Materials Science and Engineering A 551 (2012) 13–18
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The effect of oxygen and stress state on the yield behavior of commercially pure titanium M.C. Brandes a,∗ , M. Baughman c,1 , M.J. Mills b , J.C. Williams b a b c
Department of Materials Science and Engineering, The Ohio State University, 477 Watts Hall, 2041 College Rd, Columbus, OH 43210, USA Department of Materials Science and Engineering, The Ohio State University, USA Caterpillar, USA
a r t i c l e
i n f o
Article history: Received 10 November 2011 Received in revised form 10 April 2012 Accepted 17 April 2012 Available online 9 May 2012 Keywords: Titanium alloys Deformation Yield strength asymmetry Oxygen effects
a b s t r a c t Titanium alloys containing a majority volume fraction of the low temperature HCP ␣-phase have been known to display yield and creep strength asymmetries when deformed under uniaxial conditions at room temperature. This behavior has only been documented in materials alloyed with significant concentrations of aluminum (<∼10 at%); however, little work has examined the phenomenon in commercial purity alloys. In this study, the yield strengths of two commercial purity titanium alloy sheet materials (Grade 1 and Grade 4) are examined under tensile and compressive loading conditions. Yield strength asymmetry has been observed and has been found to be dependent on alloy composition and crystallite distribution relative to the deformation axis. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Deformation in HCP metals has long been known to be complex in that plasticity occurs by both slip and twinning mechanisms. While nearly all HCP alloys display crystallographically anisotropic plastic behaviors, some have been found to deform in asymmetric manners with significant differences observed between deformation in tension and compression. Although not well appreciated, titanium alloys containing a majority volume fraction of the low temperature HCP ␣-phase have been known to show yield and creep strength asymmetries when loaded under uniaxial conditions at room temperature. To date, this behavior has only been observed in alloys containing aluminum concentrations greater than approximately 10 at% [1] (also see [2,3] for comprehensive lists of references); little work has focused on nominally pure grades of titanium. The purpose of this study is to further examine the nature of strength differentials in titanium alloys through an investigation of the mechanical behaviors of commercial purity (CP) titanium alloys. Tension–compression strength asymmetries in metals have been observed as a result of both twin- and slip-based deformation mechanisms. Mechanical twinning is frequently observed in HCP
∗ Corresponding author. Tel.: +1 6146883409; fax: +1 6142921537. E-mail address: ms
[email protected] (M.C. Brandes). 1 Formerly an undergraduate researcher with the Department of Materials Science and Engineering, The Ohio State University, USA. 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.04.058
metals and has been extensively documented [4–6]. In titanium alloys several twinning modes have been identified when crystals are stressed along either [0 0 0 1] or 1 1 2¯ 0 at room temperature; these are summarized in Table 1 [7–15]. Due to the directional nature of such mechanisms, i.e. twin variants forming in response to shear stresses applied along their twinning directions will not form in response to shear stresses of the opposite sense, it is not unexpected that crystals that deform by twinning would display asymmetries in their plastic responses. In polycrystalline metals, twin induced strength differentials should be most notable in textured materials. This is indeed the case for a number of HCP metals [16–18] and has been most extensively documented in magnesium alloys [19–25]. Slip-based tension–compression flow strength asymmetries have been most thoroughly investigated in BCC metals [26–35]. Such behaviors have been largely attributed to non-planar dislocation core structures; in the case of BCC metals, the (a/2) 1 1 1 screw dislocation, in its non-glissile configuration, dissociates onto several planes at once [36–44]. Similar tendencies are also thought to exist in HCP metals in that both the c៝ + a៝ (b៝ = 1 1 2¯ 3) and a៝ (b៝ = 1 1 2¯ 0) dislocations have complex core structures. Although no experimental observations of c៝ + a៝ dislocation core structures have yet been reported, it is known that single crystals of alloys containing aluminum deform by {1 1¯ 0 1} slip in tension and {1 1 2¯ 2} slip in compression [45,46]. Additionally, several groups have utilized atomistic modeling to investigate stable 1 1 2¯ 3 core structures [47–55]; it has been found that both screw and edge components display non-planar configurations that are sensitive
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Table 1 Slip and Twinning systems in HCP titanium. Mechanism
Shear direction (1 )
Shear plane
Plane normal to 1
Notes
Slip
1 1 2¯ 0
(0 0 0 1) {1 1¯ 0 0} {1 1¯ 0 1} {1 1¯ 0 1} {1 1¯ 2 2}
– – – – –
Primary slip system in pure Ti Important cross-slip system Dominant in tension along [0 0 0 1] Dominant in compression along [0 0 0 1]
{1 1¯ 0 2} {1 1¯ 2 1} {1 1 2¯ 2} {1 1¯ 0 1}
{3 3¯ 0 5} {1 1 2¯ 1 0} {1 1 2¯ 5} {8 8¯ 0 2 7}
Tension along [0 0 0 1], compression along 1 1 2 0 Tension along [0 0 0 1], compression along 1 1 2 0 Tension along 1 1 2 0, compression along 0 0 0 1 Compression along 1 1 0 0
1 1 3¯ 0 Twin
1 1¯ 0 1 1 1 2¯ 6 1 1 2¯ 3 1 1¯ 0 2
to stress and temperature. At room temperature, the screw dislocation core spreads simultaneously along both {1 1¯ 0 1} and {1 1 2¯ 2} planes. Under forward loading, the screw core prefers to spread on two first-order pyramidal planes, {1 1¯ 0 1}, at small strains before transforming to a configuration spread on three planes, two {1 1¯ 0 1} and a {1 1 2¯ 2}, at higher strains. Under reverse loading at small strains, the core spreads in the manner described above, but at higher strains, spreading occurs primarily on a single {1 1¯ 0 1} and secondarily on a {1 1 2¯ 2} plane. While the 1 1 2¯ 3{1 1¯ 01 } edge core has yet to be examined, simulations of 1 1 2¯ 3{1 1 2¯ 2} screw dislocation core indicate that the several configurations are possible depending on temperature, applied stress, and stacking fault energy. Regardless of configuration, it is apparent that significant displacements out of the glide plane contribute greatly to the low mobility of the edge line orientation. Further, compressive loading along [0 0 0 1] may promote a core configuration that is sessile until large strains/stresses are applied to the crystal. Given that glide of the edge line orientation is the rate-limiting factor governing the expansion of a 1 1 2¯ 3 loop, these simulations provide insight to the origin of T–C asymmetry for deformation along [0 0 0 1]. In the case of the a៝ dislocation, only the screw line orientation has been found, in both simulations and experimental measurements, to spread in a non-planar fashion. The a៝ edge dislocation has been observed to be planar and compact [56–58]. Simulations of a៝ screw dislocation core by Girshick et al. and Domain indicate that the a៝ screw spreads on both the prism and basal planes by dissociation into partial dislocations on (0 0 0 1) – two parallel (a/6)1 1 2¯ 0 partials on {1 1¯ 0 0} and two (a/3)1 1¯ 0 0 Shockley partials. It should be noted that this core configuration requires significant edge component for spreading in the basal plane; no edge component is required for spreading in the prism plane. Assuming that such a structure is stable above 0 K, it is expected that crystals oriented for single prism slip would be much less sensitive to alloying than those oriented for basal slip at temperatures where interstitial species are immobile. Additionally, recent ab-initio simulations by Li, indicate that the a៝ screw dislocation core does spread such that atomic displacements occur perpendicular to the line direction. Further, it was found that there are only very subtle variations in energy, <0.1 eV, associated with stable a៝ screw dislocation core structures so that spreading may occur onto either basal, prism, or first order pyramidal planes. Therefore, it is plausible that the local solute environment might tip the balance in favor of glide on one or two systems. Simultaneous spreading of the a៝ screw dislocation core onto prism and pyramidal planes has been proposed by several researchers on the basis of experimental observations [3,59–61]. After observing cross-slip onto pyramidal planes in pure Ti single crystals deformed by prism slip (cross slip was frequently detected on {1 1¯ 0 1} planes with Schmid factors less than ∼0.1), Naka et al. suggested that a៝ dislocation cores dissociated into four parallel partial dislocations on three planes, a {1 1¯ 0 0} and two {1 1¯ 0 1}. This configuration does not seem particularly likely when one considers that oxygen is well know to induce a transition from wavy
to planar dislocation arrangements in CP Ti alloys [62,63]. Further, long, straight screw dislocations dominate the deformation microstructures of lower purity alloys, i.e. those containing greater than ∼1000 wppm interstitials [63]. Sob et al. proposed a core structure model where three partial dislocations, one of screw character and two of mixed character, spread onto one {1 1¯ 0 0} and one {1 1¯ 0 1}; it was argued that this configuration would explain the effect of oxygen on prism slip tendencies. Additionally, Neeraj et al. have suggested that a complex 1 1 2¯ 0 screw dislocation core may provide explanation for both slip behaviors and strength differentials in these materials. Noting observations of abundant cross-slip in basal slipping specimens under tensile loading and coarse planar slip under compressive loading, it was argued that the core might take different configurations dependant on the applied stress state. On the basis of phase contrast HRTEM lattice images of an a៝ dislocation in a specimen deformed by prism slip, it was proposed that a slight dissociation of the core into partials spread on the pyramidal plane would produce a structure with edge components that could produce a stress-state sensitivity. For crystals deforming by basal slip under tensile loading, it was reasoned that such dissociation would lead to composite (0 0 0 1)–{1 1¯ 0 1} slip. Under compressive loading, it was proposed that the core might take a configuration similar to that simulated by Girshick and Pettifor; basal-prism spreading would require repeated constriction in order to glide on (0 0 0 1). In the present paper, in addition to the above review of existing literature, we present new results on the behavior of CP grade Ti alloys in both tension and compression. The results show conclusively that a strength differential exists in pure, polycrystalline titanium alloys and that the magnitude of the differential depends on both slip system activity and oxygen content. 2. Experimental procedures Commercial purity ASTM Grades 1 and 4 titanium alloys were examined in this study. The Grade 1 alloy was provided by ATI Wah Chang of Albany, Oregon, and the Grade 4 alloy was provided by Titanium Metals Corporation of Henderson, Nevada. Compositions of the materials are presented in Table 2. Both alloys were obtained as unidirectionally rolled plates with nominal thicknesses of 4.5 mm (Grade 1) and 2.5 mm (Grade 4). Sections of each plate were cut, vacuum encapsulated in quartz tubing, and re-crystallization annealed. Heat-treatments low in the ␣-phase produced an eqiuaxed grained microstructures with average line intercept grain sizes of 9 m in the Grade 1 alloy (henceforth referred to as CP1) and 14 m in the Grade 4 alloy (CP4). Consistent with previously published reports [64,65], both alloys displayed similar, transverse sheet textures, after heat treatment (see Fig. 1). Test coupons were cut such that the loading axes were either parallel to the rolling directions (RD) or parallel to the transverse directions (TD) of the plates. Mechanical tests were performed on specially designed test bars with the dimensions presented in Fig. 2. Specimen dimensions were chosen to prevent buckling under
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Table 2 Impurity contents (wt%) of the CP1 and CP4 alloys. Alloy
O
N
C
H
Fe
All others
CP1 (ASTM Grade 1) CP4 (ASTM Grade 4)
0.036 0.330
0.002 0.002
0.003 0.008
<0.003 <0.005
0.025 0.090
<0.026 0.465
Fig. 1. Stereographic pole figures from the CP1 (A) and CP4 (B) materials illustrating material texture after annealing; ND, normal to the plane of the page, is normal plane of the titanium sheet while RD is the rolling direction. Pole figures were derived from EBSD scans (1 m steps between points on a square grid) over a 1 mm2 area of the sample.
compressive stresses on the basis of the secant formulation for plastically deforming, axially loaded columns [66]. For the purposes of calculation, the plastic flow of CP ␣-Ti was assumed to obey a strain rate dependent Holloman [67] form, flow = Kεn . flow is flow stress, K is a strength parameter, n is strain hardening parameter, and m is a strain rate sensitivity parameter. Flow parameters used for calculation were estimated based on those reported in [68–71]; they are as follows: K = 580 MPa, n = 0.25 for low oxygen titanium and K = 724 MPa, n = 0.1 for high oxygen titanium. Mechanical testing was performed in an MTS® Model 831 closed-loop servo-hydraulic test frame (22 kN load capacity) outfitted with a model 609 multi-axis alignment fixture. Prior to testing, the load train was carefully aligned with MTS® Easy Alignment system; once aligned, loads of up to −6.5 kN could be supported on 2 mm thick specimens with bending strains less than or equal to ∼30 microstrains. Test specimens were gripped with hydraulic wedge grips and loaded at a constant displacement rate equivalent to a strain rate of ∼10−5 s−1 ; specimens were deformed to a plastic strain level of no more than 0.004 plastic strain before unloading. MTS® Multi-purpose Testware software was utilized for both machine control and data acquisition; time, load, displacement, and strain data were continuously acquired every 50 ms during specimen loading. Strain was measured with epoxy bonded strain gages with resolutions of ∼1 m m−1 .
3. Results and discussion The results of the mechanical tests are provided in Table 3; note that yield stresses represent the stress levels at which the stress rate measured on the sample deviates from that measured during elastic loading. In agreement with previous studies, the measured moduli and yield points vary with oxygen content and specimen orientation; both alloys show increased stiffness and strength when stressed along the TD orientation as compared to the RD orientation. For specimens tested along RD, grains are primarily stressed in crystallographic directions parallel to the basal plane, and the highest resolved shear stresses lie on the systems least resistant to slip, i.e. the a៝ {1 1¯ 0 0}. For specimens stressed along TD, significant shear stresses are resolved onto both 1 1 2¯ 0 prism and 1 1 2¯ 0 basal systems. As the shear stresses necessary to activate a slip on basal planes has been found to be two to eight times those necessary to activate a៝ slip on prism planes [5,11], it is expected that the TD specimens should have greater yield strengths than the RD specimens. The yield stresses along the TD direction are ∼1.2–1.4 times greater than those measured along the RD orientation. The data presented in Table 3 provide evidence of a modest, compositionally dependent tension–compression strength asymmetry in CP titanium. While little or no yield differential is observed in the low oxygen CP1 material, the high oxygen CP4 material
Table 3 Youngs moduli (E) and yield stresses ( ys ) of the CP1 and CP4 alloys as a function of deformation axis orientation and applied stress direction. Alloy
Orientation
Applied stress
E (GPa)
ys (MPa)
CP1
RD
Ten Comp Ten Comp
104.9 108.2 119.0 122.6
175 179 237 239
Ten Comp Ten Comp
104.2 112.6 118.9 123.0
405 407 483 502
TD CP4
Fig. 2. Dimensions (in mm) of the tension–compression test bars. The thickness of the CP1 and CP4 bars were 2 and 4 mm, respectively.
RD TD
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twinning activity, they do indicate that the contributions of twinning to the plastic responses of the materials studied here are minimal. Assuming that material textures and test conditions have limited the extent of 1 1 2¯ 3 slip, the behaviors observed in specimens deformed along the TD orientation (in this orientation, significant shear stresses are resolved onto all three 1 1 2¯ 0 slip system families) suggest that a៝ slip on non-prismatic planes contributes to the measured strengths. Examination of Table 3 shows that a moderate strength asymmetry is only observed in the high oxygen CP4 material. Oxygen is well known to influence T–C strength differentials in BCC alloys (see above references for BCC T–C asymmetry). Several mechanisms have been proposed to explain these observations, including:
Fig. 3. EBSD inverse pole figure map (scan dimensions = 100 m × 100 m) of the CP1 alloy after deformation showing no evidence of twinning.
shows a strength asymmetry when stressed along the TD orientation. Given that a៝ slip on prism planes is expected as the dominant deformation mechanism for loading along the RD orientation [72], the lack of a strength differential in this orientation is consistent with published reports of the yield stresses of nominally pure titanium alloy single crystals (co ranging from 100 to 3000 wppm) yielded under tension, compression, and/or shear loading conditions [10,11,14,15,72–86]; the yield strengths of single crystals deformed by a៝ prism slip show little dependence on interstitial oxygen content. With respect to loading along TD, slip systems and deformation mechanisms other than 1 1 2¯ 0{1 1¯ 0 0} slip, may be more readily activated; as discussed in the Introduction, these include twinning, 1 1 2¯ 3 slip, and a៝ slip on (0 0 0 1) and/or {1 1¯ 0 1}. Mechanical twinning has been observed in pure, singlecrystalline titanium stressed along either [0 0 0 1] or 1 1 2¯ 0. The activation of twinning systems is known to be dependent on the direction of applied stress in that different systems are activated in response to tensile versus compressive stresses. However, the preference for mechanical twinning over dislocation glide is affected by several factors including grain size, composition, and deformation rate; twinning is suppressed as grain size is refined, oxygen content is increased, and deformation rate is slowed [72]. The investigations at hand were designed, in terms of both material structure and mechanical testing procedures, to minimize the activation of twinning systems. Although no TEM studies were performed as part of this study due to the small plastic strains to which the samples were deformed, post-mortem EBSD studies were carried out on the electro-polished gage lengths of the test bars (gage sections were polished prior to deformation). The CP1 alloy samples were mapped over 0.1 mm × 0.1 mm areas at a step size of 0.12 m, and the CP4 alloy samples were mapped over a 0.2 mm × 0.2 mm area at a step size of 0.2 m. In both cases, orientations were sampled at points according to a square grid. Little evidence of twinning was observed in either alloy; an EBSD scan of the CP1 alloy is presented in Fig. 3. In addition to EBSD experiments, specimens were imaged under secondary and channeling contrast conditions. Although slip lines could be observed in some grains, no conclusive evidence of twinning could be discerned. Although these observations do not completely eliminate the possibility of very fine-scale
• Elastic interactions between dislocations and solute atoms, which can take two forms. First, it is possible for an interstitial solute species to apply a normal stress across the slip plane of a dislocation, thus affecting the frictional stresses opposing glide. Given that the Peierls barrier governs this deformation mechanism, flow stress should show a strong dependence on temperature. Further, increasing solute concentration should strongly increase the sensitivity to temperature. Although typically not as strong as those measured in BCC metals, titanium alloys do show these expected temperature and compositional dependencies of yield stress. Second, it is possible for an interstitial atom to produce non-isotropic distortions of the lattice. Such distortions may give rise to nonlinear elastic effects that result in strength asymmetries [87]. The latter mechanism was proposed by Hirth and Cohen [31] to rationalize T–C asymmetries in iron-carbon alloys; carbon interstitials produce tetragonal lattice distortions in BCC Fe. Similar distortions are present in Ti–O alloys where interstitial oxygen preferentially stretches the ␣-Ti lattice in the c-direction [88,89]. • Solute-stacking fault interactions, which may also take two forms providing that the core of the affected dislocation dissociates into partial dislocations. The first is based on a purely elastic interaction with the solute atom whereby the planarized core of a gliding dislocation is compressed as it approaches the solute species forcing the glissile dislocation into a sessile configuration [90]. The second is a chemical interaction with the stacking fault–the so-called Suzuki effect [91]. Depending on the initial configuration of the dislocation core and the influence of alloying on SFE, this mechanism could either enhance or diminish T–C asymmetry for a given slip system. If obvious that the greatest increases in T–C asymmetry would occur when the presence of an interstitial species decreases SFE on a plane family other than that on which forward slip occurs. In titanium alloys, a possible reflection of the Suzuki mechanism is observed in the tendency of oxygen to promote pyramidal slip [63,92–95]. • Core structure modification by solutes, which qualitatively similar to the Suzuki effect. It has been proposed that solid solution alloying in BCC metals modifies the electronic and geometrical structures of dislocation cores [96–99]. Given similarities between the core structures of dislocations in BCC and HCP metals, i.e. both display complex and non-planar cores, it is logical to expect that solutes have influence over the structures of cores in ␣-Ti. As discussed above, there are small energetic differences between the various core configurations calculated by Li [58], it is not unreasonable that oxygen alloying has a significant effect core stability.
The data presented here cannot conclusively determine the mechanism by which oxygen affects dislocation glide. However, considering that oxygen stabilizes the 1 1 2¯ 0 screw line orienta-
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tion [63], oxygen may have influence over the core configuration of the a៝ screw dislocation and its behavior under stress.
[33] [34] [35] [36]
4. Conclusions [37]
The yield strength behaviors of commercial purity CP1 and CP4 titanium alloy sheet materials were observed when deformed under constant strain rate conditions. A tension–compression strength asymmetry was measured and found to be dependant on oxygen content and crystallite orientation distribution relative to the deformation axis; a significant T–C strength asymmetry was observed only in the CP4 material deformed along the TD direction. On the basis of prior studies in both HCP Ti and BCC metals, it is proposed that a៝ dislocation core effects may explain these observations Acknowledgements The authors thank John Hebda (now retired) of ATI Wah Chang and Dr. Steve Fox of Timet for providing the materials examined in this study. This research was conducted under sponsorship by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, “Center for Defect Physics,” an Energy Frontier Research Center. References [1] H. Kim, The effect of slip character on low cycle fatigue behavior of Ti–Al alloys, Carnegie Mellon University, Ph.D. Dissertation, Pittsburgh, Pennsylvania, 1982, p. 221 leaves. [2] M.C. Brandes, Ph.D. Dissertation, The Ohio State University, Columbus, Ohio, 2008. [3] T. Neeraj, M.F. Savage, J. Tatalovich, L. Kovarik, R.W. Hayes, M.J. Mills, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 85 (2005) 279–295. [4] M.H. Yoo, J.K. Lee, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 63 (1991) 987–1000. [5] P. Partridge, Metall. Rev. 12 (1967) 169. [6] M.H. Yoo, Metall. Trans. A: Phys. Metall. Mater. Sci. 12 (1981) 409–418. [7] N.E. Paton, W.A. Backofen, Trans. Metall. Soc. AIME 245 (1969) 1369. [8] N.E. Paton, W.A. Backofen, Metall. Trans. 1 (1970) 2839. [9] F. Rosi, A. Dube, B. Alexander, J. Met. (1953) 257. [10] F. Rosi, F. Perkins, L. Seigle, J. Met. 8 (1956) 115. [11] A. Akhtar, Metall. Trans. A 6 (1975) 1105–1113. [12] L.D. Kurmaeva, Y.N. Akshentsev, O.A. Elkina, V.A. Sazonova, Phys. Met. Metall. 98 (2004) 389–392. [13] N. Bozzolo, L.S. Chan, A.D. Rollett, J. Appl. Crystallogr. 43 (2010) 596–602. [14] E. Anderson, D. Jillson, S. Dunbar, J. Met. (1953) 1191. [15] E. Anderson, D. Jillson, S. Dunbar, J. Met. (1954) 697. [16] L.B. Addessio, E.K. Cerreta, G.T. Gray, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 36A (2005) 2893–2903. [17] D.W. Brown, M.A.M. Bourke, B. Clausen, T.M. Holden, C.N. Tome, R. Varma, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 34A (2003) 1439–1449. [18] J.J. Fundenberger, M.J. Philippe, F. Wagner, C. Esling, Acta Mater. 45 (1997) 4041–4055. [19] E.A. Ball, P.B. Prangnell, Scr. Metall. Mater. 31 (1994) 111. [20] S.R. Agnew, S. Viswanathan, E.A. Payzant, Q. Han, K.C. Liu, E.A. Kenik, Magnesium Alloys and Their Applications, September 27–28, 2000, Munich, Germany, 2001, p. 687. [21] R. Liu, D.L. Yin, J.T. Wang, J. Tao, X.A. Zhao, Influence of deformation processing on the tensile/compressive asymmetry in wrought Mg–3Al–Zn alloy, in: S.R.N.N.R.N.E.A.S.W.H. Agnew (Eds.), Magnesium Technology, 2010, pp. 439–444. [22] E. Sukedai, T. Yokoyama, Int. J. Mater. Res. 101 (2010) 736–740. [23] D.L. Yin, J.T. Wang, J.Q. Liu, X. Zhao, J. Alloys Compd. 478 (2009) 789–795. [24] A.A. Luo, B.R. Powell, Tensile and compressive creep of magnesium–aluminum–calcium based alloys, in: J.N. Hryn (Ed.), Magnesium Technology 2001, 2001, pp. 137–144. [25] S.R. Agnew, K.C. Liu, E.A. Kenik, S. Viswanathan, Tensile and compressive creep behavior of die cast magnesium alloy AM60B, in: H.I. Kaplan, J.N. Hryn, B. Clow (Eds.), Magnesium Technology 2000, 2000, pp. 285–290. [26] R. Lachenmar, H. Schultz, Scr. Metall. 6 (1972) 731. [27] G.L. Webb, R. Gibala, T.E. Mitchell, Metall. Trans. 5 (1974) 1581–1584. [28] K.J. Bowman, R. Gibala, Acta Metall. Mater. 40 (1992) 193–200. [29] L.N. Chang, G. Taylor, J.W. Christian, Acta Metall. 31 (1983) 37–42. [30] L.N. Chang, G. Taylor, J.W. Christian, Scr. Metall. 16 (1982) 95–98. [31] J.P. Hirth, M. Cohen, Metall. Trans. 1 (1970) 3. [32] K.V. Ravi, R. Gibala, 2nd International Conference on the Strength of Metals and Alloys, vol. 1, Cambridge, England, 1973, p. 83.
[38] [39] [40] [41] [42] [43] [44] [45] [46]
[47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64]
[65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78]
[79] [80]
[81]
[82] [83] [84] [85]
17
K.J. Bowman, R. Gibala, Scr. Metall. 20 (1986) 1451–1454. J.O. Ratka, R. Gibala, J. Met. 33 (1981) A43. D.S. Tomalin, C.J. McMahon, Acta Metall. 21 (1973) 1189–1193. C. Woodward, S.I. Rao, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 81 (2001) 1305–1316. W. Sigle, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 79 (1999) 1009–1020. V. Vitek, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 352 (1976) 109–124. H.L. Heinisch, G. Sines, Philos. Mag. 34 (1976) 945–960. D.N. Seidman, J.J. Burke, Acta Metall. 22 (1974) 1301–1314. J. Rabier, J. Grilhe, J. Phys. Chem. Solids 34 (1973) 1031–1038. G. Diener, R. Heinrich, W. Schellen, Phys. Status Solidi B: Basic Res. 44 (1971) 403. V. Vitek, R.C. Perrin, D.K. Bowen, Philos. Mag. 21 (1970) 1049. M.S. Duesbery, V. Vitek, Acta Mater. 46 (1998) 1481–1492. K.N. May, M.S. Thesis, The Ohio State University, Columbus, Ohio, 2010. K.N. May, M.C. Brandes, L.-M. Yang, M.J. Mills, J.C. Williams, Titanium 2011: science and technology, 12th Proceedings of the World Conference on Titanium, Beijing, China, 2011, in press. S. Ando, T. Gotoh, H. Tonda, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 33A (2002) 823–829. M.H. Liang, D.J. Bacon, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 53 (1986) 181–204. M.H. Liang, D.J. Bacon, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 53 (1986) 205–220. H. Numakura, Y. Minonishi, M. Koiwa, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 62 (1990) 525–543. S. Ando, M. Tsushida, H. Tonda, J. Jpn. Inst. Met. 69 (2005) 855–858. S. Ando, T. Gotoh, H. Tonda, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 33 (2002) 823–829. J.R. Morris, K.M. Ho, K.Y. Chen, G. Rengarajan, M.H. Yoo, Modell. Simul. Mater. Sci. Eng. 8 (2000) 25–35. S. Ando, T. Goto, K. Takashima, H. Tonda, J. Jpn. Inst. Met. 63 (1999) 573–576. S. Ando, K. Takashima, H. Tonda, Mater. Trans. JIM 37 (1996) 319–322. A. Girshick, D.G. Pettifor, V. Vitek, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 77 (1998) 999–1012. C. Domain, A. Legris, IUTAM Symposium on Mesoscopic Dynamics of Fracture Process and Materials Strength, vol. 41, 2004, pp. 1–420, 411. J. Li, Unpublished Research in Brandes, M.C., Ph.D. Dissertation, The Ohio State University, 2008, University of Pennsylvania, 2007–08. S. Naka, A. Lasalmonie, P. Costa, L. Kubin, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 57 (1988) 717. S. Naka, A. Lasalmonie, J. Mater. Sci. 18 (1983) 2613–2617. M. Sob, J. Kratochvil, Chekhoslovatskii Fizicheskii Zhurnal 25B (1975) 872. R.L. Jones, H. Conrad, Trans. Metall. Soc. AIME 245 (1969) 779. J.C. Williams, P.P. Tung, A.W. Sommer, Metall. Trans. 3 (1972) 2979–2984. N. Dewobroto, N. Bozzolo, T. Grosdidier, F. Wagner, Titanium’03: science and technology, in: 10th Proceedings of the World Conference on Titanium, vol. 2, Hamburg, Germany, July 13–18, 2003, 2004, p. 1212. H. Garmestani, Air Force Research Laboratory Report #AFRL-SR-AR-TR-070366 (2005). R.K. Boger, R.H. Wagoner, F. Barlat, M.G. Lee, K. Chung, Int. J. Plast. 21 (2005) 2319–2343. J. Holloman, Trans. Metall. Soc. AIME 171 (1947) 355. F. Holden, H. Ogden, R. Jaffee, J. Met. (1953) 238. A. Garde, R. Reed-Hill, Metall. Trans. 2 (1971) 2885. V. Arunacha, S.N. Monteiro, R.E. Reedhill, S. Pattanai, Metall. Trans. 3 (1972) 1009. S.N. Monteiro, A.T. Santhanam, R.E. Reed-Hill, J. Met. 20 (1968) A104. H. Conrad, Prog. Mater. Sci. 26 (1981) 123. J. Williams, R. Baggerly, N. Paton, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 33A (2002) 837. T. Sakai, Plastic Deformation of Ti and Ti–Al Alloy Single Crystals, Northwestern University, Ph.D. Dissertation, Evanston, Illinois, 1976. S. Naka, A. Lasalmonie, Mater. Sci. Eng. 56 (1982) 19. M.P. Biget, G. Saada, Philos. Mag. A: Phys. Condens. Matter Struct. Defects Mech. Prop. 59 (1989) 747–757. F. Beck, NASA Technical Report CR-134796 (1975). J.W. Fu, The Effects of Hydrogen on Slip and Twinning in Pure Titanium Single Crystals, vol Ph.D. Dissertation, The Ohio State University, Ph.D. Dissertation, Columbus, Ohio, 1975. A. Churchman, Proc. R. Soc. A 226 (1954) 216. T. Cass, Titanium’68: science and technology, in: 1st Proceedings of the World Conference on Titanium, vol. 1, London, England, May 21–24, 1968, 1968, p. 459. T. Cass, W. Spencer, Research on Deformation and Possible Strengthening Mechanisms for Solid Solution Phases of Titanium, vol Dayton, Ohio, Air Force Materials Laboratory, Martin Marietta Corporation, Orlando, Florida, 1969. T.R. Cass, Titanium’70: science and technology, in: Proceedings of the International Conference on Titanium, 1970, 1971, pp. 459–477. F. Rosi, J. Met. (1954) 58. V. Moskalenko, V. Puptsova, Fiz. Met. Metalloved. 34 (1972) 1264. M. Amateau, E. Steigerwald, The Relationship between Plastic Deformation and Fracture in Alpha Titanium, Air Force Materials Laboratory, Contract no. AF 33(615)-1682, Materials Research and Development Department, TRW Equipment Group, Cleveland, Ohio, 1966.
18 [86] [87] [88] [89]
M.C. Brandes et al. / Materials Science and Engineering A 551 (2012) 13–18
C. Brehm, P. Lehr, Mem. Sci. Rev. Metall. 68 (1971) 277. J.P. Hirth, J. Lothe, Theory Dislocations, Wiley, New York, 1982. W.L. Finlay, J.A. Snyder, Trans. AIME 188 (1950) 277. P. Lacombe, Titanium’84: science and technology, in: 5th Proceedings of the World Conference on Titanium, vol. 4, Munich, Germany, September, 1984, 1985, pp. 2705–2721. [90] W. Frank, B. Sestak, Scr. Metall. 4 (1970) 451–453. [91] H. Suzuki, J. Phys. Soc. (Jpn.) 17 (1962) 322. [92] G. Welsch, W. Bunk, Metall. Trans. 13A (1982) 889–899.
[93] Z. Liu, G. Welsch, Metall. Trans. 19A (1988) 527–542. [94] Z. Liu, G. Welsch, Titanium’88: science and technology, in: 6th Proceedings of the World Conference on Titaniums, vol. 1, Cannes, France, June 6–9, 1988, 1989, p. 99. [95] Y. Murayama, M. Mikami, S. Ishiyama, Nihon Kinzoku Gakkaishi 57 (1993) 628. [96] D.R. Trinkle, C. Woodward, Science 310 (2005) 1665–1667. [97] L. Romaner, C. Ambrosch-Draxl, R. Pippan, Phys. Rev. Lett. 104 (2010) 195503. [98] N.I. Medvedeva, Y.N. Gornostyrev, A.J. Freeman, Phys. Rev. B 72 (2005) 134107. [99] Y.Q. Feng, C.Y. Wang, J. Alloys Compd. 312 (2000) 219–227.