Dd Robertson

Modeling damage in unidirectional ceramic-matrix composites

Abstract This paper extends the modified shear-lag model developed previously to analyze the damage progression within a unidirectional fiber-reinforced ceramic-matrix composite subject to quasi-static loading. The damage mechanisms considered in this paper are matrix cracking, fiber/matrix interfacial debonding, interfacial slip and fiber failure. Crack density is determined analytically through the introduction of a ‘critical matrix strain energy’. A priori knowledge of the composites ‘proportional limit’ yields a complete closed-form stress/strain solution. The influence of the interfacial shear stress, the interfacial bond strength and the composite proportional limit on the progression of matrix cracking and interfacial debonding are reported. The unloading behavior, including stress/strain hysteresis, is also modeled in terms of interfacial frictional slip within debonded regions.

Micromechanical relations for fiber-reinforced composites using the free transverse shear approach

The formulation of a new three-dimensional micromechanical model for fiber reinforced material is presented. It is based on the relaxation of the coupling effect between the normal and shear stresses. The simplicity of the model lends itself very well to the inclusion of nonlinear behavior while maintaining the three-dimensional capability. Present nonlinear capabilities that have been added to the model include a thermoelastic-plastic analysis employing the Prandtl-Reuss flow relations with a strain hardening parameter and both isotropic and kinematic hardening. Results from the present analysis are compared in different cases with their counterparts from finite element solutions and experiment. In addition, this micromechanical analysis is extended to model a weak fiber/matrix bond.

Micromechanical analysis for thermoviscoplastic behavior of unidirectional fibrous composites

Abstract A three-dimensional micromechanics formulation for fiber-reinforced composites containing viscoplastic matrix materials is presented. The micromechanics model is based on the relaxation of the coupling effect between the normal and shear stresses. Three variations of Bodners theory of viscoplasticity are used to predict the thermoviscoplastic behavior of unidirectional metal-matrix composites; first, the original isotropic-hardening model of Bodner and Partom; second, Ramaswamys extension of the theory through the inclusion of a back stress; and third, Stouffer and Bodners extension of the theory through a special form of directional hardening. Comparisons with numerical solutions and experimental data of other researchers are made to demonstrate the accuracy of the model. Micromechanical analyses of metal-matrix composites under both in-phase and out-of-phase thermomechanical fatigue-loading conditions are also presented for comparison with experiments and previous models.

A non-linear micromechanics-based analysis of metal-matrix composite laminates

Abstract This paper presents a formulation that performs a direct assembly of a set a equations that relates ply stresses to the constituent microstresses and microstrains up through to the laminate level for any ply layup. The basic tenet of the non-linear laminate formulation in this analysis is that assumptions of the classical laminated plate (CLP) theory for the strain variation in the laminate still apply. Complete details of this analysis from the micromechanics level to the laminate level are presented, and appropriate results of the stress/strain response predictions for monotonic and cyclic applied loads are compared to their analytical and experimental counterparts from previous studies. The non-linear effects of viscoplasticity and fiber/matrix debonding are included in the present formulation, and their impact on both crossply and quasi-isotropic laminates of metal-matrix composites undergoing thermomechanical fatigue loads are examined.

Micromechanical analysis of metal matrix composite laminates with fiber/matrix interfacial damage

Abstract A nonlinear micromechanics based laminate analysis and a statistical representation for failure are combined to model the fiber/matrix interfacial damage on the composite behavior. The micromechanical analysis is based on the method of cells formulation [Aboudi (1989). Applied Mechanics Review 42(7), 193–221]. The statistical approach is based on a Gaussian distribution of the fiber-matrix interfacial stresses coupled with interfacial failure strength. This statistical representation is then modified through a linear approximation so it may be incorporated into the laminate analysis to model interfacial failure readily with minimum empirical constants. The results from the present study are compared with the experimental and finite element data of titanium-based metal matrix laminates with unidirectional and crossply layups from previous studies which demonstrate excellent agreement.

Modeling of Fatigue in Cross-Ply Ceramic Matrix Composites:

This study proposes a methodology for modeling the fatigue response of cross-ply ceramic matrix composites (CMCs). The micromechanics based analysis and failure criteria are formulated to model stress-strain hysteresis, strain ratchetting and S-N behavior specific to room-temperature cyclic loading environments. The damage mechanisms considered are matrix cracking in the 90° and 0° plies, fiber/matrix interfacial debonding, fiber fracture, and fiber pull-out. These damage modes are modeled by a set of failure criteria with a minimum reliance on empirical data which can be easily employed in a variety of numerical and analytical techniques. The predicted results are found to be in good agreement with the experimental data; however, it is observed that the assumed degradation in the frictional resistance along the fiber/matrix interface plays a dominant role in determining the fatigue response.

Incorporating fiber damage in a micromechanical analysis of metal matrix composite laminates

A micromechanics based formulation involving the method of cells is developed to analyze metal matrix composite behavior in the presence of fiber fragmentation. The effects of fiber fracture are accounted for by determining an instantaneous effective fiber modulus from a modified chain-of-bundles approach. The analysis assumes a uniform density of fiber breakage throughout the composite. This crack density is determined from Weibull statistics whose parameters may be obtained from single-fiber tests or estimated. The ultimate strength of titanium-based metal matrix composite (MMC) laminates as well as their inelastic stress-strain response in the presence of fiber fragmentation are predicted from the present analysis which are in good agreement with the experimental counterparts. Also, the applicability of the present analysis to predict the low cycle/high stress fatigue lives of MMC laminates is demonstrated.

A Simplified Approach for Modeling Fatigue of Unidirectional Ceramic Matrix Composites

An analytical methodology is developed to model the response of unidirectional ceramic matrix composites (CMCs) under monotonic and fatigue loadings at room temperature. The analysis is presented as a first step toward analyzing the fatigue behavior of CMCs at elevated temperatures. The laminate is modeled using a modified shear-lag analyses in which the microstructural damage is estimated using simple damage criteria. Moreover, the damage mechanisms considered in this study are matrix cracking, fiber/matrix interfacial debonding and slip, fiber fracture, and fiber pullout. A simple criterion for estimating the average matrix crack density is developed and compared with classical fracture mechanics techniques. Additionally, a formulation for modeling the fatigue response of ceramic composites including stress-strain hysteresis and strain ratchetting is presented. The stress-strain response under monotonic tensile loading, and the fatigue life (S-N relationship) and stress-strain hysteresis under cyclic loading obtained from the present analytical methodology are compared with their experimental counterparts. They are in good agreement with one another.

Modeling of matrix failure in ceramic matrix composites

This paper investigates failure criteria used in modeling matrix failure in unidirectional and cross-ply laminates of ceramic matrix composites. In particular, the critical matrix strain energy (CMSE) criterion, as recently introduced by the authors, is examined in detail. In principle, a failure criterion, such as CMSE, which does not require many empirical constants, is desired. This CMSE approach provides a simple closed-form estimate for the matrix crack density in ceramic matrix composites when subjected to monotonic tensile loading. The proposed criterion can be easily extended to more complex loading conditions (for example, fatigue) and laminate geometries. Other matrix failure criteria, available in the literature, are also discussed. The CMSE criterion does an adequate job of estimating the evolution of matrix damage in both unidirectional and cross-ply laminates.

Modeling behavior of cross-ply ceramic matrix composites under quasi-static loading

This paper presents a simplified analysis (model and failure criteria) for predicting the stress-strain responce of cross-ply fiber-reinforced ceramic composite laminates under quasi-static loading and unloading conditions. The model formulation is an extension of the modified shear-lag theory previously introduced by the authors for analyzing unidirectional laminates for the same loading conditions. The present formulation considers a general damage state consisting of matrix cracking in both the transverse and longitudinal plies, as well as fiber failure. These damage modes are modeled by a set of failure criteria with the minimum reliance on empirical data, and can be easily employed in a variety of numerical or analytical methods. The criteria used to estimate the extent of matrix cracking and interfacial debonding are closed-form and require the basic material properties. The failure criterion for fiber failure requires a priori knowledge of a single empirical constant. This parameter, however, may be determined without microscopic investigation of the laminate microstructure. The results from the present simplified analysis match well with the experimental data.