Micromechanics and Inhomogeneity pp 341-365 | Cite as
Thermomechanical Hysteresis and Analogous Behavior of Composites
Abstract
A stress analysis gives a simple account of the observed thermal hysteresis of copper with tungsten fibers, in terms of the frictional matrix yield stress. Initial experiments at room temperature on the mechanical hysteresis of copper with high volume fractions of tungsten fibers are reported and discussed in terms of a phenomenological model, in which the frictional matrix flow stress and the reversible matrix mean stress are both split into “elastic,” “plastic,” and “thermal” terms. The model allows separate measurements to be made of plastic friction, and the experimental results confirm Brown and Clarke’s modification of the Orowan mechanism. The possibility of extending the established mean field theory to coupled elasto-electromagnetic behavior is discussed briefly.
Keywords
Bauschinger Effect Thermal Hysteresis Thermal Residual Stress Matrix Friction Analogous BehaviorPreview
Unable to display preview. Download preview PDF.
References
- Albers, W. (1978), Physical properties and design for non-structural applications of composite materials, in Advances in Composite Materials, edited by G. Piatti, Applied Science, London, pp. 185–207.Google Scholar
- Ashby, M. F. (1966), Work hardening of dispersion-hardened crystals, Phil. Mag., 14, 1157–1178.ADSCrossRefGoogle Scholar
- Brown, L. M. (1979), Precipitation and dispersion hardening, Proceedings of the 5th International Conference on Strength of Metals and Alloys, Aachen, 27–31 August 1979, edited by P. Haasen, V. Gerold, and Kostorz, G., Pergamon, Oxford 1980, pp. 1551–1571.Google Scholar
- Brown, L. M. and Stobbs, W. M. (1971), The work-hardening of copper—silica. I. A. model based on internal stresses, with no plastic relaxation, Phil Mag., 23, 1185–1199.ADSCrossRefGoogle Scholar
- Brown, L. M. and Clarke, D. R. (1977), The workhardening of fibrous composites, with particular reference to the copper-ungsten system, Acta Metallurgica, 25, 563–70.CrossRefGoogle Scholar
- Cheskis, H. P. and Heckel, R. W. (1968), In-situ measurements of deformation behaviour of individual phases in composites by X-ray diffraction, in Metal Matrix Composites, ASTM-STP-438, ASTM, New York, pp. 76–1.Google Scholar
- Eshelby, J. D. (1957), The determination of the elastic field of an ellipsoidal inclusions, and related problems, Proc. Roy. Soc. London, A241, 376–396.MathSciNetMATHGoogle Scholar
- Eshelby, J. D. (1959), The elastic field outside an ellipsoidal inclusion, Proc. Roy. Soc. London, A252, 561–569.MathSciNetMATHGoogle Scholar
- Garrett K. W. and Rosenberg H. M. (1974), The thermal conductivity of epoxyresin/powder composite materials, J. Phys. D: Appl. Phys., 7, 1247–1258.ADSCrossRefGoogle Scholar
- Haasen, P. (1972), Mechanical, magnetic and superconductor hardening by precipitates, Mater. Sci. Engng., 9, 191–196.CrossRefGoogle Scholar
- Hashin, Z. (1970), Theory of composite materials, in Mechanics of Composite Materials, edited by F. W. Wendt, H. Liebowitz, and Perrone, N., Pergamon, Oxford, pp. 201–242.Google Scholar
- Hill, R. (1963), Elastic properties of reinforced solids: Some theoretical principles, J. Mech. Phys. Solids, 11, 357–372.ADSMATHCrossRefGoogle Scholar
- Hill, R. (1964), Theory of mechanical properties of fibre-strengthened materials. I. Elastic behaviour. II. Inelastic behaviour, J. Mech. Phys. Solids, 12, 199–219.MathSciNetADSCrossRefGoogle Scholar
- Kerner, E. H. (1956), The elastic and thermoelastic properties of composite media, Proc. Phys. Soc. London, 69B, 808.Google Scholar
- Kelly, A. and Lilholt, H. (1969), Stress—strain curve of a fibre-reinforced composite, Phil. Mag., 20, 311–328.ADSCrossRefGoogle Scholar
- Kittel, C. (1971), Introduction to Solid State Physics, 4th ed., Wiley, New York, pp. 766.Google Scholar
- Laws, N. (1973), On the thermostatics of composite materials, J. Mech. Phys. Solids, 21, 9–17.ADSCrossRefGoogle Scholar
- Lilholt, H. (1977), Hardening in two-phase materials-I. Strength contributions in fibre-reinforced copper-tungsten, Acta Metallurgica, 25, 571–585.CrossRefGoogle Scholar
- Maxwell, J. C. (1892), A Treatise of Electricity and Magnetism, vol. 1, 3rd ed., Clarendon, Oxford, pp. 440.Google Scholar
- Nye J. F. (1957), Physical Properties of Crystals, Their Representation by Tensors and Matrices, 4th ed., Clarendon, Oxford, pp. 322.MATHGoogle Scholar
- Orowan, E. (1959), Causes and effects of internal stresses, Proceedings of the Symposium on Internal Stresses and Fatigue in Metals, Detroit and Warren, 4–5 September 1958, edited by G. M. Rassweiler and W. L. Grube, Elsevier, Amsterdam, pp. 59–80.Google Scholar
- Pedersen, O. B. (1978), Transformation theory for composites, Z. Angew. Math. Mech., 58, 227–228.Google Scholar
- Pedersen, O. B. (1979), Thermoelasticity and plasticity of composite materials, Proceedings of the 3rd International Conference on Mechanical Behaviour of Materials, Vol. 3, Cambridge, 20–24 August 1979, edited by K. J. Miller and R. F. Smith, Pergamon, Oxford, pp. 263–273.Google Scholar
- Pedersen, O. B. (1983), Thermoelasticity and plasticity of composites-I. Mean field theory, Acta Metallurgica, 31, 1795–1808.CrossRefGoogle Scholar
- Pedersen, O. B. (1984), Mean field theory and the Bauschinger effect in composites, in Fundamentals of Deformation and Fracture, Proceedings of the IUTAM Eshelby Memorial Symposium, Sheffield, April 1984, edited by B. A. Bilby, K. J. Miller, and J. R. Willis, Cambridge University Press, Cambridge, 1985, pp. 263–273.Google Scholar
- Pedersen, O. B. (1985), Residual stresses and the strength of metal matrix composites, Proceedings 5th International Conference on Composite Materials, San Diego, 29 July-30 August 1985, edited by W. C. Harrigan, J. Strife, and A. K. Dhingra, The Metallurgical Society of AIME, New York, pp. 1–20.Google Scholar
- Pedersen, O. B. (1988), Dislocations and the strength of metallic composites, in Mechanical and Physical Properties of Metallic and Ceramic Composites, Proceedings 9th Rise International Symposium on Metallurgy and Materials Science, Risø National Laboratory, Roskilde, Denmark, 5–9 September 1988, edited by S. I. Andersen, H. Lilholt, and O. B. Pedersen, Rise National Laboratory, pp. 157–182.Google Scholar
- Pedersen, O. B., and Brown, L. M. (1977), Equivalence of stress and energy calculations of mean stress, Acta Metallurgica, 25, 1303–1305.CrossRefGoogle Scholar
- Pedersen, O. B. and Lisiecki, L. L. (1988), The effect of temperature on cyclic saturation in copper, Proceedings of 8th International Conference on Strength of Metals and Alloys, Tampere, 22–26 August 1988, edited by P. O. Kettunen, T. K. Lepistö, and M. E. Lehtonen, Pergamon, Oxford, pp. 719–724.Google Scholar
- Poulsen, F. W. (1985), Composite electrolytes, in Transport-Structure Relations in Fast Ion and Mixed Conductors, Proceedings 6th Rise International Symposium on Metallurgy and Materials Science, Rise National Laboratory, Roskilde, Denmark, 9–13 September 1985, edited by F. W. Poulsen, N. H. Andersen, K. Clausen, S. Skaarup, and O. T. Sorensen, Rise National Laboratory, 1988, pp. 67–78.Google Scholar
- Tanaka, K. and Mori, T. (1970), The hardening of crystals by non-deforming particles and fibres, Acta Metallurgica, 18, 931–941.CrossRefGoogle Scholar
- Tanaka, K. and Mori, T. (1971), The hardening rate of fibre-strengthened materials, Phil. Mag., 23, 737–740.ADSCrossRefGoogle Scholar
- Tanaka, K. and Mori, T. (1973), Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, 21, 571–574.CrossRefGoogle Scholar
- Taya, M. (1988), Modelling of physical properties of metallic and ceramic composites: Generalized Eshelby model, in Mechanical and Physical Properties of Metallic and Ceramic Composites, Proceedings 9th Riso International Symposium on Metallurgy and Materials Science, Rise National Laboratory, Roskilde, Denmark, 5–9 September 1988, edited by S. I. Andersen, H. Lilholt, and O. B. Pedersen, Rise National Laboratory, pp. 201–231.Google Scholar
- Taya, M. and Mura, T. (1981), On stiffness and strength of an aligned short fiber reinforced composite containing fiber-end cracks under uniaxial applied stress, J. Appl. Mech., 48, 361–367.ADSMATHCrossRefGoogle Scholar
- Truesdell, C. and Toupin, R. (1960), The classical field theories, Encyclopedia of Physics, vol. IIIl, Principles of Classical Mechanics and Field Theory, edited by S. Flügge, Springer Verlag, Berlin, pp. 226–793.Google Scholar
- Walpole, L. J. (1966), On bounds for the overall elastic moduli of inhomogeneous systems—I, J. Mech. Phys. Solids, 14, 151–162.ADSMATHCrossRefGoogle Scholar
- Wakashima, K., Otsuka, M, and Umekawa, S. (1974), Thermal expansions of heterogeneous solids containing aligned ellipsoidal inclusions, J. Composite Materials, 8, 391–404.CrossRefGoogle Scholar
- Wakashima, K., Suzuki, Y., and Umekawa, S. (1979), A micromechanical prediction of initial yield surfaces of unidirectional composites, J. Composite Materials, 13, 288–302.CrossRefGoogle Scholar
- Wilson, D. V. (1965), Reversible work-hardening in alloys of cubic metals, Acta Metallurgica, 13, 807–814.CrossRefGoogle Scholar