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Constructive and destructive interference in acoustic emission during fatigue crack propagation
Constructive and destructive interference in acoustic emission during fatigue crack propagation F. HAMEL,
J.P. BAILON
and M.N. BASSIM
Fatigue crack propagation monitoring with acoustic emission reveals the presence of maxima’and minima in the curve of the count rate as a function of the stress intensity factor. This is explained in terms of constructive and destructive interference due to specimen geometry. A theoretical model is developed and experimental proof of the validity of-the model is presented.
Introduction Acoustic emission is increasingly used as a research tool to study crack initiation and propagation during fatigue. The count rate per cycle, h, has been related to the stress intensity factor, AK, with equations similar to that of Paris for the crack propagation rate as a function of AK.’ Early investigators, namely Harris and Dunegan’ have observed that the curve AJ as a function of AK exhibits a maximum and a minimum. Similar observations were made by Hamel and Bassim and Hamel. A typical example is shown in Fig. 1 for a D6 tool steel. Harris et al attribute this behaviour to a shift in fracture mode from plane strain to plane stress in the specimens they tested, which were less than 1 mm thick. On the other hand, in the work of Hamel, specimens with sufficient thickness (12.7 mm) were used so that the fatigue crack propagates always under plane strain conditions and hence it is not possible to apply the Harris and Dunegan model. In this paper, it is shown that acoustic emission during fatigue crack propagation is influenced by the geometry of the compact tensile specimens used. This can create constructive and destructive interferences of the acoustic waves. A simplified theoretical analysis as well as an experimental method for verification of the model are presented.
a
I 10-3
’
’
’
‘1
*“I
IO
““‘-““‘“‘l’ 20
AK
40
30
[MN m-'/2]
Fig. 1 Typical acoustic emission count rate as a function for a D6 steel specimen
of
AK
values of AK where the maximum and minimum have occurred. It is evident that there exists a better correlation of the maxima and minima with the crack length than with AK. Thus, it can be assumed that they are caused by geometrical factors governing the position of the emitting source rather than crack propagation mechanisms which are governed by AK. Proposed model
Experimental
results during fatigue
Two steels were used in this investigation. One is a tool steel, D6, in the as-received state, and the other is an annealed mild steel, Type AISI 1015. Compact tensile specimens, as illustrated in Fig. 2 were used. Fatigue cracks were propagated in the specimens under constant load to fracture while the acoustic emission was monitored. Thus, it was possible to acquire acoustic emission data for the same crack length but under different AK values. A summary of all the results is shown in Table 1, which gives the crack length as well as the
The authors are at the Ecole Polytechnique Canada. Paper received 3 January 1979.
Mont&al,
Qubbec,
0041-624X/79/030125-03/$02.00 ULTRASONICS.
MAY
1979
In the proposed model it is assumed that constructive and destructive interferences due to multiple reflections on the edges of the specimen cause the occurrence of the maxima and minima observed during fatigue. Such an effect has been studied by N. Chretien’ in the case of an aluminium rod. Because of the more complex geometry of the compact tensile specimens, a more simplified approach is used in this investigation. If the crack tip, which is the emitting source, is labelled N and the transducer, assumed to be a point receiver, is M, Fig. 2 shows the direct path as well as several alternative paths which are reflections on the sides of the specimen as well as at the holes. The virtual source R, in particular, 0
1979 IPC Business Press 125
Table
1.
fatigue
Occurrence
as a function
of acoustic emission minima of AK
during
and crack length a
AK[MPa m”]
aimml
Specimen max
min
max
min
D6 c
15.0
16.8
15.4
17.5
D6 D
12.2
13.1
16.1
17.3
D6 E
18.1
18.7
16.1
16.6
D6G
-
17.6
-
17.4
D6 II
19.0
19.9
12.3
13.2
D6 12
22.8
24.0
15.7
16.7
1015
A
17.4
19.9
12.9
15.4
1015
6
20.6
22.0
13.8
15.1
1015
c
28.3
29.1
14.4
14.9
1015
D
21.0
22.7
16.4
17.8
/
/
/’
d’ P
Fig. 2
Specimen
geometry
used and position of all possible virtual
mean and standard
Dimensions
of specimen
[mm]
deviation X
for D6 specimens
17.Ok4.5
18.0-13.9
15.8kO.3
=
a+21.72
A = 60.33
17.1 kO.4
B = 49.33 c = 57.91
mean and
D =
standard
18.11
deviation for 1015 specimens
Position 21.8k4.6
23.4f4.0
14.4*
1.5
assumes that the presence of the hole will not affect the path of the acoustic wave. This assumption is justified by the presence of the pins which do not attenuate the acoustic waves to any extent and by the fact that the transducer used has a resonant frequency of 375 kHz which corresponds Table
2.
Distance
and phase shift from the transducer
Distance Crack
virtual
from transducer
of sources to crack tip
15.8k1.4
to each of the
sources [mm]
NM =
y//[(C/2)*
+ (B -
Xl21
PM =
&(C/2)2
+ (2/I - X - Bj2 1
QM =
&3C/212
+ (B - XI21
RM = &(C/2j2
+ (B + Xl21
SM = &C/212
+ (B - X-
to each of the virtual
2D121
sources
Phase shift for each source for D6
Phase shift for each source for
specimens
the mild steel [radl
[radl
length a [mm]
N
P
cl
R
S
0,
10
33.89
49.06
88.63
86.07
53.37
11
87.01
54.21
88.26
87.95
55.06
15
31.58
16
31.20
17
30.84
18
30.51
19
30.21
20
29.94
21
29.70
48.26 47.46 46.48 45.90 45.12 44.36 43.61 42.87 42.14 41.41 40.71
88.44
14
33.38 32.89 32.43 31.99
12 13
OR
5.52
19.88
18.95
5.41
20.00
19.48
5.29
20.11
20.00
0s
en
eo
OR
7.07
5.85
21.10
20.11
7.56
5.14
21.22
20.66
8.03
8.05
5.62
21.35
21.22
8.55 9.06
es 7.50
88.09
88.90
55.91
5.17
20.21
20.51
8.53
5.50
21.45
21.76
87.92
89.84
56.77
5.04
20.32
21.01
9.01
5.36
21.55
22.31
9.55
87.78
90.79
57.63
4.92
20.40
21.50
9.46
5.22
21.66
22.83
10.04
87.64
91.74
58.50
4.78
20.51
21.99
9.91
5.08
21.76
23.34
10.52
87.51
92.69
59.37
4.64
20.58
22.46
10.37
4.92
21.85
23.84
11 .oo
87.39
93.64
60.24
4.49
20.66
22.93
10.80
4.76
21.92
24.33
11.47
87.29
94.59
61.12
4.33
20.13
23.39
11.22
4.59
22.01
24.82
11.92
87.20
95.54
62.01
4.17
20.80
23.82
11.64
4.42
22.08
25.29
12.36
87.12
96.50
62.89
4.00
20.86
24.26
12.06
4.24
22.13
25.74
12.79
The minima will occur at phase shifts corresponding
126
0,
to (2n - l)n
while the maxima
will occur at 2nn. where n = 1, 2, 3,
ULTRASONICS.
MAY
1979
to a wavelength of 17 mm. This value is higher than the diameter of the hole. The speed of longitudinal waves in the steels was obtained using the pulse-echo technique with a Sperry Reflectoscope. For the D6 and 1015 Steels, values of 6500 f 200 m s-’ and 6100 * 200 ms-’ were found respectively. The wavelength h is given as: h = V/f where the frequency f was taken as 375 kHz. For the D6, the value for h was 17.3 mm while for the 1015‘it was 16.3 mm. The phase angle 8, is
Crock length [mm] Fig. 3 Variation of the root mean square of the amplitude crack length using a pulser, with a mild steel specimen
0 = 2n(X-N) x h where X is the distance from any of the virtual sources (P, Q, R and S) to the transducer M, and N is the distance NM in Fig. 2. The minima are produced when 0, is (2n - 1)a and the maxima occur at 0, equal to 2n7r, with IZan integer. Table 2 gives the distance MN, MP, MQ, MR and MS as a function of the crack length a. Also shown is 13, for the various paths in both the D6 and the mild steel. By interpolation, it is found that for the D6, there will be a minimum at a = 14.9 mm, caused by a reflection at the sides of the hole and also another minimum at 16.0 mm due to the source R. In the mild steel, these minima occur at 13.4 and 13.8 mm respectively. Another minimum for the D6 occurs at 18.4 mm and a maximum at 19.7 mm which partially cancel out. It is thus possible to conclude that the main source of interference is the presence of the hole which causes these minima and maxima to occur. Table 3. mental
Summary
fatigue
of results obtained
testing,
theroetical
from
calculation
either experior from
using
a pulser
Experimental
with
verification
To determine the presence of these maxima and minima, an acoustic emission transducer was used as a pulser to scan the crack path in compact tensile specimens for both the D6 and the mild steel. A needle was used as a waveguide and the root mean square (rms) of amplitude of the acoustic emission from another transducer, located at point M, was obtained as a function of the position of the pulser. Several scannings were made to avoid statistical errors, and typical results of one scan on the mild steel are given in Fig. 3. It is evident that there is a minimum at a crack length of 14 mm. For the D6, it was found that there is a minimum at 13 mm. In Table 3, a summary of all the results either from the theoretical model, using a pulser, or from fatigue experiments is given. All the values are in good agreement and clearly demonstrate the validity of the assumption that the geometry of the specimen can indeed influence acoustic emission measurements during fatigue and be responsible for the presence of maximum and minimum values on the curve ii’against AK.
Crack length corresponding to interference Material
D6
[mm]
Method
Acknowledgements
Fatigue Theoretical
model
Max
Min
17.1
15.8
9.8 (3R)”
14.9 (2s)* 16.0(4R)+
1015 steel
Pulser
15.0
14.0 to 16.0
Fatigue
15.8
14.4
19.7 (4R)”
13.4 (4R)”
Theoretical
model
13.8 (2s)” 18.4 (4Q)” 18.00
Pulser
14.00
*These are evaluated from Table 2. The number represents the multiple of the minimum phase shift corresponding to the associated virtual source.
ULTRASONICS.
MAY
1979
The authors acknowledge the National Research Council of Canada for support of this investigation. One of the authors, FranGois Hamel, also received a postgraduate fellowship from the same organization for completion of this work.
References 1 2 3 4
5
Sinclair, A.C.E., Connors, D.C. Mat Sci Eng 28 (1977) 263-273 Harris, D.O., Dunegan, H.L. Experimental Mechanics (February 1974) 71-81 Hamel, F. Masters thesis, Ecole Polytechnique (1978) Bassim, M.N., Hamel, F. Proc Intern Summer School on Fatigue of Materials and Structures, Sherbrooke, Quebec (July lo-19 1978) ChrBtien, N. Ultrasonics 16 (2) (1978) 69-76
127
J.P. BAILON
and M.N. BASSIM
Fatigue crack propagation monitoring with acoustic emission reveals the presence of maxima’and minima in the curve of the count rate as a function of the stress intensity factor. This is explained in terms of constructive and destructive interference due to specimen geometry. A theoretical model is developed and experimental proof of the validity of-the model is presented.
Introduction Acoustic emission is increasingly used as a research tool to study crack initiation and propagation during fatigue. The count rate per cycle, h, has been related to the stress intensity factor, AK, with equations similar to that of Paris for the crack propagation rate as a function of AK.’ Early investigators, namely Harris and Dunegan’ have observed that the curve AJ as a function of AK exhibits a maximum and a minimum. Similar observations were made by Hamel and Bassim and Hamel. A typical example is shown in Fig. 1 for a D6 tool steel. Harris et al attribute this behaviour to a shift in fracture mode from plane strain to plane stress in the specimens they tested, which were less than 1 mm thick. On the other hand, in the work of Hamel, specimens with sufficient thickness (12.7 mm) were used so that the fatigue crack propagates always under plane strain conditions and hence it is not possible to apply the Harris and Dunegan model. In this paper, it is shown that acoustic emission during fatigue crack propagation is influenced by the geometry of the compact tensile specimens used. This can create constructive and destructive interferences of the acoustic waves. A simplified theoretical analysis as well as an experimental method for verification of the model are presented.
a
I 10-3
’
’
’
‘1
*“I
IO
““‘-““‘“‘l’ 20
AK
40
30
[MN m-'/2]
Fig. 1 Typical acoustic emission count rate as a function for a D6 steel specimen
of
AK
values of AK where the maximum and minimum have occurred. It is evident that there exists a better correlation of the maxima and minima with the crack length than with AK. Thus, it can be assumed that they are caused by geometrical factors governing the position of the emitting source rather than crack propagation mechanisms which are governed by AK. Proposed model
Experimental
results during fatigue
Two steels were used in this investigation. One is a tool steel, D6, in the as-received state, and the other is an annealed mild steel, Type AISI 1015. Compact tensile specimens, as illustrated in Fig. 2 were used. Fatigue cracks were propagated in the specimens under constant load to fracture while the acoustic emission was monitored. Thus, it was possible to acquire acoustic emission data for the same crack length but under different AK values. A summary of all the results is shown in Table 1, which gives the crack length as well as the
The authors are at the Ecole Polytechnique Canada. Paper received 3 January 1979.
Mont&al,
Qubbec,
0041-624X/79/030125-03/$02.00 ULTRASONICS.
MAY
1979
In the proposed model it is assumed that constructive and destructive interferences due to multiple reflections on the edges of the specimen cause the occurrence of the maxima and minima observed during fatigue. Such an effect has been studied by N. Chretien’ in the case of an aluminium rod. Because of the more complex geometry of the compact tensile specimens, a more simplified approach is used in this investigation. If the crack tip, which is the emitting source, is labelled N and the transducer, assumed to be a point receiver, is M, Fig. 2 shows the direct path as well as several alternative paths which are reflections on the sides of the specimen as well as at the holes. The virtual source R, in particular, 0
1979 IPC Business Press 125
Table
1.
fatigue
Occurrence
as a function
of acoustic emission minima of AK
during
and crack length a
AK[MPa m”]
aimml
Specimen max
min
max
min
D6 c
15.0
16.8
15.4
17.5
D6 D
12.2
13.1
16.1
17.3
D6 E
18.1
18.7
16.1
16.6
D6G
-
17.6
-
17.4
D6 II
19.0
19.9
12.3
13.2
D6 12
22.8
24.0
15.7
16.7
1015
A
17.4
19.9
12.9
15.4
1015
6
20.6
22.0
13.8
15.1
1015
c
28.3
29.1
14.4
14.9
1015
D
21.0
22.7
16.4
17.8
/
/
/’
d’ P
Fig. 2
Specimen
geometry
used and position of all possible virtual
mean and standard
Dimensions
of specimen
[mm]
deviation X
for D6 specimens
17.Ok4.5
18.0-13.9
15.8kO.3
=
a+21.72
A = 60.33
17.1 kO.4
B = 49.33 c = 57.91
mean and
D =
standard
18.11
deviation for 1015 specimens
Position 21.8k4.6
23.4f4.0
14.4*
1.5
assumes that the presence of the hole will not affect the path of the acoustic wave. This assumption is justified by the presence of the pins which do not attenuate the acoustic waves to any extent and by the fact that the transducer used has a resonant frequency of 375 kHz which corresponds Table
2.
Distance
and phase shift from the transducer
Distance Crack
virtual
from transducer
of sources to crack tip
15.8k1.4
to each of the
sources [mm]
NM =
y//[(C/2)*
+ (B -
Xl21
PM =
&(C/2)2
+ (2/I - X - Bj2 1
QM =
&3C/212
+ (B - XI21
RM = &(C/2j2
+ (B + Xl21
SM = &C/212
+ (B - X-
to each of the virtual
2D121
sources
Phase shift for each source for D6
Phase shift for each source for
specimens
the mild steel [radl
[radl
length a [mm]
N
P
cl
R
S
0,
10
33.89
49.06
88.63
86.07
53.37
11
87.01
54.21
88.26
87.95
55.06
15
31.58
16
31.20
17
30.84
18
30.51
19
30.21
20
29.94
21
29.70
48.26 47.46 46.48 45.90 45.12 44.36 43.61 42.87 42.14 41.41 40.71
88.44
14
33.38 32.89 32.43 31.99
12 13
OR
5.52
19.88
18.95
5.41
20.00
19.48
5.29
20.11
20.00
0s
en
eo
OR
7.07
5.85
21.10
20.11
7.56
5.14
21.22
20.66
8.03
8.05
5.62
21.35
21.22
8.55 9.06
es 7.50
88.09
88.90
55.91
5.17
20.21
20.51
8.53
5.50
21.45
21.76
87.92
89.84
56.77
5.04
20.32
21.01
9.01
5.36
21.55
22.31
9.55
87.78
90.79
57.63
4.92
20.40
21.50
9.46
5.22
21.66
22.83
10.04
87.64
91.74
58.50
4.78
20.51
21.99
9.91
5.08
21.76
23.34
10.52
87.51
92.69
59.37
4.64
20.58
22.46
10.37
4.92
21.85
23.84
11 .oo
87.39
93.64
60.24
4.49
20.66
22.93
10.80
4.76
21.92
24.33
11.47
87.29
94.59
61.12
4.33
20.13
23.39
11.22
4.59
22.01
24.82
11.92
87.20
95.54
62.01
4.17
20.80
23.82
11.64
4.42
22.08
25.29
12.36
87.12
96.50
62.89
4.00
20.86
24.26
12.06
4.24
22.13
25.74
12.79
The minima will occur at phase shifts corresponding
126
0,
to (2n - l)n
while the maxima
will occur at 2nn. where n = 1, 2, 3,
ULTRASONICS.
MAY
1979
to a wavelength of 17 mm. This value is higher than the diameter of the hole. The speed of longitudinal waves in the steels was obtained using the pulse-echo technique with a Sperry Reflectoscope. For the D6 and 1015 Steels, values of 6500 f 200 m s-’ and 6100 * 200 ms-’ were found respectively. The wavelength h is given as: h = V/f where the frequency f was taken as 375 kHz. For the D6, the value for h was 17.3 mm while for the 1015‘it was 16.3 mm. The phase angle 8, is
Crock length [mm] Fig. 3 Variation of the root mean square of the amplitude crack length using a pulser, with a mild steel specimen
0 = 2n(X-N) x h where X is the distance from any of the virtual sources (P, Q, R and S) to the transducer M, and N is the distance NM in Fig. 2. The minima are produced when 0, is (2n - 1)a and the maxima occur at 0, equal to 2n7r, with IZan integer. Table 2 gives the distance MN, MP, MQ, MR and MS as a function of the crack length a. Also shown is 13, for the various paths in both the D6 and the mild steel. By interpolation, it is found that for the D6, there will be a minimum at a = 14.9 mm, caused by a reflection at the sides of the hole and also another minimum at 16.0 mm due to the source R. In the mild steel, these minima occur at 13.4 and 13.8 mm respectively. Another minimum for the D6 occurs at 18.4 mm and a maximum at 19.7 mm which partially cancel out. It is thus possible to conclude that the main source of interference is the presence of the hole which causes these minima and maxima to occur. Table 3. mental
Summary
fatigue
of results obtained
testing,
theroetical
from
calculation
either experior from
using
a pulser
Experimental
with
verification
To determine the presence of these maxima and minima, an acoustic emission transducer was used as a pulser to scan the crack path in compact tensile specimens for both the D6 and the mild steel. A needle was used as a waveguide and the root mean square (rms) of amplitude of the acoustic emission from another transducer, located at point M, was obtained as a function of the position of the pulser. Several scannings were made to avoid statistical errors, and typical results of one scan on the mild steel are given in Fig. 3. It is evident that there is a minimum at a crack length of 14 mm. For the D6, it was found that there is a minimum at 13 mm. In Table 3, a summary of all the results either from the theoretical model, using a pulser, or from fatigue experiments is given. All the values are in good agreement and clearly demonstrate the validity of the assumption that the geometry of the specimen can indeed influence acoustic emission measurements during fatigue and be responsible for the presence of maximum and minimum values on the curve ii’against AK.
Crack length corresponding to interference Material
D6
[mm]
Method
Acknowledgements
Fatigue Theoretical
model
Max
Min
17.1
15.8
9.8 (3R)”
14.9 (2s)* 16.0(4R)+
1015 steel
Pulser
15.0
14.0 to 16.0
Fatigue
15.8
14.4
19.7 (4R)”
13.4 (4R)”
Theoretical
model
13.8 (2s)” 18.4 (4Q)” 18.00
Pulser
14.00
*These are evaluated from Table 2. The number represents the multiple of the minimum phase shift corresponding to the associated virtual source.
ULTRASONICS.
MAY
1979
The authors acknowledge the National Research Council of Canada for support of this investigation. One of the authors, FranGois Hamel, also received a postgraduate fellowship from the same organization for completion of this work.
References 1 2 3 4
5
Sinclair, A.C.E., Connors, D.C. Mat Sci Eng 28 (1977) 263-273 Harris, D.O., Dunegan, H.L. Experimental Mechanics (February 1974) 71-81 Hamel, F. Masters thesis, Ecole Polytechnique (1978) Bassim, M.N., Hamel, F. Proc Intern Summer School on Fatigue of Materials and Structures, Sherbrooke, Quebec (July lo-19 1978) ChrBtien, N. Ultrasonics 16 (2) (1978) 69-76
127