- Email: [email protected]
Long-term annealing of high purity aluminum single crystals: New insights into Harper-Dorn creep
Materials Science & Engineering A 705 (2017) 1–5
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Long-term annealing of high purity aluminum single crystals: New insights into Harper-Dorn creep
MARK
⁎
K.K. Smitha, M.E. Kassnera, , P. Kumarb a b
University of Southern California, Chemical Engineering and Materials Science, OHE 430, Los Angeles, CA 90089-1453, USA Indian Institute of Science, Dept. of Materials Science, Bangalore, India
A R T I C L E I N F O
A B S T R A C T
Keywords: Annealing Harper-Dorn creep Aluminum single crystals
Single crystals of 99.999% and 99.9999% pure aluminum were annealed at high elevated temperatures (0.98Tm) for relatively long times of up to one year, the longest in the literature. Remarkably, the dislocation density remains relatively constant at a value of about 109 m−2 over a period of one year. The stability suggests some sort of “frustration” limit. This has implications towards the so-called “Harper-Dorn creep” that generally occurs at fairly high temperatures (e.g. > 0.90Tm) and very low stresses. It is possible that ordinary five-power-law creep occurs within the tradition Harper-Dorn regime with very low initial dislocation densities in aluminum. Higher initial dislocation densities, such as with this annealing study, may lead to Harper-Dorn (Newtonian) creep.
1. Introduction Long-term annealing of < 100 > and < 111 > oriented 99.999 (5 N) and 99.9999% (6 N) pure aluminum single-crystals at 0.98Tm was investigated in order to determine the change in dislocation density with various times up to one year. Note that, from Table 1, that the short-term annealed dislocation density values from other studies range from 108 m−2 to a much higher value of over 1011 m−2. The dislocation density values across different studies do not show and noticeable trend with purity as well as the annealing conditions. As-received dislocation densities were reported to be 3 × 105 m−2, 6.0 × 1010 m−2 and 6.5 × 107 m−2. Overall, the starting dislocation densities (either annealed or as-received) vary by six orders of magnitude and these values will be shown to be of the order of those observed within the so-called Harper-Dorn regime. This observation will become important in later discussions. Again, the question remains as to whether longer annealing times (up to one year) can lead to lower dislocation densities. Certainly, from pure energy considerations, we expect the dislocation density to decrease with annealing time. As Table I indicates, one year, by far, is the longest annealing time ever performed. The existence of a “frustration limit” of the dislocation density, suggested by Ardell and coworkers [7,10,11,34,38] for HarperDorn creep {low-stress and generally very high temperatures (e.g. 0.98Tm) [1]}, in which the dislocation density does not decrease below a certain value (even at very low stress), is, thus, also examined in this
⁎
Corresponding author. E-mail address: [email protected] (M.E. Kassner).
http://dx.doi.org/10.1016/j.msea.2017.08.045 Received 28 April 2017; Received in revised form 28 July 2017; Accepted 14 August 2017 Available online 18 August 2017 0921-5093/ © 2017 Published by Elsevier B.V.
work. Harper and Dorn [1] suggested low stress-exponent (n) creep at very low stresses according to
D Gb σ n εsṡ = AHD ⎛ sd ⎞ ⎛ ⎞ ⎝ kT ⎠ ⎝ G ⎠
(1)
where AHD is the Harper-Dorn coefficient, Dsd the lattice self-diffusion coefficient, G is the shear modulus, b is the Burger's vector, σ is the stress (a threshold stress was subtracted by Harper and Dorn from the applied stress to give this σ value [2]) and n has a value of 1. {Interestingly, had this (probably fictitious) threshold stress not been subtracted, three-power law creep is observed [2] instead of Newtonian creep}. Theoretically, a dislocation network creep model developed by the authors [15] in an earlier article, suggests that if the dislocation density σ varies with the steady-state stress as roughly ρss1/2 ∝ Gss , (as with classic five-power law creep) in the low stress regime (see Fig. 1), n is slightly larger than 3. On the other hand, for a constant dislocation density, n is about 1. This is roughly justified by the Orowan equation,
ε̇ = ρm b ν
(2)
If ρm is constant,
ν∝σ1,
(3)
ε ̇ ∝ σ1
(4)
But if ρm changes with stress,
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
Table 1 Average dislocation densities of aluminum in the as-received and annealed conditions. PX – polycrystal, SX – single crystal. Material
Dislocation Density (ρ)
1. 99.99% coarse-grained PX Al
6.0 5.0 6.0 4.5 2.4 1.3 1.0 3.0 6.0 4.3 6.5 2.0
5. 99.99% PX Al 6. 99.994% SX Al 7. 99.9995% SX Al 8. 99.99% SX Al 9. 99.999% SX Al 10. 99.999% PX Al 11. 99.999% SX Al 12. SX Al (purity not reported)
× × × × × × × × × × × ×
1010 m−2 1010 m−2 109 m−2 109 m−2 1011 m−2 107 m−2 108 m−2 1011 m−2 1010 m−2 1011 m−2 107 m−2 106 m−2
Conditions
Reference
As received Annealed 773 K for 10 h Annealed 823 K for 1 h Annealed 903 K for 10 h Annealed (in vacuum) 773 K for 25 min Annealed (in creep machine under < 0.00275 MPa) 823 K for 36 h Annealed 926 K for 50 h Annealed 923 K for 48 h Annealed 926 K for 50 h Annealed 698 K for 1 h Annealed 913 K for 50 h As-received
[3]
(5)
ε̇ ∝ σ n
“frustration limit” for low stress, high-temperature, creep deformation. As just mentioned, Ardell et al. suggested that the dislocation density in the in the Harper-Dorn regime is constant with changing applied stress due to a dislocation network frustration. This was suggested to be due to an inability of the dislocation network to coarsen due to Frank's rule [17], which may not be satisfied with coarsening of the dislocation network at lower values of the Frank network dislocation density.
(where 4.5 > n > 1) Hence, the observations of a constant dislocation density with decreasing stress, and a stress exponent of 1, are self-consistent for Harper-Dorn proponents. Opponents of the classical Harper-Dorn creep expect the observation of a stress-dependent dislocation density. Therefore, the nature of dislocation density variation with the stress in the Harper-Dorn regime may be the key to resolution of the existence of classical Harper-Dorn creep in aluminum. It should be mentioned that it is assumed that the strength of the structure within the Harper-Dorn regime is expected to be provided by the Frank dislocation network, just as at higher stresses and lower temperatures within the five-power-law regime [29,33]. Fig. 1 is compiled from creep studies by several investigators both supporting and refuting the existence of the classic Harper Dorn creep [5,8,9,16,18–20]. Lin et al. [16] and Barrett et al. [5] both suggested that the dislocation density remains fixed with decreasing stress, leveling out at about 108 m−2 and Harper-Dorn Creep was suggested to be observed. “Network frustration” was suggested by Lin et al. to explain the observations. Some earlier work by the authors [2,12,13,15,19] suggests that the dislocation values, in fact, continue to decrease with stress in a manner as with lower temperature and higher stress five-power-law creep of aluminum, as also did Nes [14]. Thus, an ancillary purpose of this annealing study is to check the concept of a
1014
(6)
1
where bi is the Burgers vector of the ith dislocation (link) meeting at the node in the network. Long-term annealing experiments could confirm or refute the existence of this frustration limit for the starting dislocation density. The proposed annealing experiments are simply the limit of the change is dislocation density as the stress decreases to zero. 2. Experimental procedure Single crystal aluminum samples for this study were purchased from Material–Technologie & Kristalle GmbH (MaTecK), Jülich, Germany of 5 N purity (99.999% pure) and cylindrical dimensions of 127 mm length × 25.4 mm diameter and an orientation of < 100 > or < 111 > along the length of the cylinder. 6 N purity (99.9999% pure) Al single crystals were also used with a < 100 > orientation and 19 mm Fig. 1. Steady-state dislocation density versus the modulus-compensated steady-state stress at an elevated temperature of 923 K (0.99 Tm) based on earlier work and the authors’ previous work in [2]. The data of Lin et al. [16] and that of Barrett et al. [5] suggest a lower limit of the dislocation density (ρ). The work by Barrett et al. [5] and Kumar et al. [2] may suggest a continual decrease in the dislocation density with decreasing stress. {The shear modulus (G) used was 16.96 GPa at 920 K (0.98Tm) [21]}. Note that the initial dislocation densities of Table I are of the same order as the steady-state dislocations densities at low (e.g. Harper-Dorn) stresses.
Kumar et al. (2008) Barrett et al. (1972)
1012 Dislocation Density (line length/m2 )
n
∑ bi = 0
99.999% Pure Al SX
1013
Mohamed et al. (1973) Mohamed and Ginter (1982)
1011
Kassner and McMahon (1987)
1010
Lin, Lee and Ardell (1989)
109 99.999% Pure Al - 5%Zn
108
Lin et al. Average
Blum (1993)
Barrett et al. Average
107 106
2
105
1
104 "Harper-Dorn" regime
5-Power Law regime
103 Stress due to the weight at the bottom of our specimens
102 101
10-10
10-9
10-8
10-7
10-6 σss /G
10-5
[4] [5] [6] [7] [8] [9] [32] [30]
10-4
10-3
2
10-2
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
height and 25.4 mm in diameter also from Materials-Technologie and Kristalle. The etch-pit and annealing procedures for the 5 N and 6 N crystals were identical. Five specimens were used in the annealing experiment for the 5 N single crystal and one specimen for 6 N annealing experiment. The Al single crystals were cut into individual pieces of 6–8 mm thickness (25.4 mm diameter) using the IsoMet® 1000 Precision Saw from Buehler. A 0.305 mm thick diamond saw wafer-blade was used at a slow speed of 100 rpm with oil-based lubricants. Polishing the samples consisted of using both mechanical and electro-polishing procedures. Dislocation densities were determined by surface etching. Two mechanical polishing techniques were subsequently utilized to remove the cutting damage from the IsoMet in each sample. The Ecomet III Wet Polisher/Grinder utilizing varying grades (320–1200) of 200 mm diameter CarbiMet silicon carbide grit paper discs obtained from Buehler was used to grind the specimens. Deionized (DI) water was constantly flowing onto the grit paper. Buehler MetaDi™ monocrystalline diamond suspensions, from 9 µm to 0.25 µm particle sizes, on a Struers LaboPol-2 230 mm diameter magnetic polishing wheel, were subsequently used to polish the sample to ensure all of the damage induced from the earlier silicon carbide paper was removed. DI water was also used with the diamond slurries. The samples were washed with DI water between each grinding step and compressed-air dried. Electropolishing removed any remaining surface damage from mechanical polishing and gave the aluminum crystals a damage-free surface. A total of about 2–3 mm was removed from each of the samples from the grinding and polishing steps. The electro-polishing solution consisted of a 1:9 (by volume) perchloric acid (70% ACS reagent) to methanol (99.8% anhydrous) mixture [6–8,22]. Optimal polishing conditions were ~1.6 mA and ~10 V at 0 – 5 °C. A magnetic stir bar was used to ensure a uniform dispersion of the ions from the anode surface. Dislocation densities were determined by surface etching. The etching solution [2,5,7,8,22,23] consisted of a 50:47:3 mixture of hydrochloric acid (37 vol% ACS Reagent), nitric acid (70 vol% ACS Reagent) and hydrofluoric acid (48 vol% ACS Reagent). HCl was first chilled in a beaker encapsulated by a larger beaker with ice before mixing with HNO3 and HF. The samples were etched 5–7 s with vigorous stirring to avoid localized corrosion and immediately rinsed with DI water and dried using compressed air. The etch pits are visible as squares and triangles on the surfaces of the < 100 > and < 111 > oriented crystals, respectively. Corrosion pits or over-etching of the sample was evinced by jagged or circular geometries. Electropolishing was repeated with subsequent etching in the cases of the presence of these features. Fig. 2 is a representative scanning electron micrograph (SEM) of an etched 6 N specimen after 6 months annealing at 920 K. Etch pits were used to calculate the dislocation density, as opposed to by transmission electron microscopy (TEM) partially because the dislocation densities are so low. As Nes discussed [14], a large number of TEM thin foils (e.g. 100) could be necessary to image sufficient numbers dislocations at lower density values. This is because the thin areas of the foils are small in comparison the total area associated with an individual dislocation. The authors attempted characterization of the Frank network by transmission electron microscopy (TEM), but were unsuccessful due to damage [28]. Even very small amounts of damage introduced into these low dislocation structures compromises the characterization of the network. Etch pits cannot perform orientation and Burgers vector analyses. X-ray topography is attractive (as used by Nes), but these facilities are not readily available. A question arises regarding the reliability by which the dislocations are observed by etching. This subject was investigated by Forty and Frank [31] who concluded that there can be some undercounting of dislocations in aluminum (e.g. 30–50%) by etch pits, but this does not preclude the effectiveness of this study using etch pits. Furthermore, with the exception of Nes, essentially all the studies referenced with which we compared densities, also used etch pit
Fig. 2. A scanning electron micrograph of 99.9999% purity aluminum single crystal after six months of annealing at 920 K. The < 100 > is perpendicular to the plane.
analysis. Samples were heat treated in an air furnace at 920 K (0.98 Tm) for various times: 0 days (initial dislocation density), 3 days, 10 days, 1 month, 3 months, 6 months and 1 year. A 3–550 Vulcan Multi-Stage Programmable Furnace was used for the first three months of annealing. A ramp rate of 20 °C/min was programmed to the set temperature of 920 K (0.98 Tm). The temperature was recorded using a Type-K thermocouple and a desktop computer. Each sample had an individual, soldered, thermocouple. A smaller desktop furnace was used and controlled externally by a Sigma Digital PID (three-term regulator) MDC4E temperature control unit for the remaining 9 months. The samples, again, had individual Type-K thermocouples. The samples rested on an alumina disk to provide separation from the furnace floor. The dislocation density is calculated by the equation [2,8,23,24],
ρ=
2N A
(7)
where N is the number of etch pits and A is the area over which the etch pits were counted using an optical microscope. This density (line length per unit volume) is roughly twice the density based on the number of dislocations per unit area [24]. In this work, the entire surface area of the annealed samples (507 mm2) was examined. Two kinds of etch pits were observed: large (about 6 µm) and small (3 µm) as illustrated in Fig. 2. This was also observed in our earlier work for Al single crystals [2]. The fraction of pits that are small appears to increase with annealing time from 35% in the as-received specimen to 99% after a oneyear anneal. The reported dislocation density considered both small and large etch pits. The explanation for the existence of two populations of sizes is unclear. Observing the etch pits by optical and scanning electron microscopes did not change the dislocation density measurements. Table 2 Dislocation densities associated with each annealing time period in this study. Annealing Time
5 N Average Dislocation Densities ( ρ )
6 N Average Dislocation Densities ( ρ )
Initial
2.69 × 109 m−2 range: (8.76 × 107 – 1.02 × 1010 m−2) 6.55 × 107 m−2 7.0 × 108 m−2 3.0 × 109 m−2 1.88 × 107 m−2 5.05 × 108 m−2 3.70 × 109 m−2
1.28 × 109 m−2 range: (3.54 ×108 – 4.01 ×109 m−2)
3 days 10 days 30 days 3 months 6 months 1 year
3
1.98 × 109 m−2
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
Dislocation Densities in Single Crystal Aluminum vs. Annealing Time
Fig. 3. The dislocation density versus annealing time at 920 K.
1E+12 1E+11
Present Study
Literature Averages
Dislocation Density (line length/m2 )
1E+10 1E+9 1E+8 1E+7 1E+6 1E+5
Present Study - 5N Sample Averages
1E+4
Present Study - 6N Sample Averages
1E+3
Literature Averages
1E+2
3 days 10 days 1 month 6 months 1 year
1E+1 1E+0
10-1
100
101
102
103
104
105
106
107
108
109
Time (sec)
transition from Harper-Dorn to the five power-law creep regime (see Fig. 1), the dislocation density may not correspondingly decrease due to frustration. Thus, the steady state stress may be independent of the dislocation density and a power of one may be observed. An increase in stress will place the aluminum within the five-power law regime and higher stress exponents are expected. On the other hand, if the initial density is relatively low (case 2.), as in the slowly cooled single crystals of Nes and Nost [30] (e.g. 2 × 106 m−2), increases in stress will lead to increasing dislocation densities within the Harper-Dorn regime, and five-power-law-like behavior may be observed despite being in the Harper-Dorn Regime. The increased occurs by activating the links in the network into Frank-Read sources. The modulus-compensated stress to activate a Frank-Read source can easily shown to be:
Table 2 lists the dislocation densities that are also plotted in Fig. 3 Single crystals were used in the annealing experiments so as other restoration mechanisms (e.g. grain growth [25,26]) are avoided. The one-year sample was re-polished mechanically with the 0.25 µm diamond slurry and then electropolished after removal from the furnace. The small amount of additional mechanical polishing unique to the 1 year specimens ensured that the thicker oxide layer could be fully removed with (normal) electro-polishing. The other samples (shorter annealing times) were not mechanically polished before electro-polishing. The resulting thickness of the sample disk was about 1–2 mm.
3. Results and discussion
(τ / G )F − R = 2bMρ1/2
Table 2 lists the dislocation densities that are also plotted in Fig. 3. The data suggests that the dislocation density is relatively stable during very long-time high-temperature annealing. Obviously, very high dislocation densities will recover, but coarsening of the Frank network is not observed for at least some low dislocation densities (and associated Burgers vector distributions). The dislocation density in this experiment is close to that at which constant dislocation densities are observed in Harper-Dorn creep tests by Lin et al. and Barrett et al. This trend was also very recently observed in unpublished experiments done by one of the authors [27] on 99.999% pure lithium fluoride single crystals. That study examined the effect of static annealing at 0.92Tm on the LiF crystals, The literature (as well as our data) suggests that the “starting” dislocation density varies substantially (see Table 1) in Al and often can be of the order of the expected creep-deformed steady-state dislocation density in the Harper-Dorn regime. The current study shows that these same densities may be resistant to coarsening. Also, as just mentioned, the dislocation densities observed in the Harper-Dorn regime are comparable to that at which we observed frustration or resistance to recovery under static annealing conditions. We can consider two cases for creep at very high temperatures in Al: First, the initial dislocation density is relatively high (upper part of the starting dislocation variation bracket in Fig. 1). The second case occurs when the starting dislocation density is relatively low. For each case we can have either a relatively high or low applied stress within the Harper-Dorn regime. For case 1.), as the applied stress drops from a high stress near the
(8)
where M is the Taylor factor. Modest increases in stress in a relatively high (case 1.) frustrated network near the stress associated Harper-Dorn transition to five power-law creep can cause dislocation multiplication by activating Frank read sources according to Eq. (8) and Fig. 1. FrankRead sources may not activate with small increases in stress at lower applied stresses within the Haper-Dorn regime, and Harper-Dorn behavior may persist for elevated dislocation densities at low stresses for case 1.0 with high starting dislocation densities. At low stresses associated with very low initial dislocation densities [case 2.)], modest increases in stress lead to activation of Frank-Read sources and increasing dislocation densities within the Harper-Dorn regime. So, for the same stress within the Harper- Dorn regime, the high starting dislocation density crystal will have a stress exponent of 1, while the low starting dislocation crystal will have a stress exponent of 3 or larger; behavior depends on the starting dislocation density which can vary dramatically. Unfortunately, many low-stress creep studies do not indicate the starting dislocation density prior to creep. In the study of low-stress creep by the authors [in which we did not observe 1-power (Harper-Dorn) law creep but observed 3-power instead.], the initial dislocation density was also relatively low at 6.5 × 107 m−2. Nes and Nost and Nes [14,30] that also failed to observe 1power Harper-Dorn behavior with the low starting dislocation density of 2 × 106 m−2. Of course, it must be mentioned that our observation of a “frustration” density is under zero stress and we assume that this translates to 4
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
References
the expectation of frustration under low (Harper-Dorn) stresses. Also, we observe frustration for a given starting dislocation density. We are not sure of the range of values of starting dislocation densities that will lead to this frustration. Ardell claims that the frustration model allows an accurate prediction of the creep behavior at low stresses. Ardell never fully demonstrates the viability of dislocation frustration. This strikes the authors of this study as a very difficult task. A variety of Burgers vectors, dislocation link lengths and orientations are all necessary to characterize for the network. This must be followed by a demonstration that the coarsening is impossible beyond some average link length. This task seems insurmountable despite modern computer simulations and TEM characterization techniques. It appears, as only one of several complications, that TEM cannot be performed on such low density dislocation structures because of damage introduced on the soft crystals and also because TEM examines structures at excessive magnification to characterize nodes. The authors attempted characterization of the Frank network, but were unsuccessful due to damage. Even very small amounts of damage introduced into these low dislocation structures compromises the characterization of the network. Etch pits cannot perform orientation and Burgers vector analyses. Thus, we believe frustration appears to be the only real explanation for the termination of network growth although a fundamental demonstration or proof does not appear available. Simple calculations show that the impurity levels in 5 N and 6 N single crystals is associated with more than one impurity atom per Burgers vector line length. Furthermore, this impurity level is associated with strengthening in the crystals [33]. However, any pinning to such a degree that the dislocation density is unchanged with applied stress should evince threshold behavior which is not observed. Internal stresses are not a factor in the frustration as these have been demonstrated in Cu and Al to be very low [35–37].
[1] J. Harper, J.E. Dorn, Viscous creep of aluminum near its melting temperature, Acta Metall. 5 (1957) 654–665. [2] P. Kumar, M.E. Kassner, T.G. Langdon, W. Blum, P. Eisenlohr, New observations on high temperature creep at very low stresses, Mater. Sci. Eng.: A. 510–511 (2009) 20–24. [3] B. Ya, Pines, A.F. Syrenko, Change in dislocation density in aluminum and lithium fluoride after annealing near the melting point under hydrostatic pressure, J. Mater. Sci. 3 (1968) 80–88. [4] G.K. Williamson, W.H. Hall, X-ray line broadening from filed aluminum and wolfram, Acta Metall. 1 (1953) 22–31. [5] C.R. Barrett, E.C. Muehleisen, W.D. Nix, High-temperature low stress creep of aluminum and Al-0.5%Fe, Mater. Sci. Eng.: A. 10 (1972) 33–42. [6] T.J. Ginter, F.A. Mohamed, Evidence for dynamic recrystallization during HarperDorn creep, Mater. Sci. Eng.: A. 322 (2002) 148–152. [7] S. Lee, A.J. Ardell, Dislocation link length distributions during Harper-Dorn creep of monocrystalline aluminum, Acta Metall. 34 (12) (1986) 2411–2423. [8] F.A. Mohamed, T.J. Ginter, On the nature and origin of Harper-Dorn creep, Acta Metall. 30 (1982) 1869–1881. [9] M.E. Kassner, M.E. McMahon, The dislocation microstructure of aluminum deformed to very large steady-state creep strains, Metall. Trans. 18A (1987) 835–846. [10] A.J. Ardell, Harper-Dorn creep—predictions of the dislocation network theory of high temperature deformation, Acta Metall. 45 (7) (1997) 2971–2981. [11] M.A. Przystupa, A.J. Ardell, Predictive capabilities of the dislocation-network theory of Harper-Dorn, Metall. Mater. Trans.: A 33 (2) (2002) 231–239. [12] M.E. Kassner, P. Kumar, W. Blum, Harper-Dorn creep, Int. J. Plast. 23 (2007) 980–1000. [13] W. Blum, W. Maier, Harper-Dorn creep: a myth? Phys. Status Solidi (A) 171 (1999) 467–474. [14] E. Nes, Modeling of work hardening and stress saturation in FCC metals, Progress. Mater. Sci. 41 (3) (1998) 129–193. [15] P. Kumar, M.E. Kassner, Theory for very low stress (“Harper-Dorn”) creep, Scr. Mater. 60 (2009) 60–63. [16] P. Lin, S.S. Lee, A.J. Ardell, Scaling Characteristics of Dislocation Link Length Distributions Generated During the Creep of Crystals. 37(2), 1989, pp.739–748. [17] D. Hull, D.J. Bacon, Introduction to Dislocations, 5th ed., Butterworth-Heinemann, Oxford, 2011. [18] F.A. Mohamed, K.L. Murty, J.W. Morris, Metallurgical transformations, HarperDorn Creep Al, Pb, Sn 4 (1973) 935–940. [19] P. Kumar, M.E. Kassner, T.G. Langdon, The role of Harper-Dorn creep at high temperatures and very low stresses, J. Mater. Sci. 43 (2008) 4801–4810. [20] W. Blum, Plastic deformation and fracture, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Materials Science and Technology, 6 VCH Publishers, Weinheim, Germany, 1993, p. 339. [21] P. Kumar, Creep in Pure Single and Polycrystalline Aluminum at Very Low Stresses and High Temperatures: An Evaluation of Harper-Dorn Creep (Thesis/Dissertation), University of Southern California, 2008. [22] T.J. Ginter, P.K. Chaudhury, F.A. Mohamed, An investigation of Harper-Dorn at large strains, Acta Mater. 49 (2001) 263–272. [23] Y.-C. Cheng, M. Chauhan, F.A. Mohamed, Uncovering the mystery of Harper-Dorn creep in metals, Metall. Mater. Trans.: A. 40A (2009) 80–90. [24] R.K. Ham, N.G. Sharpe, A systematic error in the determination of dislocation densities in thin films, Philos. Mag. 6 (69) (1961) 1193–1194. [25] M.E. Kassner, J. Pollard, E. Evangelista, E. Cerri, Restoration mechanisms in large strain deformation of high purity aluminum at ambient-temperature and the determination of the existence of a steady-state, Acta Metall. Mater. 42 (9) (1994) 3223–3230. [26] H.J. McQueen, W. Blum, S. Straub, M.E. Kassner, Dynamic grain growth – a restoration mechanism in 99.999% Al, Scr. Metall. Mater. 28 (1993) 1299–1304. [27] P. Kumar. Indian Institute of Science, Bangalore, India 2015. (Unpublished). [28] M.E. Kassner, C.J. Echer, Mechanical damage introduced into annealed aluminum monocrystals by conventional TEM thin-foil preparation techniques, Metallography 19 (1986) 127–132. [29] M.E. Kassner, A case for Taylor hardening during primary and steady state creep in aluminum and type 304 stainless steel, J. Mater. Sci. 25 (1990) 1997–2003. [30] E. Nes, B. Nost, Dislocation densities in slowly cooled aluminum single crystals, Philos. Mag. 124 (1966) 855–865. [31] A.J. Forty, F.C. Frank, The interpretation of etch patterns on aluminum, J. Phys. Soc. Jpn. 10 (1955) 656–663. [32] P. Kumar, Ph.D. Thesis, Dept. of Chemical Engineering and Materials Science, Univ. of Southern California, 2007. [33] M.E. Kassner, Taylor hardening in five power law creep of metals and class M alloys, Acta Mater. 52 (2004) 1–9. [34] P. Yavari, D.A. Miller, T.G. Langdon, An investigation of Harper-Dorn creep-I. mechanical and microstructural characterisitics, Acta Metall. 30 (1982) 871–879. [35] L.E. Levine, P. Geantil, B.C. Larson, J.Z. Tischler, M.E. Kassner, W. Liu, M.R. Stoudt, F. Tavazza, Disordered long-range internal stresses in deformed copper and the mechanisms underlying plastic deformation, Acta Mater. 59 (2011) 5083–5091. [36] M.E. Kassner, M.-T. Pérez-Prado, M. Long, K.S. Vecchio, Dislocation microstructures and internal stress measurements by CBED on creep deformed Cu and Al, Metall. Mater. Trans. 33A (2002) 311–318. [37] M.E. Kassner, M.-T. Perez-Prado, K.S. Vecchio, M.A. Wall, Determination of internal stresses in cyclically deformed Cu single crystals using CBED and dislocation dipole separation measurements, Acta Mater. 48 (2000) 4247–4254. [38] A.J. Ardell, Harper–Dorn creep– the dislocation network theory revisited, Scripta Mater 69 (2013), pp. 541–544.
4. Summary In summary, the aluminum single crystals were annealed for various times up to one year at 920 K (0.98 Tm). Our results show that the dislocation density is relatively constant. This may suggest that the concept of dislocation “frustration” suggested by Ardell and coworkers may be valid. This potentially explains why some low stress investigations in aluminum observe the Harper-Dorn behavior (stress exponent of one and a constant dislocation density with stress) while others observe traditional power-law (exponents of 3–4.5 with a dislocation density that varies with stress). The dislocation density can increase with increasing stress, but by the current study it may not decrease with decreasing stress due to frustration at the lower density values. If the initial density is low, increases in stress anywhere within the Harper-Dorn regime may increase the density and five-power law behavior is observed. If the initial dislocation density is relatively high (just within the Harper-Dorn regime), then increases in stress may place the new density within the five power-law regime. The density may not be able to decrease with decreasing stress due to frustration. Increases in stress from low-stress values for these higher dislocation densities Frank-Read sources may not be activated until the applied stress approaches that for five power-law creep. Thus, depending on the starting dislocation density we may observe either constant or increasing dislocation density within the Harper-Dorn regime. Hence, the observation of (or failure to observe) Harper-Dorn behavior may depend on the initial dislocation density which can vary by many orders of magnitude. This may explain a 60 year puzzle of Harper-Dorn creep. Acknowledgments The authors are grateful for support from the NSF under grant DMR1401194.
5
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Long-term annealing of high purity aluminum single crystals: New insights into Harper-Dorn creep
MARK
⁎
K.K. Smitha, M.E. Kassnera, , P. Kumarb a b
University of Southern California, Chemical Engineering and Materials Science, OHE 430, Los Angeles, CA 90089-1453, USA Indian Institute of Science, Dept. of Materials Science, Bangalore, India
A R T I C L E I N F O
A B S T R A C T
Keywords: Annealing Harper-Dorn creep Aluminum single crystals
Single crystals of 99.999% and 99.9999% pure aluminum were annealed at high elevated temperatures (0.98Tm) for relatively long times of up to one year, the longest in the literature. Remarkably, the dislocation density remains relatively constant at a value of about 109 m−2 over a period of one year. The stability suggests some sort of “frustration” limit. This has implications towards the so-called “Harper-Dorn creep” that generally occurs at fairly high temperatures (e.g. > 0.90Tm) and very low stresses. It is possible that ordinary five-power-law creep occurs within the tradition Harper-Dorn regime with very low initial dislocation densities in aluminum. Higher initial dislocation densities, such as with this annealing study, may lead to Harper-Dorn (Newtonian) creep.
1. Introduction Long-term annealing of < 100 > and < 111 > oriented 99.999 (5 N) and 99.9999% (6 N) pure aluminum single-crystals at 0.98Tm was investigated in order to determine the change in dislocation density with various times up to one year. Note that, from Table 1, that the short-term annealed dislocation density values from other studies range from 108 m−2 to a much higher value of over 1011 m−2. The dislocation density values across different studies do not show and noticeable trend with purity as well as the annealing conditions. As-received dislocation densities were reported to be 3 × 105 m−2, 6.0 × 1010 m−2 and 6.5 × 107 m−2. Overall, the starting dislocation densities (either annealed or as-received) vary by six orders of magnitude and these values will be shown to be of the order of those observed within the so-called Harper-Dorn regime. This observation will become important in later discussions. Again, the question remains as to whether longer annealing times (up to one year) can lead to lower dislocation densities. Certainly, from pure energy considerations, we expect the dislocation density to decrease with annealing time. As Table I indicates, one year, by far, is the longest annealing time ever performed. The existence of a “frustration limit” of the dislocation density, suggested by Ardell and coworkers [7,10,11,34,38] for HarperDorn creep {low-stress and generally very high temperatures (e.g. 0.98Tm) [1]}, in which the dislocation density does not decrease below a certain value (even at very low stress), is, thus, also examined in this
⁎
Corresponding author. E-mail address: [email protected] (M.E. Kassner).
http://dx.doi.org/10.1016/j.msea.2017.08.045 Received 28 April 2017; Received in revised form 28 July 2017; Accepted 14 August 2017 Available online 18 August 2017 0921-5093/ © 2017 Published by Elsevier B.V.
work. Harper and Dorn [1] suggested low stress-exponent (n) creep at very low stresses according to
D Gb σ n εsṡ = AHD ⎛ sd ⎞ ⎛ ⎞ ⎝ kT ⎠ ⎝ G ⎠
(1)
where AHD is the Harper-Dorn coefficient, Dsd the lattice self-diffusion coefficient, G is the shear modulus, b is the Burger's vector, σ is the stress (a threshold stress was subtracted by Harper and Dorn from the applied stress to give this σ value [2]) and n has a value of 1. {Interestingly, had this (probably fictitious) threshold stress not been subtracted, three-power law creep is observed [2] instead of Newtonian creep}. Theoretically, a dislocation network creep model developed by the authors [15] in an earlier article, suggests that if the dislocation density σ varies with the steady-state stress as roughly ρss1/2 ∝ Gss , (as with classic five-power law creep) in the low stress regime (see Fig. 1), n is slightly larger than 3. On the other hand, for a constant dislocation density, n is about 1. This is roughly justified by the Orowan equation,
ε̇ = ρm b ν
(2)
If ρm is constant,
ν∝σ1,
(3)
ε ̇ ∝ σ1
(4)
But if ρm changes with stress,
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
Table 1 Average dislocation densities of aluminum in the as-received and annealed conditions. PX – polycrystal, SX – single crystal. Material
Dislocation Density (ρ)
1. 99.99% coarse-grained PX Al
6.0 5.0 6.0 4.5 2.4 1.3 1.0 3.0 6.0 4.3 6.5 2.0
5. 99.99% PX Al 6. 99.994% SX Al 7. 99.9995% SX Al 8. 99.99% SX Al 9. 99.999% SX Al 10. 99.999% PX Al 11. 99.999% SX Al 12. SX Al (purity not reported)
× × × × × × × × × × × ×
1010 m−2 1010 m−2 109 m−2 109 m−2 1011 m−2 107 m−2 108 m−2 1011 m−2 1010 m−2 1011 m−2 107 m−2 106 m−2
Conditions
Reference
As received Annealed 773 K for 10 h Annealed 823 K for 1 h Annealed 903 K for 10 h Annealed (in vacuum) 773 K for 25 min Annealed (in creep machine under < 0.00275 MPa) 823 K for 36 h Annealed 926 K for 50 h Annealed 923 K for 48 h Annealed 926 K for 50 h Annealed 698 K for 1 h Annealed 913 K for 50 h As-received
[3]
(5)
ε̇ ∝ σ n
“frustration limit” for low stress, high-temperature, creep deformation. As just mentioned, Ardell et al. suggested that the dislocation density in the in the Harper-Dorn regime is constant with changing applied stress due to a dislocation network frustration. This was suggested to be due to an inability of the dislocation network to coarsen due to Frank's rule [17], which may not be satisfied with coarsening of the dislocation network at lower values of the Frank network dislocation density.
(where 4.5 > n > 1) Hence, the observations of a constant dislocation density with decreasing stress, and a stress exponent of 1, are self-consistent for Harper-Dorn proponents. Opponents of the classical Harper-Dorn creep expect the observation of a stress-dependent dislocation density. Therefore, the nature of dislocation density variation with the stress in the Harper-Dorn regime may be the key to resolution of the existence of classical Harper-Dorn creep in aluminum. It should be mentioned that it is assumed that the strength of the structure within the Harper-Dorn regime is expected to be provided by the Frank dislocation network, just as at higher stresses and lower temperatures within the five-power-law regime [29,33]. Fig. 1 is compiled from creep studies by several investigators both supporting and refuting the existence of the classic Harper Dorn creep [5,8,9,16,18–20]. Lin et al. [16] and Barrett et al. [5] both suggested that the dislocation density remains fixed with decreasing stress, leveling out at about 108 m−2 and Harper-Dorn Creep was suggested to be observed. “Network frustration” was suggested by Lin et al. to explain the observations. Some earlier work by the authors [2,12,13,15,19] suggests that the dislocation values, in fact, continue to decrease with stress in a manner as with lower temperature and higher stress five-power-law creep of aluminum, as also did Nes [14]. Thus, an ancillary purpose of this annealing study is to check the concept of a
1014
(6)
1
where bi is the Burgers vector of the ith dislocation (link) meeting at the node in the network. Long-term annealing experiments could confirm or refute the existence of this frustration limit for the starting dislocation density. The proposed annealing experiments are simply the limit of the change is dislocation density as the stress decreases to zero. 2. Experimental procedure Single crystal aluminum samples for this study were purchased from Material–Technologie & Kristalle GmbH (MaTecK), Jülich, Germany of 5 N purity (99.999% pure) and cylindrical dimensions of 127 mm length × 25.4 mm diameter and an orientation of < 100 > or < 111 > along the length of the cylinder. 6 N purity (99.9999% pure) Al single crystals were also used with a < 100 > orientation and 19 mm Fig. 1. Steady-state dislocation density versus the modulus-compensated steady-state stress at an elevated temperature of 923 K (0.99 Tm) based on earlier work and the authors’ previous work in [2]. The data of Lin et al. [16] and that of Barrett et al. [5] suggest a lower limit of the dislocation density (ρ). The work by Barrett et al. [5] and Kumar et al. [2] may suggest a continual decrease in the dislocation density with decreasing stress. {The shear modulus (G) used was 16.96 GPa at 920 K (0.98Tm) [21]}. Note that the initial dislocation densities of Table I are of the same order as the steady-state dislocations densities at low (e.g. Harper-Dorn) stresses.
Kumar et al. (2008) Barrett et al. (1972)
1012 Dislocation Density (line length/m2 )
n
∑ bi = 0
99.999% Pure Al SX
1013
Mohamed et al. (1973) Mohamed and Ginter (1982)
1011
Kassner and McMahon (1987)
1010
Lin, Lee and Ardell (1989)
109 99.999% Pure Al - 5%Zn
108
Lin et al. Average
Blum (1993)
Barrett et al. Average
107 106
2
105
1
104 "Harper-Dorn" regime
5-Power Law regime
103 Stress due to the weight at the bottom of our specimens
102 101
10-10
10-9
10-8
10-7
10-6 σss /G
10-5
[4] [5] [6] [7] [8] [9] [32] [30]
10-4
10-3
2
10-2
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
height and 25.4 mm in diameter also from Materials-Technologie and Kristalle. The etch-pit and annealing procedures for the 5 N and 6 N crystals were identical. Five specimens were used in the annealing experiment for the 5 N single crystal and one specimen for 6 N annealing experiment. The Al single crystals were cut into individual pieces of 6–8 mm thickness (25.4 mm diameter) using the IsoMet® 1000 Precision Saw from Buehler. A 0.305 mm thick diamond saw wafer-blade was used at a slow speed of 100 rpm with oil-based lubricants. Polishing the samples consisted of using both mechanical and electro-polishing procedures. Dislocation densities were determined by surface etching. Two mechanical polishing techniques were subsequently utilized to remove the cutting damage from the IsoMet in each sample. The Ecomet III Wet Polisher/Grinder utilizing varying grades (320–1200) of 200 mm diameter CarbiMet silicon carbide grit paper discs obtained from Buehler was used to grind the specimens. Deionized (DI) water was constantly flowing onto the grit paper. Buehler MetaDi™ monocrystalline diamond suspensions, from 9 µm to 0.25 µm particle sizes, on a Struers LaboPol-2 230 mm diameter magnetic polishing wheel, were subsequently used to polish the sample to ensure all of the damage induced from the earlier silicon carbide paper was removed. DI water was also used with the diamond slurries. The samples were washed with DI water between each grinding step and compressed-air dried. Electropolishing removed any remaining surface damage from mechanical polishing and gave the aluminum crystals a damage-free surface. A total of about 2–3 mm was removed from each of the samples from the grinding and polishing steps. The electro-polishing solution consisted of a 1:9 (by volume) perchloric acid (70% ACS reagent) to methanol (99.8% anhydrous) mixture [6–8,22]. Optimal polishing conditions were ~1.6 mA and ~10 V at 0 – 5 °C. A magnetic stir bar was used to ensure a uniform dispersion of the ions from the anode surface. Dislocation densities were determined by surface etching. The etching solution [2,5,7,8,22,23] consisted of a 50:47:3 mixture of hydrochloric acid (37 vol% ACS Reagent), nitric acid (70 vol% ACS Reagent) and hydrofluoric acid (48 vol% ACS Reagent). HCl was first chilled in a beaker encapsulated by a larger beaker with ice before mixing with HNO3 and HF. The samples were etched 5–7 s with vigorous stirring to avoid localized corrosion and immediately rinsed with DI water and dried using compressed air. The etch pits are visible as squares and triangles on the surfaces of the < 100 > and < 111 > oriented crystals, respectively. Corrosion pits or over-etching of the sample was evinced by jagged or circular geometries. Electropolishing was repeated with subsequent etching in the cases of the presence of these features. Fig. 2 is a representative scanning electron micrograph (SEM) of an etched 6 N specimen after 6 months annealing at 920 K. Etch pits were used to calculate the dislocation density, as opposed to by transmission electron microscopy (TEM) partially because the dislocation densities are so low. As Nes discussed [14], a large number of TEM thin foils (e.g. 100) could be necessary to image sufficient numbers dislocations at lower density values. This is because the thin areas of the foils are small in comparison the total area associated with an individual dislocation. The authors attempted characterization of the Frank network by transmission electron microscopy (TEM), but were unsuccessful due to damage [28]. Even very small amounts of damage introduced into these low dislocation structures compromises the characterization of the network. Etch pits cannot perform orientation and Burgers vector analyses. X-ray topography is attractive (as used by Nes), but these facilities are not readily available. A question arises regarding the reliability by which the dislocations are observed by etching. This subject was investigated by Forty and Frank [31] who concluded that there can be some undercounting of dislocations in aluminum (e.g. 30–50%) by etch pits, but this does not preclude the effectiveness of this study using etch pits. Furthermore, with the exception of Nes, essentially all the studies referenced with which we compared densities, also used etch pit
Fig. 2. A scanning electron micrograph of 99.9999% purity aluminum single crystal after six months of annealing at 920 K. The < 100 > is perpendicular to the plane.
analysis. Samples were heat treated in an air furnace at 920 K (0.98 Tm) for various times: 0 days (initial dislocation density), 3 days, 10 days, 1 month, 3 months, 6 months and 1 year. A 3–550 Vulcan Multi-Stage Programmable Furnace was used for the first three months of annealing. A ramp rate of 20 °C/min was programmed to the set temperature of 920 K (0.98 Tm). The temperature was recorded using a Type-K thermocouple and a desktop computer. Each sample had an individual, soldered, thermocouple. A smaller desktop furnace was used and controlled externally by a Sigma Digital PID (three-term regulator) MDC4E temperature control unit for the remaining 9 months. The samples, again, had individual Type-K thermocouples. The samples rested on an alumina disk to provide separation from the furnace floor. The dislocation density is calculated by the equation [2,8,23,24],
ρ=
2N A
(7)
where N is the number of etch pits and A is the area over which the etch pits were counted using an optical microscope. This density (line length per unit volume) is roughly twice the density based on the number of dislocations per unit area [24]. In this work, the entire surface area of the annealed samples (507 mm2) was examined. Two kinds of etch pits were observed: large (about 6 µm) and small (3 µm) as illustrated in Fig. 2. This was also observed in our earlier work for Al single crystals [2]. The fraction of pits that are small appears to increase with annealing time from 35% in the as-received specimen to 99% after a oneyear anneal. The reported dislocation density considered both small and large etch pits. The explanation for the existence of two populations of sizes is unclear. Observing the etch pits by optical and scanning electron microscopes did not change the dislocation density measurements. Table 2 Dislocation densities associated with each annealing time period in this study. Annealing Time
5 N Average Dislocation Densities ( ρ )
6 N Average Dislocation Densities ( ρ )
Initial
2.69 × 109 m−2 range: (8.76 × 107 – 1.02 × 1010 m−2) 6.55 × 107 m−2 7.0 × 108 m−2 3.0 × 109 m−2 1.88 × 107 m−2 5.05 × 108 m−2 3.70 × 109 m−2
1.28 × 109 m−2 range: (3.54 ×108 – 4.01 ×109 m−2)
3 days 10 days 30 days 3 months 6 months 1 year
3
1.98 × 109 m−2
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
Dislocation Densities in Single Crystal Aluminum vs. Annealing Time
Fig. 3. The dislocation density versus annealing time at 920 K.
1E+12 1E+11
Present Study
Literature Averages
Dislocation Density (line length/m2 )
1E+10 1E+9 1E+8 1E+7 1E+6 1E+5
Present Study - 5N Sample Averages
1E+4
Present Study - 6N Sample Averages
1E+3
Literature Averages
1E+2
3 days 10 days 1 month 6 months 1 year
1E+1 1E+0
10-1
100
101
102
103
104
105
106
107
108
109
Time (sec)
transition from Harper-Dorn to the five power-law creep regime (see Fig. 1), the dislocation density may not correspondingly decrease due to frustration. Thus, the steady state stress may be independent of the dislocation density and a power of one may be observed. An increase in stress will place the aluminum within the five-power law regime and higher stress exponents are expected. On the other hand, if the initial density is relatively low (case 2.), as in the slowly cooled single crystals of Nes and Nost [30] (e.g. 2 × 106 m−2), increases in stress will lead to increasing dislocation densities within the Harper-Dorn regime, and five-power-law-like behavior may be observed despite being in the Harper-Dorn Regime. The increased occurs by activating the links in the network into Frank-Read sources. The modulus-compensated stress to activate a Frank-Read source can easily shown to be:
Table 2 lists the dislocation densities that are also plotted in Fig. 3 Single crystals were used in the annealing experiments so as other restoration mechanisms (e.g. grain growth [25,26]) are avoided. The one-year sample was re-polished mechanically with the 0.25 µm diamond slurry and then electropolished after removal from the furnace. The small amount of additional mechanical polishing unique to the 1 year specimens ensured that the thicker oxide layer could be fully removed with (normal) electro-polishing. The other samples (shorter annealing times) were not mechanically polished before electro-polishing. The resulting thickness of the sample disk was about 1–2 mm.
3. Results and discussion
(τ / G )F − R = 2bMρ1/2
Table 2 lists the dislocation densities that are also plotted in Fig. 3. The data suggests that the dislocation density is relatively stable during very long-time high-temperature annealing. Obviously, very high dislocation densities will recover, but coarsening of the Frank network is not observed for at least some low dislocation densities (and associated Burgers vector distributions). The dislocation density in this experiment is close to that at which constant dislocation densities are observed in Harper-Dorn creep tests by Lin et al. and Barrett et al. This trend was also very recently observed in unpublished experiments done by one of the authors [27] on 99.999% pure lithium fluoride single crystals. That study examined the effect of static annealing at 0.92Tm on the LiF crystals, The literature (as well as our data) suggests that the “starting” dislocation density varies substantially (see Table 1) in Al and often can be of the order of the expected creep-deformed steady-state dislocation density in the Harper-Dorn regime. The current study shows that these same densities may be resistant to coarsening. Also, as just mentioned, the dislocation densities observed in the Harper-Dorn regime are comparable to that at which we observed frustration or resistance to recovery under static annealing conditions. We can consider two cases for creep at very high temperatures in Al: First, the initial dislocation density is relatively high (upper part of the starting dislocation variation bracket in Fig. 1). The second case occurs when the starting dislocation density is relatively low. For each case we can have either a relatively high or low applied stress within the Harper-Dorn regime. For case 1.), as the applied stress drops from a high stress near the
(8)
where M is the Taylor factor. Modest increases in stress in a relatively high (case 1.) frustrated network near the stress associated Harper-Dorn transition to five power-law creep can cause dislocation multiplication by activating Frank read sources according to Eq. (8) and Fig. 1. FrankRead sources may not activate with small increases in stress at lower applied stresses within the Haper-Dorn regime, and Harper-Dorn behavior may persist for elevated dislocation densities at low stresses for case 1.0 with high starting dislocation densities. At low stresses associated with very low initial dislocation densities [case 2.)], modest increases in stress lead to activation of Frank-Read sources and increasing dislocation densities within the Harper-Dorn regime. So, for the same stress within the Harper- Dorn regime, the high starting dislocation density crystal will have a stress exponent of 1, while the low starting dislocation crystal will have a stress exponent of 3 or larger; behavior depends on the starting dislocation density which can vary dramatically. Unfortunately, many low-stress creep studies do not indicate the starting dislocation density prior to creep. In the study of low-stress creep by the authors [in which we did not observe 1-power (Harper-Dorn) law creep but observed 3-power instead.], the initial dislocation density was also relatively low at 6.5 × 107 m−2. Nes and Nost and Nes [14,30] that also failed to observe 1power Harper-Dorn behavior with the low starting dislocation density of 2 × 106 m−2. Of course, it must be mentioned that our observation of a “frustration” density is under zero stress and we assume that this translates to 4
Materials Science & Engineering A 705 (2017) 1–5
K.K. Smith et al.
References
the expectation of frustration under low (Harper-Dorn) stresses. Also, we observe frustration for a given starting dislocation density. We are not sure of the range of values of starting dislocation densities that will lead to this frustration. Ardell claims that the frustration model allows an accurate prediction of the creep behavior at low stresses. Ardell never fully demonstrates the viability of dislocation frustration. This strikes the authors of this study as a very difficult task. A variety of Burgers vectors, dislocation link lengths and orientations are all necessary to characterize for the network. This must be followed by a demonstration that the coarsening is impossible beyond some average link length. This task seems insurmountable despite modern computer simulations and TEM characterization techniques. It appears, as only one of several complications, that TEM cannot be performed on such low density dislocation structures because of damage introduced on the soft crystals and also because TEM examines structures at excessive magnification to characterize nodes. The authors attempted characterization of the Frank network, but were unsuccessful due to damage. Even very small amounts of damage introduced into these low dislocation structures compromises the characterization of the network. Etch pits cannot perform orientation and Burgers vector analyses. Thus, we believe frustration appears to be the only real explanation for the termination of network growth although a fundamental demonstration or proof does not appear available. Simple calculations show that the impurity levels in 5 N and 6 N single crystals is associated with more than one impurity atom per Burgers vector line length. Furthermore, this impurity level is associated with strengthening in the crystals [33]. However, any pinning to such a degree that the dislocation density is unchanged with applied stress should evince threshold behavior which is not observed. Internal stresses are not a factor in the frustration as these have been demonstrated in Cu and Al to be very low [35–37].
[1] J. Harper, J.E. Dorn, Viscous creep of aluminum near its melting temperature, Acta Metall. 5 (1957) 654–665. [2] P. Kumar, M.E. Kassner, T.G. Langdon, W. Blum, P. Eisenlohr, New observations on high temperature creep at very low stresses, Mater. Sci. Eng.: A. 510–511 (2009) 20–24. [3] B. Ya, Pines, A.F. Syrenko, Change in dislocation density in aluminum and lithium fluoride after annealing near the melting point under hydrostatic pressure, J. Mater. Sci. 3 (1968) 80–88. [4] G.K. Williamson, W.H. Hall, X-ray line broadening from filed aluminum and wolfram, Acta Metall. 1 (1953) 22–31. [5] C.R. Barrett, E.C. Muehleisen, W.D. Nix, High-temperature low stress creep of aluminum and Al-0.5%Fe, Mater. Sci. Eng.: A. 10 (1972) 33–42. [6] T.J. Ginter, F.A. Mohamed, Evidence for dynamic recrystallization during HarperDorn creep, Mater. Sci. Eng.: A. 322 (2002) 148–152. [7] S. Lee, A.J. Ardell, Dislocation link length distributions during Harper-Dorn creep of monocrystalline aluminum, Acta Metall. 34 (12) (1986) 2411–2423. [8] F.A. Mohamed, T.J. Ginter, On the nature and origin of Harper-Dorn creep, Acta Metall. 30 (1982) 1869–1881. [9] M.E. Kassner, M.E. McMahon, The dislocation microstructure of aluminum deformed to very large steady-state creep strains, Metall. Trans. 18A (1987) 835–846. [10] A.J. Ardell, Harper-Dorn creep—predictions of the dislocation network theory of high temperature deformation, Acta Metall. 45 (7) (1997) 2971–2981. [11] M.A. Przystupa, A.J. Ardell, Predictive capabilities of the dislocation-network theory of Harper-Dorn, Metall. Mater. Trans.: A 33 (2) (2002) 231–239. [12] M.E. Kassner, P. Kumar, W. Blum, Harper-Dorn creep, Int. J. Plast. 23 (2007) 980–1000. [13] W. Blum, W. Maier, Harper-Dorn creep: a myth? Phys. Status Solidi (A) 171 (1999) 467–474. [14] E. Nes, Modeling of work hardening and stress saturation in FCC metals, Progress. Mater. Sci. 41 (3) (1998) 129–193. [15] P. Kumar, M.E. Kassner, Theory for very low stress (“Harper-Dorn”) creep, Scr. Mater. 60 (2009) 60–63. [16] P. Lin, S.S. Lee, A.J. Ardell, Scaling Characteristics of Dislocation Link Length Distributions Generated During the Creep of Crystals. 37(2), 1989, pp.739–748. [17] D. Hull, D.J. Bacon, Introduction to Dislocations, 5th ed., Butterworth-Heinemann, Oxford, 2011. [18] F.A. Mohamed, K.L. Murty, J.W. Morris, Metallurgical transformations, HarperDorn Creep Al, Pb, Sn 4 (1973) 935–940. [19] P. Kumar, M.E. Kassner, T.G. Langdon, The role of Harper-Dorn creep at high temperatures and very low stresses, J. Mater. Sci. 43 (2008) 4801–4810. [20] W. Blum, Plastic deformation and fracture, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Materials Science and Technology, 6 VCH Publishers, Weinheim, Germany, 1993, p. 339. [21] P. Kumar, Creep in Pure Single and Polycrystalline Aluminum at Very Low Stresses and High Temperatures: An Evaluation of Harper-Dorn Creep (Thesis/Dissertation), University of Southern California, 2008. [22] T.J. Ginter, P.K. Chaudhury, F.A. Mohamed, An investigation of Harper-Dorn at large strains, Acta Mater. 49 (2001) 263–272. [23] Y.-C. Cheng, M. Chauhan, F.A. Mohamed, Uncovering the mystery of Harper-Dorn creep in metals, Metall. Mater. Trans.: A. 40A (2009) 80–90. [24] R.K. Ham, N.G. Sharpe, A systematic error in the determination of dislocation densities in thin films, Philos. Mag. 6 (69) (1961) 1193–1194. [25] M.E. Kassner, J. Pollard, E. Evangelista, E. Cerri, Restoration mechanisms in large strain deformation of high purity aluminum at ambient-temperature and the determination of the existence of a steady-state, Acta Metall. Mater. 42 (9) (1994) 3223–3230. [26] H.J. McQueen, W. Blum, S. Straub, M.E. Kassner, Dynamic grain growth – a restoration mechanism in 99.999% Al, Scr. Metall. Mater. 28 (1993) 1299–1304. [27] P. Kumar. Indian Institute of Science, Bangalore, India 2015. (Unpublished). [28] M.E. Kassner, C.J. Echer, Mechanical damage introduced into annealed aluminum monocrystals by conventional TEM thin-foil preparation techniques, Metallography 19 (1986) 127–132. [29] M.E. Kassner, A case for Taylor hardening during primary and steady state creep in aluminum and type 304 stainless steel, J. Mater. Sci. 25 (1990) 1997–2003. [30] E. Nes, B. Nost, Dislocation densities in slowly cooled aluminum single crystals, Philos. Mag. 124 (1966) 855–865. [31] A.J. Forty, F.C. Frank, The interpretation of etch patterns on aluminum, J. Phys. Soc. Jpn. 10 (1955) 656–663. [32] P. Kumar, Ph.D. Thesis, Dept. of Chemical Engineering and Materials Science, Univ. of Southern California, 2007. [33] M.E. Kassner, Taylor hardening in five power law creep of metals and class M alloys, Acta Mater. 52 (2004) 1–9. [34] P. Yavari, D.A. Miller, T.G. Langdon, An investigation of Harper-Dorn creep-I. mechanical and microstructural characterisitics, Acta Metall. 30 (1982) 871–879. [35] L.E. Levine, P. Geantil, B.C. Larson, J.Z. Tischler, M.E. Kassner, W. Liu, M.R. Stoudt, F. Tavazza, Disordered long-range internal stresses in deformed copper and the mechanisms underlying plastic deformation, Acta Mater. 59 (2011) 5083–5091. [36] M.E. Kassner, M.-T. Pérez-Prado, M. Long, K.S. Vecchio, Dislocation microstructures and internal stress measurements by CBED on creep deformed Cu and Al, Metall. Mater. Trans. 33A (2002) 311–318. [37] M.E. Kassner, M.-T. Perez-Prado, K.S. Vecchio, M.A. Wall, Determination of internal stresses in cyclically deformed Cu single crystals using CBED and dislocation dipole separation measurements, Acta Mater. 48 (2000) 4247–4254. [38] A.J. Ardell, Harper–Dorn creep– the dislocation network theory revisited, Scripta Mater 69 (2013), pp. 541–544.
4. Summary In summary, the aluminum single crystals were annealed for various times up to one year at 920 K (0.98 Tm). Our results show that the dislocation density is relatively constant. This may suggest that the concept of dislocation “frustration” suggested by Ardell and coworkers may be valid. This potentially explains why some low stress investigations in aluminum observe the Harper-Dorn behavior (stress exponent of one and a constant dislocation density with stress) while others observe traditional power-law (exponents of 3–4.5 with a dislocation density that varies with stress). The dislocation density can increase with increasing stress, but by the current study it may not decrease with decreasing stress due to frustration at the lower density values. If the initial density is low, increases in stress anywhere within the Harper-Dorn regime may increase the density and five-power law behavior is observed. If the initial dislocation density is relatively high (just within the Harper-Dorn regime), then increases in stress may place the new density within the five power-law regime. The density may not be able to decrease with decreasing stress due to frustration. Increases in stress from low-stress values for these higher dislocation densities Frank-Read sources may not be activated until the applied stress approaches that for five power-law creep. Thus, depending on the starting dislocation density we may observe either constant or increasing dislocation density within the Harper-Dorn regime. Hence, the observation of (or failure to observe) Harper-Dorn behavior may depend on the initial dislocation density which can vary by many orders of magnitude. This may explain a 60 year puzzle of Harper-Dorn creep. Acknowledgments The authors are grateful for support from the NSF under grant DMR1401194.
5