Abstract
A review of the micromechanics of composites is given herein. This includes the concepts of geometric scales, the representative volume element, and volume averaging of state variables in the representative volume element. These concepts are first reviewed for composites composed of linear elastic constituents and then extended to include the case of composites with time dependent microcracks. A brief review is then given of recent micromechanics solutions which include the effects of damage. Results are discussed for both laminated composites and composites with one or more inelastic phases.
The development of locally averaged damage dependent constitutive equations is discussed, and evolution laws for damage accumulation are reviewed. Finally, a brief overview of the role of micromechanics in life prediction is presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jones, R.M.: Mechanics of Composite Materials. McGraw-Hill 1975.
Hill, R.: Elastic Properties of Reinforced Solids: Some Theoretical Principles. J. Mech. Phys. Solids 11 (1963) 357–372.
Hashin, Z.: Analysis of Composite Materials. J. Appl. Mech. 50 (1983) 481–505.
Eringen, A.C.: Continuum Mechanics at Atomic Scale. Crystal Lattice Defects 7 (1977) 109.
Eringen, A.C.: Theory of Nonlocal Elasticity and Some Applications. Res. Mechanica, 21 (1987) 213.
Taya, M.; Arsenault, R.J.: Metal Matrix Composites. New York: Pergamon 1989.
Eldridge, J.L.; Honecy, F.S.: Interface Characterization. HITEMP Review 1989, NASA Conference Publication 10039 (1989) 4–1–4–10.
Hashin, Z.; Rosen, B.W.: The Elastic Moduli of Fiber-Reinforced Materials. J. Appl. Mech. 31 (1964) 223.
Hill, R.: A Self-Consistent Mechanics of Composite Materials. J. Mech. Phys. Solids 13 (1965) 213–222.
Budiansky, B.: On the Elastic Moduli of Some Heterogeneous Materials. J. Mech. Phys. Solids 13 (1965) 223.
Eshelby, J.D,: The Continuum Theory of Lattice Defects. Progress in Solid State Physics, F. Seitz and D. Turnbull, Eds. New York: Academic Press 3 (1956) 79.
Mori, T.; Tanaka, K.: Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions. Acta Metallurgica 21 (1973) 571–574.
Benveniste, Y.: A New Approach to the Application of Mori-Tanaka’s Theory in Composite Materials. Mechanics of Materials 6 (1987) 147–157.
Teply, J.L.: Periodic Hexagonal Array Model for Plasticity Analysis of Composite Materials. Ph.D. Dissertation, The University of Utah 1984.
Hashin, Z.: Analysis of Orthogonally Cracked Laminates under Tension. J. Appl. Mech. (1987).
Han, Y.M.; Hahn, H.T.; Croman, R.B.: A Simplified Analysis of Transverse Ply Cracking in Cross-Ply Laminates. Composites Science and Technology 31 (1988) 165–177.
Tsai, C.-L.; Daniel, I.M.; Lee, J.-W.: Progressive Matrix Cracking of Crossply Composite Laminates Under Biaxial Loading. Microcracking-Induced Damage in Composites, G.J. Dvorak and D.C. Lagoudas, Eds., American Society of Mechanical Engineers, AMD 111 (1990) 9–18.
Highsmith, A.L.; Stinchcomb, W.W.; Reifsnider, K.L.: Stiffness Reduction Resulting from Transverse Cracking in Fiber-Reinforced Composite Laminates. Virginia Polytechnic Institute and State University, VPI-E-81.33 (1981).
Lee, J.W.; Allen, D.H.; Harris, C.E.: Internal State Variable Approach for Predicting Stiffness Reductions in Fibrous Laminated Composites with Matrix Cracks. Journal of Composite Materials 23 No. 12 (1989) 1273–1291.
Allen, D.H.; Lee, J.W.: Matrix Cracking in Laminated Composites Under Monotonic and Cyclic Loadings. Microcracking-Induced Damage in Composites, G.J. Dvorak and D.C. Lagoudas, Eds., American Society of Mechanical Engineers, AMD Vol. 111 (1990)65–76.
Lee, J.W.; Allen, D.H.: Harris, C.E.: The Upper Bounds of Reduced Axial and Shear Moduli in Cross-Ply Laminates with Matrix Cracks. Composite Materials: Fatigue and Fracture (Third Volume), ASTM STP 1110, T.K. O’Brien, Ed., American Society for Testing and Materials, Philadelphia (1991) 56–69.
Nairn, J.A.: The Strain Energy Release Rate of Composite Microcracking: A Variational Approach. J. Composite Materials 23 (1989) 1106–1127.
Lee, S.W.; Aboudi, J.: Analysis of Composite Laminates with Matrix Cracks. Report No. CCMS-88-03, Virginia Tech Center for Composite Materials and Structures (1988).
Laws, N.; Dvorak, GJ.; Hejazi, M.: Stiffness Changes in Unidirectional Composites Caused by Crack Systems. Mechanics of Materials 2, North Holland (1983) 123–137.
Whitcomb, J.D.: Analysis of Delamination Growth Near Intersecting Ply Cracks. Center for Mechanics of Composites Report No. 91-1, Texas A&M University, 1991.
Aboudi, J.: Constitutive Relations for Cracked Metal Matrix Composites. Mechanics of Materials 6 (1987) 303–315.
Aboudi, J.: Constitutive Equations for Elastoplastic Composites with Imperfect Bonding. International Journal of Plasticity 4 (1988) 103–125.
Tvergaard, V.: Micromechanical Modelling of Fibre Debonding in a Metal Reinforced by Short Fibres. Proc. IUTAM Symposium on Inelastic Deformation of Composite Materials, Troy, N.Y., G.J. Dvorak, Ed., Springer-Verlag (1990) 99–114.
Boyd, J.G.; Jones, R.H.; Allen, D.H.: The Effect of Laminate Thickness on Fiber/Matrix Debonding in Metal Matrix Composites. Anisotropy and Localization of Plastic Deformation, Proc. of Plasticity’ 91: The Third International Symposium on Plasticity and its Current Applications, J-P. Boehler and A.S. Kahn, eds., Elsevier (1991) 11–14.
Boyd, J.G.; Allen, D.H.; Highsmith, A.L.: A Self-Consistent Thermoviscoplastic Constitutive Model for Short-Fiber Composites. Microcracking-Induced Damage in Composites, G.J. Dvorak and D.C. Lagoudas, Eds., American Society of Mechanical Engineers, AMD Vol. 111 (1990) 141–150.
Boyd, J.G.; Allen, D.H.: A Thermo-Viscoplastic Micromechanics Model for Short Fiber Composites. Proc. ASME Winter Annual Meeting 1991 (to appear).
Allen, D.H.; Boyd, J.G.; Jones, R.H.: Analysis of Effects of Matrix Viscoplasticity on Damage Evolution in Metal Matrix Composites. Proc. Sixth Technical Conference, American Society for Composites, Albany, New York (1991) to appear.
Lerch, B.A.; Hull, D.R.; Leonhardt, T.A.: Microstructure of a SiC/Ti-15-3 Composite. Composites 21 No. 3 (1990) 216–224.
Cosserat, E.; Cosserat, F.: Theorie des Corps Deformable. Paris: Hermann (1909).
Erickson, J.L.; Truesdell, C: Exact Theory of Stresses and Strains in Rods and Shells, Arch. Rational Mech. Anal. 1 (1958) 295–323.
Green, A.E. Rivlin, R.S.: Multipolar Continuum Mechanics. Arch. Rational Mech. Anal. 17(1964) 113–147.
Green, A.E.; Rivlin, R.S.: Simple Force and Stress Multipole. Arch. Rational Mech. Anal. 17 (1964) 325–353.
Suquet, P.M.: Local and Global Aspects in the Mathematical Theory of Plasticity. Plasticity Today: Modelling, Methods and Applications, A. Sawczuk and G. Biahchi, Eds., Elsevier (1985) 279–310.
Stolz, C.: General Relationships between Micro and Macro Scales for the Non-Linear Behaviour of Heterogeneous Media. Modelling Small Deformations of Polycrystals, J. Gittus and J. Zarka, Eds., Elsevier (1986) 89–115.
Lo, D.C.; Allen, D.H.; Buie, K.D.: Damage Prediction in Laminated Composites with Continuum Damage Mechanics. Proc. ASCE Materials Engineering Conference, Denver (1990).
Allen, D.H.; Lo, D.C.: A Model for the Progressive Failure of Laminated Composite Structural Components. Proc. ASME Winter Annual Meeting, American Society of Mechanical Engineers (1991) to appear.
Rice, J.R.; Rudnicki, J.W.: A Note on Some Features of the Theory of Localization of Deformation. Int. J. Solids Structures 16 (1980) 597–605.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag, Berlin Heidelberg
About this paper
Cite this paper
Allen, D.H., Boyd, J.G. (1992). Micromechanics as a Basis for Damage Mechanics. In: Reddy, J.N., Reifsnider, K.L. (eds) Local Mechanics Concepts for Composite Material Systems. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84792-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-84792-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84794-3
Online ISBN: 978-3-642-84792-9
eBook Packages: Springer Book Archive