Abstract
The stress relaxation (SR) test during plastic deformation is a useful technique for studying deformation processes. SR tests were performed during plastic deformation of pure magnesium, magnesium alloys and magnesium alloys-based composites over a wide temperature interval from room temperature up to 300 °C. Various theoretical approaches were applied for the estimation of characteristic parameters of thermally activated processes and finding of stress components. The aim of this study was to reveal the main features of deformation processes in hexagonal close-packed magnesium alloys and composites. The role of solute atoms in dynamic strain aging phenomena is discussed. In ultrafine-grained magnesium, grain boundary sliding during the stress relaxation tests was observed. The paper analyzes extensive set of results obtained by authors on cast and processed magnesium materials.
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References
P. Feltham, Stress Relaxation in Alpha-Iron at Low Temperatures, Phil. Mag., 1961, 6, p 817. https://doi.org/10.1080/14786436108243341
V.I. Dotsentko, Stress Relaxation in Crystals, Phys. stat. sol. (b), 1970, 93, p 11. https://doi.org/10.1002/pssb.2220930102
E. Aifantis and W.W. Gerberich, A Theoretical Review of Stress Relaxation Testing Materials Science and Engineering, Mater. Sci. Eng., 1975, 21, p 107–113. https://doi.org/10.1016/0025-5416(75)90204-9
M. Grosbras, E. Dedieu and M. Cahoreau, Some Considerations About Stress Relaxation Experiments, Phys. stat. sol(, 1977, 42, p 449–457. https://doi.org/10.1002/pssa.2210420204
K. Hariharan and J. Jain, Stress Relaxation Test: Issues in Modelling and Interpretation, Manufact. Lett., 2020, 26, p 64–68. https://doi.org/10.1016/j.mfglet.2020.10.003
H. Conrad, Thermally Activated Deformation of Metals, JOM, 1964, 16, p 582–588. https://doi.org/10.1007/BF03378292
P. Feltham, Stress Relaxation in Magnesium at Low Temperatures, Phys. stat. sol. (b), 1963, 3, p 1340–1346. https://doi.org/10.1002/pssb.19630030805
G.A. Sargent, Stress Relaxation and Thermal Activation in Niobium, Acta Metall., 1965, 13, p 663–671. https://doi.org/10.1016/0001-6160(65)90129-X
I. Lehner, S. Chiang and D.I. Kohlstedt, Load Relaxation Studies of Four Alkali Halides, Acta Metall., 1979, 27, p 1187–1196. https://doi.org/10.1016/0001-6160(79)90136-6
A.S. Krausz and K. Krausz, Unified Constitutive laws of Plastic Deformation, Academic Press, San Diego, 1996.
J.C.M. Li, Dislocation Dynamics in Deformation and Recovery, Canad. J. Appl. Phys., 1967, 45, p 493–509. https://doi.org/10.1139/p67-043
J.C.M. Li, In: Dislocation Dynamics (Eds. A.R. Rosenfeld, G.T. Hahn, A.L. Bement, R.I. Jaffee) McGraw-Hill, p. 87, New York 1969
E.W. Hart, A Phenomenological Theory for Plastic Deformation of Polycrystalline Metals, Acta Metall., 1970, 18, p 599–610. https://doi.org/10.1016/0001-6160(70)90089-1
E.W. Hart, C.Y. Li, H. Yamaha, G.L. Wize In: Constitutive equations in Plasticity (Ed. A.S. Argon) MIY Press, Cambridge MA, 1975, p. 149
M.A. Fortes and M.E. Rosa, The Form of a Constitutive Equation of Plastic Deformation Compatible with Stress Relaxation Data, Acta Metall., 1984, 32, p 663–670. https://doi.org/10.1016/0001-6160(84)90140-8
R.W. Rohde, W.B. Jones and J.C. Swearengen, Deformation Modeling of Aluminum: Stress Relaxation, Transient Behavior, and Search for Microstructural Correlations, Acta Metall., 1981, 29, p 41–52. https://doi.org/10.1016/0001-6160(81)90085-7
E. Qrowan, Problems of Plastic Gliding, Proc. Phys. Soc., 1940, 52, p 8–22.
G. Schoeck, A. Seeger, A. Conf. Ded. Solids, Phys. Soc. London 1955, 340
H. Wolf, Die Aktivierungsenergie für die Quergleitung aufgespaltener Schraubenversetzungen, Z. Naturforschung, 1960, 15, p 180–193.
R.Y. Kuznetsov and V.A. Pavlov, Time Course of Plastic Stress Relaxation Fiz, Metal. Metaloved, 1968, 25, p 934.
U.F. Kocks, A.S. Argon and M.F. Ashby, Introduction, Prog. Mater. Sci., 1975, 19, p 1.
J. Friedel, Dislocations, Pergamon Press, Oxford, 1964, p 315
K. Ono, Temperature Dependence of Dispersed Barrier Hardening, Appl. Phys., 1968, 39, p 1803–1806. https://doi.org/10.1063/1.1656434
F.F. Lavrentev and Y.A. Pokhil, Relation of Dislocation Density in Different Slip Systems to Work-Hardening Parameters for Magnesium Crystals, Mater. Sci. Eng., 1975, 18, p 261–270. https://doi.org/10.1016/0025-5416(75)90179-2
R. de Batist and A. Callens, On the Analysis of Stress Relaxation Experiments, Phys. Stat. Sol. (a), 1974, 21, p 591–595. https://doi.org/10.1002/pssa.2210210223
G.B. Gibbs, Creep and Stress Relaxation Studies with Polycrystalline Magnesium, Phil. Mag., 1966, 13, p 317–329. https://doi.org/10.1080/14786436608212610
S.R. MacEwan, O.A. Kupcis and B. Ramaswami, An Investigation of an Incremental Unloading Technique for Estimating Internal Stress, Scripta Metall., 1969, 3, p 441–448. https://doi.org/10.1016/0036-9748(69)90128-8
P.M. Kelly and J.M. Round, Stress Relaxation and the Use of the Johnston-Gilman Equation in the Analysis of Thermally Activated Flow in A-Iron, Scripta Metall., 1968, 3, p 85–92. https://doi.org/10.1016/0036-9748(69)90206-3
W.G. Johnston and J.J. Gilman, Dislocation Velocities, Dislocation Densities and Plastic Flow in Lithium Fluorid Crystals, J. Appl. Phys., 1959, 30, p 129–144. https://doi.org/10.1063/1.1735121
A.A. Urusovskaya, G.G. Knab and Yu.Z. Estrin, Comparison of Dislocation Mobility in Lif Measured by Direct and Indirect Methods, Phys. Stat. Sol (a), 1976, 36, p 397–402. https://doi.org/10.1002/pssa.2210360143
Z. Trojanová and P. Lukáč, Step Wise Stress Relaxation in Zn-Al Single Crystals, Phys. Stat. Sol. (a), 1992, 130, p K35-39. https://doi.org/10.1002/pssa.2211300136
M. Fellner, M. Hamerský and E. Pink, A Comparison of the Portevin-Le Chatelier Effect in Constant-Strain-Rate and Constant-Stress-Rate Tests, Mater. Sci. Eng. A, 1991, 137, p 157–161. https://doi.org/10.1016/0921-5093(91)90330-P
T.W. Clyne and P.J. Whithers, An Introduction to Metal Matrix Composites, Cambridge University Press, Cambridge, UK, 1993.
R.M. Aikin Jr. and L. Christodoulou, The Role of Equiaxed Particles on the Yield Stress of Composites, Scr. Metall. Mater., 1991, 25, p 9–14. https://doi.org/10.1016/0956-716X(91)90345-2
D. Caillard, J-L. Martin, Thermally activated mechanisms in crystal plasticity, vol. 8, Pergamon, 2003.
U.F. Kocks, Realistic constitutive relations for metal plasticity. Mater. Sci. Eng. 317, 2001, 181-187. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 1 7 4 - 1
A.G. Evans and R.D. Rawlings, The Thermally Activated Deformation of Cystalline Materials, Phys. Stat. Sol., 1969, 34, p 9–31. https://doi.org/10.1002/pssb.19690340102
P. Lukáč, Solid Solution Hardening in Mg-Cd Single Crystals, Phys. Stat. Sol. (a), 1992, 131, p 377–390. https://doi.org/10.1002/pssa.2211310212
P. Lukáč, Thermally Activated Deformation Mechanisms in HCP Metals, J. Sci. Ind. Res., 1972, 32, p 569.
R. v. Mises, Mechanik der festen Körper im plastisch- deformable state. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse 1913, 582–592.
A. Couret and D. Caillard, An In Situ Study of Prismatic Glide in Magnesium—I the Rate Controlling Mechanism, Acta Metall., 1985, 33, p 1447–1454. https://doi.org/10.1016/0001-6160(85)90045-8
A. Couret and D. Caillard, An In Situ Study of Prismatic Glide in Magnesium—II Microscopic Activation Parameters, Acta Metall., 1985, 33, p 1455–1462. https://doi.org/10.1016/0001-6160(85)90046-X
A. Ahmadieh, J. Mitchell and J.E. Dorn, Lithium Alloying and Dislocation Mechanisms for Prismatic Slip in Magnesium, Trans. AIME, 1965, 233, p 1130.
J. Koike and R. Ohyama, Geometrical Criterion for the Activation of Prismatic Slip in AZ61 Mg Alloy Sheets Deformed at Room Temperature, Acta Mater., 2005, 53, p 1963–1972. https://doi.org/10.1016/j.actamat.2005.01.008
D. Buey and M. Ghazisaeidi, Atomistic Simulation of <c+a> Screw Dislocation Cross Slip in Mg, Scripta Mater., 2016, 117, p 51–54. https://doi.org/10.1016/j.scriptamat.2016.02.001
S. Ando and H. Tonda, Non-Basal Slip in Magnesium-Lithium Alloy Single Crystals, Mater. Trans. JIM, 2000, 41, p 1188–1191. https://doi.org/10.2320/matertrans1989.41.1188
H. Tonda and S. Ando, Effect of Temperature and Shear Direction on Yield Stress by 1122 <1123> Slip in HCP Metals, Metall. Mater. Trans. A, 2002, 33, p 831–836. https://doi.org/10.1007/s11661-002-1015-3
R. Ahmad, Z. Wu and W.A. Curtin, Analysis of Double Cross Slip of Pyramidal I <c+a> Dislocations and Implications for Ductility in Mg Alloys, Acta Mater., 2020, 183, p 228–241. https://doi.org/10.1016/j.actamat.2019.10.053
Z. Trojanová, P. Palček, P. Lukáč, M. Chalupová: Internal friction in magnesium alloys and magnesium alloys based composites. Magnesium Alloys, Intech, Rijeka 2017, ISBN 978-953-51-4808-1
Z. Trojanová, P. Lukáč, B. Weidenfeller and W. Riehemann, Mechanical Damping in Magnesium Prepared by Ball Milling in Medium Temperature Region, Kovove Mater., 2008, 46, p 249–256.
Z. Trojanová and P. Lukáč, Physical Aspects of Plastic Deformation in Mg-Al Alloys with Sr and Ca, Inter. J. of Mater. Research, 2009, 100, p 270–276.
W.J. McG Tegart, Activation Energies for High Temperature Creep of Polycrystalline Magnesium, Acta Metall., 1961, 9, p 614–617. https://doi.org/10.1016/0001-6160(61)90166-3
P. Eisenlohr, W. Blum and K. Milička, Dislocation Glide Velocity in Creep of Mg Alloys Derived from Dip Tests, Mater. Sci. Eng. A, 2009, 510–511, p 393–397.
S.S. Vagarali and T.G. Langdon, Deformation Mechanisms in h.c.p. Metals at Elevated Temperatures—I Creep Behavior of Magnesium, Acta metall., 1982, 29, p 1969–1962. https://doi.org/10.1016/0001-6160(81)90034-1
S.S. Vagarali and T.G. Langdon, Deformation Mechanisms in h.c.p. Metals at Elevated Temperatures—II. Creep Behavior of a Mg-0.8% Al Solid Solution Alloy, Acta metall., 1982, 30, p 1157–1170. https://doi.org/10.1016/0001-6160(82)90009-8
K. Máthis, J. Čapek, Z. Zdražilová and Z. Trojanová, Investigation of Tension–Compression Asymmetry of Magnesium by Use of the Acoustic Emission Technique, Mater. Sci. Eng., A, 2011, 528, p 5904–5907. https://doi.org/10.1016/j.msea.2011.03.114
P. Dobroň, J. Bohlen, F. Chmelík, P. Lukáč, D. Letzig and K.U. Kainer, Acoustic Emission During Stress Relaxation of Pure Magnesium and AZ Magnesium Alloys, Mater. Sci. Eng. A, 2007, 462, p 307–310. https://doi.org/10.1016/j.msea.2005.12.111
X. Liu, J. Chen and X. Liu, Effect of Twin Boundary -Dislocation and Twin Boundary -Solute Atom Interaction on Detwinning of Mg-2Gd-2Y-0.3Zr Alloy, J. Alloys. Compd., 2019, 770, p 483–89. https://doi.org/10.1016/j.jallcom.2018.08.171
M.S. Hooshmand and M. Ghazisaeidi, Solute/Twin Boundary Interaction as a New Atomic-Scale Mechanism for Dynamic Strain Aging, Acta Mater., 2020, 188, p 711–719. https://doi.org/10.1016/j.actamat.2020.01.066
Z. Pei, K. Li, J.-F. Nie and J.R. Morris, First Principle Study of the Solute Segregation in Twin Boundaries in Mg and Possible Descriptors for Mechanical Properties, Mater. Design, 2019, 165, 107574. https://doi.org/10.1016/j.matdes.2018.107574
P. Yi and M.L. Falk, Thermally Activated Twin Thinckening and Solute Softening in Magnesium Alloys-A Molecular Simulation Study, Scripta Mater., 2019, 162, p 195–199. https://doi.org/10.1016/j.scriptamat.2018.11.021
H. Zhu, S. Liu, Z. Liu and D. Li, Tailoring the Stability, Comput. Mater. Sci., 2018, 152, p 113–117.
Y.V.R.K. Sastry and R.V. Armstrong, Effect of Grain Size on the Thermal Activation Strain Rate Analysis in HCP Metals, J. Sci. Ind. Res., 1972, 32, p 314–316.
F.F. Lavrentev, The Type of Dislocation Interaction as the Factor Determining Work Hardening, Mater. Sci. Eng., 1980, 46, p 191–208. https://doi.org/10.1016/0025-5416(80)90175-5
Z. Trojanová, C.H. Cáceres, P. Lukáč and L. Čížek, Serrated Flow in Az91 Magnesium Alloy in Tension and Compression, Kovove Mater., 2008, 46, p 243–248.
L.P. Kubin and Y. Estrin, Evolution of Dislocation Densities and the Critical Condition for the Portevin - Le Châtelier Effect, Acta Metall. Mater., 1990, 38, p 697–708. https://doi.org/10.1016/0956-7151(90)90021-8
F. Chmelík, Z. Trojanová, Z. Převorovský and P. Lukáč, The Portevin-Le Châtelier Effect in Al-2.92%Mg-0.38%Mn and Linear Location of Acoustic Emission, Mater. Sci. Engn., 1993, A164, p 260–265. https://doi.org/10.1016/0921-5093(93)90674-4
J. Balík and P. Lukáč, Portevin-LeChâtelier Instabilities in Al-3Mg Conditioned by Strain Rate and Strain, Acta Metall. Mater., 1993, 41, p 1447–1454. https://doi.org/10.1016/0956-7151(93)90253-O
N. Louat, On the Theory of the Portevin-Le Châtelier Effect, Scr. Metall., 1981, 15, p 1167–1170. https://doi.org/10.1016/0036-9748(81)90290-8
J. Friedel, Dislocations, Pergamon, Oxford, 1964.
M.S. Mohebbi, A. Akbarzadeh, Y.-O. Yoon and S.-K. Kim, Stress Relaxation and Flow Behavior Of Ultra-Fine Grained AA 1050, Mechanics of Materials, 2015, 89, p 23–34. https://doi.org/10.1016/j.mechmat.2015.06.001
H. Luethy, R.A. White and O.D. Sherby, Grain Boundary Sliding and Deformation Mechanism Maps, Mater. Sci. Eng., 1979, 39(2), p 211–216. https://doi.org/10.1016/0025-5416(79)90060-0
H.J. Frost and M.F. Ashby, Deformation-mechanism Maps, Pergamon Press, Oxford, UK, 1982, p 44
A. Varma, A. Gokhale, H. Krishnaswamy, D.K. Banerjee and J. Jain, Grain Boundary Sliding and Non-Constancy Strain During Stress Relaxation of Pure Mg, Mater Sci Eng. A, 2021, 817, 141349. https://doi.org/10.1016/j.msea.2021.141349
A. Dlouhý, P. Lukáč and Z. Trojanová, Stress Relaxation, Kovove Mater., 1984, 22, p 688–694.
T. Suzuki, S. Takeuchi, H. Yoshinaga, Dislocation Dynamics and Plasticity. Springer Series in Materials Science 12, Springer-Verlag, Berlin-Heidelberg, 1991.
K. Hariharan, J. Jain and M.G. Lee, Modelling Transient Behavior During Stress Relaxation, J. Phys. Conf. Series, 2018, 1063, 012016. https://doi.org/10.1088/1742-6596/1063/1/012016
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These results were partially achieved with the use of support from the Ministry of Industry and Trade of the Czech Republic in the form of institutional funding.
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ZT contributed to supervision, investigation, conceptualization, writing—original draft, methodology, writing—review and editing. ZD contributed to investigation, methodology, review and editing. PL contributed to conceptualization, methodology, review and editing. JD ugan contributed to methodology, writing—review and editing.
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This invited article is part of a special topical focus in the Journal of Materials Engineering and Performance on Magnesium. The issue was organized by Prof. C. (Ravi) Ravindran, Dr. Raja Roy, Mr. Payam Emadi, and Mr. Bernoulli Andilab, Ryerson University.
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Trojanová, Z., Drozd, Z., Lukáč, P. et al. Stress Relaxation Tests: Modeling Issues and Applications in Magnesium Alloys and Composites. J. of Materi Eng and Perform 32, 2766–2783 (2023). https://doi.org/10.1007/s11665-022-06951-w
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DOI: https://doi.org/10.1007/s11665-022-06951-w