×

Size effects associated with skew symmetric Burgers tensor. (English) Zbl 1474.74025

Summary: This paper investigates size effect phenomena associated with the divergence of the transpose of plastic distortion in plastically deformed isotropic materials. The principle of virtual power, balance of energy, second law of thermodynamics, and codirectionality hypothesis are used to formulate the governing microforce balance and thermodynamically consistent constitutive relations for dissipative microscopic stresses associated with the plastic distortion and skew part of the Burgers tensor. It is obtained that the defect energy through the strictly skew Burgers tensor is converted to the defect energy via the divergence of the plastic distortion. The presence of material length scales in the obtained flow rule indicates that it is possible to apprehend size effects associated with the skew part of the Burgers tensor during the inhomogeneous plastic flow of solid material. Finally and amongst other things, it is shown that the dependency of the microscopic stress vector on the divergence of plastic distortion rate leads to weakening and strengthening effects in the flow rule.

MSC:

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] J. W. Hutchinson,Plasticity at the micron scale, Int. J. Solids Struct.37(2000), 225-238. · Zbl 1075.74022
[2] A. Panteghini, L. Bardella,On the finite element implementation of higher-order gradient plasticity, with focus on theories based on plastic distortion incompatibility, Comput. Methods Appl. Mech. Eng.310(2016), 840-865. · Zbl 1439.74074
[3] E. C. Aifantis,On the microstructural origin of certain inelastic models, Trans. ASME J. Eng. Mater. Tech.106(1984), 326-330.
[4] E. C. Aifantis,The physics of plastic deformation, Int. J. Plast.3(1987), 211-247. · Zbl 0616.73106
[5] H. B. Mualhaus, E. C. Aifantis,A variational principle for gradient plasticity, Int. J. Solids Struct.28(1991), 845-857. · Zbl 0749.73029
[6] P. Gudmundson,A unified treatment of strain gradient plasticity, J. Mech. Phys. Solids52 (2004), 1379-1406. · Zbl 1114.74366
[7] M. E. Gurtin,On framework for small-deformation viscoplasticity: free energy, microforces, strain gradients, Int. J. Plast.9(2003), 47-90. · Zbl 1032.74521
[8] M. E. Gurtin,A gradient theory of small-deformation isotropic plasticity that accounts for Burgers vector and dissipation due to plastic spin, J. Mech. Phys. Solids52(2004), 2545-2568. · Zbl 1084.74008
[9] M. E. Gurtin, L. Anand,A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations, J. Mech. Phys. Solids53(2005), 1624-1649. · Zbl 1120.74353
[10] E. C. Aifantis,Gradient plasticity: Handbook of Materials Behaviour Models, J. Lemaitre ed., Academic Press, 281-297, 2001.
[11] E. C. Aifantis,On the gradient approach-relation to Eringen’s nonlocal theory, Int. J. Eng. Sci.49(2011), 1367-1377.
[12] G. Mokios, E. C. Aifantis,Gradient effects in micro-/nano-identation, Materials Science and Technology28(2012), 1072-1078.
[13] E. C. Aifantis,Material mechanics: Perspectives and prospects, Acta Mech.225(2014), 999-1012.
[14] E. C. AifantisInternal length gradient (ILG) material mechanics across scales and disciplines, Adv. Appl. Mech.49(2016), 1-110.
[15] B. D. Reddy, F. Ebobisse, A. McBride,Well-posedness of a model of strain gradient plasticity for plastically irrotational materials, Int. J. Plast.24(2008), 55-73. · Zbl 1139.74009
[16] A. Borokinni, A. Akinola, O. Layeni,A theory of strain-gradient plasticity with effect of internal microforce, Theor. Appl. Mech. (Belgrade)44(2017), 1-13.
[17] M. E. Gurtin, E. Fried, L. Anand,The Mechanics and Thermodynamics of Continua, Cambridge University Press, Cambridge, 2010.
[18] L. H. Poh, R. H. J. Peerlings,The plastic rotation effect in an isotropic gradient plasticity model for applications at the meso scale, Int. J. Solids Struct.78-79(2016), 57-69.
[19] A. S. Borokinni,A gradient theory based on the Aifantis theory using the Gurtin-Anand strain gradient plasticity approach, Journal of the Mechanical Behavior of Materials27(2018), 20180012.
[20] W. Han, B. D. Reddy,Plasticity: Mathematical Theory and Numerical Analysis, SpringerVelag, New York, 2013. · Zbl 1258.74002
[21] K. E. Aifantis, J. R. Willis,The role of interfaces in enhancing the yield strength of composites and polycrystals, J. Mech. Phys. Solids53(2005), 1047-1070. · Zbl 1120.74316
[22] K. E. Aifantis, W. A. Soer, J. De Hosson, J. R. Willis,Interfaces within strain gradient plasticity: Theory and Experiments, Acta Materialia54(2006), 5077-5085
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.