Replacing Costly Methods
The development of complex composite materials is both costly and time consuming. Numerous material processing conditions and constituents have to be assembled and tested before materials emerge that might be considered for a specific application. Additionally, each application requires specific material characteristics that might be achieved with a number of material solutions.
If analytical models can predict the correct thermostructural properties as well as the correct trends in properties as functions of the constituent and processing variables, then numerical material synthesis can replace the costly fabricate it and test approach. The output of the numerical material synthesis can provide direction to the material manufacturers relative to the constituents and processing regimes on which to focus for a given material application.
CLASS II-CFCC utilizes a number of material modeling modules that can represent the characteristics of CFCC materials. These modules are integrated into a comprehensive material analysis code to provide realistic material behavior models as needed. To date, such features as material porosity, particulate reinforcement, and damage within the fiber bundle have been incorporated into the program.
Material Model
The code maintains a database of constituent and layer properties for the user. As shown in Fig. 1, the constituents include fibers, matrices, particles, and layers. These form the basic building blocks for the composite analysis. All thermoelastic properties required for thermostructural analysis and thermal analyses are provided within the data base.
The layer and bundle property prediction module utilizes the composite cylinders assemblage module for transversely isotropic, temperature-dependent fibers and matrices. The user specifies the fiber, matrix, and fiber volume fraction, and the layer properties are computed. Additional capability includes the ability to model an imperfect interface between the fiber and matrix, using the formulations developed in ref. 1 (See references at end of article). Layer strengths are estimated using one of several popular strength models, refs. 2, 3, and 4.
Ceramic matrix composites employ coatings on the fibers to protect the fibers and to influence the fiber/matrix interface strength. A multiphase composite cylinders assemblage has been incorporated into the code based upon the work in refs. 5 and 6 (Fig. 2). Up to five concentric cylinders may be modeled, each being transversely isotropic and each having its own principal coordinate system parallel to one of the three global systems (i.e., axial, radial, circumferential).
Laminated Materials
Classical lamination theory for thin plates is used to model laminated materials. The lay-ups may be fully general and need not be symmetric or balanced. Through-the-thickness properties are also computed for the laminate. The through-the-thickness properties permit supplying full 3-D material thermoelastic constants for finite-element analyses.
Once composite properties have been computed, the user may elect to apply point stresses to the material to determine how the composite will respond. General forces, moments, strains, and curvatures may be applied to the laminate. A temperature gradient may be applied, and temperature-induced stresses from the stress-free state will be computed. Layer stresses and strains, as well as the phase average fiber and matrix stresses and strains, are available. The user may track how the material will fail. At each load step, the current secant composite properties may be viewed or printed, thus permitting one to generate a piece-wise linear stress- strain curve for the composite. The basic philosophy behind the code is shown in Fig. 3. It is assumed that the model begins at the subcomposite level, with definitions of fibers, matrices, particles, and voids.
The modules compute the effective properties of the basic material building blocks, and then combine them to form a composite, using the composite material definition supplied. Output permits supplying finite-element codes with the necessary composite properties such that the entire structure may be modeled. Given critical stress or strain states from the structural analysis, CLASS II-CFCC will conduct a point stress analysis of the composite, defining the subcell level and fiber and matrix phase average stress and strain states.
Microstructure Damage Modeling
Ceramic matrix composites are prone to the accumulation of damage within the matrix within the layers. Micro-cracking occurs in the matrix, resulting in a loss of stiffness of the composite. A statistical failure criteria is currently being integrated within the code for unidirectional bundles. This damage follows an assumed damage accumulation that is based on matrix statistical strength characteristics (Fig. 4, refs. 5 and 6 [see references at end of article]).
The matrix statistical strength characteristics are supplied for the matrix within a fiber bundle. The code computes the initial bundle properties, and then applies a stress increment. Matrix stresses are then computed, and the probability of cracking the matrix is computed. For a given microcrack density, the code integrates the effect of these micro-cracks on the composite stiffness, providing an estimate of the current material stiffness. This process is continued as shown in Fig. 5, until the fiber strength is exceeded or the matrix becomes fully cracked.
Data on both unidirectional and cross-ply materials has been obtained and correlated with the model predictions. Unidirectional test data was utilized to define effective matrix strengths for the material process, and then the properties of the cross ply materials were predicted. Some typical results are shown in Figs. 6, 7, and 8. The correlations with test data are excellent. Recognize that the model input parameters were defined by using data from Fig. 6 and the [0] material from Fig. 7.
Additional data correlations will be conducted as test data become available. The objective is to identify effective in situ constituent properties, which may then be utilized to predict the performance of alternative materials constructions to determine their suitability for the applications being considered.
Summary
The analytical models are sufficiently accurate to provide good estimates of the CFCC properties, provided that input constituent properties are representative. In cases in which constituent properties are only estimates, the model can still provide very valuable information because the general trends in the predicted properties may be assumed to be correct. The use of trends and sensitivities to determine which parameters are significant can provide the necessary fabrication direction. The CLASS II-CFCC code is available to program members for utilization. By using the analytical model, one can verify that the model predicts those properties that have been measured on a given material and then trust the analysis to provide those properties that have not yet been measured. Thus the analysis provides a Data Enhancement capability that can provide a full set of thermostructural properties.
1. Hashin, Z., "Thermoelastic Properties of Fiber Reinforced Composites with Imperfect Interfaces," Mechanics of Composite Materials, 1990, Vol.8, pp.333-348.
2. Tsai, S. W., and Wu, E. M., "A General Theory of Strength for Anisotropic Materials," Journal of Composite Materials, Jan.1971, Vol.5, pp.58-80.
3. Hashin Quadratic Interaction Hashin, Z., "Failure Criteria for Unidirectional Fiber Composites," Journal of Applied Mechanics, June 1980, Vol.47, pp.329-334.
4. Rosen, B. W., "Mechanics of Composite Strengthening in Fiber Composite Materials," Am. Soc. for Metals, Metals Park, Ohio, 1965.
5. Sullivan, B.J. and Hashin, Z., "Determination of Mechanical Properties of Interfacial Region between Fiber and Matrix in Organic Matrix Composites," 3rd Int. Conf. on Composite Interfaces, Case Western Reserve, Univ. of Cleveland, OH, May 1990.
6. Yen, C.F., Buesking, K.W., "Material Modeling for Unidirectional Glass and Glass-Ceramic Matrix Composites with Progressive Matrix Damage," ASTM 4th Symposium on Composite Materials, Fatigue and Fracture, May 1991, ASTM STP 1156.
Comments to: mgc@ornl.gov
Revised: July 7, 1995
