In this paper, a damage constitutive model based on a micro-mechanical approach is established and used to predict the macro-microscopic elastic-brittle mechanical behavior of continuous fiber reinforced ceramic matrix composites (CFCC). Anisotropic damage is applied to describe the matrix phase damage which reflects all types of damage such as nucleation and coalescence of voids and micro-cracks that the matrix material undergoes. The asymptotic expansion homogenization method is used to obtain the effective mechanical properties of composites and to derive the homogenized damage elastic concentration factor and the gross stiffness matrix of unidirectional and cross-ply laminate composite materials. Internal variables are introduced to describe the evolution of the damage state and the degradation of the material stiffness. Using the proposed theory, the unidirectional composite and the cross-ply laminate composites with /03/90/03/, /03/902/03/, and /03/903/03/ stacking sequences are analyzed, and the numerical results are consistent with those of the experiments.

The scope of this book is based on the keynote lectures delivered during the Inter national Symposium on Anisotropic Behaviour of Damaged Materials ABDM, held in Krakow-Przegorzaiy, Poland, September 9-11, 2002. The Symposium was organized by the Solid Mechanics Division of the Institute of Mechanics and Machine Design - Cracow University of Technology, under aus pices of the Dean of the Faculty of Mechanical Engineering, Cracow University of Technology, Prof. S. Michalowski. The Co-organizers of the ABDM Symposium were: • Martin-Luther-Universitat Halle-Wittenberg, • Centre of Excellence for Advanced Materials and Structures AMAS at the In stitute of Fundamental Technological Research of the Polish Academy of Sci ences, Warsaw, • Committee of Mechanics of the Polish Academy of Sciences, Warsaw. Ten chapters of this book in their present form essentially exceed lectures de livered at the Symposium. They should rather be read as not only author's recent achievements in the field, but also the state of art and synthesis done by the lead ers in the mechanics community. The mixed formula of the Symposium, namely: the invited lectures and presentations of the original papers by the participants was used. 23 original papers, published in the Symposium Proceedings on CD, exhaust the full scope of the ABDM Symposium. The present book provides a survey of various damage models focusing on the damage response in anisotropic materials as well as damage-induced anisotropy.

Engineering materials show a pronounced heterogeneity on a smaller scale that influences the macroscopic constitutive behavior. Algorithms for the periodic discretization of microstructures are presented. These are used within the Nonuniform Transformation Field Analysis (NTFA) which is an order reduction based nonlinear homogenization method with micro-mechanical background. Theoretical and numerical aspects of the method are discussed and its computational efficiency is validated.

A consistent and systematic theory is developed for the analysis of damage mechanisms in metal matrix composites (MMCs). The theory involves both analytical and experimental procedures for the quantification of certain types of damage in MMCs. The analytical model involves both overall and local approaches to characterize damage in these materials. A series of experiments are conducted for micro- and macro-structural characterization of the MMC. Experiments were conducted on a titanium aluminide SiC-reinforced metal matrix composite. Center-cracked plates with laminate layups of (0/90)s, and (+/-45)s were tested under uniaxial tension. In order to investigate and model damage evolution, each of the specimens is loaded to different load levels ranging from fracture load down to 70% of the fracture load. Scanning electron microscopy (SEM) is performed on representative cross-sections of the damaged specimens. The measured crack densities are then used to define the damage parameters that are used in the theoretical model ... Metal matrix composites, Scanning electron microscopy, Damage parameters, Plasticity, Finite elements.

"Finite element modeling framework based on cohesive damage modeling, constitutive material behavior using user-material subroutines, and extended finite element method (XFEM), are developed for studying the failure behavior of continuous fiber-reinforced ceramic matrix composites (CFCCs) by the example of a silicon carbide matrix reinforced with silicon carbide fiber (SiC/SiCf) composite. This work deals with developing comprehensive numerical models for three problems: (1) fiber/matrix interface debonding and fiber pull-out, (2) mechanical behavior of a CFCC using a representative volume element (RVE) approach, and (3) microstructure image-based modeling of a CFCC using object oriented finite element analysis (OOF). Load versus displacement behavior during a fiber pull-out event was investigated using a cohesive damage model and an artificial neural network model. Mechanical behavior of a CFCC was investigated using a statistically equivalent RVE. A three-step procedure was developed for generating a randomized fiber distribution. Elastic properties and damage behavior of a CFCC were analyzed using the developed RVE models. Scattering of strength distribution in CFCCs was taken into account using a Weibull probability law. A multi-scale modeling framework was developed for evaluating the fracture behavior of a CFCC as a function of microstructural attributes. A finite element mesh of the microstructure was generated using an OOF tool. XFEM was used to study crack propagation in the microstructure and the fracture behavior was analyzed. The work performed provides a valuable procedure for developing a multi-scale framework for comprehensive damage study of CFCCs"--Abstract, page iv.

As multi-phase metal/alloy systems and polymer, ceramic, or metal matrix composite materials are increasingly being used in industry, the science and technology for these heterogeneous materials has advanced rapidly. By extending analytical and numerical models, engineers can analyze failure characteristics of the materials before they are integrat