Formulation of a Strain Based Orthotropic Elasto-Plastic Damage Theory

Abstract

A strain based orthotropic elasto-plastic damage theory is derived for solving engineering problems. The basic ideas of the formulation are first explained by the one-dimensional approach. Subsequently, the approach is generalized to develop the theory in three-dimensional space. Damage is characterized by a second order damage tensor D while its effects on mechanical properties are described by a fourth order damage effect tensor M. The concept of elastic energy equivalence is adopted to determine the stress-strain relation in terms of the effective stress and the effective strain. On the basis of the plastic flow rule and the damage potential, the elasto-plastic damage tangent tensor as well as the damage threshold function are obtained. Since the development of damage usually connects with deformation, the strain based theory is easier to use in solving structural problems. An example case of uniaxial stretching of aluminium alloy 2024T3 plate is employed to justify the applicability of the theory. The results show that the theoretical results are in good agreement with the experimental ones.

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References

1. A. L. Gurson , Continuum theory of ductile rupture by void nucleation and growth: Part I: yield criteria and flow rules for porous ductile media, J. Eng. Mat. Tech. Vol. 99, pp. 2-15, (1977).

2. V. Tvergaard , Influence of voids on shear band instabilities under plane strain conditions, Int. J. Fracture, Vol. 17, pp. 389-407 (1981).

3. V. Tvergaard , Material failure by void coalescence in localized shear band, Int. J. Solids Structures, Vol. 18, pp. 659-672 (1982).

4. R. Becker , The effect of porosity distribution on ductile failure, J. Mech. Phys. Solid, Vol. 35, No. 5, pp. 577-599 (1987).

5. J. Lemaitre , How to use damage mechanics, Nucl. Engng. Design, Vol. 80, pp. 233-246 (1984).

6. J. Lemaitre , A course on damage mechanics, Springer-Verlag (1992).

7. D. Krajcinovic , Constitutive equations for damaging materials. J. Appl. Mech., Vol. 50, pp. 355-360 (1983).

8. J. C. Simo and J. W. Ju , Strain- and stress-based continuum damage models—I. Formulations, II. Computational aspects, Int. J. Solids Structures, Vol. 23, No. 7, pp. 821-869 (1986).

9. W. H. Tai , Plastic damage and ductile fracture in mild steels, Engineering Fracture Mechanics, Vol. 37, No. 4, pp. 853-880 (1990).

10.

10. C. L. Chow and J. Wang , An anisotropic theory of continuum damage mechanics for ductile fracture, Engineering fracture mechanics, Vol. 27, No. 5, pp. 547-558 (1987).

11.

11. J. Lemaitre and J. P. Sermage , One damage law for different mechanisms, Computational mechanics 20, pp. 84-88 (1997).

12.

12. W. R. Delameter and G. Hermann , Weakening of elastic solids by doubly-periodic arrays of crack, Topics in applied continuum mechanics, Springer-Verlag (1974).

13.

13. F. Sidoroff , Description of anisotropic damage application to elasticity, IUTAM Colloquium, Physical Nonlinearities in Structural Analysis, pp. 237-244 (1981).

14.

14. E. T. Onat , Representation of mechanical behavior in the presence of internal structure damage, Eng. Frac. Mech., Vol. 25, pp. 605-614 (1986).

15.

15. E. T. Onat and F. A. Leckie , Representation of mechanical behavior in the presence of changing internal structure. J. Appl. Mech., Vol. 55, pp. 1-10 (1988).

16.

16. J. Betten , Damage tensors in continuum mechanics, J. Mech. Theor. Appl., Vol. 2, pp. 13-32 (1983).

17.

17. H. Lee , G. Li and S. Lee , Int. seminar on local approach of fracture, Moret-sur-loing, France, pp. 79-90 (1985).

18.

18. C. L. Chow and J. Wang , An anisotropic theory of elasticity for continuum damage mechanics, International Journal of Fracture, Vol. 33, pp. 3-16 (1987).

19.

19. C. Y. Tang, Modelling of craze damage in polymeric materials: A case study in polystyrene and high impact polystyrene, The Hong Kong Polytechnic University, Thesis of Ph.D. (1985).