ABSTRACT of the Doctoral Thesis

Derivation and Finite Element Implementation of Constitutive Material Laws for Multiphase Composites Based on Mori-Tanaka Approaches

by Heinz E. Pettermann (1997)

In recent years composite materials have proved highly attractive for structural applications both due to their technical merit and their economical potential. An important feature of such materials is their inherent capability for their overall properties to be tailored, i.e. the materials can be "designed" to meet certain demands.

Research in the the field of micromechanics of materials aims to obtain a deeper understanding of the behavior of composites and other inhomogeneous materials by improving the insight into the mechanisms of interaction between the constituents on the microlevel and their effect on the overall behavior.

As a foundation of the present work an overview of some basic analytical methods in micromechanics is given. One of these standard analytical approaches, viz. the Mori-Tanaka method, serves as the basis for extensions to nonaligned inclusions and nonlinear material behavior. The derivation of the pertinent equations and the computer implementation are described in detail. Examples are given in order to discuss the results, with respect to both their quality and their practical relevance for applications of such materials.

A Mori-Tanaka mean field approach for predicting the overall thermoelastic properties of multi-phase composites with given orientation distributions of the inclusion phases is derived in chapter 3. This approach is used to study the influence of the inclusion orientation distribution on the effective material properties. The aim of the present study is primarily to understand the effects of the inclusion orientations in short fiber reinforced composites and to identify the basic mechanisms of interaction between the phases which govern the overall thermo-elastic behavior.

Perfectly aligned discontinuous fibers, various orientation distributions as well as random orientations of the inclusions are studied. The overall Young's moduli, shear moduli, and coefficients of thermal expansion as well as the onset of yielding of the matrix phase under thermal and mechanical loading conditions are predicted. The results are evaluated both in terms of the orientation distributions of the inclusions and in terms of the direction dependences of the predicted overall moduli. From these findings useful information on the requirements for the design of composite materials and composite structures can be obtained.

In chapter 4 the global behavior of a two phase composite consisting of aligned thermo-elastic reinforcements embedded in an thermo-elasto-plastic matrix is described by an incremental Mori-Tanaka method. The main features of this approach are the description of the nonlinear matrix phase behavior by incremental plasticity, and an appropriate handling of the breakdown of isotropy of the matrix phase upon yielding. Using the proposed formulation for calculating both the micro scale states of the phase materials and the macro scale state of the composite, the overall thermo-elasto-plastic behavior of the composite can be evaluated for general plastic deformations. This algorithm is implemented as a material model for a finite element code, allowing structural analyses of composite components. To obtain an efficient algorithm an implicit solving strategy is used.

The applicability of the method is shown by investigating a continuously reinforced metal matrix composite. Material characterization under various simple loading conditions and a structural analysis of a hybrid component consisting of a monolithic and a composite part are performed. As a further potential application the investigation of the global deformation behavior of a functionally graded material is demonstrated. The latter application also requires a formulation for thermo-elasto-plastic inclusions in an thermo-elastic matrix phase which is obtained in analogy to the introduced MMC type description.

revised 970305 (hjb)