Normalized diagrams for micromechanical estimates of the elastic response of composite materials
- PDF / 1,444,376 Bytes
- 13 Pages / 612 x 792 pts (letter) Page_size
- 55 Downloads / 146 Views
DUCTION
expensive than the aforementioned analytical approaches in terms of both modeling effort and computational requirements. The purpose of the present work is to provide easy access to a number of well-known analytical descriptions of the influence on the overall elastic moduli of two-phase materials of (1) the elastic moduli of constituents, (2) the inclusion morphology, (3) the inclusion orientation, and (4) the volume fraction of reinforcement. The models forming the basis of the diagrams comprise Hashin–Shtrikman (H–S)-type bounds,[1,16,17] Mori–Tanaka-type mean-field approaches,[4,18] and classical self-consistent schemes (SCSs).[2,3] The mathematical expressions corresponding to these models are discussed first in the context of relevant microstructural features. The resulting predictions are then compared with experimental measurements available in the literature for a variety of composite materials. This aspect is central to the validation of the models and of the underlying assumptions made in their formulation. Finally, normalized diagrams are developed that allow one to conduct assessments of the overall elastic response of a wide range of composites and porous materials without the need to perform lengthy calculations. These diagrams facilitate access to proven micromechanical methods, provide a new tool for microstructural tailoring of composites, and help in gaining, by visual inspection, an intuitive understanding of the influence of microstructural features on the elastic response.
PROCESSING of optimum composite materials for structural applications requires an insight into the relationship between microstructural parameters (such as the orientation, morphology, and volume fraction of reinforcements) and the overall mechanical behavior. Quantitative estimates of the influence of microstructural features on the mechanical response can be performed within the framework of analytical and semianalytical models from solid mechanics, an approach known as continuum micromechanics of materials. For thermoelastic material properties, this field of research reached its maturity in the 1960s and 1970s with the work of Hashin and Shtrikman,[1] Hill,[2] Budiansky,[3] Mori and Tanaka,[4] as well as Christensen and Lo.[5] Comprehensive textbooks have been available for more than a decade.[6,7] The resulting models, however, have only found limited practical use in materials design, as they require more of a background in continuum mechanics and are mathematically more complex than the rule-of-mixture approaches that continue to be widely used. The mathematical complexity of the preceding micromechanical models ranges from simple scalar equations to systems of tensor equations. Although the predictions made on the basis of sophisticated models are more accurate and general than those based on simplified models, some algebra has to be done to solve the sets of equations associated with them. In addition to analytical and semianalytical descriptions, numerically based approaches for predicting the thermomechani
Data Loading...
