ME355 Winter 2015 Hw#7 Due: March 6, 2015 Review questions

ME355
Winter 2015
Hw#7
Due: March 6, 2015
Review questions (no need to turn in these, just make sure you can answer the
following questions through reviewing the lecture notes or reading the textbook)
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Difference between thermoplastics, thermosets, and elastomers in terms of
their structure, properties (Tg, bonding, branchness/networking
arrangement, mechanical strength, ductility, etc) and response to heat
Glass transition temperature Tg, and its physical significance
Different types of polymer additives and their functions
Processing techniques for polymers and reinforced plastics
Functions of the matrix and reinforcing phases in composites
Advantages and disadvantages of composites
Prediction of longitudinal properties of fiber reinforced composites
 Processing techniques for reinforced plastics (lecture on May 19)
Recycling challenges of plastics
Numerical Problems (to be turned in):
P1: For a given fiber reinforced composite with the following properties:
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Young’s modulus of fiber: E f
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Young’s modulus of matrix: Em
Fiber volume fraction: V f
Assuming that the fiber and matrix are isotropic, prove (with appropriate
sketches):
1) the Young’s modulus of the composite ( Ec ) in the longitudinal direction
(along the fiber direction) is:
Ec  E f V f  Em (1  V f )
(2) the load percentage carried by the fiber in the longitudinal direction is:
Ff
E fVf

Fc E f V f  Em (1  V f )
(3) the Young’s modulus of the composite ( Ec ) in the transverse direction
(perpendicular to the fiber direction) satisfies:
1 Vf 1  Vf
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Ec E f
Em
(4) the fiber does not enhance the load carrying capacity of the composites in
the transverse direction.
P2. In Example 10.4, what would be the percentage of the load supported by the
fibers if their strength is 1250 MPa and the matrix strength is 240 MPa? What if
the strength is unaffected, but the elastic modulus of the fiber is 600 GPa while
the matrix is 50 GPa?
P3. Calculate the elastic modulus and percentage of load supported by fibers in a
composite with an epoxy matrix (E = 10 GPa), with 20% fibers made of (a) highmodulus carbon and (b) Kevlar 29.
(refer to Table 10.4 on P609 for modulus of the different fibers)
P4. Calculate the stress in the fibers and in the matrix for P3. Assume that the cross
sectional area is 50 mm2 and Fc = 2000 N.
P5. Consider a composite consisting of reinforcing fibers with Ef = 300 GPa. If the
allowable fiber stress is 200 MPa and the matrix strength is 50 MPa, what should
be the matrix stiffness so that the fibers and matrix fail simultaneously?
Answer keys to numerical problems:
P2:
No effect, 75%
P3:
(a) 91 GPa, 91%;
(b) 20.4 GPa, 61%
(refer to Table 10.4 on P609 for modulus of the different fibers)
P4:
(a) 182 MPa in fiber, 4.5 MPa in matrix
(b) 122 MPa in fiber, 19.5 MPa in matrix
P5:
75 GPa