Sage Journals: Discover world-class research

Abstract

We present a design sensitivity analysis, which supports the shape optimization of the tool used in thermoset composite manufacturing. The method provides a systematic way to predict the optimal tool geometry that leads to the minimum difference between desired and final shapes of the manufactured part. The design process is formalized by integrating process modeling, design sensitivity analysis, and numerical optimization into a single framework. The process modeling is based on a transient coupled thermo-chemo-viscoelastic finite element scheme, which accurately capturest he evolution of residual stresses throughout the manufacturing process, and their effect on the final shape of the composite part. Design sensitivity information is extracted efficiently from the primal analysis using an analytical, direct differentiation method. The sensitivities are then provided to a numerical optimization program to improve the tool design. Optimization results are presented for two specific applications involving mold design for cross-ply laminates and L-shaped composite parts.

Keywords

thermoset composites dimensional accuracy design sensitivity analysis shape optimization finite elements

Get full access to this article

View all access options for this article.

References

1. Pagliuso, S. (1982). Warpage, a nightmare for composite parts producers. In: Proceedings of the 4th International Conference on Composite Materials (ICCM-4). Tokyo, Japan. pp. 1617–1623.

2. Zhu, Q. , Li, M. , Geubelle, P.H. and Tucker III, C.L. (2000). Dimensional accuracy of thermoset composites: simulation of process-induced residual stresses. To appear in Journal of Composite Materials.

3. Weitsman, Y. (1980). Optimal cool-down in linear viscoelasticity. Journal of Applied Mechanics, 47: 35–39.

4. White, S.R. and Hahn, H.T. (1992). Cure cycle optimization for the reduction of processinginduced residual stress in composite materials. Journal of Composite Materials, 27(14): 1352–1378.

5. Olivier, P. and Cottu, J.P. (1998). Optimization of the co-curing of two different composites with the aim of minimizing residual curing stress levels. Composites Science and Technology, 58: 645–651.

6. Reuter, R.C., Jr. (June 1988). Evaluation and controls of residual states in curved, composite panels. In: Proceedings of the Fourth Japan-U.S. Conference on Composite Materials. Washington, D.C. pp. 742–751.

7. Fernlund, G. and Poursartip, A. (1999). The effect of tooling material, cure cycle, and tool surface finish on spring-in of autoclave processed curved composite parts. In: Proceedings of the 12th International Conference on Composite Materials (ICCM-12). Paris, France. p. 708–708. 5–9 July.

8. Li, M. , Zhu, Q. , Geubelle, P.H. and Tucker III, C.L. (2001). Optimal curing for thermoset matrix composites: thermochemical considerations. Polymer Composites, 22(1): 118–131.

9. Morthland, T.E. , Byrne, P.E. , Tortorelli, D.A. and Dantzig, J.A. (August 1995). Optimal riser design for metal castings. Metallurgical and Materials Transactions B, 26B: 871–885.

10.

10. Johnston, A. , Hubert, P. , Nelson, K. and Poursartip, A. (1998). A sensitivity analysis of factors affecting the warpage of a composite structure. In: Proceedings of 43rd International SAMPE Symposium and Exhibition. CA, USA: Anaheim. May 31–June 4.

11.

11. Fernlund, G. , Poursartip, A. , Nelson, K. , Wilenski, M. and Swanstrom, F. (1999). Process modeling for dimensional control–sensitivity analysis of a composite spar process. In: Proceedings of 44th International SAMPE Symposium and Exhibition. Long Beach, California. pp. 1744–1755. 23–27 May.

12.

12. Christensen, R.M. (1971). Theory of Viscoelasticity. New York: Academic Press.

13.

13. Taylor, R.L. , Pister, K.S. and Goudreau, G.L. (1970). Thermomechanical analysis of viscoelastic solids. International Journal for Numerical Methods in Engineering, 2(1): 45–59.

14.

14. Tortorelli, D.A. , Tiller, M.M. and Dantzig, J.A. (1994). Optimal design of nonlinear parabolic systems. Part I: Fixed spatial domain with applications to process optimization. Computer Methods in Applied Mechanics and Engineering, 113: 141–155.

15.

15. Tortorelli, D.A. , Tomasko, J.A. , Morthland, T.E. and Dantzig, J.A. (1994). Optimal design of nonlinear parabolic systems. Part II: Variable spatial domain with applications to casting optimization. Computer Methods in Applied Mechanics and Engineering, 113: 157–172.

16.

16. Michaleris, P. , Tortorelli, D.A. and Vidal, C.A. (1994). Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity. International Journal for Numerical Methods in Engineering, 37: 2471–2499.

17.

17. Engineering, V. (1992). DOT Users Manual, Version 3.00. Goleta, CA: Vanderplaats, Miura and Associates, Inc.

18.

18. Kim, K.S. and Hahn, H.T. (1989). Residual stress development during processing of graphite/ epoxy composites. Composites Science and Technology, 36(2): 121–132.

19.

19. Oakeshott, J.L. and Lemoine, D. (1998). Experimental study of spring forward in cured laminated U-channelsmade from unidirectionally reinforced carbon fiber-epoxy prepregs. Plastics, Rubber and Composites Processing and Applications, 27(4): 190–199.

20.

20. Radford, D.W. and Diefendorf, R.J. (1993). Shape instabilities in composites resulting from laminate anisotropy. Journal of Reinforced Plastics and Composites, 12(1): 58–75.

21.

21. Huang, C.K. and Yang, S.Y. (1997). Study on accuracy of angled advanced composite tools. Materials and Manufacturing Process, 12(3): 473–486.

22.

22. Lee, C.C. (1995). A finite element study of bond-line-read-out. Journal of Reinforced Plastics and Composites, 14: 1226–1249.