Statistical Physics I (8.044) Spring 2009 Assignment 7
April 1, 2009 Due April 8, 2009
Please remember to put your name and section number at the top of what you turn in.
Readings
The reading for Chapter V of 8.044 is Adkins, Chapters 4, 5.1-5.5 and 7, an
Statistical Physics I (8.044) Spring 2009 Assignment 4
February 25, 2009 in. Due Thursday March 5, 2009 Please remember to put your name and section number at the top of what you turn
Readings
By now you should have completed your reading of the Notes on
8.18 The fatigue data for a brass alloy are given as follows:
Stress Amplitude (MPa)
Cycles to Failure
310
2 105
223
1 106
191
3 106
168
1 107
153
3 107
143
1 108
134
3 108
127
1 109
(a) Make an SN plot (stress amplitude versus logarithm cycles to failure
8.8 A large plate is fabricated from a steel alloy that has a plane strain fracture toughness of
55 MPa m (50 ksi in. ). If, during service use, the plate is exposed to a tensile stress of 200 MPa (29,000 psi),
determine the minimum length of a surface cr
8.3 If the specific surface energy for soda-lime glass is 0.30 J/m2, using data contained in Table 12.5,
compute the critical stress required for the propagation of a surface crack of length 0.05 mm.
Solution
We may determine the critical stress required
8.29 For a cylindrical S-590 alloy specimen (Figure 8.31) originally 10 mm (0.40 in.) in diameter and
500 mm (20 in.) long, what tensile load is necessary to produce a total elongation of 145 mm (5.7 in.) after 2,000 h
at 730C (1350F)? Assume that the sum
8.17 A 12.5 mm (0.50 in.) diameter cylindrical rod fabricated from a 2014-T6 alloy (Figure 8.34) is
subjected to a repeated tension-compression load cycling along its axis. Compute the maximum and minimum
loads that will be applied to yield a fatigue life
These values are smaller than those for the metal alloys given in Table 8.3, which range from 0.93 to 43.1 mm.
2 - ratio is used. The four polymers are ranked
(b) Relative to the leak-before-break criterion, the K Ic
y
according to values of this ratio as
On the basis of these results, the fatigue lifetime for specimen C will be greater than specimen B, which in turn
will be greater than specimen A. This conclusion is based upon the following S-N plot on which curves are plotted
for two m values.
at 600C (873 K) and 300 MPa. It is first necessary to determine
(b) We are now asked to estimate
s
'
the value of K 2 , which is accomplished using the first expression above, the value of Qc, and one value each of
and T1). Thus,
and T (say
s1
s
exp
8.D4 Consider an S-590 alloy component (Figure 8.32) that is subjected to a stress of 200 MPa (29,000
psi). At what temperature will the rupture lifetime be 500 h?
Solution
We are asked in this problem to calculate the temperature at which the rupture lif
8.16 An 8.0 mm (0.31 in.) diameter cylindrical rod fabricated from a red brass alloy (Figure 8.34) is
subjected to reversed tension-compression load cycling along its axis. If the maximum tensile and compressive
loads are +7500 N (1700 lbf) and -7500 N (-
8.22 Three identical fatigue specimens (denoted A, B, and C) are fabricated from a nonferrous alloy.
Each is subjected to one of the maximum-minimum stress cycles listed below; the frequency is the same for all
three tests.
Specimen
max (MPa)
min (MPa)
A
(b) The average of the maximum and minimum impact energies from the data is
Average =
89.3 J 25 J
= 57.2 J
2
As indicated on the plot by the one set of dashed lines, the ductile-to-brittle transition temperature according to this
criterion is about 75C.
(
Crack Initiation and Propagation
Factors That Affect Fatigue Life
8.24 Briefly explain the difference between fatigue striations and beachmarks both in terms of (a) size
and (b) origin.
Solution
(a) With regard to size, beachmarks are normally of macrosco
Generalized Creep Behavior
8.26 Give the approximate temperature at which creep deformation becomes an important consideration
for each of the following metals: nickel, copper, iron, tungsten, lead, and aluminum.
Solution
Creep becomes important at about
8.27 The following creep data were taken on an aluminum alloy at 400 C (750F) and a constant stress
of 25 MPa (3660 psi). Plot the data as strain versus time, then determine the steady-state or minimum creep rate.
Note: The initial and instantaneous strai
Data Extrapolation Methods
8.D3 An S-590 alloy component (Figure 8.32) must have a creep rupture lifetime of at least 100 days at
500C (773 K). Compute the maximum allowable stress level.
Solution
This problem asks that we compute the maximum allowable st
8.2 Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by
the propagation of an elliptically shaped surface crack of length 0.25 mm (0.01 in.) and having a tip radius of
curvature of 1.2 10-3 mm (4.7 10-5
8.31 A cylindrical component constructed from an S-590 alloy (Figure 8.30) has a diameter of 12 mm
(0.50 in.). Determine the maximum load that may be applied for it to survive 500 h at 925 C (F).
Solution
We are asked in this problem to determine the maxi
8.30 If a component fabricated from an S-590 alloy (Figure 8.30) is to be exposed to a tensile stress of
300 MPa (43,500 psi) at 650C (1200F), estimate its rupture lifetime.
Solution
This problem asks us to calculate the rupture lifetime of a component fa
8.6 Some aircraft component is fabricated from an aluminum alloy that has a plane strain fracture
toughness of 35 MPa m (31.9 ksi in. ). It has been determined that fracture results at a stress of 250 MPa
(36,250 psi) when the maximum (or critical) intern
Principles of Fracture Mechanics
8.D2 (a) For the thin-walled spherical tank discussed in Design Example 8.1, on the basis of critical
crack size criterion [as addressed in part (a)], rank the following polymers from longest to shortest critical crack
len
8.34 Steady-state creep rate data are given below for nickel at 1000 C (1273 K):
(s1)
s
[MPa (psi)]
104
15 (2175)
6
10
4.5 (650)
If it is known that the activation energy for creep is 272,000 J/mol, compute the steady-state creep rate at a
temperature o
8.4 A polystyrene component must not fail when a tensile stress of 1.25 MPa (180 psi) is applied.
Determine the maximum allowable surface crack length if the surface energy of polystyrene is 0.50 J/m2 (2.86
10-3 in.-lbf/in.2). Assume a modulus of elastic
*23-7. A 10 pC charge and a -6 C charge are separated by 40 mm. What is the force between
them. The spheres are placed in contact for a few moments and then separated again by
40 mm. What is the new force? Is it attractive or repulsive?
9 2 2 .5 .5
F=(9 X
23-4. Assume that the radius ofthe electron's orbit around the proton in a hydrogen atom is
approximater 5 .2 X 10"11 n1. What is the electrostatic force of attraction?
9 109N- 2IC2 .5 10'19 1.5 1049:
F:%; F=3.52X10'8N
(5.2 X 10 In)