Fiber Strength Theory

With an understanding of the gross behavior of a filamentary structure, a proper assessment of the mechanical and geometric properties of the constituent materials is possible. In particular, the use of fiber strength, the binding resin matrix, and the interface may be placed in a perspective based on the results of a mathematical analysis. They provide accurate guidelines for the design of RPs. 

A macroscopic theory of strength is based on a phenomenological approach. No direct reference to the mode of deformation and fracture is made. Essentially, this approach employs the mathematical theories of elasticity and tries to establish a yield or failure criterion. Among the most popular strength theories are those based on maximum stress, maximum strain, and maximum work. 

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Stephen W. Tsai, Strength Theories of Filamentary Structures, in Fundamental Aspects of Fiber Reinforced Plastic Conposites, Conference Proceedings, R. T. Schwartz and H. S. Schwartz (Editors), Dayton, Ohio, 24-26 May 1966, Wiley interscience. New York, 1966, pp. 3-11. 

Jung, T., Subramanian, R.V. and Manoranjan, V.S. (1993). Prediction of fiber strength at the critical length A simulation theory and experimental verification for bimodally distributed carbon fiber strength. J. Mater. Sci. 28, 4489-4496. 

Tsai SW. Strength theories of filamentary structures. In Schwartz RT, Schwartz HS, editors. Fundamental aspects of fiber reinforced plastic composites. New York, USA Wiley Interscience 1968. pp. 3—11. 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

In the push out test [93], the fiber is pushed into the matrix rather than being pulled out. The test allows the measurement of two quantities, Fdcb (the force at which debonding occurs) and F/., (the force needed to push the fiber through the matrix sample if it is thin enough). The bond shear strength Tdeb is calculated using the shear lag theory ... 

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