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07.06.2023
UCK236E - COMPOSITE MATERIALS
FINAL EXAM
1) (40 pts) A unidirectional graphite/epoxy specimen is loaded by a uniaxial stress of 200
MPa along the x-axis. The fibers of the composite are at an angle of 50° to this axis. A
strain gage (the small black rectangle shown on the x direction of the schematic) is
placed to measure strain in the direction of the applied stress. The composite has the
following properties as referenced to the fiber direction.
E1 = 143 GPa
G12 = 6.0 GPa
ν12 = 0.28
E2 = 9.8 GPa
Find the following stress and strains:
a. Determine the stresses along and perpendicular to the fibers.
b. Determine the strains along and perpendicular to the fibers. What will the
value be read from the strain gage at these loading condition
c. Determine the strains along and perpendicular to y-axis.
d. If the strain gage was removed and re-attached on the direction of 1. At the same
loading conditions what will be the value of strain measured on the strain gage?
e. If the stress is applied on the y direction as 200 MPa, then what will you read in
the strain gage as strain value placed still in the x direction (no change in the
strain gage placement).
HINT: According to your lamina considering the fiber angle with the global axes, define
your transformation matrices and all matrices needed to calculate the stress and strains.
Then by using these, calculate every special condition asked in the question. Do not
forget to draw each schematic for each condition by showing the applied stresses, global
axes, local axes even they do not change if in the asked version. This will help you to
see the solution easier.
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Student Number:
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07.06.2023
2) (30 pts) A carbon/epoxy lamina is clamped between rigid plates in a mold as in Figure
while curing at a temperature of 125°C. After curing, the lamina/mold assembly (still
clamped together) is cooled from 125°C to 25°C. The cooling process occurs in moist
air and the lamina absorbs 0.5% of its weight in moisture. The lamina has the following
properties:
E1 = 140 GPa
E2 = 10 GPa
ν12 = 0.3
G12 = 7 GPa
α1= -0.3x10-6/K
α2=28x10-6/K
β1=0
β2=0.44
Assuming that the lamina properties do not change over this temperature range and that
the lamina is initially dry and stress free, determine the residual hygrothermal stresses
in the lamina at 25°C for angles of fiber as θ=0° and 45°.
3) (30 pts) The packing of the fibers is presented in the figure below for a graphite epoxy
composite. The properties of the graphite epoxy is given a below:
E1 = 230 GPa (fiber in L direction), fiber = 17.2 kN/m3
Ematrix = 3.45 GPa, matrix = 12.0 kN/m3
Plot the L and T direction specific sttiffness and the weight density of the composite as
a function of fiber radius for a UD composite
Unit Volume
HINT: Consider the max fiber diameter that can be calculated in such a unit cell as presented
on the schematic up. (0 rfiber  rfibermax)