1. MSM Lab . ( Graduate Student )
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MSM Lab . ( Graduate Student )

2. Problem 8.1
To provide some perspective on the dimensions of atomic defects, consider a metal specimen that has a dislocation density of 𝟏 𝟎 𝟓 𝒎 𝒎 −𝟐 . Suppose that all the dislocations in 𝟏𝟎𝟎𝟎𝒎 𝒎 𝟑 𝟏𝒄 𝒎 𝟑 were some how removed and linked end to end. How far (in miles) would this chain extend? Now suppose that the density is increased to 𝟏 𝟎 𝟗 𝒎 𝒎 −𝟐 by cold working. What would be the chain length of dislocations in 𝟏𝟎𝟎𝟎𝒎 𝒎 𝟑 of materials? 2

3. Problem 8.7
One slip system for the BCC crystal structure is {110}<111>. Sketch a {110}-type plane for the BCC structure, representing atom positions with circles. Now, using arrows, indicate two different <111> slip directions within this plane.
 Prob. 8.5,8.6 3

4. =18.6𝑀𝑃𝑎 =10.17𝑀𝑃𝑎  Prob. 8.13 Problem 8.12
Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 43.1º and 47.9º, respectively, with the tensile axis. If the critical resolved shear stress is 20.7MPa, will an applied stress of 38MPa cause the single crystal to yield? If not, what stress will be necessary?
=18.6𝑀𝑃𝑎
=10.17𝑀𝑃𝑎
 Prob. 8.13 4

5. Problem 8.14
Consider a single crystal of silver oriented such that a tensile stress is applied along the [001] direction. If slip occurs on a (111) plane and in a [101] direction and is initiated at an applied tensile stress of 1.1 MPa, compute the critical resolved shear stress. 5

6. Problem 8.14
Consider a single crystal of silver oriented such that a tensile stress is applied along the [001] direction. If slip occurs on a (111) plane and in a [101] direction and is initiated at an applied tensile stress of 1.1 MPa, compute the critical resolved shear stress.
 Prob. 8.15, 8.16, 8.17 6

7. Problem 8.24
The lower yield point for an iron that has an average grain diameter of 𝟓∗𝟏 𝟎 −𝟐 𝒎𝒎 is 135MPa. At a grain diameter of 𝟖∗𝟏 𝟎 −𝟐 𝒎𝒎, the yield point increase to 260MPa. At what grain diameter will the lower yield point be 205MPa? 7

8. Problem 8.29
Two previously undeformed specimens of the same metal are to be plastically deformed by reducing their cross-sectional areas. One has a circular cross section, and the other is rectangular; during deformation the circular cross section is to remain circular, and the rectangular is to remain as such. Their original and deformed dimensions are as follows. Which of these specimens will be the hardest after plastic deformation, and why?
Circular(dia.mm)
Rectangular(mm)
Original
15.2
125*175
Deformed
11.4
75*200 8

9. Problem 8.29
Two previously undeformed specimens of the same metal are to be plastically deformed by reducing their cross-sectional areas. One has a circular cross section, and the other is rectangular; during deformation the circular cross section is to remain circular, and the rectangular is to remain as such. Their original and deformed dimensions are as follows. Which of these specimens will be the hardest after plastic deformation, and why?
Prob. 8.27, 8.30,
8.31, 8.32 9

10. Problem 8.41
A non-cold-worked brass specimen of average grain size mm has a yield strength of 160MPa. Estimate the yield strength of this alloy after it has been heated to 600℃ for 1000 s, if it is known that the value of ky is 12.0 MPa*mm1/2
𝜎 0 = 𝜎 𝑦 − 𝑘 𝑦 𝑑 − 1 2
 Prob. 8.37, 8.38 , 8.39 10

11. Problem 9.3
If the specific surface energy for soda-lime glass is 0.30J/m2, E=69GPa. then, compute the critical stress required for the propagation of a surface crack of length 0.05mm
= 𝟐∗𝟔𝟗∗ 𝟏𝟎 𝟗 𝑵/ 𝒎 𝟐 ∗𝟎.𝟑𝟎𝑵/𝒎 𝝅 𝟎.𝟎𝟓∗ 𝟏𝟎 −𝟑 𝒎 𝟐
 Prob. 9.4, 9.5, 9.6, 9.10 11

12. Problem 9.17
A fatigue test was conducted in which the mean stress was 70MPa, and the stress amplitude was 210MPa.
Compute the maximum and minimum stress levels. 12

13. Problem 9.17
A fatigue test was conducted in which the mean stress was 70MPa, and the stress amplitude was 210MPa.
(b) Compute the stress ratio. 13

14. Problem 9.17
A fatigue test was conducted in which the mean stress was 70MPa, and the stress amplitude was 210MPa.
(c) Compute the magnitude of the stress range.
 Prob. 9.18, 9.19, 9.24 14

15. Problem 9.37
(a) Estimate the activation energy for creep for the low carbon-nickel alloy having the steady-state creep behavior ,Ýε s1 = 0.01 %/1000 h = 1 x 10−7 (h)−1 and Ýε s2 = 0.8 %/1000 h = 0.8 x 10−5 (h)−1. Use data taken at a stress level of 55MPa and temperatures of 427 ℃ and 538 ℃. Assume that the stress exponent n is independent of temperature. 15

16. Problem 9.37
(b) Estimate 𝝐 𝒔 at 649 ℃
 Prob. 9.36, 9.38 16