A micromechanical model for interpenetrating multiphase composites

Abstract The dependence relation between the macroscopic effective property and the microstructure of interpenetrating multiphase composites is investigated in this paper. The effective elastic moduli of such composites cannot be calculated from conventional micromechanics methods based on Eshelby’s tensor because an interpenetrating phase cannot be extracted as dispersed inclusions. Employing the concept of connectivity, a micromechanical cell model is presented for estimating the effective elastic moduli of composites reinforced with either dispersed inclusions or interpenetrating networks. The model includes the main features of stress transfer of interpenetrating microstructures. The Mori–Tanaka method and the iso-stress and iso-strain assumptions are adopted in an appropriate manner of combination, rendering the calculation of effective moduli quite easy and accurate.

[1]  Wade Babcock,et al.  Computational materials science , 2004 .

[2]  Siegfried Schmauder,et al.  Self-consistent matricity model to simulate the mechanical behaviour of interpenetrating microstructures , 1999 .

[3]  Jaromír Slavík,et al.  COMPUTATIONAL MECHANICS I , 2004 .

[4]  M. Lethiecq,et al.  Effective electroelastic moduli of 3-3(0-3) piezocomposites , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[5]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[6]  S. Torquato.  Random Heterogeneous Materials , 2002 .

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

[8]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

[9]  L. Gibson,et al.  The mechanical behaviour of interpenetrating phase composites – II: a case study of a three-dimensionally printed material , 2000 .

[10]  S. Torquato,et al.  Elastic Properties and Structure of Interpenetrating Boron Carbide/Aluminum Multiphase Composites , 2004 .

[11]  L. Walpole,et al.  On the overall elastic moduli of composite materials , 1969 .

[12]  L. E. Cross,et al.  Connectivity and piezoelectric-pyroelectric composites , 1978 .

[13]  L. Gibson,et al.  The mechanical behaviour of interpenetrating phase composites – I: modelling , 2000 .

[14]  S. Torquato,et al.  GEOMETRICAL-PARAMETER BOUNDS ON THE EFFECTIVE MODULI OF COMPOSITES , 1995 .

[15]  Siegfried Schmauder,et al.  SIMULATION OF INTERPENETRATING MICROSTRUCTURES BY SELF CONSISTENT MATRICITY MODELS , 1998 .

[16]  Interpenetrating Phase Composites , 1992 .