Mechanics of Materials 2010 Part 5 pptx
Mechanics of Materials 2010 Part 5 pptx
... Saouma Mechanics of Materials II
Draft
6 FUNDAMENTAL LAWS of CONTINUUM MECHANICS
6.3.2 †Moment of Momentum Principle
25 The moment of momentum principle states that the time rate of change of the ... P
2
(5. 5-a)
C
A·dr = 0 along a closed contour line (5. 5-b)
5. 3 Integration by Parts
5 The integration by part formula is
b
a
u(x)v
(x)dx = u(x)v(x)|
b
a
−
b
a...
High Cycle Fatigue: A Mechanics of Materials Perspective part 5 doc
... field of “gigacycle fatigue,” indicating lives of the order of 10
9
cycles or higher,
data have been generated indicating that some materials do not have a fatigue limit
within the range of cycles ... to understand the very long-life
of materials and the apparent lack of a fatigue limit using ultrasonic test machines [5] .
They show that in higher strength materials such as...
High Cycle Fatigue: A Mechanics of Materials Perspective part 17 pptx
... = 0 .5
R
= 0.8
HCF
LCF
R = 0.1
R
= 0 .5
R
= 0 .5
700
790
900
53 4
639
910
(A)
(B)
(C)
Figure 4.9. Schematic showing amplitudes of LCF and HCF fatigue limit stresses.
LCF–HCF Interactions 151
10
100
1000
1 ... 151
10
100
1000
1 10 100 1000 10,000
c = 5 μm, short crack
c = 5 μm, long crack
c = 50 0 μm, short crack
c = 50 0 μm, long crack
Stress (MPa)
Crack length, a (μm)
K
th...
High Cycle Fatigue: A Mechanics of Materials Perspective part 24 pptx
... +a
0
(5. 10)
Notch Fatigue 2 25
Evaluation of Figures 5. 6 and 5. 7 points out some of the difficulties in making generaliza-
tions about the transition from crack initiation to crack propagation, particularly ... form
k
f
=1+
k
t
−1
1+
a
m
r
(5. 3)
The equation of Peterson [4] is
k
f
=1+
k
t
−1
1+
a
m
r
(5. 4)
The equation of Heywood [5] is
k
f
=
k
t
1+2
a
m
r
(5. 5)
whe...
High Cycle Fatigue: A Mechanics of Materials Perspective part 26 pptx
... Equation (5. 11). Numerical
results showing the stress distributions ahead of a circular notch of radius r, and of a
crack of length a, are shown in Figure 5. 23, for three different values of a/a
0
; ... parameter has the form for an S–N type curve,
FIN = 65 739N
−06779
+4335N
−004 15
(5. 25)
To apply the parameter to notch data, the average value of the parameter over a di...
High Cycle Fatigue: A Mechanics of Materials Perspective part 27 pptx
... strength of a steel is easily calculated
from Equations (5. 48) and (5. 49). The results, in terms of the parameter
√
area, are
presented in Figure 5. 29 which shows that for all but the softest of steels, ... as
a
D
=
a
0
2
a
N
=
a
∗
2
=
k
2
t
a
0
2
(5. 39)
246 Effects of Damage on HCF Properties
0
100
200
300
400
50 0
10
4
10
5
10
6
10
7
R = –1
R = 0.1
R = 0 .5
Predicted...
High Cycle Fatigue: A Mechanics of Materials Perspective part 38 pptx
... as-FODed
Bending S, with SR
Figure 7.34. Prediction of the HCF capability of specimens with FOD using the unnotched stresses.
0
0 .5
1
1 .5
2
2 .5
3
3 .5
4
0 5 10 15 20 25 30
Peak local stress predictions
Axial ... there is no model for values of k
f
.
362 Effects of Damage on HCF Properties
0
0 .5
1
1 .5
2
2 .5
3
3 .5
4
0
5
10 15 20 25 30
Un-notched predictions
S
un-n...
Mechanics of Materials 1 Part 5 pps
...
9.3 758 )
-
(1. 25 W
-
6. 258 )
1
-
EI
x
103
1
=-
(1 .56 W+ 15. 6 258 )
EI
x
103
Now the total horizontal deflection
of
A
=
0
-3.1 25 W+ 5. 2088
+
1 .56
W+
15. 6 258
=
0
-
1 .56 5 ...
=
-
[
+
0.06 258 ~~
El
2
1
=
-!-
{["':"
x
0.02 25+ 0.06 258
x
0. 15
El
x
0.01 +0.06 258 (-0.1)
1
=-
{
(1. 25
x
2. 25 W+6. 25
x...
Mechanics of Materials 1 Part 9 pptx
... integral part of this expression is the first moment of area of the shaded parts
of
Fig. 3.23(a) about the vertical axis and evaluation of this integral allows the determination
of
M
for ...
distribution being given by eqns.
(10 .5)
and
(10.6)t
as:
(3.42)
(3.43)
E.J.
Hem,
Mechanics
of
Materials
I,
Butterworth-Heinernann,
1997.
66
Mechanics
of
Materials...
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