Mech 473 Homework Assignment #1
1. Because Mg is a low-density material (r = 1.738 g/cm3) with a low melting temperature (670 o
C) and boiling point, it has been considered for use in an aerospace vehicle intended to enter the outer space environment. Is this a good material design?
What other material might be considered? (2)
2. You would like to place a 3 foot diameter microsatellite into orbit, for which many aerospace companies and space agencies currently have a need. This satellite will contain delicate electronic equipment that will send and receive radio signals from earth. What properties of the materials for the satellite will be required and what kind of materials might be considered? (2)
3. Calculate the lattice parameter and theoretical density of silicon assuming that it has the diamond cubic structure and an atomic radius of 1.176 Angstroms. (1)
4. Calculate the theoretical density of GaAs, which is a compound semiconductor having the zinc blende structure, given that the atomic mass of Ga is 69.723 g/mole and As is
74.921 g/mole and that the radius of the Ga ion is 0.62 A and the radius of the As ion is
2.22 A. (2)
5. The coefficient for linear thermal expansion for Al is 23.6x10exp(-6) / o
C. If a 200 mm long, 100 mm diameter rod is heated from 20 o
C to 100 o
C, what are the dimensions
(length and diameter) of the rod at 100 o
C? Is there a stress on the rod? (2)
6. If an application requires materials to support loads at 250 degrees C, determine whether gold, copper, iron and titanium will likely creep. (2)
7. Determine the Miller indices of the directions shown in the figure below. (2)
8. Determine the Miller indices of the planes shown in the figure below. (1.5)

9. Determine the Miller Bravais indices for the directions in the hexagonal lattice shown below. (1.5)
10. Determine the Miller Bravais indices for the planes in the hexagonal lattice shown below. (1.5)

11. What are the indices of the four directions of the form <111> that lie in the
  plane of a cubic cell? (2)
12. Calculate the length of the dislocation Burgers vector in BCC iron (low temperature),
FCC iron, FCC aluminum, Tungsten, and germanium. (2)
13. Calculate the length of the dislocation Burgers vector for Silicon given that its (111) plane has a width of 3.135 Angstroms. (1)
14. A slight misalignment of an optoelectronic device during fabrication leaves a grain boundary passing through the optically active region having a width of 20 nm. If the two grains approach each other at an angle of 10 degrees, how many dislocations, N, could exist to short out the device? (2)
15. A single crystal of an BCC metal is oriented so that the [001] direction is parallel to an applied stress. If the critical resolved shear stress is 12,000 psi, calculate the magnitude of the applied stress required to cause slip to begin in the
 
direction in the ( 110 ) , ( 011 ) , and ( 10 1 ) slip planes. (2)
16. The strength of titanium is found to be 65,000 psi when the grain size is 17 x 10 -6 m and 82,000 psi when the grain size is 0.8 x 10
-6
m. Determine the constants in the Hall-
Petch equation and the strength of the titanium when the grain size is reduced to
0.2 x 10
-6
m. (1.5)
17. When a 3000 kg load is applied to a 100 mm diameter ball in a Brinell test of a steel, an indentation of 3.1 mm is produced. Estimate the tensile strength of the steel. (1)
18. A three point bend test is performed on a block of silicon carbide that is 10 cm long,
1.5 cm wide, and 0.6 cm thick and is resting on two supports that are 7.5 cm apart. The sample breaks when a deflection of 0.09 mm is recorded. The flexural modulus for silicon carbide is 480 GPa. Assume that no plastic deformation occurs. Calculate a) the force that caused the fracture and b) the flexural strength. (2)

19. For a two inch thick material with K
Ic
= 50 ksi sqrt(inch),
 ys
= 100 ksi, and
 des
= 40 ksi, determine the critical crack length in an infinitely long and wide plate for a through thickness a) edge and b) center crack assuming that the correction factor, f , for the edge crack is 1.12 and for the center crack is 1.0. (2)
20. The acrylic polymer from which the figure below was obtained is subjected to an alternating stress between 15 MPa and 0 MPa. The largest surface cracks initially detected by non-destructive testing are 0.001 mm in length. From the graph calculate the constants C and n for the steady state fatigue equation. If the critical fracture toughness of the polymer is 2 MPa sqrt(in), calculate the critical flaw size, a c
and the number of cycles, N , required before failure occurs, which is given by the equation below. Let f =
1.0. (2)
N

2

( a c
( 2
)

( 2
 n ) / n ) Cf
2 n


( a i

) n

( 2 n
 n
/ 2
) / 2

21. In a fatigue test, the maximum stress applied in tension is 80,000 psi and the minimum stress in compression is 20,000 psi. Determine the stress range, stress amplitude, mean stress and stress ratio, R. (2)
22. Calculate the fatigue limit of a steel that has an ultimate tensile strength of 160 ks when the stress ratio, R = 0 and a 50 per cent probability of enduring the stress for the life

of the component. Use a safety factor of 2. Determine the diameter of the rod to be used to carry a fluctuating load of 20,000 lb-force. (1)
23. The activation energy for self-diffusion in copper is 49,300 cal/mol. A copper specimen creeps at 0.002 in/in –h when a stress of 15,000 psi is applied at 600 o
C. If the creep rate is dependent on self-diffusion, determine the creep rate if the temperature is
800 o
C. (1)
24. When a stress of 20,000 psi is applied to a material heated to 900 o
C, rupture occurs in 25,000 h. If the activation energy for rupture is 35,000 cal/mol, determine the rupture time if the temperature is reduced to 800 o
C. (1)