Introduction

• Most composite materials exhibit nonlinear stress-strain behavior in at least one of the principal material directions[1]
• Sources of material nonlinearity: (1) Matrix material response, such as viscoelastic behavior in polymeric matrices or (2) Microstructural characteristics, such as micro-cracks
• Under large strain deformation, fiber orientation change greatly affects the stress-strain response and the ultimate strength of composite laminates[2][3]
• No prior research conducted on effect of deformation-induced fiber orientation change on laminate during multi-axial/general loading scenario

[1] Robert M. Jones and Harold S. Morgan, AIAA Journal, Vol. 15 (12), 1977
[2] Michael R. Wisnom, Composites, Vol. 26 (1), 1995
[3] C.T. Sun and Changming Zhu, Composites Science and Technology, 60, 2337-2345, 2000

Research Objectives

• Develop multi-axial formulation describing relationship between strains and change in orientation
• Incorporate formulation in incremental laminate analysis to calculate angle step-by-step and update effective properties accordingly
• Develop algorithm for implementation in CMAP-NL: a nonlinear laminate analysis code
• Create a comprehensive numerical tool able to simulate the large displacement behavior of thermoplastic composites by accounting for the change in local fiber orientation

Approach

• Obtain general analytical solution based on uniaxial angle rotation-strain relationships from literature to keep track of varying angle
• Validate multi-axial formulation
• Develop algorithm based on incremental laminate analysis
• In incremental analysis, nonlinear response of laminate generated through summation of piece-wise linear increments in stress over pre-determined load schedule

Uni-Axial & Multi-Axial Formulation

• Combination of four loading cases would simulate general multi-axial loading scenario:

General Formulation

Subroutine Algorithm

Conclusion

• Derived general equation relating change in fiber orientation during multi-axial loading
• Developed subroutine for implementation in nonlinear laminate analysis code CMAP-NL

Future Work

• Experimental validation including tension and shear tests
• Incorporate UMAT in LS-DYNA to explore multi-axial loads and how rotation is affected correspondingly
• Investigate the influence of residual stresses due to thermal effects on the nonlinear response of the material

Acknowledgements

This work is supported by the University of Delaware Center for Composite Materials under the guidance of Dr. John W. Gillespie and Dr. Bazle Z. (Gama) Haque.