Chapter 6 Mechanics of Multidirectional Carbon-Carbon Composite Materials John J. Kibler Materials Sciences Corporation Blue Bell, Pennsylvania Abstract 170 Symbols 170 Introduction 170 Background 172 Characteristics of CC Materials 175 Description of Model 176 Method of Analysis 179 Multidirectional Composite Model 179 Degraded Properties Model 181 Thin CC Composites 182 Property Predictions and Data Correlation 183 Effects of Degraded Properties 188 Concluding Remarks 191 References 193 Abstract This chapter describes the mechanics of analyzing carbon-carbon (CC) composite materials from the structural analyst's point of view. The peculiarities of CC material as well as their influences upon the material behavior are discussed. Many assumptions must be made regarding some of the material parameters; an intelligent approach to making those assumptions is presented. Material models for evaluating thermoelastic properties of fiber composite materials having a spatial distribution of fiber orientations are discussed. The approach is to construct a material model with a finite number of fiber orientations in a repeating unit cell. This basic material model is a mini-mechanical model based upon the concept that a material system can be regarded as an assemblage of unit cells. Symbols Ea modulus in axial fiber direction, Msi 3r modulus in transverse fiber direction, Msi Ez composite modulus in a fiber (z) direction, Msi GA fiber ^ial shear modulus, Msi Al/l .\ thermal expansion in axial fiber direction Al/lx thermal expansion in transverse direction VAT Poisson's ratio in axial direction Vtt Poisson's ratio in transverse direction Introduction The successful use of CC materials in numerous applications has led the engineering community to view CC as a viable material for other applications. Because this material is expensive and not a simple off-the-shelf material, the type of composite which is best suited for any given application must be considered; that is, one cannot simply place an order for a given number of pounds of CC composite. As with most composites, the reinforcement type and complexity must be defined to determine which is best suited for the application. Then the user must define the environment and the complexity of the stress states which must be carried by the material. Given a definition of the desired material type, the user must work with the material manufacturers to develop the specific material and processing approach for the given application. The complexity of the material needed for a given application must be defined. For instance, if the loading is primarily in one plane and attachment loads will not be significant, then a two dimensionally reinforced material may be the right choice. However, three-dimensional reinforcement may be a better choice if the loading is complex or if the part must be relatively thick. Three-dimensional (3-D) materials, braids, and multiaxial weaves all provide reinforcement in more than two directions and therefore may be capable of carrying more complex loading conditions. The penalty for using a multidimensional weave is the increase in material costs and the reduction of in-plane properties in order to add fibers in the extra directions. Consequently, material selection is a major part of the development of new applications for these complex materials. These comments are true not only for CC materials but also for multidirectional composites in general. Therefore, the ability to synthesize material properties and to predict the performance (and, hence weaknesses) of a structure made of these materials is both necessary and important to the development of new materials. It should be obvious that the efficient use of materials and material development dollars requires that the material be designed for (at a minimum) each generic component. Analysis of these materials requires that the analyst understand the structure and the performance of the materials under given conditions. In this chapter, CC from an engineering mechanics point of view is addressed; descriptions of analytical models that are capable of modeling the material at the subcell level also are discussed. Even if the material to be used for a given application is defined, the structural analyst is faced with the question of how to analyze the structure using this material and how to determine its potential failure modes. The peculiarities of CC material which make it unique from an analyst's point are discussed first. The influence of these characteristics on mechanical and thermal properties is noted, followed by approaches to modeling the material. Thermal protection materials for such high-performance applications as rocket nozzles and reentry vehicle nose tips can be fabricated with a wide range of constituent mechanical and thermal properties and with various internal geometries utilizing three-dimensional arrays of fibers. The performance of the resulting material will be a function of such variables as choice of fiber (or fibers, in combination), weave parameters, type of matrix material, and the temperature, pressure history, and number of cycles experienced during the fabrication process. Because of the large number of variables and the high unit cost for test specimens (particularly when the material under consideration is of the CC class), direct evaluation of the relative performance capability of candidate materials is expected to be a time-consuming and costly approach. The alternative approach is the utilization of reliable material guidance models. The mini-mechanics approach to modeling composite materials is a balance between the micro- and macro-mechanics approaches. A macro-mechanics material model treats a composite as a homogeneous but anisotropic material. Using this effective material, the heterogeneity of the composite material is ignored and, consequently, realistic (microlevel) failure mechanisms are difficult to be treated as part of the design failure criterion. A macro-mechanics approach cannot be utilized as a predictive tool for the thermomechanical properties of materials not yet fabricated or tested, and this approach is of limited assistance in the development of new materials. The macro-mechanics approach, however, does permit structural design analyses to be performed using state-of-the-art analytical techniques. At the other extreme, a micro-mechanics model treats each distinct subregion of the material in an attempt to find a detailed solution for the local stresses and strains. With this approach, failure prediction becomes dependent upon details of the internal geometry such as fiber placement within a fiber bundle. This results in a complex methodology which is sensitive to local variables that are not readily defined by the material construction parameters. However, micro-mechanics solutions for specific regions within the unit cell can provide an important function in the construction of a material model. The mini-mechanics model developments described herein were incorporated into computer codes for treatment of properties of CC materials reinforced by fibers in three or more spatial directions. Comparisons between the predicted and experimental results demonstrate excellent agreement for elastic constants and thermal expansion coefficients. A combination of micro- and mini-mechanics approaches is used at Materials Sciences Corporation (MSC) for modeling these materials. In particular, a model for fiber bundle and matrix properties was incorporated into a laminate analysis model for predicting properties. The success of this approach is discussed in a following section. Background A large number of alternative methods to define the effective properties of composite structural materials exist; however, the work in the area of threedimensional composites is quite limited. Certain methods for structural composites can play a role in material modeling for the more complex composites. These composites may be defined as quasiregular arrays of yams (characteristically carbon or graphite) oriented in three or more nonplanar directions and embedded within a matrix of phenolic, carbon, or graphite. There is a regularity to the internal geometry; however, numerous geometric imperfections do exist. Nonuniformity is found in filament spacing within the impregnated yarn bundle and in voids and microcracks within the matrix. |