Page 230 - Mechanical Behavior of Materials

Problems and Questions 231

(a) Determine all nonzero strain components if the temperature remains constant.
(b) Determine all nonzero strain components if the temperature decreases by 25 C while
◦
the given stresses are present.
(c) Compare the strain values from (a) and (b), and comment on the trends in the values.
5.32 A plate of magnesium alloy is subjected to in-plane stresses of σ x = 80, σ y = 30, and
τ xy = 50 MPa, with the other stress components being zero. The coefficient of thermal
expansion for the alloy is 26 × 10 −6 ◦
/ C. Proceed as in Prob. 5.31(a), (b), and (c).
5.33 For the situation of Example 5.3(e), consider the possibility of a temperature change T in
addition to the stress σ z =−75 MPa being applied.
(a) For a temperature increase, how would you expect the value of σ y to qualitatively
change, as to its magnitude becoming larger or smaller? For a temperature decrease?
(b) Calculate the temperature change that would cause the copper alloy block to be on the
verge of losing contact with the walls in the y-direction. The coefficient of thermal
◦
expansion for the alloy is 16.5 × 10 −6 1/ C.
Section 5.4 3
5.34 Name two materials that fit into each of the following categories: (a) isotropic, (b) transversely
isotropic, and (c) orthotropic. Try to think of your own examples rather than using those from
the text.
5.35 A composite material is made with a titanium alloy matrix and 35%, by volume, of
unidirectional SiC fibers. Estimate the elastic constants E X , E Y , G XY , ν XY , and ν YX .
5.36 A composite material is to be made by extruding 50% by volume of unidirectional type
E-glass fibers in an epoxy matrix.
(a) Estimate the composite properties E X , E Y , G XY , ν XY , and ν XY , where X is the fiber
direction. Fiber (reinforcement) and the matrix properties are given in Table 5.3(a) and
in the note below the table.
(b) Compare your values with the data given in Table 5.3(b) for a similar composite with
60% unidirectional fibers. Are the differences qualitatively what you would expect
from the different fiber volumes?
5.37 For the epoxy reinforced with 60% unidirectional E-glass fibers in Table 5.3, use the
reinforcement and matrix properties given in Table 5.3(a), and in the note below the table, to
estimate the composite properties E X , E Y , G XY , ν XY , and ν YX . How well do your estimates
compare with the experimental values in Table 5.3(b)? Can you suggest reasons for any
discrepancies?
5.38 Proceed as in the previous problem, except change the fiber material to Kevlar 49.
5.39 Proceed as in Prob. 5.37, except change the fiber material to T-300 graphite.
5.40 Proceed as in Prob. 5.37, except change the fiber material to GY-70 graphite.
5.41 For unidirectional E-glass fibers used to reinforce epoxy, employ the reinforcement and matrix
properties given in Table 5.3(a), and in the note below the table, to estimate E X and E Y for
several volume fractions of reinforcement ranging from zero to 100%. Plot curves of E X
versus V r , and E Y versus V r , on the same graph, and comment on the trends.

3
Materials properties for these problems may be found in Tables 5.2 and 5.3, including the footnote to the latter.