Question

Use Halpin-Tsai. A composite is made of unidirectionally aligned carbon fibers in a glass-ceramic matrix. The following data are available: Ef1 = 280 GPa, Ef2 = 40 GPa, Em = 70 GPa, νf1 = 0.2, νm = 0.3, Gf12 = 18 GPa a. Compute the elastic modulus in the longitudinal and transverse directions. b. Compute the two Poisson’s ratios. c. Compute the principal shear modulus, G12.

Answer 1

Given,

Also from property Table,

NB : Since the value of Gm and are not given they are taken from property table. if you have some other value in the question which you missed to post you can substitute and modify the answer.

a.

Longitudinal Elastic Modulus

From Halpin Tsai Curve fitting,

and for Vf >0.5 from Hewitt Malherbe equation, we have

(NB: for circular fiber in square array , we can approximate ,but for now we are using the above value)

,(if we calculate using ,we'll get )

Transverse Elastic Modulus,

b)

we have,

c)

From Halpin Tsai Curve fitting,

and for Vf >0.5 from Hewitt Malherbe equation, we have

,(if we calculate using ,we'll get )

Shear Modulus,

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