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Comparison of several methods of JIc determination
Engineering Frorrurr Printed in the U.S.A.
Merhunrc~
Vol. 22. No. 6, pp.
I117-I
0013-7944/85 $3.00 + .oa Pergamon Press Ltd.
119. 1985
TECHNICAL
COMPARISON
Northeast
OF SEVERAL
NOTE
METHODS
OF J,, DETERMINATION
ZU-HAN LA1 and CHANG-XIANG MA University of Technology, Shenyang, People’s Republic of China
have been several standards of J,, test methods; for example, Chinese Standard GB2038-80, American Standard ASTM E813-81 and Japanese Standard JSME SOOI-81. These are based on the multispecimen method. There are several alternatives for constructing the blunting line used in the multispecimen method. These are shown as follows: Chinese Standard:
THERE
J
=
t(oo.2
+
e)Aa, (1)
or
J = 3ofsAa,
Ufs =
I(ao.2
+
m)r
where ub is the ultimate tensile strength. and Au. the crack growth. According to Kobayashi et al.111:
According to Miyamoto[2]: J = 4ufsAa.
(31
SZW = nti,
(41
According to O’Brien and Ferguson[3]:
where n = f to 1 and 8 is the crack tip opening displacement, factor r, 0.40 s r s 0.45. Lastly, according to ASTM:
which can be measured as usual by using the rotational
J = Zof,Aa.
(51
Several researchers[2, 31 had reported that the blunting line given by (5) may not be suitable for soft materials and that the J,, value obtained by ASTM recommendation is usually larger than the values obtained by the other methods. One obvious reason for the discrepancy is that different definitions of blunting line had been used by different methods. Only the single specimen method does not need blunting line construction. In this report, we compare these different alternatives with our own single specimen method, which had been published in (41. An interpretation of the results is then given. The strengths of the materials used in this research are shown in Table 1. The specimens used in fracture mechanic tests are prepared according to GB2038-80 and the validity criterion of Jt, is satisfied. In Figs. l-3, straight line R represents the linear regression of multispecimen data points. Here we do not eliminate those points where Aa c 0.15 mm. This is similar to JSME Standard. The maximum Au is less than 1 mm. On the other hand, according to ASTM Standard, these points with Au s 0.15 mm must be abandoned. But we find that this does not introduce significant change of the results obtained here. The symbols in the figures are respectively: (A) blunting line given by O’Brien-Ferguson’s method (r = 0.45, n = 4). (B) blunting line J = 41r,~Aa, (C) blunting line J = i
Aa.
(D) blunting line J = 3uf,Aa, (E) blunting line J = 2uf.A~. The values of J,, obtained by the above methods are shown in Table 2. The figures in Table 2 demonstrate clearly that the first five methods give fairly well agreement with one another, while the last one (method 6) always gives somewhat of an overestimation of J,,. Now it is worth analyzing the reason for such a discrepancy. In our single specimen method, J,, is the toughness at the initiation pont of ductile tearing. It occurs just after the SZW had attained its maximum width. The agreement shown by the first five methods is not accidental, and it indicates that they all give the toughness at or very near to the crack initiation. Table 3 shows the maximum SZW at crack initiation obtained by the blunting line J = 2u,.Aa. 1117
1118
Technical Note Table 1. Strengths of the materials 00
2
Material
(MPa)
45* carbon steel 40 Cr 20 CrMnTi
510.9 620.8 750.2
ABCD
0
0.1
0.2
749.3 753.2 815.0
E
0.3
0.4
0.5
0.6
Ail
mm
Fig. 1. Linear regression of JR - Aa of 45* carbon steel and the blunting lines.
20 CrMnTi I (J
1
0.1
0.2
0.3
0.4
I
0.5
0.6
ba
mm
Fig. 2. Linear regression of J R - Aa of 2OCrMnTi and the blunting lines
1119
Technical Note
ABCD
0
at
0.2
E
0.3
0.4
a5
AlI nn
Fig. 3. Linear regression of JR - Au of 40Cr and the blunting lines.
Table 2. Comparison
Material 20 CrMnTi 45* 40 Cr
Method 1, single specimen method (1) (2) (1) (2) (1) (2)
112.1 166.9 117.9 132.8 129.4 164.0
of J,, (KPa m or KN m- ’ ) obtained by six different methods Method 2, using A
Method 3, using B
Method 4, using C
Method 5, using D
Method 6, using E
105.3 179.7 124.8 136.8 141.0 150.7
106.7 176.9 132.4 135.7 154.2 157.2
114.0 189.9 135.3 139.0 162.5 165.2
114.0 189.3 143.9 148.7 169.6 172.0
129.9 219.9 173.8 182.1 212.1 212.0
Table 3. Apparent SZW at crack initiation obtained by method 6 SZW at crack initiation (mm)
Material 20 CrMnTi 40 Cr 45*
0.09 0.15 0.14
Actually, the maximum SZW measured on the fracture surface or obtained by methods 2-5 lies between 0.05 to 0.09 mm. Therefore the values of Jt, of these steels according to method 6 are the J values at Au equal to 0.09 to 0.15 mm, which is beyond the physical crack initiation point.
REFERENCES 111H. Kobayashi, T. Mura, Proc. ICF Internarional Symposium on Fracture Mechanics (Beijing) 1983, p. 517. PI H. Miyamoto, H. Kobayashi, and N. Ohtsuka, Proc. ICFInrernationnl Symposium on Fracrure Mechanics (Beijing) 1983, p. 550. [31 D. M.-O’Brien, W. G. Ferguson, Inr. J. Fracture 20, No. 2, R39 (1982). 141 Z. H. Lai, L. J. Chen, J. M. Zhang, C. X. Ma and J. X. Zhao, Engng Fracfure and J. M. Zhang, J. Testing Eval. 11, No. 5, 340 (1983). (Received
15 Nol,ember
1984)
Mech. 17, 395 (1983); Z. H. Lai
Merhunrc~
Vol. 22. No. 6, pp.
I117-I
0013-7944/85 $3.00 + .oa Pergamon Press Ltd.
119. 1985
TECHNICAL
COMPARISON
Northeast
OF SEVERAL
NOTE
METHODS
OF J,, DETERMINATION
ZU-HAN LA1 and CHANG-XIANG MA University of Technology, Shenyang, People’s Republic of China
have been several standards of J,, test methods; for example, Chinese Standard GB2038-80, American Standard ASTM E813-81 and Japanese Standard JSME SOOI-81. These are based on the multispecimen method. There are several alternatives for constructing the blunting line used in the multispecimen method. These are shown as follows: Chinese Standard:
THERE
J
=
t(oo.2
+
e)Aa, (1)
or
J = 3ofsAa,
Ufs =
I(ao.2
+
m)r
where ub is the ultimate tensile strength. and Au. the crack growth. According to Kobayashi et al.111:
According to Miyamoto[2]: J = 4ufsAa.
(31
SZW = nti,
(41
According to O’Brien and Ferguson[3]:
where n = f to 1 and 8 is the crack tip opening displacement, factor r, 0.40 s r s 0.45. Lastly, according to ASTM:
which can be measured as usual by using the rotational
J = Zof,Aa.
(51
Several researchers[2, 31 had reported that the blunting line given by (5) may not be suitable for soft materials and that the J,, value obtained by ASTM recommendation is usually larger than the values obtained by the other methods. One obvious reason for the discrepancy is that different definitions of blunting line had been used by different methods. Only the single specimen method does not need blunting line construction. In this report, we compare these different alternatives with our own single specimen method, which had been published in (41. An interpretation of the results is then given. The strengths of the materials used in this research are shown in Table 1. The specimens used in fracture mechanic tests are prepared according to GB2038-80 and the validity criterion of Jt, is satisfied. In Figs. l-3, straight line R represents the linear regression of multispecimen data points. Here we do not eliminate those points where Aa c 0.15 mm. This is similar to JSME Standard. The maximum Au is less than 1 mm. On the other hand, according to ASTM Standard, these points with Au s 0.15 mm must be abandoned. But we find that this does not introduce significant change of the results obtained here. The symbols in the figures are respectively: (A) blunting line given by O’Brien-Ferguson’s method (r = 0.45, n = 4). (B) blunting line J = 41r,~Aa, (C) blunting line J = i
Aa.
(D) blunting line J = 3uf,Aa, (E) blunting line J = 2uf.A~. The values of J,, obtained by the above methods are shown in Table 2. The figures in Table 2 demonstrate clearly that the first five methods give fairly well agreement with one another, while the last one (method 6) always gives somewhat of an overestimation of J,,. Now it is worth analyzing the reason for such a discrepancy. In our single specimen method, J,, is the toughness at the initiation pont of ductile tearing. It occurs just after the SZW had attained its maximum width. The agreement shown by the first five methods is not accidental, and it indicates that they all give the toughness at or very near to the crack initiation. Table 3 shows the maximum SZW at crack initiation obtained by the blunting line J = 2u,.Aa. 1117
1118
Technical Note Table 1. Strengths of the materials 00
2
Material
(MPa)
45* carbon steel 40 Cr 20 CrMnTi
510.9 620.8 750.2
ABCD
0
0.1
0.2
749.3 753.2 815.0
E
0.3
0.4
0.5
0.6
Ail
mm
Fig. 1. Linear regression of JR - Aa of 45* carbon steel and the blunting lines.
20 CrMnTi I (J
1
0.1
0.2
0.3
0.4
I
0.5
0.6
ba
mm
Fig. 2. Linear regression of J R - Aa of 2OCrMnTi and the blunting lines
1119
Technical Note
ABCD
0
at
0.2
E
0.3
0.4
a5
AlI nn
Fig. 3. Linear regression of JR - Au of 40Cr and the blunting lines.
Table 2. Comparison
Material 20 CrMnTi 45* 40 Cr
Method 1, single specimen method (1) (2) (1) (2) (1) (2)
112.1 166.9 117.9 132.8 129.4 164.0
of J,, (KPa m or KN m- ’ ) obtained by six different methods Method 2, using A
Method 3, using B
Method 4, using C
Method 5, using D
Method 6, using E
105.3 179.7 124.8 136.8 141.0 150.7
106.7 176.9 132.4 135.7 154.2 157.2
114.0 189.9 135.3 139.0 162.5 165.2
114.0 189.3 143.9 148.7 169.6 172.0
129.9 219.9 173.8 182.1 212.1 212.0
Table 3. Apparent SZW at crack initiation obtained by method 6 SZW at crack initiation (mm)
Material 20 CrMnTi 40 Cr 45*
0.09 0.15 0.14
Actually, the maximum SZW measured on the fracture surface or obtained by methods 2-5 lies between 0.05 to 0.09 mm. Therefore the values of Jt, of these steels according to method 6 are the J values at Au equal to 0.09 to 0.15 mm, which is beyond the physical crack initiation point.
REFERENCES 111H. Kobayashi, T. Mura, Proc. ICF Internarional Symposium on Fracture Mechanics (Beijing) 1983, p. 517. PI H. Miyamoto, H. Kobayashi, and N. Ohtsuka, Proc. ICFInrernationnl Symposium on Fracrure Mechanics (Beijing) 1983, p. 550. [31 D. M.-O’Brien, W. G. Ferguson, Inr. J. Fracture 20, No. 2, R39 (1982). 141 Z. H. Lai, L. J. Chen, J. M. Zhang, C. X. Ma and J. X. Zhao, Engng Fracfure and J. M. Zhang, J. Testing Eval. 11, No. 5, 340 (1983). (Received
15 Nol,ember
1984)
Mech. 17, 395 (1983); Z. H. Lai