Modeling and Design

With the advent of powerful computers and robust software, computational modeling has emerged as a very informative and cost effective tool for materials design and analysis. Modeling often can both eliminate costly experiments and provide more information than can be obtained experimentally. Computational modeling has clearly played an important role in FGM research to date, and because of the considerable complexity involved, is expected to play an even greater role in future developments. This chapter introduces some of the common approaches used in modeling FGMs, identifies the major difficulties involved, and, it is hoped, provides useful guidance for future simulation efforts. It focuses mainly on continuum models of the bulk response of FGMs due to thermal or mechanical loading.

[1]  Subra Suresh,et al.  Elasto-plastic deformation of compositionally graded metal-ceramic composites , 1997 .

[2]  S. Suresh,et al.  Fundamentals of functionally graded materials , 1998 .

[3]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[4]  Panos Tsakiropoulos,et al.  A generalized law of mixtures , 1994 .

[5]  Salvatore Torquato,et al.  Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties , 1991 .

[6]  W. Voigt.  Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper , 1889 .

[7]  Hideaki Tsukamoto,et al.  A Unified Micromechanical Approach toward Thermomechanical Tailoring of Metal Matrix Composites. , 1992 .

[8]  F. Jones,et al.  Single fibre fragmentation test for assessing adhesion in fibre reinforced composites , 1998 .

[9]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[10]  S. Shtrikman,et al.  A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials , 1962 .

[11]  K. S. Ravichandran,et al.  Elastic Properties of Two‐Phase Composites , 1994 .

[12]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[13]  S. B. Biner.  A numerical analysis of time dependent stress fields ahead of stationary interface cracks at creep regime—Part I. Interface cracks in bimaterials , 1997 .

[14]  Robert J. Asaro,et al.  A micromechanical study of residual stresses in functionally graded materials , 1997 .

[15]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[16]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  Hugh A. Bruck,et al.  Evaluating microstructural and damage effects in rule-of-mixtures predictions of the mechanical properties of Ni-Al2O3 composites , 1999 .

[18]  Steven M. Arnold,et al.  Thermoelastic theory for the response of materials functionally graded in two directions with applications to the free-edge problem , 1995 .

[19]  Joseph R. Zuiker,et al.  The effective properties of functionally graded composites—I. Extension of the mori-tanaka method to linearly varying fields , 1994 .

[20]  C. Nan.  Physics of inhomogeneous inorganic materials , 1993 .

[21]  J. Gurland,et al.  The law of mixtures applied to the plastic deformation of two- phase alloys of coarse microstructures , 1988 .

[22]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[23]  S. Y. Lee,et al.  Mechanical Performance of ZrO2-Ni Functionally Graded Material by Powder Metallurgy , 1997 .

[24]  Richard L. Williamson,et al.  Finite element analysis of thermal residual stresses at graded ceramic‐metal interfaces. Part I. Model description and geometrical effects , 1993 .

[25]  E. H. Kerner.  The Elastic and Thermo-elastic Properties of Composite Media , 1956 .