Skip to main content
SpringerLink
Log in

A mathematical model and numerical estimation of setting stresses in polymer composites molded under hydrostatic pressure

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

The effect of compression molding (i.e. molding under hydrostatic pressure) on the magnitude and distribution of setting stresses in particle-reinforced polymer composites is investigated using the finite element method. Models based on fairly random arrangements of the reinforcing particles are used, with different particle size gradations, as well as different aggregate-to-resin ratios. An analytical expression of the maximum setting stresses in these composites is introduced. A non-linear constrained optimization technique is used to obtain the mathematical model parameters which aid in a reasonable numerical estimation of the maximum setting stresses in real systems. The numerical results show that externally applied hydrostatic pressure helps diminish some of the local setting stresses. However, this relief becomes insignificant at the interface between aggregate particles and the resin domains where local setting stresses are maximum. This indicates that the practice of compression molding does not have a significant effect in reducing local setting stresses in ordinary polymer concrele systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A.M. Boriek, J.E. Akin and C.D. Armeniades, Setting Stress Distribution in Particle Reinforced Polymer Composites,Journal of Composite Materials, 10 (1988) 986–1002.

    Google Scholar 

  2. A.M. Boriek, J.E. Akin and C.D. Armeniades, Setting Stress Distribution in Polymer Composites Reinforced with Multiple Sized-Aggregate,Journal of ASCE, Materials Division, 1 (1989) 217–236.

    Google Scholar 

  3. A.M. Boriek, M.M. El-Alem, J.E. Akin and C.D. Armeniades, A Theoretical Model for Voids Distribution in Polymer Composites and Their Effect on Setting Stresses,Journal of Probabilistic Engineering Mechanics 5 (3) (1990) 129–137.

    Google Scholar 

  4. A.M. Boriek, Modeling of Setting Stresses in Particle Reinforced Polymer Composites Using Finite Element Analysis, Ph.D. Thesis, Rice University (1989).

  5. A.M. Boriek and C.D. Armeniades, Minimization of Setting Stresses Using Realistic Models for Particle Reinforced Polymer Composites, Presented in the Twenty-Third Annual Pittsburgh Conference on Modeling and Simulation; April 30-May 1, 1992.

  6. ASTM standands in building codes, vol, II, American Society for Testing and Materials, ASTM, 1988.

  7. R.D. Henshell, PAFEC 75 Theory, Results, PAFEC Ltd., Nottingham (1975).

    Google Scholar 

  8. PAFEC Data preparation Manual, PAFEC Ltd., Nottingham, U.K. (1986).

  9. E. Haque, Physicochemical Interaction between Montmorillonite and Polymerizing Systems: Effect on Particle-Reinforced Composites, Ph.D. Thesis, Rice University (1986).

  10. A. Goldstein, Constructive Real Analysis, New York: Harper and Row (1967).

    Google Scholar 

  11. E. Zeidler, Nonlinear Functional Analysis and Its Applications, Vol. III. New York: Springer-Verlag (1984).

    Google Scholar 

  12. J.E. Dennis and R.B. Schnabet, Numerical methods for Unconstrained Optimization and Nonlinear Equations, Englewood Cliffs, NJ: Prentice-Hall, 129–133 (1983).

    Google Scholar 

  13. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, New York: John Wiley & Sons (1968).

    Google Scholar 

  14. R. Fletcher, Practical Methods of Optimization, New York: John Wiley & Sons (1987).

    Google Scholar 

  15. P.E. Gill, W. Murray, M.A. Saunders and M.H. Wright,User's guide for QPSOL, a Fortran package for quadratic programming, version 3.2, System Optimization Laboratory, Stanford University, CA, TR SOL 84–6, September (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Materials Science, Rice University, P.O. Box 1892, 77251-1892, Houston, TX, USA

    A. M. Boriek

  2. Department of Mathematical Sciences, Reice University, P.O. Box 1892, 77251-1892, Houston, TX, USA

    A. S. El-Bakry

  3. Department of Chemical Engineering, Rice University, P.O. Box 1892, 77251-1892, Houston, TX, USA

    C. D. Armeniades

Authors
  1. A. M. Boriek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. El-Bakry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. D. Armeniades
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boriek, A.M., El-Bakry, A.S. & Armeniades, C.D. A mathematical model and numerical estimation of setting stresses in polymer composites molded under hydrostatic pressure. J Eng Math 26, 509–524 (1992). https://doi.org/10.1007/BF00042767

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00042767

Keywords

Search

Navigation