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Strain gradient plasticity: energetic or dissipative?

Fleck, NA and Willis, JR (2015) Strain gradient plasticity: energetic or dissipative? Acta Mechanica Sinica/Lixue Xuebao, 31. pp. 465-472. ISSN 0567-7718

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Abstract

© 2015, The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg. For an infinite slab of strain gradient sensitive material subjected to plane-strain tensile loading, computation established and analysis confirmed that passivation of the lateral boundaries at some stage of loading inhibits plastic deformation upon further loading. This result is not surprising in itself except that, remarkably, if the gradient terms contribute to the dissipation, the plastic deformation is switched off completely and only resumes at a clearly defined higher load, corresponding to a total strain ε c , say. The analysis presented in this paper confirms the delay of plastic deformation following passivation and determines the exact manner in which the plastic flow resumes. The plastic strain rate is continuous at the exact point ε c of resumption of plastic flow and, for the first small increment Δε=ε-εc in the imposed total strain, the corresponding increment in plastic strain, Δε p , is proportional to (Δε) 2 . The constant A in the relation Δε p (0)=A(Δε) 2 , where Δε p (0) denotes the plastic strain increment at the centre of the slab, has been determined explicitly; it depends on the hardening modulus of the material. The presence of energetic gradient terms has no effect on the value of ε c unless the dissipative terms are absent, in which case passivation reduces the rate of plastic deformation but introduces no delay. This qualitative effect of dissipative gradient terms opens the possibility of experimental discrimination of their presence or absence. The analysis employs an incremental variational formulation that is likely to find use in other problems.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div C > Materials Engineering
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:43
Last Modified: 18 Nov 2017 22:09
DOI: