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 K.K. Smith a , M.E. Kassner a, ⁎ , P. Kumar b a University of Southern California, Chemical Engineering and Materials Science, OHE 430, Los Angeles, CA 90089-1453, USA b Indian Institute of Science, Dept. of Materials Science, Bangalore, India ARTICLE INFO Keywords: Annealing Harper-Dorn creep Aluminum single crystals ABSTRACT Single crystals of 99.999% and 99.9999% pure aluminum were annealed at high elevated temperatures (0.98T m ) 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 10 9 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. > 0.90T m ) 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 0.98T m 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 10 8 m -2 to a much higher value of over 10 11 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 × 10 5 m -2 , 6.0 × 10 10 m -2 and 6.5 × 10 7 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 an- nealing 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 Harper- Dorn creep {low-stress and generally very high temperatures (e.g. 0.98T m ) [1]}, in which the dislocation density does not decrease below a certain value (even at very low stress), is, thus, also examined in this work. Harper and Dorn [1] suggested low stress-exponent (n) creep at very low stresses according to = ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ε A D Gb kT σ G ̇ ss HD sd n (1) where A HD is the Harper-Dorn coefficient, D sd 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. {Inter- estingly, had this (probably fictitious) threshold stress not been sub- tracted, 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 varies with the steady-state stress as roughly ∝ ρ ss σ 1/2 G ss , (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, = b ε̇ ρ ν m (2) If ρ m is constant, ∝ ν σ , 1 (3) ∝ ε σ ̇ 1 (4) But if ρ m changes with stress, 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 ⁎ Corresponding author. E-mail address: kassner@usc.edu (M.E. Kassner). Materials Science & Engineering A 705 (2017) 1–5 Available online 18 August 2017 0921-5093/ © 2017 Published by Elsevier B.V. MARK