Abstract
Three-dimensional, thermomechanical constitutive equations and an associated correspondence principle are developed for a linear viscoelastic, unidirectional composite with growing damage. The type of damage modeled is transverse cracking, which is commonly observed in laminates consisting of unidirectional fiber layers. The equations allow for aging. First, the constitutive equations without damage are summarized. They are then modified to allow for time-dependent damage by means of a correspondence principle. This principle relates elastic and viscoelastic solutions in the time-plane; the familiar correspondence principle based on the Laplace transform is not applicable because of the aging and crack growth. Some existing, simplified micromechanical models for elastic media are extended to viscoelasticity and then used to demonstrate that the requirements of the correspondence principle are quite-well satisfied for realistic material behavior. The correspondence principle is developed in the Appendix. It generalizes a previously-developed principle for plane stress in fiber-composites to three-dimensional conditions, and is not limited to the specific type of damage covered in the body of the paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Daniel, I.M. and Ishai, O., Engineering Mechanics of Composite Materials, Oxford, New York, 1994.
Ferry, J.D., Viscoelastic Properties of Polymers, 3rd edn, John Wiley & Sons, New York, 1980.
Gibson, R.F., Principles of Composite Material Mechanics, McGraw-Hill, New York, 1994.
Ha, K. and Schapery, R.A., ‘A three-dimensional viscoelastic constitutive model for particulate composites with growing damage and its experimental validation’, International Journal of Solids and Structures 35, 1998, 3497–3517.
Han, W.H. and McKenna, G.B., ‘Plasticizer effects on physical aging of epoxy’, SPE ANTEC II, 1997, 1539–1545.
Han, W.H. and McKenna, G.B., ‘The influence of moisture on the physical aging response of epoxy: Experimental results and modeling considerations’, in Recent Developments in Durability Analysis of Composite Systems, A.H. Cardon, H. Fukuda, K.L. Reifsnider and G. Verchery (eds), A.A. Balkema, Rotterdam, 2000, 153–158.
Hashin, Z., ‘Analysis of composite materials-A survey’, Journal of Applied Mechanics 50, 1983, 481–505.
Hashin, Z., ‘Analysis of cracked laminates: A variational approach’, Mechanics of Materials 4, 1985, 121–136.
Lee, J.-W., Allen, D.H. and Harris, C.E., ‘The upper bounds of reduced axial and shear moduli in cross-ply laminates with matrix cracks’, in Composite Materials: Fatigue and Fracture, Vol. 3, ASTM STP 1110, T.K. O'Brien (ed.), American Society for Testing and Materials, Philadelphia, PA, 1991, 56–69.
Lemaitre, J., A Course on Damage Mechanics, Springer-Verlag, Berlin, 1992.
Lifshitz, J.M. and Rotem, A., ‘Time-dependent longitudinal strength of unidirectional fibrous composites’, Fiber Science and Technology 3, 1970, 1–20.
Lou, Y.C. and Schapery, R.A., ‘Viscoelastic characterization of a non-linear fiber-reinforced plastic’, Journal of Composite Materials 5, 1971, 208–234.
Lu, H., Zhang, X. and Knauss, W.G., ‘Uniaxial shear and Poisson relaxation and their conversion to bulk relaxation: Studies on Poly (methyl methacrylate)’, Polymer Engineering and Science 37, 1997, 1053–1064.
McKenna, G.B., ‘On the physics required for prediction of long term performance of polymers and their composites’, Journal on Research of the National Institute of Standards and Technology 99, 1994, 169–189.
Miyano, Y., Nakada, M., Kasamori, M. and Muki, R., ‘Effect of physical aging on the creep deformation of an epoxy resin’, Mechanics of Time-Dependent Materials 4, 2000, 9–20.
Moore, R.H. and Dillard, D.A., ‘Time-dependent matrix cracking in cross-ply laminates’, Composites Science and Technology 39, 1990, 1–12.
Noh, J. and Whitcomb, J.D., ‘Efficient techniques for predicting viscoelastic behavior of sublaminates’, in Proceedings of the American Society for Composites (ASC), September 24–27, O.O. Ochoa, T.K. O'Brien, D. Lagoudas and H.J. Sue (eds), Technomic Publishing Company, Lancaster, PA, 2000, 334–342.
Noh, J. and Whitcomb, J.D., ‘Effect of various parameters on the effective properties of a cracked ply’, Journal of Composite Materials 35, 2001a, 689–712.
Noh, J. and Whitcomb, J.D., ‘Effect of transverse matrix cracks on the relaxation moduli of linear viscoelastic laminates’, in Proceedings of the American Society for Composites (ASC), September 9–12, M.W. Hyer and A.C. Loos (eds), Technomic Publishing Company, Lancaster, PA, 2001b, Paper No. 099 on CD-Rom.
Park, S.W. and Schapery, R.A., ‘A viscoelastic constitutive model for particulate composites with growing damage’, International Journal of Solids and Structures 34, 1997, 931–947.
Park, S.W., Kim, Y.R. and Schapery, R.A., ‘A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete’, Mechanics of Materials 24, 1996, 241–255.
Raghaven, J. and Meshii, M., ‘Time-dependent damage in carbon fibre-reinforced polymer composites’, Composites Part A 27A, 1996, 1223–1227.
Schapery, R.A., ‘On the characterization of non-linear viscoelastic materials’, Polymer Engineering and Science 9, 1969, 295–310.
Schapery, R.A., ‘Viscoelastic behavior and analysis of composite materials’, in Mechanics of Composite Materials, G.P. Sendeckyj (ed.), Academic Press, New York, 1974, 85–168.
Schapery, R.A., ‘On viscoelastic deformation and failure behavior of composite materials with distributed flaws’, in Advances in Aerospace Structures and Materials, ASME Vol. AD-01, S.S. Wang and W.J. Renton (eds), ASME, New York, 1981, 5–20.
Schapery, R.A., ‘Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media’, International Journal of Fracture 25, 1984, 195–223.
Schapery, R.A., ‘Nonlinear viscoelastic and viscoplastic constitutive equations based on thermodynamics’, Mechanics of Time Dependent Materials 1, 1997a, 209–240.
Schapery, R.A., ‘Non-linear viscoelastic constitutive equations for polymers and polymeric composites with distributed damage’, in The Lazar M. Kachanov Symposium on Inelasticity and Damage in Solids Subject to Microstructural Change, I.J. Jordaan, R. Seshadri and I.L. Meglis (eds), Memorial University of Newfoundland, St. Johns, 1997b, 35–45.
Schapery, R.A., ‘Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage’, International Journal of Fracture 97, 1999, 33–66.
Schapery, R.A., and Sicking, D.L., ‘On nonlinear constitutive equations for elastic and viscoelastic composites with growing damage’, in Mechanical Behavior of Materials, A. Bakker (ed.), Delft University Press, Delft, 1995, 45–76.
Srirengan, K. and Whitcomb, J.D., ‘Finite element based degradation model for composites with transverse cracks’, Journal of Thermoplastic Composite Materials 11, 1998, 113–123.
Struik, L.C.E., Physical Aging in Amorphous Polymers and Other Materials, Elsevier, Amsterdam, 1978.
Whitney, J.M., Structural Analysis of Laminated Anisotropic Plates, Technomic, Lancaster, PA, 1987, 12.
Zocher, M.A., Allen, D.H. and Groves, S.E., ‘Stress analysis of a matrix-cracked viscoelastic laminate’, International Journal of Solids and Structures 34, 1997, 3235–3257.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schapery, R. Homogenized Constitutive Equations for Linear Viscoelastic Unidirectional Composites with Growing Transverse Cracks. Mechanics of Time-Dependent Materials 6, 101–131 (2002). https://doi.org/10.1023/A:1015077128800
Issue Date:
DOI: https://doi.org/10.1023/A:1015077128800