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w ratio on crack initiation values of cod and j-integral
En&wing t~rwrrwe Mechonb~s Printed in Great Britain.
Vol. 23. No. 5. PP. 925-928. 1986
0013-794486 $3.00 + .OO 0 1986 Pergamon Press Ltd.
TECHNICAL THE EFFECT
Department
NOTE
OF a/W RATIO ON CRACK INITIATION COD AND J-INTEGRAL
VALUES
OF
QINGFEN Ll, LlMlN ZHOU and SHOUREN LI of Mechanical Engineering, Harbin Shipbuilding Engineering Institute, Harbin, China
Abstract-The effect of the crack length/specimen width ratio (a/W) on the crack initiation values of crack opening displacement (COD) and J-integral were investigated. A series of tests was performed on a high-strength and high-toughness alloy steel where the ratio a/W was varied from about 0.1 to 0.5, keeping W constant. Two clip gauges were used. P-V and P-A plots were simultaneously obtained on the same specimen. The COD values were obtained from both PV and P-A plots. The J-integral values were calculated according to the “single-point method.” The results indicate that Ji and hi values of shallow cracks are significantly higher than those of deep cracks. Si is insensitive to a/W when a/W 2 0.2 and becomes dependent on a/W as a/W S 0.15. 1. INTRODUCTION MUCH PREVIOUS work has shown that the initiation value of COD, Si, is insensitive to a/WI, investigations have shown that for a/W < 0.19, Si and Ji values are much larger than those Therefore, it is worthwhile to investigate the effect of n/W on ai and Ji for both a/W L 0.2 and In the present work, the tests were carried out in six groups of three-point-bend specimens was varied from 0.1 to 0.5.
21. However, recent of deep cracks[3, 41. a/W < 0.2. where the ratio a/W
2. EXPERIMENTAL PROCEDURE (a) Material and specimens A Chinese alloy steel was used. The chemical compositions and mechanical properties are given in Table I. Test pieces were of B = 12.5 mm, W = 25 mm, S = 4W and knife edge of thickness z = 1.8 mm. a was varied from 2.5 to 12.5 mm. (b) Tests Specimens were loaded, and P-V and P-A plots were simultaneously recorded on an X-Y-Y recorder. Two clip gauges were used. One was used to measure the crack mouth displacement V and the other was to measure the loadpoint displacement A. Six series of & and Ji values were obtained from both P-V and P-A plots. After off-loading, specimen crack fronts were marked by heat tinting and then specimens were broken at low temperature. Crack length a and crack extension Au measurements were made according to the seven-point-average procedure. All tests were made at room temperature. (c) Determination of Ji, 6, and rp The J-integral values were calculated according to the “single-point used:
method”[5] and the following formulas were
J=
in which MJPA J, = ~ B(W - a) ’
p=
(2)
E
67r(I - v2)a; ’
M, = 0.2227 + 2.6839CalW) - 2.3119(~IW)~.
(3) (4)
From the P-V plot, the COD values 6” were calculated according to the formula Yp(W - a,v, 6” = 6”e + s” = K2 (I - v21 + P 2a,E yp(W - a) + a + z ’ where S: and S; are the elastic and plastic component
of s” respectively. 925
(5)
926
Technical Note Table 1. Composition and properties of the tested steel Chemical analysis C
0.19
Ni 4.15
Cr 1.44
W 0.93
Mn 0.41
Si 0.35
s P cu 0.06 0.013 0.04
Mechanical properties Yield strength Ultimate strength Elongation
83.8 kg/mm’ 96.7 kg/mm’ 20.1%
From the P-A plots, the COD values 6’ were calculated according to the formula 6.
=
6-\
+
c..
_
e
K’(1- 6 + Ed’+’ - &J, 2a,E
W
For a/W 2 0.2, there is good agreement between these two sets of 6 values. (All the relative differences between 6” and 6* are within 5%.) We therefore take 6 = (6” + 6”)/2. For a/W < 0.2, the plastic flow spreads to the surface of the beam and the flanks of the shallow cracks were slightly curved. The COD cannot be accurately obtained from a clip gauge measurement at the mouth of the crack[3]. In these circumstances, we take 6 = 6*. According to recent work[4, 61, we take r = 0.45 in our calculation. 3. RESULTS AND DISCUSSION Experimental results of COD and J-integral values are shown in Figs. 1 and 2 as a function of crack growth Aa. The initiation values of COD as a function of a/W are given in Fig. 3. Table 2 gives the values of J, and &.
Symbol A A 0 0 X 0
0.7 -
0.6 -
8=2Aa
0.3
0.4
0.5
0.6
Aotmm) Fig. I. Experimental
results of COD.
0.7
O/W Group A Group B
GroupC Group D GroupE Group F
0.8
0.5 0.4 0.3 0.2
0.15 0.1
0.9
I 1.0
Technical Note
927
0.13
Symbol A a 0 0 X
1
0.i
,-
GroupA Group B GroupC Group D GroupE Group F
q
O/W 0.5 0.4 0.3 0 2 0 15 0 I
0.1 3-
J =2uyAa
O.! j-
-z0.4 E
I-
h Y * O.?s-
0
0.1
0.2
I
I
0.3
0.4
I
0.5
I
0.6
0.7
0.6
0.9
1.0
Aatmm) Fig. 2. Experimental
results of J-integral.
The results show that 6i increases slightly with decreasing a/W, it is insensitive to a/W when a/W 3 0.2, and becomes dependent on a/W as u/W s 0.15. 6;for shallow cracks (a/WS 0.15) is about twice that of the deeper cracks. Ji increases with decreasing a/W and is much higher for shallow-notch specimens than for the deep ones. These results clearly show that shallow cracks can exhibit significantly higher toughness values than those obtained for deep cracks. As a consequence, the assessment of the significance of many shallow defects (in practice, defects are often in the form of shallow surface cracks) by the normal method is unduly conservative. This is in agreement with [3], [4] and [7].
6
Fig. 3. hi as a function of a/W.
928
Technical Note Table 2. J, and 6, values triw
6, (mm)
J, (kg/mm)
0.5
0.105
0.4 0.3 0.2 0.15 0.1
0.114 0.140 0.149 0.250 0.295
IS.3 16.5 l8.S 19.0 22.2 23.0
4. CONCLUSIONS I. 6, increases slightly with decreasing a/W when u/W 2 0.2 and becomes dependent on u/W as ul W C 0.15. 2. The values of Ji and 6; for shallow cracks (al W s 0.15) are significantly higher than those for the deep ones. This result shows that small cracks can exhibit significantly higher toughness and therefore shows the importance of small cracks in engineering design. REFERENCES
[II P. M. S. T. de Castro, .I. Spurrier and P. Hancock, An experimental study of the crack length/specimen width (a/W) ratio dependence of the crack opening displacement (COD) test using small-scale specimens, Fracture Mechanics (C. W. Smith, Ed.) ASTM STP 677, 486-491 (1979). VI T. Ingham, G. R. Egan, D. Elliott and T. C. Harrison, The effect of geometry on the interpretation of COD test data. Instn. Mech. Engrs. C54l41, 200. [31 B. Collerell, Q. F. Li, D. Z. Zhang and Y. W. Mai, On the effect of plastic constraint on ductile tearing in a structural steel, Engng Fract. Mech. 21, 239-244 (1985). [41 Qing-fen Li, A study about Ji and 6; in three-point bend specimens with deep and shallow notches, Engng Fract. Mech. 22, 9-16 (1985).
[51 Shen Wai, Single-point method of calculating J-integral, J. Huazhong Engng Inst. 2 (1978). 161 Wu Shang-xian, Plastic rotational factor and J-COD relationship of three-point bend specimen, Engng Fracf. Mech. 18, 83-95 (1983).
171 C. G. Chipperfield, Some observation on ductile crack initiation and propagation in fracture toughness specimens, in Proceedings Special&s Meeting on Elusto-plastic Fracture Mechanics, OECP Nuclear Energy Agency. Dareshury, 1978, Vol. 2, p. 15.
Vol. 23. No. 5. PP. 925-928. 1986
0013-794486 $3.00 + .OO 0 1986 Pergamon Press Ltd.
TECHNICAL THE EFFECT
Department
NOTE
OF a/W RATIO ON CRACK INITIATION COD AND J-INTEGRAL
VALUES
OF
QINGFEN Ll, LlMlN ZHOU and SHOUREN LI of Mechanical Engineering, Harbin Shipbuilding Engineering Institute, Harbin, China
Abstract-The effect of the crack length/specimen width ratio (a/W) on the crack initiation values of crack opening displacement (COD) and J-integral were investigated. A series of tests was performed on a high-strength and high-toughness alloy steel where the ratio a/W was varied from about 0.1 to 0.5, keeping W constant. Two clip gauges were used. P-V and P-A plots were simultaneously obtained on the same specimen. The COD values were obtained from both PV and P-A plots. The J-integral values were calculated according to the “single-point method.” The results indicate that Ji and hi values of shallow cracks are significantly higher than those of deep cracks. Si is insensitive to a/W when a/W 2 0.2 and becomes dependent on a/W as a/W S 0.15. 1. INTRODUCTION MUCH PREVIOUS work has shown that the initiation value of COD, Si, is insensitive to a/WI, investigations have shown that for a/W < 0.19, Si and Ji values are much larger than those Therefore, it is worthwhile to investigate the effect of n/W on ai and Ji for both a/W L 0.2 and In the present work, the tests were carried out in six groups of three-point-bend specimens was varied from 0.1 to 0.5.
21. However, recent of deep cracks[3, 41. a/W < 0.2. where the ratio a/W
2. EXPERIMENTAL PROCEDURE (a) Material and specimens A Chinese alloy steel was used. The chemical compositions and mechanical properties are given in Table I. Test pieces were of B = 12.5 mm, W = 25 mm, S = 4W and knife edge of thickness z = 1.8 mm. a was varied from 2.5 to 12.5 mm. (b) Tests Specimens were loaded, and P-V and P-A plots were simultaneously recorded on an X-Y-Y recorder. Two clip gauges were used. One was used to measure the crack mouth displacement V and the other was to measure the loadpoint displacement A. Six series of & and Ji values were obtained from both P-V and P-A plots. After off-loading, specimen crack fronts were marked by heat tinting and then specimens were broken at low temperature. Crack length a and crack extension Au measurements were made according to the seven-point-average procedure. All tests were made at room temperature. (c) Determination of Ji, 6, and rp The J-integral values were calculated according to the “single-point used:
method”[5] and the following formulas were
J=
in which MJPA J, = ~ B(W - a) ’
p=
(2)
E
67r(I - v2)a; ’
M, = 0.2227 + 2.6839CalW) - 2.3119(~IW)~.
(3) (4)
From the P-V plot, the COD values 6” were calculated according to the formula Yp(W - a,v, 6” = 6”e + s” = K2 (I - v21 + P 2a,E yp(W - a) + a + z ’ where S: and S; are the elastic and plastic component
of s” respectively. 925
(5)
926
Technical Note Table 1. Composition and properties of the tested steel Chemical analysis C
0.19
Ni 4.15
Cr 1.44
W 0.93
Mn 0.41
Si 0.35
s P cu 0.06 0.013 0.04
Mechanical properties Yield strength Ultimate strength Elongation
83.8 kg/mm’ 96.7 kg/mm’ 20.1%
From the P-A plots, the COD values 6’ were calculated according to the formula 6.
=
6-\
+
c..
_
e
K’(1- 6 + Ed’+’ - &J, 2a,E
W
For a/W 2 0.2, there is good agreement between these two sets of 6 values. (All the relative differences between 6” and 6* are within 5%.) We therefore take 6 = (6” + 6”)/2. For a/W < 0.2, the plastic flow spreads to the surface of the beam and the flanks of the shallow cracks were slightly curved. The COD cannot be accurately obtained from a clip gauge measurement at the mouth of the crack[3]. In these circumstances, we take 6 = 6*. According to recent work[4, 61, we take r = 0.45 in our calculation. 3. RESULTS AND DISCUSSION Experimental results of COD and J-integral values are shown in Figs. 1 and 2 as a function of crack growth Aa. The initiation values of COD as a function of a/W are given in Fig. 3. Table 2 gives the values of J, and &.
Symbol A A 0 0 X 0
0.7 -
0.6 -
8=2Aa
0.3
0.4
0.5
0.6
Aotmm) Fig. I. Experimental
results of COD.
0.7
O/W Group A Group B
GroupC Group D GroupE Group F
0.8
0.5 0.4 0.3 0.2
0.15 0.1
0.9
I 1.0
Technical Note
927
0.13
Symbol A a 0 0 X
1
0.i
,-
GroupA Group B GroupC Group D GroupE Group F
q
O/W 0.5 0.4 0.3 0 2 0 15 0 I
0.1 3-
J =2uyAa
O.! j-
-z0.4 E
I-
h Y * O.?s-
0
0.1
0.2
I
I
0.3
0.4
I
0.5
I
0.6
0.7
0.6
0.9
1.0
Aatmm) Fig. 2. Experimental
results of J-integral.
The results show that 6i increases slightly with decreasing a/W, it is insensitive to a/W when a/W 3 0.2, and becomes dependent on a/W as u/W s 0.15. 6;for shallow cracks (a/WS 0.15) is about twice that of the deeper cracks. Ji increases with decreasing a/W and is much higher for shallow-notch specimens than for the deep ones. These results clearly show that shallow cracks can exhibit significantly higher toughness values than those obtained for deep cracks. As a consequence, the assessment of the significance of many shallow defects (in practice, defects are often in the form of shallow surface cracks) by the normal method is unduly conservative. This is in agreement with [3], [4] and [7].
6
Fig. 3. hi as a function of a/W.
928
Technical Note Table 2. J, and 6, values triw
6, (mm)
J, (kg/mm)
0.5
0.105
0.4 0.3 0.2 0.15 0.1
0.114 0.140 0.149 0.250 0.295
IS.3 16.5 l8.S 19.0 22.2 23.0
4. CONCLUSIONS I. 6, increases slightly with decreasing a/W when u/W 2 0.2 and becomes dependent on u/W as ul W C 0.15. 2. The values of Ji and 6; for shallow cracks (al W s 0.15) are significantly higher than those for the deep ones. This result shows that small cracks can exhibit significantly higher toughness and therefore shows the importance of small cracks in engineering design. REFERENCES
[II P. M. S. T. de Castro, .I. Spurrier and P. Hancock, An experimental study of the crack length/specimen width (a/W) ratio dependence of the crack opening displacement (COD) test using small-scale specimens, Fracture Mechanics (C. W. Smith, Ed.) ASTM STP 677, 486-491 (1979). VI T. Ingham, G. R. Egan, D. Elliott and T. C. Harrison, The effect of geometry on the interpretation of COD test data. Instn. Mech. Engrs. C54l41, 200. [31 B. Collerell, Q. F. Li, D. Z. Zhang and Y. W. Mai, On the effect of plastic constraint on ductile tearing in a structural steel, Engng Fract. Mech. 21, 239-244 (1985). [41 Qing-fen Li, A study about Ji and 6; in three-point bend specimens with deep and shallow notches, Engng Fract. Mech. 22, 9-16 (1985).
[51 Shen Wai, Single-point method of calculating J-integral, J. Huazhong Engng Inst. 2 (1978). 161 Wu Shang-xian, Plastic rotational factor and J-COD relationship of three-point bend specimen, Engng Fracf. Mech. 18, 83-95 (1983).
171 C. G. Chipperfield, Some observation on ductile crack initiation and propagation in fracture toughness specimens, in Proceedings Special&s Meeting on Elusto-plastic Fracture Mechanics, OECP Nuclear Energy Agency. Dareshury, 1978, Vol. 2, p. 15.