Concept explainers
Derive an equation showing the relationship between the elastic modulus of a layered composite of made of plastic matrix and unidirectional fibers subjected to isostress conditions.
Answer to Problem 47AAP
The equation of elastic modulus of the layered composite is
Explanation of Solution
For the isostress conditions, the stress on the composite will be equal to stress on the matrix and stress on the fiber respectively.
Here, stress on the composite is
Also, the total change in length of the composite will be equal to summation of changes in lengths of the matrix and fiber respectively.
Here, total change in length of the composite is
Rewrite Equation (II) in terms of volumes.
Here, volumes of the fiber and matrix are
Rewrite Equation (III) in terms of stress and modulus using Hooke's law.
Here, modulus of elasticity of the composite, fiber and matrix are
Divide Equation (IV) by
Thus, the equation of elastic modulus of the layered composite is
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