The structural and residual stress of fibrous composites can be evaluated by measuring the strain in embedded particles which are sensitive to X-ray diffraction. The main advantage is that three-dimensional stresses in the interior can be measured. To evaluate the stress in the material a micromechanical model is proposed for the effective stressstrain relationship between the strain in the particles and the stress in the composite. The consistency of the model is checked by Finite-Element computations of representative volume elements. The predictions of the model are compared with experimental results and conclusions about the validity of the model are drawn.
1. Hahn, H. T. and N. J. Pagano. “Curing Stresses in Composite Laminates,”Journal of Composite Materials,9:91-106, 1975.
2.
2. Hahn, H. T.“Residual Stresses in Polymer Composite Laminates,”Journal of Composite Materials,10:266-278, 1976.
3.
3. Hahn, H. T.“Effects of Residual Stresses in Polymer Matrix Composites,”Journal of the Astronautical Sciences,32(3):253-267, 1984.
4.
4. Hahn, H. T.“Hygrothermal Damage in Graphite/Epoxy Laminates,”Journal of Engineering Materials and Technology,109:3-11, 1987.
5.
5. Pagano, N. J. and R. B. Pipes. “On the Calculation of Interlaminar Normal Stresses in Composite Laminate,”Journal of Composite Materials,8:65-81, 1974.
6.
6. Barrett, C. S. and P. Predecki. “Stress Measurement in Polymeric Materials by X-Ray Diffraction,”Polymer Engineering and Science,16:602-608, 1976.
7.
7. Barrett, C. S.“Diffraction Technique for Stress Measurement in Polymeric Materials,”Advances in X-Ray Analysis,20:329-336, 1977.
8.
8. Barrett, C. S. and P. Predecki. “Stress Measurement in Graphite/Epoxy Uniaxial Composites by X-Rays,”Polymer Composites,1:2-6, 1980.
9.
9. Predecki, P. and C. S. Barrett. “Stress Measurement in Graphite/Epoxy Composites by X-Ray Diffraction from Fillers,”Journal of Composite Materials,13:61-71, 1979.
10.
10. Predecki, P. and C. S. Barrett. “Residual Stresses in Resin Matrix Composites,” in E. Kula, editor, 28th Sagamore Army Materials Research Conference,pp. 409-424, Lake Placid, July 13-17, 1981.
11.
11. Predecki, P. and C. S. Barrett. “Detection of Moisture in Graphite/Epoxy Laminates by X-Ray Diffraction,”Journal of Composite Materials,16:260-267, 1982.
12.
12. Barrett, C. S. and P. Predecki. “X-Ray Diffraction Evaluation of Adhesive Bonds and Stress Measurements with Diffracting Paint,”Advances in X-Ray Analysis,24:231-238, 1983.
13.
13. Predecki, P. and C. S. Barrett. “Stress Determination in an Adhesive Bonded Joint by X-Ray Diffraction,”Advances in X-Ray Analysis,27:251-260, 1984.
14.
14. Hauk, V. M. and E. Macherauch. “The Suitable Performance of X-Ray Stress Evaluations (xse),” in V. Hauk and E. Macherauch, editors, Eigenspannungen und Lastspannungen, Moderne Ermittlung—Ergebnisse—Bewertung,Härterei-Technische Mitteilungen. Carl Hanser, München, Wien, 1982.
15.
15. Hauk, V., A. Troost and D. Ley. “Evaluation of (Residual) Stresses in Semicrystalline Polymers by X-Rays,”Advances in Polymer Technology,7:389-396, 1987.
16.
16. Wörtler, M. “Interlaminare Spannungskonzentrationen in Faserverbundwerkstoffen,” Ph.D. thesis, University of Karlsruhe, 1988.
17.
17. Prinz, B. and E. Schnack. “Determination of Stress Gradients in Fibrous Composites by X-Ray Diffraction from Fillers,”Journal of Composite Materials,31(9):852-873, 1997.
18.
18. Hauk, V.“Structural and Residual Stress Analysis by X-Ray Diffraction on Polymeric Materials and Composites,”Advances in X-Ray Analysis,42-42, 1999.
19.
19. Hauk, V. M. and E. Macherauch. “A Useful Guide for X-Ray Stress Evaluation,”Advances in XRay Analysis,27:81-99, 1984.
20.
20. Hauk, V., editor. Structural and Residual Stress Analysis by Nondestructive Methods.Elsevier, 1997.
21.
21. Hill, R.“A Self-Consistent Mechanics of Composite Materials,”Journal of the Mechanics and Physics of Solids,13:213-222, 1965.
22.
22. Eshelby, J. D.“The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,”Proceedings Royal Society London A,241:376-396, 1957.
23.
23. Hashin, Z.“The Elastic Moduli of Heterogeneous Materials,”Journal of Applied Mechanics,29:143-150, 1962.
24.
24. Christensen, R. M.Mechanics of Composite Materials.John Wiley & Sons, 1979.
25.
25. Christensen, R. M. and K. H. Lo. “Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models,”Journal of the Mechanics and Physics of Solids,27:315-330, 1979.
26.
26. Christensen, R. M.Personal communication, 1998.
27.
27. Voigt, W. “Über die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper,”Annalen der Physik und Chemie,38:573-587, 1889.
28.
28. Reuss, A. “Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle,”Zeitschrift für angewandte Mathematik und Mechanik,9:49-58, 1929.
29.
29. Hashin, Z. and S. Shtrikman. “A Variational Approach of the Theory of the Elastic Behaviour of Multiphase Materials,”Journal of the Mechanics and Physics of Solids,11:127-140, 1963.
30.
30. Brinksmeier, E., A. Horns and J. Mell. “Numerik der Kreuzkorrelationsmethode zur relativen Peaklagebestimmung in der röntgenographischen Eigenspannungsmessung,”Zeitschrift für Metallkunde,72:579-581, 1981.
31.
31. Reinsch, C. H.“Smoothing by Spline Functions,”Numerische Mathematik,10:173-183, 1967.
32.
32. Reinsch, C. H.“Smoothing by Spline Functions II,”Numerische Mathematik,16:451-454, 1971.
