Question

a fiberglass-epoxy reinforced plastic with longitudinally aligned fibers are subjected to a tensile loading (pc). the composite consists of 35% fibers by area/volume. the elastic modulus of the fibers is 175 gpa, and the elastic modulus of the epoxy matrix is 70 gpa. (a) calculate the elastic modulus of the combined composite, and (b) the fraction of the load that is supported by the fibers

Answer 1

The elastic modulus of a composite material can be calculated using the rule of mixtures. The elastic modulus of the combined composite is 68.25 GPa. Therefore, the fraction of the load supported by the fibers is 0.35.

Step-by-step explanation:

The elastic modulus of a composite material can be calculated using the rule of mixtures. For a composite with longitudinally aligned fibers, the elastic modulus of the composite can be calculated using the formula:

Ec = Vf * Ef + Vm * Em

Where:
Ec is the elastic modulus of the composite
Vf is the volume fraction of fibers
Ef is the elastic modulus of the fibers
Vm is the volume fraction of matrix
Em is the elastic modulus of the matrix

Using the given values, the elastic modulus of the composite is:

Ec = 0.35 * 175 GPa + 0.65 * 70 GPa = 68.25 GPa

To calculate the fraction of the load supported by the fibers, we can use the same concept of volume fractions:

Fiber fraction = Vf = 0.35
Matrix fraction = Vm = 0.65

Therefore, the fraction of the load supported by the fibers is 0.35.