ = σ0 + αMG1.5SvbθLABfLAB + K(1 − fLAB)Sv/2 (5) where σ0 is the flow stress (20 MPa), α is a constant (0.24), M is the Taylor factor (3.0[9]), G is the shear modulus (45 GPa), b is the Burgers vector (0.256 nm), K is the Hall-Petch slope of coarsegrained Cu (140 MPa·μm1/2), Sv is the surface area per unit volume (Sv=2 d [11]), θLAB and fLAB are the average misorientation angle and the fraction of low angle dislocation boundaries that are misoriented less than critical angle, respectively. Equation (2) can thus be rewritten: σtotal = fdis(σ0 + αMG 1.5Sdis v bθdis LABfdis LAB + K (1 − fdis LAB)Sdis v /2) + ftwin(σ0 + K/√ d + fsb(σ0+ αMG 1.5Ssb v bθsb LABfsb LAB + K (1 − fsb LAB)Ssb v /2) (6) By inserting the parameters of the three different microstructures given in Table 2, Eq. (6) gives a flow stress of 640 MPa, which is very close to the measured tensile yield strength of 620 MPa[3]. 4. Conclusions 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 (DSregion, NT-region, and SB-region) have been quanti- fied and the strengthening mechanism has been discussed. The following conclusions are drawn:
F.Yan et al.:J.Mater.Sci.Technol.,2011,27(8),673-679 679 (1)The microstructures in the DS-region and SB- [7]F.Dalla Torre,R.Lapovok,J.Sandlin and P.Thom- region are characterized by extended boundaries,in- son:Acta Mater.,2004,52,4819. terconnecting dislocation boundaries and isolated dis- [8]A.P.Zhilyaev,S.Swaminathan,A.A.Gimazov,T.R. locations in the volume between the boundaries. McNelley and T.G.Langdon:J.Mater.Sci.,2008,43. (2)The DS-region microstructure in the LN-DPD 7451. Cu shows:i)a smaller boundary spacing(121 nm);ii) [9]X.Molodova,G.Gottstein,M.Winning and R. a lower misorientation angle (3.8).iii)a lower frac- Hellmig:Mater.Sci.Eng.A,2007,460-461,204. 10]N.Hansen:Scripta Mater.,2004,51,801. tion of high angle boundaries (~0)and iv)a higher dislocation density (5.6x1015 m-2)compared with Cu [11]D.A.Hughes and N.Hansen:Acta Mater.,2000,48, 2985. sample processed by low strain rate deformation at 12 L.Liu and I.Baker:Scripta Metall.,1993,28,197. room temperaturel12-15,18-22,24,25] [13]W.Q.Cao,C.F.Gu,E.V.Pereloma and C.H.J.Davies: (3)The boundaries in the NT-region are deviated Mater.Sci.Eng.A,2008,492,74. from the perfect 53 relationship (60/)up to [14]J.Gubicza,L.Balogh,R.J.Hellmig,Y.Estrin and T. a maximum value of 9o.Based on the boundary pa- Ungar:Mater.Sci.Eng.A,2005,400-401,334. rameters and the deviation angles,the density of the [15]Y.Zhang,N.R.Tao and K.Lu:Acta Mater.,2008, excess dislocations in the boundaries was estimated 56.2429. tobe1.7×1016m-2 16]E.Orowan:Proc.Phys.Soc.,1940,52,8. (4)The boundaries in the SB-region are mainly [17 J.W.Christian and S.Mahajan:Prog.Mater.Sci., 1995.39.1. low angle dislocation boundaries that are spaced [18 S.C.Baik,R.J.Hellmig,Y.Estrin and H.S.Kim:Z. <50 nm.The dislocation density was estimated to Metallkd.,2003,94.754. be1.6×1016m-2. 19 F.Dalla Torre,A.Gazder,C.Gu,C.Davies and E. (5)The flow stress-structural parameters relation- Pereloma:Metall.Mater.Trans.A.2007,38.1080. ship has been established based on the linear additiv- [20]M.Shaarbaf and M.Toroghinejad:Metall.Mater. ity of the weighted contributions from three types of Trans.A.2009,40,1693. microstructures in the LN-DPD Cu sample. 21 B.L.Li,N.Shigeiri,N.Tsuji and Y.Minamino:Mater. Sci.Forum,2006,503-504,615. 22 A.Belyakov,T.Sakai,H.Miura and K.Tsuzaki:Phi- Acknowledgements los.Mag.A,2001,81,2629 The authors acknowledge the Danish National Re- [23]F.J.Humphreys,Y.Huang,I.Brough and C.Harris: J.Microsc.,1999,195,212 search Foundation and the National Natural Science Foundation of China (Grant No.50911130230)for the [24]O.V.Mishin and G.Gottstein:Philos.Mag.A,1998, Danish-Chinese center for Nanometals,within which this 78,373 study was performed.Thanks Dr.X.Huang and Dr. 25 O.V.Mishin,D.Juul Jensen and N.Hansen:Mater. W.Pantleon for constructive discussion.This project Sci.Emg.A,2003,342,320. was sponsored by MOST international S&T project [26]G.R.Canova,C.Fressengeas,A.Molinari and U.F. (2010DFB54010),SRF for ROCS,SEM,and the Young Kocks:Acta Metall.,1988.36.1961. Merit Scholar of Institute of Metal Research.Chinese [27]J.Weertman and S.S.Hecker:Mech.Mater.,1983,2, 89. Academy of Science,China. [28]T.Zhu,J.Li,A.Samanta,H.G.Kim and S.Suresh: Proc.Natl.Acad.Sci.USA.2007.104.3031. REFERENCES 29 M.Sennour,S.Lartigue-Korinek,Y.Champion and M.J.Hytch:Philos.Mag.,2007,87,1465 [1 Y.S.Li,N.R.Tao and K.Lu:Acta Mater.,2008,56, [30]L.Lu,Y.F.Shen,X.H.Chen,L.H.Qian and K.Lu: 230. Science,2004,304,422. [2]C.S.Hong,N.R.Tao,X.Huang and K.Lu:Acta [31]L.Lu,X.Chen,X.Huang and K.Lu:Science,2009, Mater.,2010,58,3103. 323,607. 3]W.S.Zhao,N.R.Tao,J.Y.Guo,Q.H.Lu and K.Lu: [32 J.Gil Sevillano:Proceeding of the 25th Riso Inter- Scripta Mater.,2005,53,745. national symposium on Materials Science:Evolution 4]Y.S.Li,Y.Zhang,N.R.Tao and K.Lu:Acta Mater., of Deformation Microstructures in 3D,Riso National 2009.57,761. Laboratory,Roskilde,Denmark,1. 5 Q.Liu:J.Appl.Cryst.,1994,27,755 33 J.M.Martinez-Esnaola,M.Montagnat,P.Duval and 6]H.W.Zhang,X.Huang and N.Hansen:Acta Mater., J.Gil Sevillano:Scripta Mater.,2004,50,273. 2008,56.5451. [34 N.Hansen:Mater.Sci.Eng.,2005,409,39
F. Yan et al.: J. Mater. Sci. Technol., 2011, 27(8), 673–679 679 (1) The microstructures in the DS-region and SBregion are characterized by extended boundaries, interconnecting dislocation boundaries and isolated dislocations in the volume between the boundaries. (2) The DS-region microstructure in the LN-DPD Cu shows: i) a smaller boundary spacing (121 nm); ii) a lower misorientation angle (3.8◦), iii) a lower fraction of high angle boundaries (∼0) and iv) a higher dislocation density (5.6×1015 m−2) compared with Cu sample processed by low strain rate deformation at room temperature[12–15,18–22,24,25]. (3) The boundaries in the NT-region are deviated from the perfect Σ3 relationship (60◦/) up to a maximum value of 9◦. Based on the boundary parameters and the deviation angles, the density of the excess dislocations in the boundaries was estimated to be 1.7×1016 m−2. (4) The boundaries in the SB-region are mainly low angle dislocation boundaries that are spaced <50 nm. The dislocation density was estimated to be 1.6×1016 m−2. (5) The flow stress-structural parameters relationship has been established based on the linear additivity of the weighted contributions from three types of microstructures in the LN-DPD Cu sample. Acknowledgements The authors acknowledge the Danish National Research Foundation and the National Natural Science Foundation of China (Grant No. 50911130230) for the Danish-Chinese center for Nanometals, within which this study was performed. Thanks Dr. X. Huang and Dr. W. Pantleon for constructive discussion. This project was sponsored by MOST international S&T project (2010DFB54010), SRF for ROCS, SEM, and the Young Merit Scholar of Institute of Metal Research, Chinese Academy of Science, China. REFERENCES [1 ] Y.S. Li, N.R. Tao and K. Lu: Acta Mater., 2008, 56, 230. [2 ] C.S. Hong, N.R. Tao, X. Huang and K. Lu: Acta Mater., 2010, 58, 3103. [3 ] W.S. Zhao, N.R. Tao, J.Y. Guo, Q.H. Lu and K. Lu: Scripta Mater., 2005, 53, 745. [4 ] Y.S. Li, Y. Zhang, N.R. Tao and K. Lu: Acta Mater., 2009, 57, 761. [5 ] Q. Liu: J. Appl. Cryst., 1994, 27, 755. [6 ] H.W. Zhang, X. Huang and N. Hansen: Acta Mater., 2008, 56, 5451. [7 ] F. Dalla Torre, R. Lapovok, J. Sandlin and P. Thomson: Acta Mater., 2004, 52, 4819. [8 ] A.P. Zhilyaev, S. Swaminathan, A.A. Gimazov, T.R. McNelley and T.G. Langdon: J. Mater. Sci., 2008, 43, 7451. [9 ] X. Molodova, G. Gottstein, M. Winning and R. Hellmig: Mater. Sci. Eng. A, 2007, 460-461, 204. [10] N. Hansen: Scripta Mater., 2004, 51, 801. [11] D.A. Hughes and N. Hansen: Acta Mater., 2000, 48, 2985. [12] L. Liu and I. Baker: Scripta Metall., 1993, 28, 197. [13] W.Q. Cao, C.F. Gu, E.V. Pereloma and C.H.J. Davies: Mater. Sci. Eng. A, 2008, 492, 74. [14] J. Gubicza, L. Balogh, R.J. Hellmig, Y. Estrin and T. Ung´ar: Mater. Sci. Eng. A, 2005, 400-401, 334. [15] Y. Zhang, N.R. Tao and K. Lu: Acta Mater., 2008, 56, 2429. [16] E. Orowan: Proc. Phys. Soc., 1940, 52, 8. [17] J.W. Christian and S. Mahajan: Prog. Mater. Sci., 1995, 39, 1. [18] S.C. Baik, R.J. Hellmig, Y. Estrin and H.S. Kim: Z. Metallkd., 2003, 94, 754. [19] F. Dalla Torre, A. Gazder, C. Gu, C. Davies and E. Pereloma: Metall. Mater. Trans. A, 2007, 38, 1080. [20] M. Shaarbaf and M. Toroghinejad: Metall. Mater. Trans. A, 2009, 40, 1693. [21] B.L. Li, N. Shigeiri, N. Tsuji and Y. Minamino: Mater. Sci. Forum, 2006, 503-504, 615. [22] A. Belyakov, T. Sakai, H. Miura and K. Tsuzaki: Philos. Mag. A, 2001, 81, 2629. [23] F.J. Humphreys, Y. Huang, I. Brough and C. Harris: J. Microsc., 1999, 195, 212. [24] O.V. Mishin and G. Gottstein: Philos. Mag. A, 1998, 78, 373 [25] O.V. Mishin, D. Juul Jensen and N. Hansen: Mater. Sci. Eng. A, 2003, 342, 320. [26] G.R. Canova, C. Fressengeas, A. Molinari and U.F. Kocks: Acta Metall., 1988, 36, 1961. [27] J. Weertman and S.S. Hecker: Mech. Mater., 1983, 2, 89. [28] T. Zhu, J. Li, A. Samanta, H.G. Kim and S. Suresh: Proc. Natl. Acad. Sci. USA, 2007, 104, 3031. [29] M. Sennour, S. Lartigue-Korinek, Y. Champion and M.J. H¨ytch: Philos. Mag., 2007, 87, 1465 [30] L. Lu, Y.F. Shen, X.H. Chen, L.H. Qian and K. Lu: Science, 2004, 304, 422. [31] L. Lu, X. Chen, X. Huang and K. Lu: Science, 2009, 323, 607. [32] J. Gil Sevillano: Proceeding of the 25th Risø International symposium on Materials Science: Evolution of Deformation Microstructures in 3D, Risø National Laboratory, Roskilde, Denmark, 1. [33] J.M. Mart´ınez-Esnaola, M. Montagnat, P. Duval and J. Gil Sevillano: Scripta Mater., 2004, 50, 273. [34] N. Hansen: Mater. Sci. Eng., 2005, 409, 39
