Analytical description plastic strain distribution of plane sample in tension

Y.Y. Deryugin1
1Institute of Strength Physics and Materials Science
Abstract
The method for analytical description of the non-uniform plastic deformation in the local zone of a flat specimen under tension is proposed, which allows theoretically to describe the shape of the neck and the strain distribution in that zone. It allows simulating the real distribution non-uniform deformation and the shape of the neck according to the experimental measurements. That task is actual in connection with the important problem of solid mechanics associated with the transition from experimental curves “loading – elongation” to the diagrams of “stress-strain” for the material in the zone of minimum cross section of the specimen where plastic deformation is very non-uniform and is developing with a maximum speed.
Received: 20 December 2011   Revised: 19 January 2012   Accepted: 24 January 2012
Views: 56   Downloads: 12
References
1.
M.N. Gusev, I.S. Osipov, “Features of deformation-plasticbehavior of metals and alloys irradiated by neutrons inreactors the BBP-K and БН-350,” Bulletin of Udmurtuniversity.Physics, 4, 104-112 (2007) [in Russian].
2.
L.S. Derevyagina, V.E. Panin, A. Gordienko, Physicalmesomechanics. 10(4), 59-71 (2007) [in Russian].
3.
Strain hardening and destruction of polycrystallinemetals, Ed. V.I. Trefilov (Naukova Dumka, Kiev, 1987).(in Russian).
4.
T.M. Poletika, A.P. Pshenichnikov, JTP 79(3), 54-58(2009) [in Russian].
5.
W.H. Peters, W.F. Ranson, Optical Engineering 21, 427(1982).
6.
M.A. Sutton, W.J. Wolters, W.H. Peters, W.F. Ranson, S.R.McNeil, 1(3), 133 (1982).
7.
V.E. Panin, V.S. Pleshanov, V.V. Kibitkin, S. Sapozhnikov,Defectoscope 2, 80 (1998) [in Russian].
8.
S.V. Panin, V.I. Syryamkin, P.S. Lyubutin, Auto-metry41(2), 44 (2005) [in Russian].
9.
J.D. Eshelby, “Continuum theory of defects,” Solid StatePhysics, 3, (1956).
10.
R. de Wit, Linear theory of static disclinations. In:Fundamental aspects of dislocation, ed. by J.A. Simons,R. de Wit, R. Bullough, Nat. Bur. Stand. (US) Spec. Publ.317, vol. I, 651-673 (1970).
11.
V.A. Likhachev, A.E. Volkov, V.E. Shudegov, Continuumtheory of defects (Leningrad. Univ., Leningrad 1986) [inRussian].
12.
R. Gallagher The Finite Element Method. Basics.Springer-Verlag, (1984).
13.
S.L. Crouch, A.M. Starfield, Boundary element methodsin solid mechanics (London: George Allen & Unwin,1983).
14.
Ye.Ye. Deryugin, G. Lasko, S. Schmauder, „RelaxationElement Method in Mechanics of Deformed Solid”. In:Wilhelm U. Oster. Computational Materials (NY: NovaScience Publisher, 2009) 479-545.
15.
A.V. Panin, A.A. Son, Y.F. Ivanov, V.I. Kopylov, PhysicalMesomechanics 7(3), 5-16 (2004) [in Russian].
16.
M.J. Vygodskii Handbook on higher mathematics (AST:Astrel, Moscow, 2005) [in Russian].
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1.
Периг А.В., Бондаренко С.И., Бондаренко Е.А., Письма о материалах 2(2 (6)), 103-106 (2012).