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1

Kassner, M. E., P. Kumar, and W. Blum. "Harper–Dorn creep." International Journal of Plasticity 23, no. 6 (June 2007): 980–1000. http://dx.doi.org/10.1016/j.ijplas.2006.10.006.

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2

Wang, J. N., and M. Toriumi. "Harper-Dorn creep in feldspar." Materials Science and Engineering: A 187, no. 1 (October 1994): 97–100. http://dx.doi.org/10.1016/0921-5093(94)90335-2.

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3

Wang, Jian N. "Harper-Dorn creep in olivine." Materials Science and Engineering: A 183, no. 1-2 (June 1994): 267–72. http://dx.doi.org/10.1016/0921-5093(94)90911-3.

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4

Blum, W., and W. Maier. "Harper-Dorn Creep — a Myth?" physica status solidi (a) 171, no. 2 (February 1999): 467–74. http://dx.doi.org/10.1002/(sici)1521-396x(199902)171:2<467::aid-pssa467>3.0.co;2-8.

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5

Nes, E., W. Blum, and P. Eisenlohr. "Harper-dorn creep and specimen size." Metallurgical and Materials Transactions A 33, no. 2 (February 2002): 305–10. http://dx.doi.org/10.1007/s11661-002-0091-8.

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6

Novotný, J., J. Fiala, and J. Čadek. "Harper-Dorn creep in alpha-zirconium." Acta Metallurgica 33, no. 5 (May 1985): 905–11. http://dx.doi.org/10.1016/0001-6160(85)90115-4.

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7

Ruano, O. A., J. Wadsworth, and O. D. Sherby. "Harper-dorn creep in pure metals." Acta Metallurgica 36, no. 4 (April 1988): 1117–28. http://dx.doi.org/10.1016/0001-6160(88)90165-4.

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8

Nabarro, F. R. N. "The mechanism of Harper-Dorn creep." Acta Metallurgica 37, no. 8 (August 1989): 2217–22. http://dx.doi.org/10.1016/0001-6160(89)90147-8.

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9

Nabarro, F. R. N. "Harper-Dorn Creep - A Legend Attenuated?" physica status solidi (a) 182, no. 2 (December 2000): 627–29. http://dx.doi.org/10.1002/1521-396x(200012)182:2<627::aid-pssa627>3.0.co;2-e.

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10

Kassner, Michael E. "New Developments in Understanding Harper–Dorn, Five-Power Law Creep and Power-Law Breakdown." Metals 10, no. 10 (September 25, 2020): 1284. http://dx.doi.org/10.3390/met10101284.

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This paper discusses recent developments in creep, over a wide range of temperature, that may change our understanding of creep. The five-power law creep exponent (3.5–7) has never been explained in fundamental terms. The best the scientific community has done is to develop a natural three power-law creep equation that falls short of rationalizing the higher stress exponents that are typically five. This inability has persisted for many decades. Computational work examining the stress-dependence of the climb rate of edge dislocations may rationalize the phenomenological creep equations. Harper–Dorn creep, “discovered” over 60 years ago, has been immersed in controversy. Some investigators have insisted that a stress exponent of one is reasonable. Others believe that the observation of a stress exponent of one is a consequence of dislocation network frustration. Others believe the stress exponent is artificial due to the inclusion of restoration mechanisms, such as dynamic recrystallization or grain growth that is not of any consequence in the five power-law regime. Also, the experiments in the Harper–Dorn regime, which accumulate strain very slowly (sometimes over a year), may not have attained a true steady state. New theories suggest that the absence or presence of Harper–Dorn may be a consequence of the initial dislocation density. Novel experimental work suggests that power-law breakdown may be a consequence of a supersaturation of vacancies which increase self-diffusion.
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11

Mohamed, Farghalli A. "Harper–Dorn creep: Controversy, requirements, and origin." Materials Science and Engineering: A 463, no. 1-2 (August 2007): 177–84. http://dx.doi.org/10.1016/j.msea.2006.06.142.

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12

Wolfenstine, J., O. A. Ruano, J. Wadsworth, and O. D. Sherby. "Harper-dorn creep in single crystalline NaCl." Scripta Metallurgica et Materialia 25, no. 9 (September 1991): 2065–70. http://dx.doi.org/10.1016/0956-716x(91)90275-6.

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13

Wang, J. N. "A microphysical model of Harper-Dorn creep." Acta Materialia 44, no. 3 (March 1996): 855–62. http://dx.doi.org/10.1016/1359-6454(95)00281-2.

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14

Kumar, P., and M. E. Kassner. "Theory for very low stress (“Harper–Dorn”) creep." Scripta Materialia 60, no. 1 (January 2009): 60–63. http://dx.doi.org/10.1016/j.scriptamat.2008.08.033.

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15

Ardell, Alan J. "Harper–Dorn creep – The dislocation network theory revisited." Scripta Materialia 69, no. 7 (October 2013): 541–44. http://dx.doi.org/10.1016/j.scriptamat.2013.06.022.

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16

Ginter, Timothy J., and Farghalli A. Mohamed. "Evidence for dynamic recrystallization during Harper–Dorn creep." Materials Science and Engineering: A 322, no. 1-2 (January 2002): 148–52. http://dx.doi.org/10.1016/s0921-5093(01)01127-3.

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17

Ruano, O. A., J. Wolfenstine, J. Wadsworth, and O. D. Sherby. "Harper-Dorn and power law creep in uranium dioxide." Acta Metallurgica et Materialia 39, no. 4 (April 1991): 661–68. http://dx.doi.org/10.1016/0956-7151(91)90134-m.

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18

Wolfenstine, J., O. A. Ruano, J. Wadsworth, and O. D. Sherby. "Harper-dorn creep in class I solid solution alloys." Scripta Metallurgica et Materialia 24, no. 5 (May 1990): 903–6. http://dx.doi.org/10.1016/0956-716x(90)90134-3.

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19

Ginter, T. J., P. K. Chaudhury, and F. A. Mohamed. "An investigation of Harper–Dorn creep at large strains." Acta Materialia 49, no. 2 (January 2001): 263–72. http://dx.doi.org/10.1016/s1359-6454(00)00316-5.

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20

Raj, S. V. "On the grain size dependence of Harper-Dorn creep." Materials Science and Engineering 96 (December 1987): 57–64. http://dx.doi.org/10.1016/0025-5416(87)90540-4.

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21

Cheng, Yu-Ching, Manish Chauhan, and Farghalli A. Mohamed. "Uncovering the Mystery of Harper–Dorn Creep in Metals." Metallurgical and Materials Transactions A 40, no. 1 (November 4, 2008): 80–90. http://dx.doi.org/10.1007/s11661-008-9680-5.

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22

Wang, Jian N. "Comments on the internal stress model of Harper-Dorn creep." Scripta Metallurgica et Materialia 29, no. 10 (November 1993): 1267–70. http://dx.doi.org/10.1016/0956-716x(93)90121-8.

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23

Meyrick, Glyn. "On the dislocation density in aluminum during Harper-Dorn creep." Scripta Metallurgica 23, no. 12 (December 1989): 2025–28. http://dx.doi.org/10.1016/0036-9748(89)90225-1.

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24

Wang, Jian N. "Experimental Evidence for Harper-Dorn Creep in Mn-Zn Ferrite." Journal of the American Ceramic Society 77, no. 11 (November 1994): 3036–38. http://dx.doi.org/10.1111/j.1151-2916.1994.tb04544.x.

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25

Przystupa, M. A., and A. J. Ardell. "Predictive capabilities of the dislocation-network theory of Harper-Dorn creep." Metallurgical and Materials Transactions A 33, no. 2 (February 2002): 231–39. http://dx.doi.org/10.1007/s11661-002-0085-6.

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26

Wang, Jian N. "On the transition from power law creep to Harper-Dorn creep." Scripta Metallurgica et Materialia 29, no. 6 (September 1993): 733–36. http://dx.doi.org/10.1016/0956-716x(93)90217-g.

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27

Wang, Jian N. "Harper-dorn creep in polycrystalline ferrite, beryllia, alumina, calcite and olivine." Scripta Metallurgica et Materialia 30, no. 7 (April 1994): 859–62. http://dx.doi.org/10.1016/0956-716x(94)90404-9.

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28

Raj, S. V. "On the importance of surface dislocation sources in Harper-Dorn creep." Scripta Metallurgica 19, no. 9 (September 1985): 1069–73. http://dx.doi.org/10.1016/0036-9748(85)90011-0.

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29

Raman, V., and S. V. Raj. "An analysis of Harper-Dorn creep based on specimen size effects." Scripta Metallurgica 19, no. 5 (May 1985): 629–34. http://dx.doi.org/10.1016/0036-9748(85)90350-3.

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30

Wang, Jian N. "Harper-Dorn creep in single crystals of lead, rutile and ice." Philosophical Magazine Letters 70, no. 2 (August 1994): 81–85. http://dx.doi.org/10.1080/09500839408241276.

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31

Ruano, Oscar A., Jeffrey Wolfenstine, Jeffrey Wadsworth, and Oleg D. Sherby. "Harper-Dorn and Power-Law Creep in Single-Crystalline Magnesium Oxide." Journal of the American Ceramic Society 75, no. 7 (July 1992): 1737–41. http://dx.doi.org/10.1111/j.1151-2916.1992.tb07190.x.

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32

Wang, J. N., T. Shimamoto, and M. Toriumi. "Harper-Dorn creep in polycrystalline MgCI2-6H2O, CaTiO3 and (Co0.5Mg0.5)O." Journal of Materials Science Letters 13, no. 20 (1994): 1451–53. http://dx.doi.org/10.1007/bf00419132.

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33

Hou, Qing Yu, and Jing Tao Wang. "Deformation Mechanism in the Mg-Gd-Y Alloys Predicted by Deformation Mechanism Maps." Advanced Materials Research 146-147 (October 2010): 225–32. http://dx.doi.org/10.4028/www.scientific.net/amr.146-147.225.

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Deformation mechanism maps at 0-883 K and shear strain rate of 10-10-10+6 s-1 were built from available rate equations for deformation mechanisms in pure magnesium or magnesium alloys. It can be found that the grain size has little effect on the fields of plasticity and phonon or electron drag, though it has important influence on the fields of power-law creep, diffusion creep, and Harper-Dorn creep in the maps within the present range of temperature, strain rate, and grain size. A larger grain size is helpful to increase the field range of power-law creep but decrease that of diffusion creep when the grain size is smaller than ~204 μm. Harper-Dorn creep dominates the deformation competed to diffusion creep in the grain size range of ~204-255 μm. The maps include only plasticity, phonon or electron drag, and power-law creep when the grain size is higher than ~255 μm, then the grain size has little influence on the maps. Comparison between the reported data for the Mg-Gd-Y alloys and the maps built from available rate equations, it can be conclude that the maps are an effective tool to predict or achieve a comprehensive understanding of the deformation behavior of the Mg-Gd-Y alloys and to classify systematically their discrepancies in the deformation mechanism. However, differences exist in the deformation mechanisms of the alloys observed by the reported data and that predicted by the maps. Therefore, refinement of the maps from the viewpoint of mechanical twining, DRX, and adiabatic shear are necessary.
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34

Tsujino, Noriyoshi, Andreea Mârza, and Daisuke Yamazaki. "Pressure dependence of Si diffusion in γ-Fe." American Mineralogist 105, no. 3 (March 1, 2020): 319–24. http://dx.doi.org/10.2138/am-2020-7197.

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Abstract The pressure dependence of Si diffusion in γ-Fe was investigated at pressures of 5–15 GPa and temperatures of 1473–1673 K using the Kawai-type multi-anvil apparatus to estimate the rate of mass transportation for the chemical homogenization of the Earth's inner core and those of small terrestrial planets and large satellites. The obtained diffusion coefficients D were fitted to the equation D = D0 exp[−(E* + PV*)/(RT)], where D0 is a constant, E* is the activation energy, P is the pressure, V* is the activation volume, R is the gas constant, and T is the absolute temperature. The least-squares analysis yielded D0 = 10-1.17±0.54 m2/s, E* = 336 ± 16 kJ/mol, and V* = 4.3 ± 0.2 cm3/mol. Moreover, the pressure and temperature dependences of diffusion coefficients of Si in γ-Fe can also be expressed well using homologous temperature scaling, which is expressed as D = D0exp{–g[Tm(P)]/T}, where g is a constant, Tm(P) is the melting temperature at pressure P, and D0 and g are 10-1.0±0.3 m2/s and 22.0 ± 0.7, respectively. The present study indicates that even for 1 billion years, the maximum diffusion length of Si under conditions in planetary and satellite cores is less than ∼1.2 km. Additionally, the estimated strain of plastic deformation in the Earth's inner core, caused by the Harper–Dorn creep, reaches more than 103 at a stress level of 103–104 Pa, although the inner core might be slightly deformed by other mechanisms. The chemical heterogeneity of the inner core can be reduced only via plastic deformation by the Harper–Dorn creep.
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35

Langdon, Terence G. "The Significance of Diffusion Creep and Harper-Dorn Creep at Low Stresses." Key Engineering Materials 171-174 (October 1999): 205–12. http://dx.doi.org/10.4028/www.scientific.net/kem.171-174.205.

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36

Wang, J. N., and T. G. Langdon. "An evaluation of the rate-controlling flow process in Harper-Dorn creep." Acta Metallurgica et Materialia 42, no. 7 (July 1994): 2487–92. http://dx.doi.org/10.1016/0956-7151(94)90328-x.

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37

Wang, Jian N. "Dependence of dislocation density in Harper-Dorn creep on the peierls stress." Scripta Metallurgica et Materialia 29, no. 11 (December 1993): 1505–8. http://dx.doi.org/10.1016/0956-716x(93)90345-s.

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38

Chokshi, Atul H. "The effect of pipe diffusion on harper-dorn creep at low stresses." Scripta Metallurgica 19, no. 4 (April 1985): 529–34. http://dx.doi.org/10.1016/0036-9748(85)90128-0.

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39

Viernstein, Bernhard, and Ernst Kozeschnik. "Integrated Physical-Constitutive Computational Framework for Plastic Deformation Modeling." Metals 10, no. 7 (June 30, 2020): 869. http://dx.doi.org/10.3390/met10070869.

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An integrated framework for deformation modeling has been developed, which combines a physical state parameter-based formulation for microstructure evolution during plastic deformation processes with constitutive creep models of polycrystalline materials. The implementations of power law, Coble, Nabarro–Herring and Harper–Dorn creep and grain boundary sliding are described and their contributions to the entire stress response at a virtual applied strain rate are discussed. The present framework simultaneously allows calculating the plastic deformation under prescribed strain rate or constant stress, as well as stress relaxation after preceding stress or strain loading. The framework is successfully applied for the construction of deformation mechanism maps.
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40

Murty, K. L. "Significance and Role of Deformation Micromechanisms in Life-Predictive Modeling of Aging Structures." Applied Mechanics Reviews 46, no. 5 (May 1, 1993): 194–200. http://dx.doi.org/10.1115/1.3120336.

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Transitional creep mechanisms are exhibited by materials used in power systems and a thorough knowledge of these is a prerequisite in reliable extrapolations of short-term data to service conditions mainly due to the dominance of viscous creep mechanisms such as Nabarro-Herring, Coble and more importantly Harper-Dorn creep at low stresses. The paper summarizes the deformation mechanisms pertinent to various classes of materials. It is shown that blind extrapolation of the short-term laboratory test results to long-term service conditions leads to nonconservative predictions of the creep-rates and life times of the structural materials. Application of such transitional creep mechanisms to the prediction of dimensional changes of Zircaloy cladding in light water reactors is summarized.
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41

ARDELL, A. J. "HARPER-DORN CREEP—PREDICTIONS OF THE DISLOCATION NETWORK THEORY OF HIGH TEMPERATURE DEFORMATION." Acta Materialia 45, no. 7 (July 1997): 2971–81. http://dx.doi.org/10.1016/s1359-6454(96)00397-7.

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42

Wang, J. N. "Newtonian flow process in polycrystalline silicon carbides: diffusional creep or Harper-Dorn creep?" Journal of Materials Science 29, no. 23 (December 1994): 6139–46. http://dx.doi.org/10.1007/bf00354553.

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43

Novotny, J., J. Fiala, and J. Čadek. "On Harper-Dorn creep in alpha iron at homologous temperatures 0.40 to 0.54." Scripta Metallurgica 19, no. 7 (July 1985): 867–70. http://dx.doi.org/10.1016/0036-9748(85)90209-1.

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44

Owen, David M., and Terence G. Langdon. "Low stress creep behavior: An examination of Nabarro—Herring and Harper—Dorn creep." Materials Science and Engineering: A 216, no. 1-2 (October 1996): 20–29. http://dx.doi.org/10.1016/0921-5093(96)10382-8.

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45

Kumar, Praveen, Michael E. Kassner, and Terence G. Langdon. "The role of Harper–Dorn creep at high temperatures and very low stresses." Journal of Materials Science 43, no. 14 (July 2008): 4801–10. http://dx.doi.org/10.1007/s10853-008-2680-4.

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46

Wang, Jian Nong. "Establishment of a steady dislocation density by the Peierls stress in Harper-Dorn creep." Philosophical Magazine A 71, no. 1 (January 1995): 115–26. http://dx.doi.org/10.1080/01418619508242959.

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47

Singh, Shobhit Pratap, Praveen Kumar, and Michael E. Kassner. "Frustration of the dislocation density in NaCl and its implication on “Harper-Dorn” creep." Materials Science and Engineering: A 799 (January 2021): 140360. http://dx.doi.org/10.1016/j.msea.2020.140360.

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48

Kumar, Praveen, Michael E. Kassner, and Terence G. Langdon. "Fifty years of Harper–Dorn creep: a viable creep mechanism or a Californian artifact?" Journal of Materials Science 42, no. 2 (January 4, 2007): 409–20. http://dx.doi.org/10.1007/s10853-006-0782-4.

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49

Fiala, Jaroslav, and Terence G. Langdon. "An examination of the metals deforming by Harper-Dorn creep at high homologous temperatures." Materials Science and Engineering: A 151, no. 2 (May 1992): 147–51. http://dx.doi.org/10.1016/0921-5093(92)90202-c.

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50

Kloc, Luboš, and Jaroslav Fiala. "Harper–Dorn creep in metals at intermediate temperatures revisited: Constant structure test of pure Al." Materials Science and Engineering: A 410-411 (November 2005): 38–41. http://dx.doi.org/10.1016/j.msea.2005.08.102.

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