Of unidirectional composites

The difference between the bounds defined by the simple models can be large, so that more advanced theories are needed to predict the transverse modulus of unidirectional composites from the constituent properties and fiber volume fractions (1). The Halpia-Tsai equations (50) provide one example of these advanced theories ia which the rule of mixtures expressions for the extensional modulus and Poisson s ratio are complemented by the equation... 

In this Example the angle, 6, was set at 25°. Fig. 3.11 shows the variation of the moduli and Poisson s Ratio values for all angles between 0° and 90°. This gives an interesting overview of the performance of unidirectional composites when subjected to off-axis loading. 

Hong T. Hahn and Stephen W. Tsai, Nonlinear Elastic Behavior of Unidirectional Composite Laminae. Journal of Composite Materials, January 1973, pp. 102-118. 

J. M. Whitney, Elastic Moduli of Unidirectional Composites with Anisotropic Filaments, Journal of Composite Materials, April 1967, pp. 188-193. 

R. L. Foye, An Evaluation of Various Engineering Estimates of the Transverse Properties of Unidirectional Composites, Proceedings of the 10th National Sympo-... 

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

G. C. Sih and E. P. Chen, Fracture Analysis of Unidirectional Composites, Journal of Composite Materials, April 1973, pp. 230-244. 

Reinforce injected parts locally. A more lightweight part can be made by reinforcing it at specific spots with an insert of unidirectional composite manufactured, for example, by filament winding. 

The properties of unidirectional composites in the fibre direction can compete with those of current metals and alloys. The highest-performance engineering plastics compete with magnesium and aluminium alloys. 

Cui, W.C. and Wisnom, M.R. (1992). Contact finite element analysis of three- and four-point short beam bending of unidirectional composites. Composites Sci. Technol. 45, 323-334. 

Petit, P.H. (1969). A simplified method of determining the in-plane shear stress-strain response of unidirectional composites. In Composite Materials Testing and Design, ASTM STP 460, ASTM, Philadelphia, PA, pp. 83-93. 

Pindera, M.J., Choksi, G., Hidde, J.S. and Herakovich, C.T. (1987). A methodology for accurate shear characterization of unidirectional composites. J. Composites Mater. 21, 1164-1184. 

Rosen, B.W. (1972). A simple procedure for experimental determination of the longitudinal shear modulus of unidirectional composites. J. Composites Mater. 6, 552-554. 

Sims, D.F. (1973). In-plane shear stress-strain response of unidirectional composite materials. J. Composite Mater. 7, 124-128. 

Nairn J.A. (1990). Fracture mechanics of unidirectional composites. J. Reinf. Plast. Compo.sites9,91-101. 

Waas, A.M. (1992). Effect of interphase on compressive strength of unidirectional composites. J. Appl. Mech. 59, S183-S188. 

Figure 26. Cross-sectional shrinkage as a function of heating rate during carbonization of unidirectional composites fabricated with high-modulus PAN-based fibers and pitch matrix under three conditions of pressure and sulfur content (20).

Figure 27. Flexural strength and bulk density of unidirectional composites subjected to graphitizing heat treatments either for each densification cycle or after the densification cycles were completed (20,52) The matrix was a coal-tar binder pitch with 10 wt.-% sulfur the high-modulus PAN-based fiber was Sigrafil HM.

An essential step in developing an interactive reliability model requires formulating a deterministic failure criterion that reflects the limit state behavior of the material. Miki et al.,21 and de Roo and Paluch22 have adopted this approach in computing the reliability of unidirectional composites. In both articles, the Tsai-Wu failure criterion is adopted, where different failure behavior is allowed in tension and compression, both in the fiber direction and... 

Tsukrov 1, Novak J. Micromechanical modelling of transverse moduli of unidirectional composites with non-circular elastic fibres. In Brebbia C A, de Wilde WP, editors. High performance stmctures and composites. Southampton, Boston WIT Press 2002. 

Hsiao HM, Daniel IM. Effect of fibre waviness on stiffness and strength reduction of unidirectional composites under compressive loading. Compos Sci Technol 1996 56 581-93. 

Perevozchikov VG, Limonov VA, Protasov VD, Tamuzh VP. Static and fatigue strength of unidirectional composites under the combined effect of shear stress and transverse tension—compression stresses. Mech Compos Mater 1989 24(5) 638—44. 

N. K. Naik and R. S. Kumar, Compressive strength of unidirectional composites evaluation and comparison of prediction models. Compos. Struct., 46 [3] 299-308 (1999). 

The Halpin-Tsai model is a well-known composite theory to predict the stiffness of unidirectional composites as a functional of aspect ratio. In this model, the lorrgitudi-nal Ejj and transverse engineering modtrli are expressed in the following general form ... 

Micromechanics are a study of mechanical properties of unidirectional composites in terms of those of constituent materials. In particular, the properties to be discussed are elastic modulus, hydrothermal expansion coefficients and strengths. In discussing composites properties it is important to define a volume element which is small enough to show the microscopic structural details, yet large enough to present the overall behavior of the composite. Such a volume element is called the Representative Volume Element (RVE). A simple representative volume element can consists of a fiber embedded in a matrix block, as shown in Fig. 9.3. 

Chamberlain [114] derived an alternate model for transverse expansion of unidirectional composites using thick-walled cylinder equations for the case of a fiber embedded in a cylindrical matrix section. The radial displacements on the outside of the cylinder were related to in the radial direction. The expression for a is given by the following equation ... 

Figure 4.4 Design of unidirectional composite laminae Halpin-Tsai rule of mixtures. Relationship of weight to volume fraction.

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