Shear band formation in plane strain

Hutchinson, J. W.; Tvergaard, V.

Affiliations

¹Division of Applied Sciences, Harvard University, Cambridge, MA 02138, U.S.A.

²Department of Solid Mechanics, Technical University of Denmark, Lyngby, Denmark

Abstract

The growth of a single shear band in an infinite block of an incompressible solid undergoing plane strain tension or compression is studied for three material models—nonlinear elasticity, kinematic hardening plasticity and a plasticity theory based on yield surface corner development. The study includes analyses of bifurcation and post-bifurcation behaviour as well as the sensitivity of shear band growth to material imperfections. Depending on their orientation and on details of the material model, shear bands may form gradually with relatively limited localization of strain or they may localize catastrophically with an attendant strong sensitivity to initial imperfections in the form of material inhomogeneity.

Links

DOI: 10.1016/0020-7683(81)90053-6

WoS: A1981LQ25700001

Cited Works (1)

Year	Entry
1978	Needleman A, Rice JR. Limits to ductility set by plastic flow localization. In: Koistinen DP, Wang N-M, eds. Mechanics of Sheet Metal Forming: Material Behavior and Deformation Analysis. New York, NY: Plenum PRess; 1978:237-267.

Cited By (13)

Year	Entry
2016	Klingbeil D, Svendsen B, Reusch F. Gurson-based modelling of ductile damage and failure during cyclic loading processes at large deformation. Eng Fract Mech. July 2016;160:95-123.
2007	Kuroda M, Tvergaard V. Effects of texture on shear band formation in plane strain tension/compression and bending. Int J Plast. February 2007;23(2):244-272.
2019	Muhammad W, Ali U, Brahme AP, Kang J, Mishra RK, Inal K. Experimental analyses and numerical modeling of texture evolution and the development of surface roughness during bending of an extruded aluminum alloy using a multiscale modeling framework. Int J Plast. June 2019;117:93-121.
1982	Triantafyllidis N, Needleman A, Tvergaard V. On the development of shear bands in pure bending. Int J Solids Struct. 1982;18(2):121-138.
2001	Evans AG, Suo Z, Wang RZ, Aksay IA, He MY, Hutchinson JW. Model for the robust mechanical behavior of nacre. J Mater Res. September 2001;16(9):2475-2484.
1982	Tvergaard V. Influence of void nucleation on ductile shear fracture at a free surface. J Mech Phys Solids. December 1982;30(6):399-425.
1987	Tvergaard V. Effect of yield surface curvature and void nucleation on plastic flow localization. J Mech Phys Solids. 1987;35(1):43-60.
2013	Mattei L, Daniel D, Guiglionda G, Klöcker H, Driver J. Strain localization and damage mechanisms during bending of AA6016 sheet. Mater Sci Eng. January 1, 2013;A559:812-821.
1985	Mear ME, Hutchinson JW. Influence of yield surface curvature on flow localization in dilatant plasticity. Mech Mater. 1985;4(3-4):395-407.
1987	Tvergaard V. Ductile shear fracture at the surface of a bent specimen. Mech Mater. 1987;6(1):53-69.
2003	Lievers WB, Pilkey AK, Worswick MJ. The co-operative role of voids and shear bands in strain localization during bending. Mech Mater. July 2003;35(7):661-674.
2001	Lievers WB. Effect of Void Damage and Shear Band Development on the Bendability of AA6111 Automotive Aluminum Alloy Sheet [Master's thesis]. Ottawa, ON: Carleton University; May 9, 2001.
2001	Thomson CIA. Modeling the Effects of Particle Clustering on Ductile Failure [PhD thesis]. Ottawa, ON: Carleton University; May 2001.