ARTICLE
Influence of pre-tension on torsion of microscale Cu wires: a study via strain gradient theory
Xinbing Ma 1
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Jiangsu University, Faculty of Civil Engineering and Mechanics, Zhenjiang, Jiangsu Province
Online publish date: 2019-10-15
Publish date: 2019-10-15
Submission date: 2019-01-14
Acceptance date: 2019-06-17
 
Journal of Theoretical and Applied Mechanics 2019;57(4):1055–1065
KEYWORDS
ABSTRACT
Nonproportional plastic deformations on the microscale are an emerging topic. A simplified theory of strain gradient elasto-plasticity is developed to study the evolution of yield strength in a copper wire sequentially experiencing tension and torsion. The pre-tension deformation and stress are inherited to the upcoming torsion process, resulting in a nonproportional loading condition. With consideration of the extra hardening effect due to strain gradient, pre-tension weakens the extra hardening effect of the strain gradient and the dependence on the wire radius. Cyclic torsion behavior is also investigated. Anomalous Bauschinger effect and plastic softening are found.
 
REFERENCES (28)
1.
Bardella L., Panteghini A., 2015, Modelling the torsion of thin metal wires by distortion gradient plasticity, Journal of the Mechanics and Physics of Solids, 78, 467-492.
 
2.
Chakravarthy S.S., Curtin W.A., 2011, Stress-gradient plasticity, Proceedings of the National Academy of Sciences of the United States of America, 108, 38, 15716-15720.
 
3.
Dunstan D.J., Ehrler B., Bossis R., Joly S., P’ng K.M.Y., Bushby A.J., 2009, Elastic limit and strain hardening of thin wires in torsion, Physical Review Letters, 103, 15, 155501, DOI: 10.1103/PhysRevLett.103.155501.
 
4.
Eleftheriadis I., Neuhäuser H., Aifantis E., 2012, Torsional prestrain gradient and size dependence of initial yield for < 100 > Cu-Mn single crystals in tension, Journal of the Mechanical Behavior of Materials, 21, 3-4, 95-99.
 
5.
Fertig R.S., Baker S.P., 2009, Simulation of dislocations and strength in thin films: a review, Progress in Materials Science, 54, 6, 874-908.
 
6.
Fleck N.A., Hutchinson J.W., 1997, Strain gradient plasticity, Advances in Applied Mechanics, 33, 295-361.
 
7.
Fleck N.A., Hutchinson J.W., 2001, A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49, 10, 2245-2271.
 
8.
Fleck N.A., Hutchinson J.W., Willis J.R., 2014, Strain gradient plasticity under non-proportional loading, Proceedings of the Royal Society, 470, 20140267.
 
9.
Fleck N.A., Muller G., Ashby M., Hutchinson J., 1994, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia, 42, 2, 475-487.
 
10.
Fleck N.A.,Willis J.R., 2009, A mathematical basis for strain-gradient plasticity theory. Part II: Tensorial plastic multiplier, Journal of the Mechanics and Physics of Solids, 57, 7, 1045-1057.
 
11.
Forest S., Sievert R., 2003, Elastoviscoplastic constitutive frameworks for generalized continua, Acta Mechanica, 160, 1-2, 71-111.
 
12.
Gao H., Huang Y., 2003, Geometrically necessary dislocation and size-dependent plasticity, Scripta Materialia, 48, 2, 113-118.
 
13.
Gao H., Huang Y., 2016, Taylor-based nonlocal theory of plasticity, International Journal of Solids and Structures, 38, 15, 2615-2637.
 
14.
Gudmundson P., 2004, A unified treatment of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, , 52, 6, 1379-406.
 
15.
Idiart M.I., Fleck N.A., 2010, Size effects in the torsion of thin metal wires, Modelling and Simulation in Materials Science and Engineering, 18, 1, 015009.
 
16.
Janssens K.G.F., 2018, Proportionally and non-proportionally perturbed fatigue of stainless steel, International Journal of Fatigue, 110, 42-48.
 
17.
Kiener D., Motz C., Grosinger W., Weygand D., Pippan R., 2010, Cyclic response of copper single crystal micro-beams, Scripta Materialia, 63, 5, 500-503.
 
18.
Liu D., He Y., Dunstan D.J., Zhang B., Gan Z., Hu P., Ding H., 2013a, Anomalous plasticity in the cyclic torsion of micron scale metallic wires, Physical Review Letters, 110, 24, 244301, DOI: 10.1103/PhysRevLett.110.244301.
 
19.
Liu D., He Y., Dunstan D.J., Zhang B., Gan Z., Hu P., Ding H., 2013b, Toward a further understanding of size effects in the torsion of thin metal wires: an experimental and theoretical assessment, International Journal of Plasticity, 41, 1, 30-52, DOI: 10.1016/j.ijplas.2012.08.007.
 
20.
Liu D., He Y., Shen L., Lei J., Guo S., Peng K., 2015, Accounting for the recoverable plasticity and size effect in the cyclic torsion of thin metallic wires using strain gradient plasticity, Materials Science and Engineering: A, 647, 84-90, DOI: 10.1016/j.msea.2015.08.063.
 
21.
Liu J., Soh A. K., 2016, Strain gradient elasto-plasticity with a new Taylor-based yield function, Acta Mechanica, 227, 10, 3031–3048.
 
22.
Nicola L., Xiang Y., Vlassak J., der Giessen E.V., Needleman A., 2006, Plastic deformation of freestanding thin films: experiments and modeling, Journal of the Mechanics and Physics of Solids, 54, 10, 2089-2110.
 
23.
Nix W.D., Gao H., 1998, Indentation size effects in crystalline materials: a law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 46, 3, 411-425.
 
24.
Ozhoga-Maslovskaja O., Naumenko K., Altenbach H., Prygorniev O., 2015, Micromechanical simulation of grain boundary cavitation in copper considering non-proportional loading, Computational Materials Science, 96, 178-184.
 
25.
Pejkowski L., 2017, On the material’s sensitivity to non-proportionality of fatigue loading, Archives of Civil and Mechanical Engineering, 17, 3, 711-727.
 
26.
Stölken J.S., Evans A.G., 1998, A microbend test method for measuring the plasticity length scale, Acta Materialia, 46, 14, 5109-5115.
 
27.
Xiang Y., Vlassak J., 2006, Bauschinger and size effects in thin-film plasticity, Acta Materialia, 54, 20, 5449-5460.
 
28.
Yang Y., Vormwald M., 2017, Fatigue crack growth simulation under cyclic non-proportional mixed mode loading, International Journal of Fatigue, 102, 37-47.
 
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