On the elasto-plastic stress concentration at a circular hole in an anisotropic sheet
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The classical problem of determining the stress concentration factor at a circular hole embedded in an infinite sheet subjected to remote uniform tension is investigated. A finite strain elasto-plastic deformation theory based on Hill's new anisotropic flow theory  is used. It is shown that the governing field equations can be reduced to a single first order differential equation from which the stress concentration factor is obtained by a standard numerical method. The solution covers the entire elasto-plastic range and is valid for any strain hardening function. Comparison with experimental results, for a few materials, shows good agreement.
With a pure power hardening law and within the framework of small strain plasticity, our results agree with those obtained from a more general solution discovered by Budiansky .
- Budiansky, B., Mangasarian, D. L. (1960) Plastic stress concentration at a circular hole in an infinite sheet subjected to equal biaxial tension. J. Appl. Mech. 82: pp. 59-64
- Budiansky, B. (1971) An exact solution to an elastic-plastic stress-concentration problem. PMM 35: pp. 40-48
- Hill, R.: The mathematical theory of plasticity, Chapt. XII. Oxford University Press 1950.
- Lee Wu, M. H.: Analysis of plane-plastic-stress problems with axial symmetry in strain-hardening range. NACA TR 1021 (1951).
- Yang, W. H. (1969) Axisymmetric plane stress problems in anisotropic plasticity. J. Appl. Mech. 36: pp. 7-14
- Parmar, A., Mellor, P. B. (1978) Plastic expansion of a circular hole in sheet metal subjected to biaxial tensile stress. Int. J. Mech. Sci. 20: pp. 707-720
- Hill, R. (1979) Theoretical plasticity of textured aggregates. Math. Proc. Camb. Phil. Soc. 85: pp. 179-191
- Budiansky, B.: Private communication (1979).
- Nadai, A.: Theory of flow and fracture of solids, pp. 472–481. McGraw-Hill 1950.
- Durban, D. (1979) Large strain solution for pressurized elasto/plastic tubes. J. Appl. Mech. 46: pp. 228-230
- On the elasto-plastic stress concentration at a circular hole in an anisotropic sheet
Volume 43, Issue 1-2 , pp 73-84
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