STRESS INTENSITY FACTOR SOLUTIONS
Fracture Toughness Testing of Metals
(a)
(b)
(c)
(d)
(e)
FIGURE
Common test specimen geometries: (a) compact specimen, (b) disk-shaped compact specimen,
(c) single-edge-notched bend (SE(B)) specimen, (d) middle tension (MT) panel, (e) arc-shaped specimen, (f)
single-edge-notched tension specimen, (g) double-edge-notched tension panel, (h) edge-cracked plate in pure
bending, and (i) edge-cracked plate in combined bending and tension.
Fracture Mechanics: Fundamentals and Applications
(f)
(g)
(h)
(i)
FIGURE A7.1 (
)
Fracture Toughness Testing of Metals
ABLE
Nondimensional
Solutions for
kness
ks in Flat Plates [8, 55]
(a) Compact specimen
2
2
0.886 4.64
3/ 2
1
3
13.32
14.72
4
5.60
(b) Disk-shaped compact specimen
2
2
0.76 4.8
3/ 2
1
3
11.58
4
11.43
4.08
(c) Single-edge-notched bend specimen loaded in three-point bending
3
21 2
2
3/ 2
1
1.99
1
2.15 3.93
2.7
(d) Middle tension (MT) panel
2
sec
4
2
1 0.025
4
0.06
(e) Arc shaped specimen
2
3
1.9 1.1
1 0.25 1
1
1
2
where
2
3.74
3/ 2
1
6.30
3
6.32
2.43
(f) Single-edge-notched tension panel
2 tan
cos
2
3
0.752 2.02
0.37 1 sin
2
2
(g) Double-edge-notched tension (DENT) panel
2
1
2
1.122 0.561
0.205
3
0.471
4
0.190
(
)
Fracture Mechanics: Fundamentals and Applications
Fracture Mechanics: Fundamentals and Applications
ABLE
ABLE
(h) Edge-cracked plate subject to pure bending
(h) Edge-cracked plate subject to pure bending
3/ 2
3/ 2
6 2 tan
2
6 2 tan
0.923 0.199 1 sin
2
0.923 0.199 1 sin
2
cos
2
2
cos
4
4
2
(i) Edge-cracked plate subject to combined bending and tension
(i) Edge-cracked plate subject to combined bending and tension
11
where
are given
givenabove
aboveinin(f)(f)and
and(h),
(h),respectively.
respectively.
where and
and are
aa See Figure A7.1 for a definition of the dimensions for each configuration.
See Figure A7.1 for a definition of the dimensions for each configuration.
ABLE
ABLE
Nondimensional Load
forfor
Nondimensional
LoadLine
LineCompliance
ComplianceSolutions
Solutions
Plates [55]
Plates
Nondimensional Compliance:
Nondimensional
Compliance:
kness
kness ks in
ksFlat
in Flat
where
where
(a) Compact
Compact specimen
(a)
specimen
1
1
1
1
2
2
2
2.163 12.219
2.163 12.219
20.065
20.065
2
3
0.9925
0.9925
4
3
5
4
20.609
20.609
9.9314
9.9314
5
(b) Single-edge-notched bend (SENB) specimen loaded in three-point bending
(b) Single-edge-notched bend (SENB) specimen loaded in three-point bending
3
(1
3
(1
3
3
2
)
2
) 0.25 0.6
0.25 0.6
2
2
2
2(1
(1
)
1.5
) 1.5
(c) Middle tension (MT) panel
(c) Middle tension (MT) panel
1.071 0.250
2
1.071 0.250
2
1
1
2
0.357
0.357
(d) Single-edge-notched tension specimen
(d) Single-edge-notched tension specimen
2
4
14
1
(e) Double-edge-notched tension panel
2
2
2
2
2
5.58 19.57
5.58 19.57
2
36.82
36.82
3
2 0.121
0.121
4
b
b
5
30.047
04 .008
0.008
0.047
0.99
1
1.3 1.2
1
0.7
1.3 1.2
For side-grooved
specimens,
should be replaced by an effective thickness:
(
)2
where
is the net thickness.
(
)2
where of the
is dimensions
the net thickness.
See Figure A7.1 for a definition
for each configuration.
See Figure A7.1 for a definition of the dimensions for each configuration.
2
0.7
8
ln sec
8
2
ln sec
4
123.77
12.77
1.071
ln 1
5
1.071
ln 1
2
0.99
4
(e) Double-edge-notched tension panel
4
0.0629 0.0610 cos
0.0019 cos
4
2
2
2
4
0.0629 0.0610 cos
0.0019 cos
2
2
2
a For side-grooved specimens,
should be replaced by an effective thickness:
a
3
2 .94
34
34.94
2
4
These solutions have the following form:
(
where ,
, and
(A9.1)
)
are geometry factors.
ABLE
ess-Intensity Solution for a Semielliptical Surface Flaw in a Flat Plate for
(
)
,
,
,
where
1.65
1 1.464
2
1
1
2
3
1.13 0.09
0.89
0.2
0.54
2
3
4
24
1.0
0.65
0.5
14 1.0
1/ 4
2
cos
2
sin
2
1/ 2
sec
s - Membrane (tensile) stress
s - Bending stress
2
2
1
2
(1 sin )2
0.1 0.35
1
(
2
1
)(sin )
where
0.2
3
0.6
6
1
1 0.34
2
1
0.11
2
1
1
2
1.22 0.12
0.75
2
0.55 1.05
1.5
0.47
Application to Structures
ABLE
ess-Intensity Solution for a Semielliptical Surface Flaw in a Flat Plate for
(
)
,
,
>1
,
where
1.65
1 1.464
2
1
4
2
3
1 0.04
1
4
2
0.2
4
0.11
3
2
1
(1 sin )2
0.1 0.35
1/ 4
2
sin
2
cos
2
1/ 2
sec
2
0.2
s - Membrane (tensile) stress
s - Bending stress
0.6
2
1
1
2
1
11
12
2
2
where
3
6
11
21
22
0.04 0.41
0.75
12
21
0.55 1.93
1.5
1.38
2.11 0.77
0.75
22
0.55 0.72
1.5
0.14
Fracture Mechanics: Fundamentals and Applications
ABLE
ess-Intensity Solution for an Elliptical Buried Flaw in a Flat Plate [10].
where
M 2l 2
(M1
l 4)
3
1/ 2
2
sec
f
2
0.05
2
1.5
0.11
0.29
3
1.5
0.23
4
1
For /
| cos |
1 4
1:
1.65
1 1.464
1/ 4
2
s - Membrane (tensile) stress
cos
1
2
sin
2
1
For / > 1:
1.65
1 1.464
1/ 4
2
sin
2
cos
2
1
Tables A9.6 to A9.15 list fully plastic and displacement solutions for selected geometries from
the original EPRI plastic fracture handbook [23]. Note that the total and displacement are obtained
by including the elastic contribution. Refer to Section 9.3.1 for the complete estimation procedure.
Application to Structures
ABLE
ess-Intensity Solution for a Quarter-Elliptical Corner Cr k in a Flat Plate
for
(
)
2
1
4
2
(
1
3
2
1
1 2
)(sin )
1.65
1 1.464
1.08 0.03
1
1.06
0.3
0.44
2
15
0.5 0.25
3
14.8 1
2
(1 sin )3
1
1
0.08
0.4
2
1
0.08 0.15
2
(1 cos )3
1/ 4
2
cos 2
s - Membrane (tensile) stress
s - Bending stress
sin 2
1/ 2
sec
2
2
1
2
where
1
(
2
0.2
3
(1 sin )2
0.1 0.35
1
)(sin )
0.6
12
1
1 0.34
2
1
0.11
2
1
1
2
1.22 0.12
0.75
2
0.64 1.05
1.5
0.47
Fracture Mechanics: Fundamentals and Applications
ABLE
ess-Intensity Solution for a Quarter-Elliptical Corner Cr k
in a Flat Plate for
(
)
2
1
4
2
(
1
3
2
1
1 2
)(sin )
1.65
1 1.464
1.08 0.03
1
2
0.375
2
2
0.25
3
2
(1 sin )3
1
1
0.08 0.4
2
1
0.08 0.15
2
s - Membrane (tensile) stress
s - Bending stress
(1 cos )3
1/ 4
2
sin 2
cos 2
1/ 2
sec
2
where
2
0.2
0.6
3
12
2
1
1
11
12
2
1
21
22
2
11
0.04 0.41
0.75
12
21
0.55 1.93
1.5
1.38
2.11 0.77
0.75
22
0.64 0.72
1.5
0.14