Limit Plastic State of Notched Stripes with Stress State Dependent Properties

Abstract:

Article Preview

Behavior of isotropic media with stress state dependent plastic properties is studied in this paper. One of the possible general approaches to the formulation of constitutive equations of these materials is demonstrated. The derived equations are applied to the problem of tension of a notched stripe under plane stress conditions. Some general equations of stress state dependence of plastic properties of materials that can be used with large variety of models are derived in the case of hyperbolic constitutive equations. Theoretical results are compared with FEM solution of this problem for the Drucker-Prager material model.

Info:

Periodical:

Edited by:

Robert V. Goldstein, Dr. Yeong-Maw Hwang, Yeau Ren Jeng and Cho-Pei Jiang

Pages:

79-88

Citation:

E.V. Lomakin and A.M. Melnikov, "Limit Plastic State of Notched Stripes with Stress State Dependent Properties", Key Engineering Materials, Vol. 528, pp. 79-88, 2013

Online since:

November 2012

Export:

Price:

$41.00

[1] D.C. Drucker and W. Prager, Soil Mechanics and Plastic Analysis or Limit Design, Quarterly. Appl. Math. 10 2 (1952) 157–165.

DOI: https://doi.org/10.1090/qam/48291

[2] V.V. Novozhilov, On Plastic Cavitation, J. Appl. Math. Mech. 29 4 (1965) 811–819.

[3] R.J. Green, A Plasticity Theory for Porous Solids, Int. J. Mech. Sci. 14 4 (1972) 215-226.

[4] A.L. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part 1 — Yield Criteria and Flow Rules for Porous Ductile Media, Trans. of ASME. J. Eng. Mater. Techn. 99 (1977) 2–15.

DOI: https://doi.org/10.2172/7351470

[5] V. Tvergaard and A. Needleman, Analysis of the Cup-Cone Fracture in a Round Tensile Bar, Acta. Metall. Mater. 32 (1984) 157–169.

DOI: https://doi.org/10.1016/0001-6160(84)90213-x

[6] E.V. Lomakin, Nonlinear Deformation of Materials whose Resistance Depends on the Form of the Stressed State, Mech. Solids. 15 4 (1980) 69–75.

[7] E.V. Lomakin, Dependence of the Limit State of Composite and Polymer Materials on the Type of the Stress State. 1. Experimental Dependencies and Determining Equations, Mech. Comp. Mater. 24 1 (1988) 1–7.

DOI: https://doi.org/10.1007/bf00608152

[8] E.V. Lomakin, Constitutive Relations of Deformation Theory for Dilatant Media, Mech. Solids. 26 6 (1991) 64–72.

[9] E.V. Lomakin, Mechanics of Media with Stress-State Dependent Properties, Phys. Mesomech. 10 5 (2007) 41-52.

[10] A.M. Freudental and H. Geiringer, The Mathematical Theories of the Inelastic Continuum, in Handbuch der Physik. Bd. VI. Elastiziätt und Plastizität, Ed. by S. Flügge (Springer, Berlin, 1958, pp.229-433.

DOI: https://doi.org/10.1007/978-3-642-45887-3_3

[11] E. V. Lomakin, A. M. Melnikov, Plane Stress State Problems for Notched Bodies whose Plastic Properties Depend on the Form of the Stress State, Mech. Sol. 46 1 (2011) 62-69.

DOI: https://doi.org/10.3103/s0025654411010092

[12] J. W. Hutchinson, Plastic Stress and Strain Fields at a Crack Tip. J. Mech. Phys. Solids. 16 (1968) 337–347.