MATERIALS AEROSPACE LABORATORY (ASE 324L)
Final December 14, 2001 2-4 pm WRW 113
Please attempt all four questions. The points assigned to each question are shown in ( ). This is a closed notes/homework/book exam. Space for your answers is provided in this booklet.
NAME:
Section
T
W
Th
(circle one)
1. The compliance matrix of a unidirectional fiber reinforced composite is given by
1 E1 12 E1 0 21 E2 1 E2 0 0 1 G12 0
E1 = 39, E2 = 8.7,G12 = 3.8 GPa and 12 = 0.28
(a) Describe what experiments you would conduct in order to determine all the quantities in the compliance matrix. (6) (b) Show how the transverse modulus is controlled by the fiber and matrix moduli and the respective fiber volume fractions. (4) (c) The fiber and matrix moduli are 200 and 4 GPa, respectively. Find the volume fraction of fibers that was used in this composite. (3) (d) A panel is subjected to the stress state shown below. The shear stress increases in proportion to the normal stress a through = 1.5 a . Determine the ratio of b : a that should be applied so that the transverse strain is always zero. Determine the levels of a and when the panel fails at a fiber strain of 1.5%. (7)
b
a
a
b
2. Shown below are three beams. They are identical except that one is notched and one is cracked. The height and thickness are h=2 in. and b=0.5 in., respectively. The 6M unnotched height h1 = 0.75h . The stress at the root of the notch is n = 2.5 2 due to the bh1 stress concentration there. The stress intensity factor for an edge cracked beam with a 1.12 * 6M crack length a is K = a . 2 bh
(a) Determine which of the three beams fails first if one set is made of aluminum and the other steel. Indicate what the dominant failure mechanism is for each each material. (10)
Material Toughness (ksiin) 59 31 Yield Strength (ksi) 297 47
Steel Aluminum
K . 2r Determine the size of the plastic zone ahead of the cracked steel and aluminum bars and use this information to further explain the results in (a). (10)
(b) The normal stress a distance r ahead of a crack is given by =
M
h
M
M
h
h1
M
M
h
h1
M
Thickness=b
3. The S-N curve of a material follows the relationship a = fat +
b . Nc (a) Explain what the terms in the expression are and how the material properties in it are found. (5) (b) Mean stress effects in this material are accounted for by the Goodman line fat = 1 m . Explain how you would conduct experiments to fat uts determine the effect of mean stress and how it appears on S-N curves. (3) (c) The pressure vessel shown below is subjected to an internal pressure p and an axial compressive force F . It has a radius R = 72in. and wall thickness t = 0.05in. The pressure fluctuates between p0 and zero. The force is R 2 p0 applied continuously at a level F = . The ultimate tensile strength and 2 endurance limit of the material are 140 and 70 ksi, respectively, with b = 200 ksi and c = 0.15. How many more cycles can be applied at p0 = 310 psi if the following pressure/load history has already been applied? (10)
Pressure p0 (ksi) 0.25 0.28 0.33 0.36 Cycles
6.96E+05 6.84E+04 1.75E+03 3.37E+02
(d) If F = R 2 p0 , indicate what the main change would be to your calculations in (c) above. (2) Hint: Ignore any potential biaxial stress effects and recall that the axial stress due pR to an internal pressure p is = . 2t
t F R F
4. We have all seen windshields that have been struck by a stone. Quite often there are several cracks emanating from the impact zone as shown schematically below (for example, there are 8 cracks in this case). After some time, one crack often dominates and grows out of the star burst zone. Since the driving stress (often residual stress) may be constant, environmentally assisted crack growth is a possible mechanism. (a) Explain how you would characteriz...