A Quadratic Yield Function for Fiber-Reinforced Composites

Abstract

A simple, 3-D yield function that is quadratic in stresses was proposed to describe the plastic behavior of fiber composites. It relaxes the two usually used assumptions that hydrostatic stress does not influence plastic deformation and that the total plastic dilatation is incompressible. It is also general in nature to allow for composites with various fiber volume fractions and different fiber arrays. The applicability of this quadratic yield function to fiber composites was examined, and the accuracy of the elasto-plasticity model was verified by using the macro stress-strain data generated by a 3-D nonlinear micromechanics model. Because this anisotropic plasticity model is simple and is in the general form of those widely used in existing numerical plasticity codes, it can easily be incorporated into the existing codes with little effort.

References

1. Griffin, O. H. , M. P. Kamat and C. T. Herakovich . 1981. "Three-Dimensional Inelastic Finite Element Analysis of Laminated Composites," J. Composite Materials, 5:543-560.

2. Dvorak, G. J. and Y. A. Bahei-El-Din . 1982. "Plasticity Analysis of Fibrous Composites," J. Appl. Mech., 49:327-335.

3. Chen, J. K. and C. T. Sun . 1987. "Nonlinear Analysis of Interlaminar Stress in Graphite/Epoxy Laminates with and without Delamination Cracks," Composite Structures, 8:271-285.

4. Aboudi, J. 1987. "Closed Form Constitutive Equations for Metal Matrix Composites," Int. J. Engng. Sci. 25(9):1229-1240.

5. Pindera, M. J. , C. T. Herakovich , W. Becker and J. Aboudi . 1990. "Nonlinear Response of Unidirectional Boron/Aluminum," J. Composite Materials, 24:2-21.

6. Hansen, A. C. , D. M. Blackketter and D. E. Walrath . 1991. "An Invariant Based Flow Rule for Anisotropic Plasticity Applied to Composite Materials," J. Appl. Mech., 58:881-888.

7. Chen, J. L. and C. T. Sun . 1993. "A Plastic Potential Function Suitable for Anisotropic Fiber Composites," J. Composite Materials, 27:1379-1390.

8. Xie, M. and D. F. Adams . 1995. "A Plasticity Model for Unidirectional Composite Materials and Its Application in Modeling Composites Testing," Composite Science and Technology, 54(1):11-22.

9. Adams, D. F. and D. A. Crane . 1984. "Finite Element Micromechanics Analysis of a Unidirectional Composite Including Longitudinal Shear Loading," Computers & Structures, 18(6): 1153-1165.

10.

10. Sun, C. T. and J. L. Chen . 1989. "A Simple Flow Rule for Characterizing Nonlinear Behavior of Fiber Composites," J. Composite Materials, 23:1009-1020.

11.

11. Vaziri, R. , M. D. Olson and D. L. Anderson . 1991. "A Plasticity-Based Constitutive Model for Fibre-Reinforced Composite Laminates," J. Composite Materials, 25:512-535.