Skip to main content
SpringerLink
Log in

Symmetric Laminates

  • Chapter
  • First Online:
Micromechanics of Composite Materials

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 186))

  • 4537 Accesses

Abstract

Laminated plates and shells are made by laying up and co-curing unidirectionally reinforced fibrous composite plies or laminae, which have different in-plane orientation and are ordered in a certain stacking sequence. Ply thicknesses are material system specific and their final magnitudes may depend on the fabrication procedure. Most polymer matrix composites are made using pre-impregnated or prepreg tapes or sheets, reinforced by tows consisting of many small diameter (<20 μm) fibers, which typically form ∼0.127 mm (0.005 in.) thick plies. Metal matrix laminates are often reinforced by monolayers of large diameter (150 μm) filaments, which yield ply thicknesses of ~0.200 mm (0.008 in.). Therefore, many plies are required to build up section thicknesses required in larger structures.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alberski, T.C. (2000). Ph.D. Dissertation, Rensselaer Polytechnic Institute.

    Google Scholar 

  • Ambartsumyan, S. A. (1970). Theory of anisotropic plates. Strength, stability, vibration (T. Cheron, Trans.). Stamford: Technomic Publishing.

    Google Scholar 

  • Bahei-El-Din, Y. A., Dvorak, G. J., & Wu, J.-F. (1992). Dimensional stability of metal-matrix laminates. Composites Science and Technology, 43, 207–219.

    Article  Google Scholar 

  • Christensen, R. M., & DeTeresa, S. J. (1992). Elimination/minimization of edge-induced stress singularities in fiber composite laminates. International Journal of Solids and Structures, 29, 1221–1231.

    Article  MATH  Google Scholar 

  • Christensen, R. M., & Zywicz, E. (1990). A three-dimensional constitutive theory for fiber composite laminated media. ASME Journal of Applied Mechanics, 57, 948–955.

    Article  Google Scholar 

  • Christensen, R. M. (1998) Two theoretical elasticity micromechanics models. J. Elasticity, 50, 15–25.

    Article  MATH  Google Scholar 

  • Daniel, I. M., & Ishai, O. (2006). Engineering mechanics of composite materials (2nd ed.). New York: Oxford University Press.

    Google Scholar 

  • Dvorak, G. J., Prochazka, P., & Srinivas, M. V. (1999). Design and fabrication of submerged cylindrical laminates I. International Journal of Solids and Structures, 36, 3917–3943.

    Article  MATH  Google Scholar 

  • Eshelby, J. D., Read, W. T., & Shockley, W. (1953). Anisotropic elasticity with applications to dislocation theory. Acta Metallurgica, 1, 251–259.

    Article  Google Scholar 

  • Flanagan, G. (1994). An efficient stress function approximation for the free-edge stresses in laminates. International Journal of Solids and Structures, 31, 941–952.

    Article  MATH  Google Scholar 

  • Hayashi, T. (1967). Analytical study of interlaminar shear stresses in a laminate composite plate. Transactions. Japan Society for Aeronautical and Space Sciences, 10, 43–48.

    Google Scholar 

  • Herakovich, C. T. (1998). Mechanics of fibrous composites. New York: Wiley.

    Google Scholar 

  • Kassapoglou, C., & Lagace, P. A. (1986). An efficient method for the calculation of interlaminar stresses in composite materials. ASME Journal of Applied Mechanics, 53, 744–750.

    Article  MATH  Google Scholar 

  • Kim, T., & Atluri, S. N. (1995a). Analysis of edge stresses in composite laminates under combined thermo-mechanical loading, using a complementary energy approach. Computational Mechanics, 16, 83–97.

    Article  MATH  Google Scholar 

  • Kim, T., & Atluri, S. N. (1995b). Optimal through-thickness temperature gradients for control of interlaminar stresses in composites. AIAA Journal, 33, 730–738.

    Article  MATH  Google Scholar 

  • Kovarik, V. (1989). Stresses in layered shells of revolution. Prague: Academia.

    MATH  Google Scholar 

  • Lekhnitskii, S. G. (1968). Anisotropic plates (Translated from 2nd Russian edition by S. W. Tsai, & T. Cheron, Gordon and Breach).

    Google Scholar 

  • Librescu, L. (1975). Elastostatics and kinetics of anisotropic and heterogeneous shell-type structures. Leyden: Noordhoff.

    MATH  Google Scholar 

  • Noor, A. K., & Burton, W. S. (1989). Assessment of shear deformation theories for multilayer composite plates. Applied Mechanics Reviews, 42, 1–13.

    Article  Google Scholar 

  • Ochoa, O. O., & Reddy, J. N. (1992). Finite element analysis of composite laminates. Dordrecht: Kluwer.

    Book  Google Scholar 

  • Pagano, N. J. (1969). Exact solutions for composite laminates in cylindrical bending. Journal of Composite Materials, 3, 398–411.

    Article  Google Scholar 

  • Pagano, N. J. (1978a). Stress fields in composite laminates. International Journal of Solids and Structures, 14, 385–400.

    Article  MATH  Google Scholar 

  • Pagano, N. J. (1978b). Free edge stress fields in composite laminates. International Journal of Solids and Structures, 14, 401–406.

    Article  MATH  Google Scholar 

  • Pagano, N. J., & Pipes, R. B. (1970). Interlaminar stresses in composite laminates under uniform axial extension. Journal of Composite Materials, 4, 538–548.

    Google Scholar 

  • Panc, V. (1975). Theories of elastic plates. Leyden: Noordhoff.

    Book  MATH  Google Scholar 

  • Reddy, J. N. (1997). Mechanics of laminated composite plates: Theory and analysis. New York: CRC Press.

    MATH  Google Scholar 

  • Reissner, E. (1950). On a variational theorem in elasticity. Journal of Mathematics and Physics, 29, 90–95.

    MathSciNet  MATH  Google Scholar 

  • Rose, C. A., & Herakovich, C. T. (1993). An approximate solution for interlaminar stresses in composite laminates. Composites Engineering, 3, 271–285.

    Article  Google Scholar 

  • Stroh, A. N. (1958). Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 3, 625–646.

    Article  MathSciNet  MATH  Google Scholar 

  • Suvorov, A. P., & Dvorak, G. J. (2001). Optimized fiber prestress for reduction of free edge stresses in composite laminates. International Journal of Solids and Structures, 38, 6751–6786.

    Article  MATH  Google Scholar 

  • Ting, T. C. T. (1996). Anisotropic elasticity: Theory and applications. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Vel, S. S., & Batra, R. C. (2000). The generalized plane strain deformations of thick anisotropic composite laminated plates. International Journal of Solids and Structures, 37, 715–733.

    Article  MATH  Google Scholar 

  • Wang, S. S., & Choi, I. (1982). Boundary-layer effects in composite laminates: Part I – Free-edge stress singularities. ASME Journal of Applied Mechanics, 49, 541–548.

    Article  MATH  Google Scholar 

  • Whitney, J. M. (1987). Structural analysis of laminated anisotropic plates. Lancaster: Technomic Publications Co.

    Google Scholar 

  • Yin, W. L. (1994a). Free-edge effects in anisotropic laminates under extension, bending and twisting, Part I: A stress-function-based variational approach. Journal of Applied Mechanics, 61, 410–415.

    Article  MATH  Google Scholar 

  • Yin, W. L. (1994b). Free-edge effects in anisotropic laminates under extension, bending and twisting, Part II: Eigenfunction analysis and the results for symmetric laminates. Journal of Applied Mechanics, 61, 416–421.

    Article  Google Scholar 

  • Bailey, J. E., Curtis, P. T., & Parvizi, A. (1979). On the transverse cracking and longitudinal splitting behaviour of glass and carbon fibre reinforced epoxy cross ply laminates and the effect of Poisson and thermally generated strain. Proceedings of the Royal Society of London, A366, 599.

    Google Scholar 

  • Budiansky, B., & Fleck, N. A. (1993). Compressive failure of fiber composites. Journal of the Mechanics and Physics of Solids, 41, 183–211.

    Article  Google Scholar 

  • Budiansky, B., & Fleck, N. A. (1994). Compressive kinking of fiber composites A topic review. Applied Mechanics Reviews, 47(6), Part 2, S246–S250.

    Google Scholar 

  • Chen, W., & Ravichandran, G. (1996). Static and dynamic compressive behavior of aluminum nitride under moderate confinement. Journal of the American Ceramic Society, 79, 579–584.

    Article  Google Scholar 

  • Chen, W., & Ravichandran, G. (1997). Dynamic compressive behavior of a glass ceramic under lateral confinement. Journal of the Mechanics and Physics of Solids, 45, 1303–1328.

    Article  Google Scholar 

  • Chen, W., & Ravichandran, G. (2000). Failure mode transition in ceramics under dynamic multiaxial compression. International Journal of Fracture, 101(1–2), 141–159.

    Article  Google Scholar 

  • Chen, W. W., Rajendran, A. M., Song, B., & Nie, Xu. (2007). Dynamic fracture of ceramics in armor applications. Journal of the American Ceramic Society, 90, 1005–1018.

    Article  Google Scholar 

  • Christensen, R. M. (2012). www.FailureCriteria.com

  • Christensen, R. M., & DeTeresa, S. J. (1997). The kink band mechanism for the compressive failure of fiber composite materials. ASME Journal of Applied Mechanics, 64, 1–6.

    Article  MATH  Google Scholar 

  • Cook, T. S., & Erdogan, F. (1972). Stresses in bonded materials with a crack perpendicular to the interface. International Journal of Engineering Science, 10, 677–697.

    Article  MATH  Google Scholar 

  • Crossman, F. W., & Wang, A. S. D. (1982). The dependence of transverse cracking and delamination on ply thickness in graphite/epoxy laminates. In Damage in Composite Materials (ASTM STP 775, p. 118). West Conshohocken: American Society for Testing and Materials.

    Google Scholar 

  • Delale, F., & Erdogan, F. (1979). Bonded orthotropic strips with cracks. International Journal of Fracture, 15, 343–364.

    Google Scholar 

  • Dvorak, G. J., & Prochazka, P. (1996). Thick-walled composite cylinders with optimal fiber prestress. Composites, 27B, 643–649.

    Google Scholar 

  • Dvorak, G. J., & Suvorov, A. (2000). Effect of fiber prestress on residual stresses and onset of damage in symmetric laminates. Composites Science and Technology, 60, 1929–1939.

    Article  Google Scholar 

  • Fleck, N. A. (1997). Compressive failure of fiber composites. In J. W. Hutchinson & T. Y. Wu (Eds.), Advances in applied mechanics (Vol. 33). New York: Academic.

    Google Scholar 

  • Garrett, K. W., & Bailey, J. E. (1977). Multiple transverse fracture in 90 ° cross-ply laminates of glass fibre-reinforced polyester. Journal of Materials Science, 12, 157–168.

    Article  Google Scholar 

  • Gooch, W. (2010). 2011 overview of the development of ceramic armor technology: Past, present and future. 35th International Conference on Advanced Ceramics & Composites, American Ceramic Society.

    Google Scholar 

  • Gudmundson, P., & Zhang, W. (1993). An analytical model for thermoelastic properties of composite laminates containing transverse cracks. International Journal of Solids and Structures, 30, 3211–3231.

    Article  MATH  Google Scholar 

  • Gupta, V., Argon, A. S., & Suo, Z. (1992). Crack deflection at an interface between two orthotropic media. ASME Journal of Applied Mechanics, 59, S79–S87.

    Article  Google Scholar 

  • Hashin, Z. (1985). Analysis of cracked laminates: A variational approach. Mechanics of Materials, 4, 121–136.

    Article  Google Scholar 

  • Hauver, G. E., Rapacki, E. J., Netherwood, P. H., & Benck, R. F. (2005). Interface defeat of long-rod projectiles by ceramic armor (Report ARL-TR-3950). U.S. Army Research Laboratory.

    Google Scholar 

  • Highsmith, A. L., & Reifsnider, K. L. (1982). Stiffness reduction mechanisms in composite laminates. In Damage in Composite Materials (ASTM STP 775, pp. 103–117). West Conshohocken: American Society for Testing and Materials.

    Google Scholar 

  • Ho, S., & Suo, Z. (1993). Tunneling cracks in constrained layers. ASME Journal of Applied Mechanics, 69, 890–894.

    Article  Google Scholar 

  • Kardomateas, G. A., & Philobox, M. S. (1995). Buckling of thick orthotropic cylindrical shells under combined external pressure and axial compression. AIAA Journal, 33, 1946–1953.

    Article  MATH  Google Scholar 

  • Kyriakides, S., Arseculeratne, R., Perry, E. J., & Liechti, K. M. (1995). On the compressive failure of fiber reinforced composites. International Journal of Solids and Structures, 32, 689–738.

    Article  MATH  Google Scholar 

  • Laws, N., & Dvorak, G. J. (1988). Progressive transverse cracking in composite laminates. Journal of Composite Materials, 22, 900–916.

    Article  Google Scholar 

  • Lu, M.-C., & Erdogan, F. (1983). Stress intensity factors in two bonded elastic layers containing cracks perpendicular to an interface, I. Analysis, II. Solution and results. Engineering Fracture Mechanics, 18, 491–528.

    Article  Google Scholar 

  • Luo, J., & Sun, C. T. (1991). Global-local methods for thermoelastic analysis of thick fiber-wound cylinders. Journal of Composite Materials, 25, 453–468.

    Google Scholar 

  • Malaise, F., Tranchet, J.-Y., & Collombet, F. (2000). Effects of dynamic confinement on the penetration resistance of ceramics against long rods. In M. D. Furnish, L. C. Chhabildas, & R. S. Hixson (Eds.), Shock compression of condensed matter-1999 (pp. 1121–1140). New York: AP Press.

    Google Scholar 

  • McCartney, L. N., & Schoeppner, G. N. (2002). Predicting the effect of non-uniform ply cracking on the thermoelastic properties of cross-ply laminates. Composites Science and Technology, 62, 1841–1856.

    Article  Google Scholar 

  • Nairn, J. A. (2006). On the calculation of energy release rates for cracked laminates with residual stress. International Journal of Fracture, 139, 267–293.

    Article  MATH  Google Scholar 

  • Praveen, G. N., & Reddy, J. N. (1998). Transverse matrix cracks in cross-ply laminates: Stress transfer, stiffness reduction and crack opening profiles. Acta Mechanica, 130, 227–248.

    Article  MATH  Google Scholar 

  • Sarva, S., Nemat-Nasser, S., McGee, J., & Isaacs, J. (2007). The effect of thin membrane restraint on the ballistic performance of armor grade ceramic tiles. International Journal of Impact Engineering, 34, 277–302.

    Article  Google Scholar 

  • Srinivas, M. V., Dvorak, G. J., & Prochazka, P. (1999). Design and fabrication of submerged cylindrical laminates-II: Effect of fiber prestress. International Journal of Solids and Structures, 36(26), 3945–3976.

    Article  MATH  Google Scholar 

  • Sun, C. T., & Li, S. (1988). Three-dimensional effective elastic constants for thick laminates. Journal of Composite Materials, 22, 629–639.

    Article  Google Scholar 

  • Suvorov, A., & Dvorak, G. J. (2001a). Optimized fiber prestress for reduction of free edge stresses in composite laminates. International Journal of Solids and Structures, 38, 6751–6786.

    Article  MATH  Google Scholar 

  • Suvorov, A., & Dvorak, G. J. (2001b). Optimal design of prestressed laminate/ceramic plate assemblies. Meccanica, 36, 87–109.

    Article  MATH  Google Scholar 

  • Suvorov, A., & Dvorak, G. J. (2002). Stress relaxation in prestressed composite laminates. ASME Journal of Applied Mechanics, 69, 459–469.

    Article  MATH  Google Scholar 

  • Wang, A. D. S. (1984). Fracture mechanics of sublaminate cracks in composite materials. Composites Technology Review, 6, 45.

    Article  Google Scholar 

  • Zhang, D., Ye, J., & Lam, D. (2007). Properties degradation induced by transverse cracks in general symmetric laminates. International Journal of Solids and Structures, 44, 5499–5517.

    Article  MATH  Google Scholar 

  • Christensen, R. M. (1998). Two theoretical elasticity micromechanics models. Journal of Elasticity, 50, 15–25.

    Article  MATH  Google Scholar 

  • Dvorak, G. J., & Teply, J. (1985). Periodic hexagonal array models for plasticity analysis of composite materials. In A. Sawczuk & V. Bianchi (Eds.), Plasticity today: Modeling, methods and applications (W. Olszak memorial volume, pp. 623–642). Amsterdam: Elsevier Scientific Publishing Company.

    Google Scholar 

  • Dvorak, G. J., & Johnson, W. S. (1980). Fatigue of metal matrix composites. International Journal of Fracture, 16, 585–607.

    Article  Google Scholar 

  • Dvorak, G. J., & Laws, N. (1987). Analysis of progressive matrix cracking in composite laminates. II. First ply failure. Journal of Composite Materials, 21, 309–329.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical, Aeronautical and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    George J. Dvorak

Authors
  1. George J. Dvorak
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Dvorak, G.J. (2013). Symmetric Laminates. In: Micromechanics of Composite Materials. Solid Mechanics and Its Applications, vol 186. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4101-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-4101-0_10

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4100-3

  • Online ISBN: 978-94-007-4101-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation