Alain Burr

Micro-mechanics and continuum damage mechanics

SummaryContinuum Damage Mechanics has been applied successfully to technical problems since the idea was introduced by Kachanov almost 40 years ago. In keeping with the traditions of mechanics, the formulation was based on the results of mechanical tests on specimens whose size is measured in centimeters. To model the observations which describe the deterioration of material properties it was found necessary to introduce internal variables referred to as ‘damage’. The approach is phenomenological, with only a minimal attempt to provide a physical interpretation of damage. For this reason the approach has had little appeal to those whose interest is in the physical mechanisms which cause material deterioration. In this presentation a description is given of attempts to develop continuum damage mechanics so that the relationship with the physical mechanism approach is less abrupt. The procedure is illustrated with reference to ceramic matrix composites.

Matrix cracking and debonding of ceramic-matrix composites

The effects of matrix cracking and debonding which occur in ceramic-matrix composites are described by a micromechanical model. The cracking and debonding processes induce loss of stiffness, inelastic strains, hysteresis loops and crack closure. These features are analysed within the framework of Continuum Mechanics by the introduction of internal variables identified in the micromechanical analysis. The evolution laws of the internal variables can be determined by combining the experimental data with micromechanical modeling. The influences of residual stress fields due to processing are also included. Comparisons are made between theoretical predictions and the results of experiments performed on layered materials.

On the mechanical behaviour under cyclic loading of ceramic matrix composites

Abstract In this paper, a constitutive law is presented to model the mechanical behaviour of ceramic matrix composites. It allows matrix-cracking, interfacial debonding, sliding and wear to be accounted for in the framework of continuum mechanics. Based upon micromechanical studies, a 1D and 2D model was derived. An application was performed on a [0,90] SiC/SiC composite.

The behavior of ceramic-matrix composites under thermo-mechanical cyclic conditions

The thermo-mechanical behavior of ceramic-matrix composites is analyzed in the framework of continuum damage mechanics through the introduction of internal variables. The choice of these variables is based upon the study of a micromechanical model describing the degradation mechanisms that have been observed in the material. The model identification is performed by studying two tension tests. The model is then used to predict the result of a Iosipescu shear test. An extension for cyclic and thermal loadings is presented.

Ultimate tensile strength during fatigue of fiber-reinforced ceramic-matrix composites

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Ultimate tensile strength during fatigue of fiber-reinforced ceramic-matrix composites François Hild, Alain Burr

Isochronous analysis of the behaviour of ceramic-matrix composites under thermomechanical cyclic loading conditions

The design of components made of ceramic-matrix composites requires computations of both fatigue and creep responses. Micromechanical analyses under monotonic loading conditions have been integrated within the framework of continuum thermodynamics. The extension to creep and/or fatigue loadings usually leads to a description of the state of the material with a large number of internal variables. In the present paper, an isochronous approach is presented in order to decrease this number, and therefore to give an answer with current computational facilities in a time equivalent to calculations for monotonic loading conditions. The main objective of this paper is to present and illustrate an original method that allows the designer to simplify the computation of the long-term analyses (i.e. fatigue, creep) to reduce the CPU time down to a monotonic analysis.

On the continuum description of damage in fiber-reinforced composites

In this paper, the derivation of a mechanism-based constitutive law is presented to model the mechanical behavior of fiber-reinforced composites. It allows to account for matrix-cracking, inter facial debonding and sliding in the framework of Continuum Damage Mechanics. Applications are performed on a unidirectional SiC/SiC composite and on concrete specimens.

Damage, Fatigue, and Failure of Ceramic-Matrix Composites

Matrix cracking, interfacial debonding and sliding, fiber breakage and fiber pullout induced loss of stiffness, inelastic strains, hysteresis loops, and crack closure. These mechanisms are analyzed within the framework ofcontinuum mechanics through the introduction of internal variables. Two models that are faithful to the micromechanical analysis are studied. They provide guidance on the choice of the relevant internal variables to describe the mechanical behavior of unidirectional fiber-reinforced composites. Ultimate strength properties of fiber-reinforced composites are derived and compared with results related to localization. Extensions to cyclic load histories are discussed in terms of ultimate strength reached after cycling.

On the mechanical behavior of fiber-reinforced composites

Abstract In this paper, the derivation of the state potential is presented to model the mechanical behavior of fiber-reinforced composites. It allows matrixcracking, interfacial debonding and sliding to be accounted for in the framework of Continuum Damage Mechanics. An application is performed on a unidirectional SiC/SiC composite.

SECTION 10.7 – Behavior of Ceramic—Matrix Composites under Thermomechanical Cyclic Loading Conditions

This chapter proposes a constitutive law for ceramic-matrix composites (CMCs) which models matrix cracking, interface sliding and wear, fiber breakage, and fiber pullout and creep. These different mechanisms induce loss of stiffness, inelastic strains, creep strains, hysteresis loops, and crack closure. The features are analyzed within the framework of continuum damage mechanics (CDM) by the introduction of physical internal variables. The focus is to develop a continuum description of the damage processes which is mechanism-based and which is used to describe the behavior of CMCs under the conditions of multiaxial stress occurring in practice. By combining CDM with micromechanical studies which are mechanism based, constitutive equations are developed which lend themselves to the finite element procedures commonly used in practice. The CDM formulation applied to reinforced composites is written within the framework of the continuum thermodynamics. The chapter demonstrates matrix cracking, sliding occurs at the fiber-matrix interface which causes inelastic deformations. The model is integrated into a finite element system (ABAQUS) and is used to estimate the behavior of a representative structures under monotonic, cyclic, and creep loading conditions.