MNSMS  Vol.4 No.3 , July 2014
Micromechanical Analysis of Thermal Expansion Coefficients
Author(s) Christian Karch
ABSTRACT
Thermal expansion coefficients play an important role in the design and analysis of composite structures. A detailed analysis of thermo-mechanical distortion can be performed on microscopic level of a structure. However, for a design and analysis of large structures, the knowledge of effective material properties is essential. Thus, either a theoretical prediction or a numerical estimation of the effective properties is indispensable. In some simple cases, exact analytical solutions for the effective properties can be derived. Moreover, bounds on the effective values exist. However, in dealing with complex heterogeneous composites, numerical methods are becoming increasingly important and more widely used, because of the limiting applicability of the existing (semi-)analytical approaches. In this study, finite-element methods for the calculation of effective thermal expansion coefficients of composites with arbitrary geometrical inclusion configurations are discussed and applied to a heterogeneous lightning protection coating made from Dexmet&#174 copper foil 3CU7-100FA and HexPly&#174 epoxy resin M21. A short overview of some often used (semi-)analytical formulas for effective thermal expansion coefficients of heterogeneous composites is given in addition.

Cite this paper
Karch, C. (2014) Micromechanical Analysis of Thermal Expansion Coefficients. Modeling and Numerical Simulation of Material Science, 4, 104-118. doi: 10.4236/mnsms.2014.43012.
References
[1]   Hashin, Z. (1983) Analysis of Composite Material—A Survey. Journal of Applied Mechanics, 50, 481-505.
http://dx.doi.org/10.1115/1.3167081

[2]   Nemat-Nasser, S. and Hor, H. (1999) Micromechanics. Elsevier, Amsterdam.

[3]   Hill, R. (1963) Elastic Properties of Reinforced Solids: Some Theoretical Principles. Journal of the Mechanics and Physics of Solids, 11, 357-372.
http://dx.doi.org/10.1016/0022-5096(63)90036-X

[4]   Geers, M., Kouznetseva, V. and Brekelsman, M. (2011) Scale Transition in Solid Mechanics Based on Computational Homogenization. CSIM Lecture Notes, Eindhoven University of Technology, Eindhoven.

[5]   Hyer, M.W. (2009) Stress Analysis of Fiber-Reinforced Composite Materials. DEStech Publications, Inc., Lancaster.

[6]   Voigt, W. (1889) Theoretische Studien über die Elastizit?tsverh?ltnisse der Krystalle. Annalen der Physik, 38, 573-587.
http://dx.doi.org/10.1002/andp.18892741206

[7]   Reuss, A. (1922) Berechnung der Flie?grenze von Kristallen auf Grund der Plastizit?tsbedingung für Einkristalle. Zeitschrift für angewandte Mathematik und Mechanik, 9, 49-58.

[8]   Turner, P.S. (1946) Thermal Expansion Stresses in Reinforces Plastics. Journal of Research of the National Bureau of Standards, 37, 239-250.
http://dx.doi.org/10.6028/jres.037.015

[9]   Levin, V.M. (1967) Thermal Expansion Coefficient of Heterogeneous Materials. Mechanics of Solids, 2, 58-61.

[10]   Hashin, Z. and Shtrikman, S.A. (1962) A Variational Approach to the Theory of the Elastic Behavior of Polycrystals. Journal of the Mechanics and Physics of Solids, 20, 343-352.
http://dx.doi.org/10.1016/0022-5096(62)90005-4

[11]   Rosen, B.W. and Hashin, Z. (1970) Effective Thermal Expansion Coefficients and Specific Heat of Composite Materials. International Journal of Engineering, 8, 157-173.
http://dx.doi.org/10.1016/0020-7225(70)90066-2

[12]   Schapery, R.A. (1968) Thermal Expansion Coefficient of Composite Materials Based on Energy Principles. Journal of Composite Materials, 2, 380-404.
http://dx.doi.org/10.1177/002199836800200308

[13]   Van Fo Fy, G.A. (1966) Elastic Constants and Thermal Expansion of Certain Bodies with Inhomogeneous Regular Structure. Soviet Physics, Doklady, 11, 176-182.

[14]   Budiansky, B. (1970) Thermal and Thermoelastic Properties of Isotropic Composites. Journal of Composite Materials, 4, 286-295.
http://dx.doi.org/10.1177/002199837000400301

[15]   Chamberlain, N.J. (1968) Derivation of Expansion Coefficients for a Fibre Reinforced Composites. BAC SON(P) Report 33, British Aircraft Corporation, London.

[16]   Karch, C. and Wulbrand, W. (2013) Thermomechanical Damage of Protected CFRP Structures Caused by Lightning Continuous Currents, SEA2013-20.1. International Conference on Lightning and Static Electricity (ICOLSE), Seattle, 2013, 20.1-20.13.

[17]   Lepetit, B., Escure, C., Guinard, S., Revel, I. and Peres, G. (2011) Thermo-Mechanical Effects Induced by Lightning on Carbon Fiber Composite Materials. International Conference on Lightning and Static Electricity (ICOLSE), Oxford, 2011.

[18]   Karch, C. and Wulbrand, W. (2013) Contributions of Lightning Current Pulses to Mechanical Damage of Protected CFRP Structures: Part 1—Theoretical Survey. CTO/IW-SE-2013-063, EADS, Munich.

[19]   Barbero, E.J. (2011) Introduction to Composite Materials Design. CRC Press, New York.

[20]   Kelly, A. (1989) Conciseencyclopaedia of Composite Materials. Pergamon Press, Oxford.

[21]   Khare, G.A., Chandra, N. and Silvain, J.-F. (2008) Application of Eshelby’s Tensor and Rotation Matrix for the Evaluation of Thermal Transport Properties Composites. Mechanics of Advanced Materials and Structures, 15, 117-129.

[22]   Milton, G.W. (2002) The Theory of Composites. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511613357

 
 
Top