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A new method for measurement of fracture toughness KIC by three point bend specimen
Engineering Fracture Mechanics Printed in Great Britain.
Vol. 45,
No.
2. pp.
141-147,
0013-7944/93 $6.00 + 0.00 Ii‘ 1993 Pergamon Press Ltd.
1993
A NEW METHOD FOR MEASUREMENT OF FRACTURE TOUGHNESS K,, BY THREE POINT BEND SPECIMEN ZHU Department
of Basic Sciences.
ZHE-MING
Fuxin
Mining
Institute,
Fuxin
123000, P.R.C.
Abstract-The relationship between the three point bend (TPB) specimen size and the measured fracture toughness K,, value is analyzed by the theory of crack opening displacement (COD). According to the concept of plane strain fracture toughness K,,, a new formula for K,, is presented. For small-scale or large-scale TPB specimens, the K,, values of material can all be obtained from the new formula and the corresponding curve of load versus crack mouth opening displacement (CMOD). For large-scale specimens, the new formula is compatible with the ASTM standard.
1. INTRODUCTION of fracture toughness value, K,c, of material by three point bend (TPB) specimen, the specimen sizes must satisfy the conditions that B > 2S(K,,/q,.)* and (W - a) > 2S(K,,/q,.)* [l]. The experimental work may be difficult for the following reasons. (1) When the yield strength of some metals is low or fracture toughness is high, the specimen size will need to be very large for measurement of the effective fracture toughness K,,. It will not be convenient for experimental work. (2) Sometimes the measurement of K,, must take place in a specified medium or under a specified temperature; it may not be possible to perform the experiment for a large-scale specimen. (3) If the K,, value of the material cannot be estimated before measurement, in order to satisfy the size condition, a large number of specimens of different sizes is needed for measurement of K,,. Therefore, the amount of experimental work will be increased. If K,, can also be measured by a small-scale specimen, the above mentioned difficulties will not exist. Here, a new method is put forward, by which the K,, may be measured by a single small-scale TPB specimen. This makes a significant contribution to economy and efficiency. The principle and calculation method are presented in the following. IN THE MEASUREMENT
2. PRINCIPLE
AND CALCULATION
METHOD
A TPB specimen is shown in Fig. 1. The unflawed stress 0 of the crack tip is a = aPS/[aB( W - a)“] = ~PS/(u*BW*),
(1)
where 1 -a/W,
cc =(W-a)jW=
Let us introduce a new parameter
VS which is taken as
(2)
CMOD (VI
Fig. 2. Load versus CMOD record of large enough specimen.
Fig. I. TPB specimen. I41
142
ZHU
Fig. 3. (r-KS
ZHE-MING
line.
where V is the crack mouth opening displacement (CMOD); I’S approaches the opening displacement of point N which is & from the crack tip. If the specimen is large enough, or it fractures in the linear elastic state, the corresponding plot of load P versus CMOD V is as shown in Fig. 2. We have PC -=P,
V(. (3)
VB’
where C is the critical point of fracture in Fig. 2. Pg. P, and V,, Vc are the loads and CMODs, respectively. From eq. (1) we have cc P, -z-, (4) GB PB where oc and crBare the unflawed stresses of the crack tip which correspond respectively. From eq. (2) we have vs, v< vs,=v,*
to points C and B,
(5)
where I’S, and VSB are the parameters VS which correspond to points C and B, respectively. From eqs (3), (4) and (5) we obtain gc --=---bB - 8. (6) vsc KS, Equation (6) indicates that for a large enough TPB specimen cr is in linear relation with VS as shown in Fig. 3. fl is the slope of this line. According to similar theory, the fl values of geometrically similar specimens are a certainty for a material. The law is verified by experiments of No. 45 steel. The results of tests are shown in Table I. The relationship between the crack tip opening displacement (CTOD) 6 and CMOD V is (Fig. 4) (5 r(W-u) I/==r(W-a)+a or ril -a/B) r(1 -a/W)+a/IV
6=
v
(7)
’
where r is the rotation factor, and in the critical state the factor r approaches for instance DD-19 [3] has suggested r = l/3. Table I. V,. and b values of TPB specimen T, B, U’ a/W V, B
(mm) unit length MPa mm unit length
TZ
7.3
Td
(S/W T,
a constant [2],
= 4) T6
T7
T”
6, 12 0.504 72.5
8. 16 0.501 73.8
10, 20 0.495 72.0
12, 24 0.498 73.1
15, 30 0.501 70.8
25, 50 0.497 70.2
40, 80 0.501 73.1
60. 120 0.498 71.7
71.2
72.6
71.1
70.7
71.9
70.9
71.3
72.2
Measurement of fracture toughness by three point bend specimen
143
When 6 = & (6, is a certainty for a material), eq. (7) can be written as
4-4w>
&=
v
r(1 -a/W)+a/W
(8)
”
Equation (8) indicates that for the geometrically similar TPB specimens the critical CMOD values Vc are a certainty for a material. The law is verified by experiments on No. 45 steel; the results of tests are shown in Table 1. The formula for the stress intensity factor of a TPB specimen is A4 K, = Bw)‘zf
(a/W)
= h’afif
(a/W).
Now we assume that there are two large enough specimens among a group of geometrically similar TPB specimens with various sizes, and they all fracture in the linear elastic state; we have K,, =
42
=
Kc,
(10)
where K,, and K,* are the critical stress intensity factors of these two specimens, respectively. Substituting eq. (9) into eq. (lo), and noting f(a,/W,) =f(a,/W,) for proportional specimens, we have acIJK=ac2JK or
(11) where ac, , acZ and W, , W, are the critical unflawed stresses of the crack tip and the widths of these two specimens, respectively. From eq. (2) we can obtain the corresponding ratio of critical VS of these two specimens as VSc, V,,I& Vc, Ja, =-----. m -V&2 = v,,/Ja, vc2 fi Considering the critical CMOD V,, = Vc2 and a2/a, = W,/ W, for proportional eq. (12) can be written as -
specimens. (13)
From eqs (11) and (13) we have acI
ac2
vscl=vs,2*
(14)
Equation (14) indicates that for large enough and geometrically similar TPB specimens the ratios of the critical unflawed stress of the crack tip to the critical parameter VS are a certainty for a material. The corresponding relationship between ac and VS, is plotted by line OD in Fig. 5. Comparing with eq. (6) the slope of line OD is equal to the slope of line a-VS of one of these geometrically similar specimens. These two lines will naturally coincide.
Fig. 5. ur-KS,
curve of geometrically similar specimens.
144
ZHU
ZHE-MING
.Ti WC 12mm . r,
‘6
/
T,
ByElmm
W=
16 mm
T3’
B-IOmm
W=
20
mm
T,
Byl2mm
W-
24
mm
Ts
B-15mm
W=
30
mm
T,
Bz25mm
W:
50
mm
T,
B-40mm
W=
80
mm
T,
El=60mm
W=
120 mm 35
“S Fig, 6. The o C’S curve of No. 45 steel small-scale fractured
umt length
(-XT-)
specimen and compar~on specimens.
with the 0, . I ‘S, values nl
However, when the specimen size is smaller, because of plastic deformation, it is fractured under large displacement. The relationship between u(. and VS,. is not linear. and is plotted by curve DE in Fig. 5. On the a,-KS,. curve, the critical point of fracture will depend on the specimen size. From eqs (11) and (13) we obtain that (TV,and P’S,, are inversely proportional to V:%. The point of cc and VSc will move to the point 0 along the o~.~VS,. curve as the specimen size increases. Obviously the whole oc-L’S, curve ODE is practically the B-VS curve of the small-scale specimen of which E is the critical point of fracture. The reason is that if the cc.- P’S,.curve is ODE’ (OD portion will coincide) as shown in Fig. 5, E’ is the critical point of fracture of this small-scale specimen. the coordinates (L’S,., , CJ<,~ ) of point E’ are equal to the coordinates ( F’S,, CT(. ) of point E, so the points E’ and E will coincide, and the whole curves ODE’ and ODE will coincide. The law is verified by experiments of No. 45 steel, and the results of tests are plotted in Fig. 6. According to the concept of plane strain fracture toughness K,,., the stress intensity factor K, equals K,c only when the specimen fractures in the linear elastic state. For a small-scale specimen which fractures in the nonlinear elastic state, K, does not equal K,,., but we can obtain K, (which equals K,c) of a large enough specimen from the load versus CMOD curve of this small-scale specimen. The process is derived in the following. We arbitrarily locate one point A in the linear portion (line OD) of the curve ODE (Fig. 5). A is the critical point of fracture, and the corresponding specimen is large enough and is similar to the specimen of which E is the critical point of fracture. From eq. (9), the K,,, of the specimen of which A is the critical point of fracture can be written as
(15) where (TV,., , uA and W, are the critical unflawed stress of the crack tip. crack length and width of the specimen of which A is the critical point of fracture. Since the rr( --V.S,. curve of geometrically similar specimens is practically the (r-k’s curve of this small-scale specimen of which E is the critical point of fracture, we obtain
(16) where gA and P,4 are the unflawed stress and the load of point A on the 0 - VS curve, and S,. B, and W, are the sizes of this small-scale specimen. From eqs (2), ( 13) and (16) we have
Measurement of fracture toughness by three point bend specimen
Substituting eqs (16) and (17) into eq. (15) and noting f(aE/ W,) =f(a,/ specimens, we obtain
145
WA) for proportional
(18)
KM= When S/W = 4, we have
(19) where P, and VE/VA can be obtained from the load versus CMOD curve of this small-scale specimen. According to ASTM E399 standard [l], the formula of K,, for this small-scale specimen of which E is the critical point of fracture is KIE =
#f($)
.
(20)
E
E
From eqs (18) and (20) we have
where PA/VA is the slope of the linear portion of the P-V curve, and PE/ VE is the slope of the secant line OE of the P-V curve. Let us define m and m’ as m = PA/VA
(22)
m’= PEIVE.
(23)
From eqs (22) and (23), eq. (21) can be written as
KA = 4, =
3 K,E.
Equation (24) indicates the relationship between the K,, value of material and the K,, value of measurement using a small-scale TPB specimen. Since m 2 m’, we have K,, > I&.
(25)
When a specimen fractures in the linear elastic state (i.e. OE is in the linear state), m = m’, eq. (24) can be written as K,, = K,E.
(26)
So, eq. (21) or (24) is compatible with ASTM E399 standard [I] for the plane strain fracture toughness K,, , and they are suitable not only for a small-scale specimen but also for a large-scale
specimen. 3. EXPERIMENTAL
RESULTS
The material employed in the test is shown in Table 2. The small-scale TPB specimen data are as follows: B = 10 mm, W = 20 mm, a = 9.9 mm, S/W = 4. The load versus CMOD record of this small-scale specimen is shown in Fig. 7. The critical point of fracture that we determined is E, and P, = 1302 kg, VE = 72 unit lengths. From eq. (20) we obtain K,E = 94.37 MPa,,&. Table 2 Material No. 45 steel
Heat treatment Normalizine.
HRC (MPa) 52.3
oh (MPa) 804
& (MPa&) 101
146
ZHU
ZHE-MING
1600
/I
1200
-6%
1000
1
a
I-
800
T7
B
J
600 t
I 0
IO
li 20
I
CMOD
Fig. 7. Load
I 40
30
P versus CMOD
V Curd
V record
I 50
I 60
I 70
I 80
1 90
length)
of a small-scale
TPB specimen
Table 3 Material
Heat treatment
No. 45 steel 45MnSiV
860 900 440 650
34CrNi3Mo
We arbitrarily lengths. Substituting
C normalizing ‘C quenching C tempering C tempering
Actual K,,. (MPaJG)
Eq. (21)
z,,. (MPa&)
g,jL (MPa)
vh (MPa)
294 1471
549 1648
70.7 71.9 83.7
69.5 84.5
539
716
121~ 138
122.8
locate one point A in the linear portion, and P, = 400 kg, V,4= 20.8 unit the values of P,. V,. P,, Vt and K,, into eq. (21). we obtain K,, = 100.36 MPa,/m.
Comparing it with the actual K,, value, we find that the K,, value calculated according to eq. (21) has a good accuracy. By using small-scale TPB specimens. we have measured the K,, values of three other materials according to eq. (21) or (24). The results of tests are shown in Table 3.
4. THE FORMULA
CONDITIONS
Equation (21) or (24) is derived at the condition for which CTOD 6c is a certainty for a material, but according to ref. [4], the value S,. of a specimen for which B = 2 mm has a big difference from the values 6,. of specimens for which B > 5 mm. Therefore, during measurement of fracture toughness value K,,., the width B of the specimen should be bigger than 5 mm. The lower bound of the specimen size has yet to be studied further for measurement of an effective K,,. value. Since the CMOD V is measured by a clip-gage attached to the crack mouth of a TPB specimen, and in eq. (7) or (8), the distance of the clip-gage location from the specimen surface has not been considered, so during the test, we should try to decrease the distance, or directly stick the clip-gage on the crack mouth of the specimen using glue-water. The determination of the critical point is important for the measurement of fracture toughness K,c, because it determines the value nr’ of eq. (24). It should be performed as follows. (1) For fracture at indication of “pop-in” or crack burst, the determination of the critical point should be performed according to ASTM E399 standard [I]. (2) For fracture at no indication of “pop-in” or crack burst, the determination of the critical point should be performed according to the method of CTOD measurement [3]. 5. CONCLUSIONS (1) The new method for measurement of fracture toughness K,, values using TPB specimens is based upon the idea that the a-KS curve of the small-scale specimen contains all the o-VS curves of geometrically similar specimens with larger sizes.
Measurement of fracture toughness by three point bend specimen
147
(2)For the small-scale specimen, the fracture toughness value K,, measured according to ASTM E399 standard is less than the actual K,,[5], for instance K,E= 94.37 MPaJ;f; < 101 MPa fi. However, according to eq. (21) or (24), the K,,value is very close to the actual K,c. (3) The procedure of the present work can be referred to for other kinds of specimens (for instance, the compact specimen, C-specimen, etc.) which are utilized for measurement of the fracture toughness value K,,. REFERENCES Standard method of test for plane strain fracture toughness of materials, ASTM E399-81 (1982). [ii T. Ingham, G. R. Egum, D. Elliott and T. C. Harrison, The effection geometry on the interpretation of COD test data. Conference on Practical Application of Fracture Mechanics to Pressure-Vessel Technology, London, C 54/71 (May 1971). [31 Methods for crack opening displacement (COD) testing. British Standard Institution Draft for Development 19, London (1972). [41 R. F. Smith and J. F. Knott, Crack opening displacement and fibrous fracture in mildsteel. Conference on Practical Application of Fracture Mechanics to Pressure-Vessel Technology, London, C 9/71 (May 1971). PI Luo Ligeng, Jin Zhiying and Wang Degen, The measurement of fracture toughness K,, in large scale yielding. New Meral Mater. 5, 61-67 (1978) [in Chinese]. (Received
29 July 1992)
Vol. 45,
No.
2. pp.
141-147,
0013-7944/93 $6.00 + 0.00 Ii‘ 1993 Pergamon Press Ltd.
1993
A NEW METHOD FOR MEASUREMENT OF FRACTURE TOUGHNESS K,, BY THREE POINT BEND SPECIMEN ZHU Department
of Basic Sciences.
ZHE-MING
Fuxin
Mining
Institute,
Fuxin
123000, P.R.C.
Abstract-The relationship between the three point bend (TPB) specimen size and the measured fracture toughness K,, value is analyzed by the theory of crack opening displacement (COD). According to the concept of plane strain fracture toughness K,,, a new formula for K,, is presented. For small-scale or large-scale TPB specimens, the K,, values of material can all be obtained from the new formula and the corresponding curve of load versus crack mouth opening displacement (CMOD). For large-scale specimens, the new formula is compatible with the ASTM standard.
1. INTRODUCTION of fracture toughness value, K,c, of material by three point bend (TPB) specimen, the specimen sizes must satisfy the conditions that B > 2S(K,,/q,.)* and (W - a) > 2S(K,,/q,.)* [l]. The experimental work may be difficult for the following reasons. (1) When the yield strength of some metals is low or fracture toughness is high, the specimen size will need to be very large for measurement of the effective fracture toughness K,,. It will not be convenient for experimental work. (2) Sometimes the measurement of K,, must take place in a specified medium or under a specified temperature; it may not be possible to perform the experiment for a large-scale specimen. (3) If the K,, value of the material cannot be estimated before measurement, in order to satisfy the size condition, a large number of specimens of different sizes is needed for measurement of K,,. Therefore, the amount of experimental work will be increased. If K,, can also be measured by a small-scale specimen, the above mentioned difficulties will not exist. Here, a new method is put forward, by which the K,, may be measured by a single small-scale TPB specimen. This makes a significant contribution to economy and efficiency. The principle and calculation method are presented in the following. IN THE MEASUREMENT
2. PRINCIPLE
AND CALCULATION
METHOD
A TPB specimen is shown in Fig. 1. The unflawed stress 0 of the crack tip is a = aPS/[aB( W - a)“] = ~PS/(u*BW*),
(1)
where 1 -a/W,
cc =(W-a)jW=
Let us introduce a new parameter
VS which is taken as
(2)
CMOD (VI
Fig. 2. Load versus CMOD record of large enough specimen.
Fig. I. TPB specimen. I41
142
ZHU
Fig. 3. (r-KS
ZHE-MING
line.
where V is the crack mouth opening displacement (CMOD); I’S approaches the opening displacement of point N which is & from the crack tip. If the specimen is large enough, or it fractures in the linear elastic state, the corresponding plot of load P versus CMOD V is as shown in Fig. 2. We have PC -=P,
V(. (3)
VB’
where C is the critical point of fracture in Fig. 2. Pg. P, and V,, Vc are the loads and CMODs, respectively. From eq. (1) we have cc P, -z-, (4) GB PB where oc and crBare the unflawed stresses of the crack tip which correspond respectively. From eq. (2) we have vs, v< vs,=v,*
to points C and B,
(5)
where I’S, and VSB are the parameters VS which correspond to points C and B, respectively. From eqs (3), (4) and (5) we obtain gc --=---bB - 8. (6) vsc KS, Equation (6) indicates that for a large enough TPB specimen cr is in linear relation with VS as shown in Fig. 3. fl is the slope of this line. According to similar theory, the fl values of geometrically similar specimens are a certainty for a material. The law is verified by experiments of No. 45 steel. The results of tests are shown in Table I. The relationship between the crack tip opening displacement (CTOD) 6 and CMOD V is (Fig. 4) (5 r(W-u) I/==r(W-a)+a or ril -a/B) r(1 -a/W)+a/IV
6=
v
(7)
’
where r is the rotation factor, and in the critical state the factor r approaches for instance DD-19 [3] has suggested r = l/3. Table I. V,. and b values of TPB specimen T, B, U’ a/W V, B
(mm) unit length MPa mm unit length
TZ
7.3
Td
(S/W T,
a constant [2],
= 4) T6
T7
T”
6, 12 0.504 72.5
8. 16 0.501 73.8
10, 20 0.495 72.0
12, 24 0.498 73.1
15, 30 0.501 70.8
25, 50 0.497 70.2
40, 80 0.501 73.1
60. 120 0.498 71.7
71.2
72.6
71.1
70.7
71.9
70.9
71.3
72.2
Measurement of fracture toughness by three point bend specimen
143
When 6 = & (6, is a certainty for a material), eq. (7) can be written as
4-4w>
&=
v
r(1 -a/W)+a/W
(8)
”
Equation (8) indicates that for the geometrically similar TPB specimens the critical CMOD values Vc are a certainty for a material. The law is verified by experiments on No. 45 steel; the results of tests are shown in Table 1. The formula for the stress intensity factor of a TPB specimen is A4 K, = Bw)‘zf
(a/W)
= h’afif
(a/W).
Now we assume that there are two large enough specimens among a group of geometrically similar TPB specimens with various sizes, and they all fracture in the linear elastic state; we have K,, =
42
=
Kc,
(10)
where K,, and K,* are the critical stress intensity factors of these two specimens, respectively. Substituting eq. (9) into eq. (lo), and noting f(a,/W,) =f(a,/W,) for proportional specimens, we have acIJK=ac2JK or
(11) where ac, , acZ and W, , W, are the critical unflawed stresses of the crack tip and the widths of these two specimens, respectively. From eq. (2) we can obtain the corresponding ratio of critical VS of these two specimens as VSc, V,,I& Vc, Ja, =-----. m -V&2 = v,,/Ja, vc2 fi Considering the critical CMOD V,, = Vc2 and a2/a, = W,/ W, for proportional eq. (12) can be written as -
specimens. (13)
From eqs (11) and (13) we have acI
ac2
vscl=vs,2*
(14)
Equation (14) indicates that for large enough and geometrically similar TPB specimens the ratios of the critical unflawed stress of the crack tip to the critical parameter VS are a certainty for a material. The corresponding relationship between ac and VS, is plotted by line OD in Fig. 5. Comparing with eq. (6) the slope of line OD is equal to the slope of line a-VS of one of these geometrically similar specimens. These two lines will naturally coincide.
Fig. 5. ur-KS,
curve of geometrically similar specimens.
144
ZHU
ZHE-MING
.Ti WC 12mm . r,
‘6
/
T,
ByElmm
W=
16 mm
T3’
B-IOmm
W=
20
mm
T,
Byl2mm
W-
24
mm
Ts
B-15mm
W=
30
mm
T,
Bz25mm
W:
50
mm
T,
B-40mm
W=
80
mm
T,
El=60mm
W=
120 mm 35
“S Fig, 6. The o C’S curve of No. 45 steel small-scale fractured
umt length
(-XT-)
specimen and compar~on specimens.
with the 0, . I ‘S, values nl
However, when the specimen size is smaller, because of plastic deformation, it is fractured under large displacement. The relationship between u(. and VS,. is not linear. and is plotted by curve DE in Fig. 5. On the a,-KS,. curve, the critical point of fracture will depend on the specimen size. From eqs (11) and (13) we obtain that (TV,and P’S,, are inversely proportional to V:%. The point of cc and VSc will move to the point 0 along the o~.~VS,. curve as the specimen size increases. Obviously the whole oc-L’S, curve ODE is practically the B-VS curve of the small-scale specimen of which E is the critical point of fracture. The reason is that if the cc.- P’S,.curve is ODE’ (OD portion will coincide) as shown in Fig. 5, E’ is the critical point of fracture of this small-scale specimen. the coordinates (L’S,., , CJ<,~ ) of point E’ are equal to the coordinates ( F’S,, CT(. ) of point E, so the points E’ and E will coincide, and the whole curves ODE’ and ODE will coincide. The law is verified by experiments of No. 45 steel, and the results of tests are plotted in Fig. 6. According to the concept of plane strain fracture toughness K,,., the stress intensity factor K, equals K,c only when the specimen fractures in the linear elastic state. For a small-scale specimen which fractures in the nonlinear elastic state, K, does not equal K,,., but we can obtain K, (which equals K,c) of a large enough specimen from the load versus CMOD curve of this small-scale specimen. The process is derived in the following. We arbitrarily locate one point A in the linear portion (line OD) of the curve ODE (Fig. 5). A is the critical point of fracture, and the corresponding specimen is large enough and is similar to the specimen of which E is the critical point of fracture. From eq. (9), the K,,, of the specimen of which A is the critical point of fracture can be written as
(15) where (TV,., , uA and W, are the critical unflawed stress of the crack tip. crack length and width of the specimen of which A is the critical point of fracture. Since the rr( --V.S,. curve of geometrically similar specimens is practically the (r-k’s curve of this small-scale specimen of which E is the critical point of fracture, we obtain
(16) where gA and P,4 are the unflawed stress and the load of point A on the 0 - VS curve, and S,. B, and W, are the sizes of this small-scale specimen. From eqs (2), ( 13) and (16) we have
Measurement of fracture toughness by three point bend specimen
Substituting eqs (16) and (17) into eq. (15) and noting f(aE/ W,) =f(a,/ specimens, we obtain
145
WA) for proportional
(18)
KM= When S/W = 4, we have
(19) where P, and VE/VA can be obtained from the load versus CMOD curve of this small-scale specimen. According to ASTM E399 standard [l], the formula of K,, for this small-scale specimen of which E is the critical point of fracture is KIE =
#f($)
.
(20)
E
E
From eqs (18) and (20) we have
where PA/VA is the slope of the linear portion of the P-V curve, and PE/ VE is the slope of the secant line OE of the P-V curve. Let us define m and m’ as m = PA/VA
(22)
m’= PEIVE.
(23)
From eqs (22) and (23), eq. (21) can be written as
KA = 4, =
3 K,E.
Equation (24) indicates the relationship between the K,, value of material and the K,, value of measurement using a small-scale TPB specimen. Since m 2 m’, we have K,, > I&.
(25)
When a specimen fractures in the linear elastic state (i.e. OE is in the linear state), m = m’, eq. (24) can be written as K,, = K,E.
(26)
So, eq. (21) or (24) is compatible with ASTM E399 standard [I] for the plane strain fracture toughness K,, , and they are suitable not only for a small-scale specimen but also for a large-scale
specimen. 3. EXPERIMENTAL
RESULTS
The material employed in the test is shown in Table 2. The small-scale TPB specimen data are as follows: B = 10 mm, W = 20 mm, a = 9.9 mm, S/W = 4. The load versus CMOD record of this small-scale specimen is shown in Fig. 7. The critical point of fracture that we determined is E, and P, = 1302 kg, VE = 72 unit lengths. From eq. (20) we obtain K,E = 94.37 MPa,,&. Table 2 Material No. 45 steel
Heat treatment Normalizine.
HRC (MPa) 52.3
oh (MPa) 804
& (MPa&) 101
146
ZHU
ZHE-MING
1600
/I
1200
-6%
1000
1
a
I-
800
T7
B
J
600 t
I 0
IO
li 20
I
CMOD
Fig. 7. Load
I 40
30
P versus CMOD
V Curd
V record
I 50
I 60
I 70
I 80
1 90
length)
of a small-scale
TPB specimen
Table 3 Material
Heat treatment
No. 45 steel 45MnSiV
860 900 440 650
34CrNi3Mo
We arbitrarily lengths. Substituting
C normalizing ‘C quenching C tempering C tempering
Actual K,,. (MPaJG)
Eq. (21)
z,,. (MPa&)
g,jL (MPa)
vh (MPa)
294 1471
549 1648
70.7 71.9 83.7
69.5 84.5
539
716
121~ 138
122.8
locate one point A in the linear portion, and P, = 400 kg, V,4= 20.8 unit the values of P,. V,. P,, Vt and K,, into eq. (21). we obtain K,, = 100.36 MPa,/m.
Comparing it with the actual K,, value, we find that the K,, value calculated according to eq. (21) has a good accuracy. By using small-scale TPB specimens. we have measured the K,, values of three other materials according to eq. (21) or (24). The results of tests are shown in Table 3.
4. THE FORMULA
CONDITIONS
Equation (21) or (24) is derived at the condition for which CTOD 6c is a certainty for a material, but according to ref. [4], the value S,. of a specimen for which B = 2 mm has a big difference from the values 6,. of specimens for which B > 5 mm. Therefore, during measurement of fracture toughness value K,,., the width B of the specimen should be bigger than 5 mm. The lower bound of the specimen size has yet to be studied further for measurement of an effective K,,. value. Since the CMOD V is measured by a clip-gage attached to the crack mouth of a TPB specimen, and in eq. (7) or (8), the distance of the clip-gage location from the specimen surface has not been considered, so during the test, we should try to decrease the distance, or directly stick the clip-gage on the crack mouth of the specimen using glue-water. The determination of the critical point is important for the measurement of fracture toughness K,c, because it determines the value nr’ of eq. (24). It should be performed as follows. (1) For fracture at indication of “pop-in” or crack burst, the determination of the critical point should be performed according to ASTM E399 standard [I]. (2) For fracture at no indication of “pop-in” or crack burst, the determination of the critical point should be performed according to the method of CTOD measurement [3]. 5. CONCLUSIONS (1) The new method for measurement of fracture toughness K,, values using TPB specimens is based upon the idea that the a-KS curve of the small-scale specimen contains all the o-VS curves of geometrically similar specimens with larger sizes.
Measurement of fracture toughness by three point bend specimen
147
(2)For the small-scale specimen, the fracture toughness value K,, measured according to ASTM E399 standard is less than the actual K,,[5], for instance K,E= 94.37 MPaJ;f; < 101 MPa fi. However, according to eq. (21) or (24), the K,,value is very close to the actual K,c. (3) The procedure of the present work can be referred to for other kinds of specimens (for instance, the compact specimen, C-specimen, etc.) which are utilized for measurement of the fracture toughness value K,,. REFERENCES Standard method of test for plane strain fracture toughness of materials, ASTM E399-81 (1982). [ii T. Ingham, G. R. Egum, D. Elliott and T. C. Harrison, The effection geometry on the interpretation of COD test data. Conference on Practical Application of Fracture Mechanics to Pressure-Vessel Technology, London, C 54/71 (May 1971). [31 Methods for crack opening displacement (COD) testing. British Standard Institution Draft for Development 19, London (1972). [41 R. F. Smith and J. F. Knott, Crack opening displacement and fibrous fracture in mildsteel. Conference on Practical Application of Fracture Mechanics to Pressure-Vessel Technology, London, C 9/71 (May 1971). PI Luo Ligeng, Jin Zhiying and Wang Degen, The measurement of fracture toughness K,, in large scale yielding. New Meral Mater. 5, 61-67 (1978) [in Chinese]. (Received
29 July 1992)