Microstructure Lectures

by

Ronald D. Kriz, Associate Professor
Engineering Science and Mechanics
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061


Table of Contents:

  1. Introduction
  2. Cracks: Atomistic - at Interfaces - in a Continuum
  3. Cracks Near Interfaces Between Dissimilar Isotropic Materials
  4. Introduction to Mechanical Behavior of Anisotropic Laminates
  5. Laminate Singularities Caused by Anisotropy: "Free-Edge Problem"
  6. Laminate Singularities Caused by Ply Cracks
  7. Cracks Near Interfaces Between Dissimilar Anisotropic Materials

    ------ Extension to a Homogeneous Continuum ------

  8. Cracks in Homogeneous Isotropic Materials
  9. Cracks in Homogeneous Anisotropic Materials
  10. Wave Propagation in Homogeneous Isotropic/Anisotropic Materials
  11. References

11.0 References

  1. Kriz, R.D., "Influence of Ply Cracks on Fracture Strength of Graphite/Epoxy Laminates at 76K", Effects of Defects in Composite Materials, ASTM STP 836, American Society for Testing and Materials, pp. 250-265, 1984.

  2. Broeck, D., Elementary Engineering Fracture Mechanics, Kluwer Academic Publishers Group, 1982.

  3. Eftis, J., Subramonian, N., and Liebowitz, H., "Crack Border Stress and Displacement Equations Revisited," Engineering Fracture Mechanics, Vol. 9, pp. 189-210, 1977.

  4. Williams, M. L., "The Stresses Around a Fault of Crack in Dissimilar Media," Bulletin of the Seismological Society of America, Vol. 49, No. 2, pp. 199-204, April, 1959

  5. Zak, A. R., and Williams, M. L., "Crack Point Stress Singularities at a Bi-Material Interface," GALCIT SM 62-1, California Institute of Technology, January, 1962.

  6. Nye, J. F., Physical Properties of Crystals, Oxford University Press, London, 1957.

  7. Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, Holden-Day, San Francisco, 1963.

  8. Frederick, D. and Chang, T. S., Continuum Mechanics, Scientific Publishers, Inc. Boston, 1972.

  9. Kriz, R.D. and Ledbetter, H.M., "Elastic Representation Surfaces of Unidirectional Graphite/Epoxy Composites," Recent Advances in Composites in the United States and Japan, ASTM STP 864, J.R. Vinson and M. Taya, Eds. American Society for Testing and Materials, Philadelphia, pp. 661-675, 1985.

  10. Kriz, R.D. and Stinchcomb, W.S., "Elastic Moduli of Transversely Isotropic Fibers and Their Composites," Experimental Mechanics, Vol. 19, pp. 41-49, 1979.

  11. Golfein, S., "Investigation of Structure of Graphite FIbers with the Goal of Improving Their Mechanical Properties," Internal Report AD-A013 524, Army Mobility Equipment Research and Development Center, Fort Belvoir, Virginia, 1974.

  12. Barnet, F.R. and Norr, M.K., "A Three-dimensional Structural Model for a High Modulus Pan-based Carbon Fibre," Composites, pp. 93-99, 1976.

  13. Ledbetter, H.M. and Kriz, R.D., "Elastic Wave Surfaces in Solids," Phys. Stat. Sol. (b) 114, p. 475, 1982.

  14. Musgrave, M.J.P., "On an Elastodynamic Classification of Orthorhombic Media," Proc. R. Soc. Lond. A374, p. 401, 1981.

  15. Kriz, R.D. and Ledbetter, M.M., "Elastic-wave Surfaces in Anisotropic Media," Rheology of Anisotropic Materials, C. Huet, D. Fourgoin, S. Richmond, Eds. CR 19 Coll. GFR Paris Nov. 1984 Editions CEPADUES, Toulouse, pp. 79-92, 1986.

  16. Kriz, R.D. and Heyliger, P.R., "Finite Element Model of Stress Wave Topology in Unidirectional Graphite/Epoxy: Wave Velocities and Flux Deviations,"Review of Progress in Quantitative Nondestructive Evaluation, Vol.8A, Plenum Publishing Corp., pg 141-148, 1989.

  17. Kriz, R.D. and Gary J.M., "Numerical Simulation and Visualization Models of Stress Wave propagation in Graphite/Epoxy Composites,"Review of Progress in Quantitative Nondestructive Evaluation, Vol.9, Plenum Publishing Corp., pg 125-132, 1990.

  18. Vandenbossche, B. and Kriz, R.D.,and Oshima, T." Stress Wave Displacement Polarizations and Attenuation in Unidirectional Composites: Theory and Experiment, "J. Research In Nondestructive Evaluation, Vol. 8, No. 2, pp. 101-123, 1996.

  19. Jones, B., Mechanics of Composite Materials, McGraw Hill, 1975.

  20. Ashton, J.E. and Whitney, J.M., "Theory of Laminated Plates", Technomic Publishing Co., Inc., Stamford Conn., 1969.

  21. Kriz, R.D. and Stinchcomb, W.W., "Effects of Moisture, Residual Thermal Curing Stresses, and Mechanical Load on the Damage Development in Quasi-Isotropic Laminates," Damage in Composite Materials, ASTM STP 775, American Society for Testing and Materials, 1982, pp.63-80.

  22. Kriz, R.D., "Edge Stresses in Woven Laminates at Low Temperatures," Composite Materials: Fatique and Fracture, Second Volume, ASTM STP 1012, Paul A Lagace, Ed., American Society for Testing and Materials, 1989, pp. 150-161.

  23. R. B. Pipes and N.J. Pagano, "Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension", J. Composite Materials, Vol. 4, pp.538-548, 1970.

  24. Stroh, A.N., "Steady State Problems in Anisotropic Elasticity,", J. Mathematics and Physics, Vol. 41, pp. 77-103, 1962.

  25. Ting, T.C.T and Chou, S.C., "Stress Singularities in Laminated Composites," Fracture of Composite Materials, eds. G.C. Sih and V.P. Tamuzs, 1982, Martinus Nijhoff, Proceedins of the 2nd USA-USSR Symposium, Lehigh Univ., Bethlehem, PA, March 9-12, 1981, pp. 265-277, 1982.

  26. Ting, T.C.T. and Hoang, P.H., "Singularities at the Tip of a Crack Normal to the Interface of an Anisotropic Layered Composite," Int. J. Solids and Structures, Vol. 20, No. 5, pp. 439-454, 1984.

  27. Tewary, V. K. and Kriz, R. D., "Generalized Plane strain Analysis of Bimaterial Composite a Free Surface Normal to the Interface", Journal of Material Research, Vol. 13, pp. 2609-2622, 1991.

  28. Tewary, V.K. and R. D. Kriz, "Effect of a Free Surface on Stress Distribution in a Bimaterial Composite", NIST Special Publication 802, National Institute of Standards and Technology, U.S. Gov. Printing Office, Washington D.C., March 1991.

  29. Benzley, S.E., "Representation of Singularities with Isoparametric Finite Elements," Int. J. Numerical Methods in Engineering, Vol. 8, pp. 537-545, 1974.

  30. Mirza, F.A. and Olson, M.D., "The Mixed Finite Element Method in Plane Elasticity," Int. J. Numerical Methods in Engineering, Vol. 15, pp. 273-289, 1980.

  31. Heyliger, P.R. and Kriz, R.D., "Stress Intensity Factors by Enriched Mixed Finite Elements," Int. J. Numerical Methods in Engineering, Vol. 28, 1461-1473, 1989.

Send comments to: rkriz@vt.edu
Ronald D. Kriz, Short Bio
Engineering Science and Mechanics
College of Engineering
Virginia Tech
Blacksburg, Virginia 24061

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