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Influence of specimen size on the crack-opening stretch zone
Materials Science and Engineering, 70 (1985) 111-122
111
Influence of S p e c i m e n Size on the Crack-opening Stretch Zone S. K. PUTATUNDA and J. M. RIGSBEE
Department of Metallurgy and Mining Engineering, University of Illinois, Urbana, IL 61801 (U.S.A.) (Received May 11, 1984)
ABSTRACT
An investigation has been carried out to find the influence o f specimen size (thickness and width) on the blunting line in the Jxc test procedure (where Jic is the critical value o f the elastic-plastic toughness parameter). Compact tension specimens prepared from aircraft quality A I S I 4340 steel heat treated to a yield strength level o f 1000 MPa were used. The Jic values were determined by two different methods, i.e. (i) multiple-specimen resistance curve and (ii) by measurement o f the critical stretch zone width on the fracture surface. This investigation shows that the stretch zone size ahead o f the crack tip during blunting as well as the post-crack-initiation stage is independent o f specimen size. The slope o f the blunting line was f o u n d to be 1.2, compared with 2. 0 (eqn. (2)) in the standard Ji¢ test procedure. Ji¢ values obtained by measurement o f the critical stretch zone size were found to be in good agreement with the Jxc value obtained by the multiple-specimen resistance curve method. J, the crack-opening displacement COD and the stretch zone size (Aa)sz were f o u n d to be related by the expressions J = 0.6o0(COD) and COD ~ 1.86(Aa)~z (where Oo is the flow stress).
J where the crack advance line intersects the blunting line (Fig. 1). During the initial loading of a precracked specimen, crack tip blunting causes formation of a stretched zone prior to material separation (Fig. 2). Landes and Begley [2] reported that the apparent crack extension (Aa)sz associated with this stretch zone can be approximated by assuming the stretch zone size to be equal to half the crack-opening displacement COD. This can be expressed as (Aa)s: ~
I-w Z
½(COD)
(I)
STEP 3
~
"~
tO
~'~ST EP 2
"r
~STEPI
. ~
~STEP
4
/START
(a)
CRACK EXTENSION
~
Ao
LE TEARING
J V,~KCRA~KBLUNTING 1. INTRODUCTION
--0~
I
,
~
INITIAL
SHARP CRACK
;~4..(,,,o},:z I , ~,
~
BLUNTING TEARING
I
~
S T A B L E TEARING
i
The J integral is increasingly used as a fracture parameter for characterization of elasticplastic behavior of engineering materials. The value Jic [ 1 ], which is the critical value of the elastic-plastic fracture toughness parameter, is usually determined by a resistance curve technique (Ja curve) where the J values are plotted as a function of crack extension. The Jic fracture toughness is taken as the value of 0025-5416/85/$3.30
PRIOR TO
(b) ~z~o~.i Fig. 1. (a) Four steps of ductile fracture process on a resistance curve: start, sharp crack, no loading; step 1, crack tip blunting; step 2, initiation of stable crack growth, JIc; step 3, stable crack growth; step 4, ductile instability. (b) Schematic diagram of a JR curve. © Elsevier Sequoia/Printed in The Netherlands
112 Crack
growth
direction
0
T
Fatigue -
//
//
precracked region
Fig. 2. Schematic section profile of the stretch zone:
CTOD, crack-tip-opening displacement.
The crack-opening displacement is then related to J by the following relation: J = may(COD)
(2)
where ay is the yield strength of the material and m is a constraint factor. The flow stress a0 customarily is substituted for the yield strength o~ in this equation to take into account the strain-hardening effect [ 3 ]. Combining eqns. (1) and (2) results in a blunting line equation given by J = 2mao(Aa)sz
(3)
In the standard Ji~ test procedure [4] the value of m is assumed to be equal to unity. However, it has been recently reported that the value of m depends on the material [ 5 - 7 ] , the state of stress [8] and the specimen size [9]. Thus an assumption of a uniform m value of about unity may not be valid for all classes of materials and all specimen sizes. Since evaluation of a proper blunting line is essential for determination of the Jic fracture toughness parameter, this aspect needs closer and systematic examination and is a main objective of this paper. Blunting at the crack tip is caused by the plastic deformation ahead of the crack tip. The specimen size parameters, thickness and width [ 10, 11 ] have been reported to influence the plastic zone size and therefore could affect the blunting process and consequently the size of the stretch zone. However, in very few investigations has the effect of the specimen size on the stretch zone been examined, and those in which this has been done are not conclusive [9, 12]. This aspect was therefore examined in the present investigation. The multiple-specimen J a curve technique has its own limitations since several specimens identical in all respects are required to obtain
a single J1c value. Therefore, emphasis is now on the determination of Jic by a single-specimen technique. The most difficult part of such a method is the identification of the crack initiation point and this problem has not yet been satisfactorily resolved. Recently, several workers [ 1 2 - 1 4 ] have att e m p t e d to correlate the Jic fracture toughness with the critical stretch zone size (Aa)szc as measured on the fracture surface of the specimens (post-crack-initiation stage). Several empirical relationships [ 1 2 - 1 4 ] have been proposed relating Jic to the critical stretch zone size. However, such a correlation, although very important and useful, has so far not been clearly established and needs further investigation. In the present investigation the critical stretch zone size was measured in the specimens which had stable crack extensions to determine whether sufficient correlation exists between the critical stretch zone size and Jic to allow this procedure to be used to estimate the Ji¢ fracture toughness. The objectives of the present investigation were as follows: first, to find out the effect of specimen thickness and width on stretch zone size; second, to determine a valid size-independent blunting line equation; lastly, to examine whether the Ji¢ fracture toughness can be determined through the measurement of the critical stretch zone size. Compact tension specimens {with TL orientation, i.e. the load was applied in the transverse direction and the crack propagated in the longitudinal direction) prepared from aircraft quality AISI 4340 steel and heat treated to a yield strength level of 1000 MPa were used in the present investigation. The multiple-specimen JR curve method was used to determine unambiguous JI~ values for specimens of three different thicknesses and three different widths. In addition, several specimens of each size (thickness and width) were loaded to different levels of blunting (without any stable crack extension) and were used to evaluate the blunting line from measurements of their stretch zone.
2. EXPERIMENTAL PROCEDURE 2.1. Material
The aircraft quality AISI 4340 steel plate was available in the form of a hot-rolled plate 12.5 mm thick with an identifiable rolling
113 TABLE 1 Chemical composition Element Amount (wt.%) of element
C 0.43
Cr 0.81
S 0.10
Mn 0.73
Ni
P
Si
1.81
0.006
0.36
TABLE 2
TABLE 3
Mechanical properties
Specimen designation
Ultimate tensile strength Yield strength Elongation Reduction in area Brinell hardness
1070 MN m-2 1014 MN m-2 11.5% 50.8% 320-+ 20 HB
direction. The chemical composition of the material and its mechanical properties after heat t r e a t m e n t are given in Tables 1 and 2 respectively. 2.2. Specimen preparation Modified c o m p a c t tension specimens with TL orientation were prepared as described in A S T M Standard E 813-81 [4]. Six series of specimens were investigated. In the first three series the specimen_ width was held constant (W ~ 100 mm) and three thicknesses were studied (B ~ 12 mm, B ~ 6 nlm and B ~ 4 mm). In the n e x t three series the thickness was held constant (B ~ 12 mm) but the width was varied (W ~ 150 mm, W ~ 100 mm and W ~ 62.5 mm). The dimensions of the specimens are given in Table 3 together with the scheme for classification. After fabrication, the specimens were austenitized at 816 °C for 1 h and t he n quenched in oil. I m m edi at el y after quenching, t h e y were t e m p e r e d at 649 °C for 1 h and then air cooled to r o o m temperature. All the specimens were heat treated in an identical manner. The specimens were then ground on b o t h surfaces. 2.3. Fracture toughness measurements A multiple-specimen JR curve m e t h o d was e m p l o y e d to determine the Jic fracture toughness. Measurement of fracture toughness involves simultaneous m e a s u r e m e n t of load, load-line displacement and crack extensions. F r o m these measurements, J values were calculated using the standard relationship [4].
Mo 0.222
A1 0.050
Group Series
Width (mm)
Thickness (mm)
Number of specimens
1 1 1
601-609 401-410 251-259
150 100 62.5
12 12 12
9 10 9
2 2
411-419 421-429
100 100
6 4
9 9
The specimens were initially precracked in fatigue up to an a~ W value of a b o u t 0.55 f r o m the initial n o t c h a/W value of a b o u t 0.30. The last 2 m m of fatigue cracking were carried out at a AK level of 25 MN m -3/2, which conf o r m e d to the standard specification [4]. T hen the specimens were m o n o t o n i c a l l y loaded t o different amounts of load displacem e n t (which correspond to different amounts of crack extension) and unloaded. After the specimens had been unloaded, t h e y were again cracked in fatigue and finally fractured in liquid nitrogen. This was done t o retain fractographic features for subsequent analysis by scanning electron m i croscopy (SEM). On the fracture surface the physical crack extension Aa and the original crack length a0 were measured with the help of a traveling microscope. An average of nine readings across the specimen thickness was taken to obtain a0 and Aa (physical) for subsequent c o m p u t a t i o n of J values. The J values were calculated from the area under the load displacement curve and appropriately corrected using the Merkle and Corten [15] relationship. On a J versus Aa diagram a least-squares fit straight line was obtained. This was ext e n d e d to the blunting line given by J = 2Uo Aa and the J~c values were det erm i ned for the three thickness series and the three width series.
(3a)
114
2.4. Measurement o f stretch zone size In order to measure the stretch zone size on the fracture surface, a fractographic sample of the fracture surface area was cut from each of the specimens: the fracture surface included the crack front, the stretch zone, the stable crack growth region and the post-fatigue crack growth region. The samples were then cleaned in acetone and the fracture surfaces were examined by SEM. It should be noted that because of lack of clarity the boundaries of the respective fracture surface regions could not be identified and measured on all the specimens. The specimen data for measurements which were carried out with confidence are given in Figs. 5 and 6. These samples showed the following regions on the fractured surface: (1) fatigue-precracked region, (2) stretch zone, (3) stable crack extension, (4) post-fatigue crack and (5) liquid nitrogen fracture stage. These features are schematically shown in Fig. 3. The stretch zone at the start of crack extension is referred to as the critical stretch zone (Aa)szc. (Aa)szc is expected to depend only on the J value at the start of crack extension, i.e. Ji~ does not increase with subsequent loading. The crack extension starts at the mid-thickness region at JIc and then spreads toward the surfaces at progressively higher J values. When the stretch zone is interpreted, it must be remembered that the stretch zone at the mid-thickness and near the specimen surface forms at two different J levels in the specimen. Thus the stretch zone values measured only near the mid-thickness of t h e specimen are expected to correlate with Jxc.
Secondly, to check for consistency, the stretch zone size needs to be measured on both halves of the specimen. The formation of stretch zones at two different J levels in the midthickness and surface of the specimen will contribute to scatter in these measurements. On the basis of the above considerations a number of specimens of different sizes (thickness and widths) were examined and the stretch zone size was measured at 20-25 points near the mid-thickness region of each half of the specimen. An initial statistical analysis of the stretch zone size measurement showed that a minimum of 25 readings is necessary for the measurement of the stretch zone with a 95% confidence limit. The size of the stretch zone in each specimen was determined by holding the specimen at 45 ° to the incident SEM beam. In this position the stretch zone could be clearly seen and the measurements were carried out in the mid-thickness portion of the crack front with confidence. The measured stretch zone values had to be multiplied by a factor sec 45 ° to convert to actual values. The stretch zone was clearly demarcated by a featureless region bounded by a fatigue precrack on one side and a stable crack extension region on the other side. The stretch zone region appeared as a dark band against a white background, the width of which could be measured sufficiently accurately. This is shown in Fig. 4. The stable crack extension region was characterized by the presence of microvoid coalescence, which enables it to be distinguished from the stretch zone.
3. R E S U L T S A N D D I S C U S S I O N -FATIGUE- PRECRACKED PORTION
- - S T A B L E CRACK EXTENSION
ST ETN CH ZR O E~~IItL IQ I UD IN TIROGE FR NACTURE POS FT A-TG IUC ERACK Fig. 3. V a r i o u s f r a c t o g r a p h i c f e a t u r e s o n t h e specim e n surface.
The results of the present investigation will be presented and discussed in the following order: first, the effect of the size parameters B and W on the stretch zone size; next, the relationship between the stretch zone and the blunting line; finally, the correlation between Jic and the critical stretch zone size (Aa)szc. Various fractographic features will also be discussed. 3.1. E f f ect o f thickness and width on stretch zone size As was mentioned in Section 2.2, the stretch zone was measured in specimens with
115
T STABLE CRACK EXTENStON
L STRETCH ZONE
FATIGUE PRECRACK
,t
l
STABLE CRACK EXTENSION
STRETCH ZONE
T FATIGUE ~ C R AC~
Fig. 4. Microfractographs of (a) a s p e c i m e n 12 m m thick and (b) a s p e c i m e n 4 m m thick, showing the stretch zone, stable crack e x t e n s i o n and fatigue precrack. (Magnification, 400×.)
116 O.15 l
r
r
i
i
BLUNTING LIN E_~ SLOPE 2 I =
"•
O.10
~J
~~/~
I
'
I
'
I
~,?.
.\~
MEAN VALUE= +
+
0
~_~:
. . . . . . .
•
__
g
<3
+&
• e-~_
o+
• ° O
o
= _-~_
•
o
_,
. . . . . . .
o
O.O5
/
/ I
O 80
-
/ ..../.~..,,~o m
'-
i
~
t
I
80
~
I
t
160
I
240
i
I
320
J (kJ m -2)
!
/. 0
I
i CONVE]NTIONA L
320
--" 'E240
i
H/
0.05
J O.10
(AO)sz
Fig. 6. E f f e c t o f the s p e c i m e n size on the critical s t r e t c h zone.
....
,
I O. 15
(mm -I)
Fig. 5. E f f e c t o f the s p e c i m e n size o n t h e s t r e t c h zone.
Symbol
W (ram)
B (ram)
o • +
~62.5 ~100 >`150
~12 ~12 ~12
•
~100
>-4
[]
=100
>`6
different thicknesses B of a b o u t 12, 6 and 4 mm. All these specimens had a c ons t ant width W of a b o u t 100 mm. Figures 5 and 6 show plots of stretch zone size v e r s u s J and critical stretch zone size v e r s u s J respectively for three specimen thicknesses and three specimen widths. It is evident f r om these figures that the specimen thickness has no apparent influence on the stretch zone size. The reason for the observed scatter in the stretch zone values has already been m e n t i o n e d in Section 2. The thickness effect on stretch zone size has been studied by earlier workers [9, 12, 16 ]. However, the results r e p o r t e d in the literature are o f t e n c o n t r a d i c t o r y and conflicting. Gilmore e t al. [9] r e p o r t a larger value o f stretch zone size in 12.7 m m specimens prepared f r om martensitic stainless steel H T8 0 than for 2.5 m m specimens of the same material. In contrast, Ohji e t al. [16] and Kobayashi e t al. [12] f o u n d the stretch zone
Symbol o
W (mm) ~62.5
B (mm) ~12
•
>`100
~-12
+
>`150
~.12
•
>`100
~4
[]
~100
~6
width to be virtually i n d e p e n d e n t of specimen thickness. The results of the present investigation also show that the specimen thickness has little influence on the stretch zone, which is in agreement with the results report ed by Ohji e t al. and Kobayashi e t al. Figures 5 and 6 also show the effect of the specimen width on the stretch zone size. All these specimens had a constant thickness B of a b o u t 12 mm. The stretch zone sizes as measured on these specimens are comparable with the measured values on specimens with different thicknesses. It is clear from Figs. 5 and 6 that specimen width also has little or virtually no effect on the stretch zone size when loaded t o comparative J values. However, the scatter in the measured stretch zone values is somewhat lower than was f o u n d for the specimens with varying thicknesses. Very few studies have been c o n d u c t e d to date to study the influence of the specimen width on the stretch zone size. One of the present authors and coworkers [17] in a previous publication found that the width had no effect on the stretch zone size in a material that undergoes simultaneous pop-in and stable crack extension. Our results also show t hat
117 the specimen width has no apparent influence on the stretch zone size, although this material did not undergo any pop-in type of crack extension.
The JR curves of these specimens with different thicknesses and widths have been determined by the multiple-specimen technique and have been reported in another publication [18]. Figures 7 and 8 show the multiplespecimen JR curves for these specimens. It is clear that with the conventional blunting line (J -- 2(Aa)szOo) the Jic value for different thicknesses varies from 62 kJ m -2 for specimens 4 m m thick to 78 kJ m -2 for specimens 12 mm thick. However, if the blunting line J = 1.2(Aa)szOo obtained by the stretch zone size measurement were to be used, the scatter in the Jic values is reduced. (The Jic values vary between 68 and 80 kJ m-e.) The blunting line obtained by stretch zone size measurements when used in the plot of JR curves for three different widths W of about 150, 100 and 62.5 mm gives J~c values within -+10% of the mean value of 76 kJ m -e. It is imperative to note that all these specimens had a constant thickness (B ~ 12 ram) and had square or flat fracture present on them. None of these specimens (constant thickness B ~ 12 mm) had any shear lips. Thus it appears that the blunting line obtained by stretch zone measurements is more appropriate in determining the Ji~ values for specimens instead of
3.2. Stretch zone size and blunting line The stretch zone values obtained from direct measurements on the specimen surfaces are compared with the conventional blunting line in Fig. 5. As was mentioned earlier, these specimens were loaded to different levels of blunting such that no stable crack extensions were present on them. The data points plotted in Fig. 5 are an average of 2 0 - 2 5 measurements taken on each specimen in the midthickness region. The conventional blunting line represented by eqn. (3) has a slope of J/oo(Aa)sz = 2. The (Aa)~ values measured on the specimen surfaces, however, fall within the two limits shown as broken lines in Fig. 5. These data points lie between a line of slope 1.5 and a line of slope 1.0, and the mean value of the slope of the line passing through these points is about 1.2 compared with a slope of 2 for the conventional blunting line used in the standard J1~ test procedure.
I
'
I
I
'
I
'
I '
VBLUNTING LINE J= 2O'oAa
32O
r /
I,
I
/
I /!NEWBLUNTiNOL,NE //joe,~o
L Ill
240
L.-o.m
e~
m,',
OFFSETLINE
FII:
~/
32.0 ~-
' -
,
~l~,;'i
~',/
l
k
-
I
7 ° /
:
-
I/i"J;> ~
0
;i
l
'
I
! 1.5 m m
o /
°~oo~""
"
I
I
ov ~
I
o
i
I
~ OFFSET
Ill I II/ !I
I
,
I
,
0.8
I 1.2
i
I 1.6
Ao (mm)
Fig. 7. Multiple-specimen JR curve for three different thicknesses (constant width W = 100 ram): I, B ~4mm;o,B~ 6mm;A,B ~ 12ram.
0
I
I 0 1 C~-~I (9' .
-
I
I OFFSET
0.4
'
,J=2°oAa
///
i
0[
I
i.....--BLUNTING LINE
I-I I ;
! III
~
I l / I~O-15mm I I I #OFFSET LINE 240 F I /--~-NEW I BLUNTING LINE
'E
~^I I I ~ . ,
I
r LINE I I 0.4
0.8 a o (mm)
1.2
1.6
Fig. 8. M u l t i p l e - s p e c i m e n JR c u r v e f o r t h r e e d i f f e r e n t w i d t h s ( c o n s t a n t t h i c k n e s s B = 12 r a m ) : o, W 6 2 . 5 r a m ; i , W ~ 1 0 0 m m ; +, W ~- 1 5 0 r a m .
118
using a standard blunting line with a slope of 2 for all materials. The slope of the blunting line has previously been studied by several workers [5-7, 9]. Mills [5] has reported that the value of the constraint factor m depends on the material. For a low strain-hardening material the value of m is reported to be equal to u n i t y [5, 6], whereas for a material with a high strain-hardening coefficient the value of m lies between 2 and 3 [5]. Gilmore et al. [9] reported a size-dependent value for the constraint factor m. For specimens 12.7 m m thick prepared from a martensitic stainless steel, they reported an m value in the range 0.8-0.95, but for specimens of the same material with a smaller thickness (B ~ 2.5 mm) they f o u n d a higher m value of about 2.6-2.8. Broek [19] found an m value of the order of 1.1 for all aluminum alloys. Liu and Kobayashi [20] reported a value for the constraint factor in the range 1.1-1.5. Others have found an m value in the range 0.79-3.0. The results of Kobayashi et al. [21], however, show a constraint factor of the order of 0.60. A two-dimensional analysis by Shih [8] correlating J and the crack-opening displacem e n t predicts the value of the constraint factor m to equal about 1.4 for a low strainhardening material. The material used in the present investigation had a very low strainhardening coefficient (n ~ 0.03). Our results, however, indicate that the constraint factor m is independent of size and has a value of approximately 0.6 and is thus in agreement with the results reported by Kobayashi et al. [211. 3.3. Critical stretch z o n e size and J~¢
The stretch zone forms during the loading of the precracked specimens and attains a critical value at the initiation of fracture. This critical value of the stretch zone size remains unaffected by continued stable crack growth [12] and is defined as (Aa)sze. The critical stretch zone size was measured in the mid-thickness region in all the specimens which had stable crack extension present on them. Figure 6 shows a diagram of these (Aa)szc values against J for different thicknesses and widths. As was mentioned earlier, these (Aa)szc values were f o u n d to be independent of specimen size (thickness and width). The mean value of (Aa)szc when used
TABLE 4 Comparison of fracture toughness values obtained by various methods
Method
Mean value of fracture toughness JIc (kJ m -2)
KIc (MPa m 1/2)
Multiple-specimen resistance 68 curve with conventional blunting line
124
Multiple-specimen resistance 76 curve wtih new blunting line J = 1.2o0(Aa)sz
132
Stretch zone measurements
143
90
in Fig. 5 and extrapolated to the new blunting line with slope 1.2 (the blunting line obtained by direct measurements on the specimen surfaces on the specimens without any stable crack growth as reported in Section 3.2) gives a Jic value of 90 kJ m -2, which is about 18% higher than the mean value 76 kJ m -2 obtained by the multiple-specimen resistance curve m e t h o d (Table 4). However, in terms of Kic the fracture toughness value is only 10% higher than the mean value of 132 MPa m 1/2. It is evident from Fig. 5 that, when this mean critical stretch zone size value is extrapolated to the conventional blunting line represented by J = 2o0(Aa)sz, it gives a considerably higher Jic value and consequently a higher value of Kic (Jie ~ 150 kJ m -2) than the value obtained by the multiple-specimen resistance curve methods. It therefore appears that the critical stretch zone size measurements can be used for this class of materials for a determination of the KI~ fracture toughness provided that the correct blunting line is used in J1e tests. Several other workers [22-25] have found reasonable agreement between the critical stretch zone size and Kic. Our results also show that a good estimation of Kic is possible by proper and elaborate measurements of critical stretch zone sizes. Several empirical relationships have been proposed by some workers [13, 14, 24] for Kie and (Aa)sze. Two of these models, namely those of Fujita et al. [24] and Yin et al. [13], were examined for our test data. However,
119
when the measured (Aa)szc values were used in these equations, the Kxc values estimated were found to be much higher (200 and 180 MPa m 1/2) than those obtained from Ji¢ by the multiple-specimen resistance curve method.
=0.50 [
3.4. J versus crack-opening displacement relationship
r :0.45
The crack-opening displacements were calculated using Dover's equation [26] for compact tension specimens. In all these calculations the value of the rotational factor r used depended on the extent of stable crack growth on the specimens. For specimens loaded to a high crack extension (Aa >~ 1.50 mm) or high levels of load-line displacement, the value of the rotational factor r was taken as 0.50. Similarly, for specimens loaded to crack extensions of approximately 1.0-1.5 mm, the r value was taken as 0.45. For specimens loaded to crack extensions of between 0.5 and 1.0 mm the r value was taken as 0.40. This is illustrated in Fig. 9. This m e t h o d was
r --0.40
/
L 0.5
1.0 AO (mm)
J
1.50
Fig. 9. R o t a t i o n a l f a c t o r r vs. stable crack e x t e n s i o n .
0.50
E
o.2o
C
+
0.10
/
0 0
'-~MEAN SLOPE = 0.60
I
I 0. I0
I
I 0.20
I
I 0.30
J
1 0.40
COD (ram) Fig. 10. I n t e r r e l a t i o n b e t w e e n J a n d t h e c r a c k - o p e n i n g d i s p l a c e m e n t COD. Symbol
W (mm)
B (mm)
© • + • []
~-62.5 ~100 ~150 ~100 ~100
~12 ~12 ~12 ~4 ~-6
120
adopted since there is no standard relationship for the determination of the crack-opening displacement for c o m p a c t tension specimens and the value of the rotational factor r has been reported to be in the range 0 . 3 2 0.50 [26]. The crack-opening displacement values calculated by the above m e t h o d are plotted in Fig. 10 against J/oo. J values were calculated for each specimen from the load displacement area and corrected appropriately using the Merkle and Corten relationship [15]. The slope of the least-squares fit line joining these data points was found to be about 0.60 and the J versus crack-opening displacement relationship was found to be expressed as J = 0.6a0(COD) for this material. As was mentioned earlier, the value for m has
'
I
'
I
'
I
1
0.40
(1)
z
+
E E a o
been reported to be in the range 0 . 7 - 3 . 0 for different materials. Simpson [27] reported an m value of about 1.08 for Zr-2.5wt.%Nb. Our results show that there is a good correlation between J and crack-opening displacement. The constraint factor m has a value of 0.6 for this material. Figure 11 is a plot of the crack-opening displacement versus stretch zone size. It is evident from this figure that a good correlation exists between the crack-opening displacement and (Aa)sz; the slope of the line of leastsquares fit was found to be a b o u t 1.86, which is slightly lower than the analytical value of 2 predicted by Landes and Begley [2]. Similar patterns of results have been reported by other workers [28, 29]. The good correlation between J, crack-opening displacement and
o 0
0.30
GO T Z t-- UJ
+
I.U
o
z
v
+
0
+
0
113
0.20
+o
°
+
0
0
SPECIMENS LOADED UP TO BLUNTING
0. I0
,,,~MEAN 0
l
0
SLOPE= 1.86 I
0.05
~
=f
(Aa)szc I
0.10
~
I
0.15
(Ao)sz (mm) Fig. 11. C r a c k - o p e n i n g d i s p l a c e m e n t C O D vs. s t r e t c h z o n e size.
Symbol
W (mm)
B (ram)
O • + • Q
~62.5 ~100 ~150 ~100 ~100
~12 ~12 ~12 ~4 ~6
121
(Aa)~ confirms the fact that the stretch zone measurements in the present investigation are reliable and can be related directly to the toughness parameters J and crack-opening displacement.
3.5. Fractographic features The various regions present on the fractured surface were described earlier and are illustrated in Fig. 4. In general, the fractographic features which define a given region of the fracture surface were the same for all specimens. In the fatigue-precracked region the striation markings were not very clearly visible. This is probably because the last 2 m m of the fatigue cracking were carried out at a low AK level of 25 MN m -312. At such low AK levels, striations are difficult to observe because of their fine spacing. At high magnifications (3600X), however, sometimes microvoids and striation markings were observed. The stretched zone could be clearly seen as a wide dark band in a bright background as shown in Fig. 4. The stretch zone has been reported either to be characterized by glide markings or to have a featureless appearance [30]. In the present investigation, examination of the stretch zone at a high magnification revealed the presence of microvoids. The stable cracked region is characterized by the presence of very fine equiaxed dimples: These are clearly visible as shown in Fig. 4. In between a few of the voids, some inclusions could be seen. Parallel ridges perpendicular to the crack front were also observed. The ridges were typical of a TL orientation where the crack propagation takes place along the axes of stringer-type inclusions.
4. CONCLUSIONS
Specimen size (thickness and width) has virtually no influence on the stretch zone size obtained by direct measurements on the specimen fracture surface. The blunting line is best represented by the relation J = 1.2(Aa)szo0 for AISI 4340 steel heat treated to a yield strength of 1000 MPa. A good correlation exists between the critical value of the stretch zone and Kic, and computation of/{ic is possible by measurements
of the critical stretch zone size for this material. The crack-opening displacement and (Aa)sz are related by COD = 1.86(Aa)sz for compact tension specimens in the thickness and width ranges investigated in this investigation. The new blunting line obtained by measurement of the stretch zone size in this investigation can give a size-independent Jic value. The Jic value obtained by measurement of the stretch zone size is about 18% higher than the Jic value obtained by the multiple-specimen resistance curve method.
ACKNOWLEDGMENTS
The authors would like to thank Professor H. T. Corten for many helpful discussions concerning this work. One of the authors (S.K.P.) acknowledges the help and support of the Department of Metallurgy, University of Illinois at Urbana-Champaign, for completion of this work and the Materials Engineering Research Laboratory for the mechanical testing facilities. Part of the support for this work was provided by the Council for International Exchange of Scholars, Washington, DC, which is gratefully acknowledged.
REFERENCES 1 J. A. Begley and J. D. Landes, Proc. Natl. Symp. on Fracture Mechanics, in A S T M Spec. Tech. Publ. 514, 1972, p. 1. 2 J. D. Landes and J. A. Begley, Proc. 8th Conf. on Fracture Analysis, in A S T M Spec. Tech. Publ. 560, 1974, p. 170. 3 J. F. Knott, Met. Sci., 14 (1980) 327. 4 A S T M Stand. E 813-81, in 1983 Annual Book o f A S T M Standards, Vol. 03.01, ASTM, Philadelphia, PA, 1983, p. 762. 5 W. J. Mills, J. Test. Eval., 9 (1981) 56. 6 R. L. Tobler, Proc. 9th Conf. on Cracks and Fracture, in A S T M Spec. Tech. Publ. 601, 1976, p. 346. 7 H. P. Keller and D. Munz, Proc. lOth Conf. on Flow Growth and Fracture, in A S T M Spec. Tech. Publ. 631, 1977, p. 217. 8 C. F. Shih, J. Mech. Phys. Solids, 29 (1981) 305. 9 C. M. Gilmore, V. Provenzano, F. A. Smidt and J. R. Hawthorne, Met. Sci., 17 (1983) 177. 10 S. Banerjee, Eng. Fract. Mech., 15 (1981) 343. 11 S. K. Putatunda and S. Banerjee, Eng. Fract. Mech., 19 (1984) 507. 12 H. Kobayashi, H. Nakamura and H. Nakazawa, in
122
13 14
15 16
17 18 19 20 21
K. J. Miller and R. F. Smith (eds.), Proc. 3rd Int. Conf. on the Mechanical Behaviour o f Materials, Cambridge, Cambridgeshire, August 20-24, 1979, Pergamon, Oxford, 1979, p. 529. S. W. Yin, R. A. Gerbrands and M. Hartevelt, Eng. Fract. Mech., 18 (1981) 1025. P. N. Duy, in R. Roberts (ed.), Proc. 13th Conf. on Fracture Mechanics, in A S T M Spec. Tech. Publ. 743, 1981, p. 543. J. G. Merkle and H. T. Corten, J. Press. Vessel Technol., 56 (1974) 286. K. Ohji, K. Ogura, Y. Mutoh, H. Itogawa, H. Uchida and M. Honki, J. Mater. Sci. Soc. Jpn., 27 (1978) 31. S. K. Putatunda, A. K. Mallik and S. Banerjee, Trans. Indian Inst. Met., to be published. S. K. Putatunda, J. M. Rigsbee and H. T. Corten, J. Test. Eval., to be published. D. Broek, Eng. Fract. Mech., 6 (1974) 173. H. W. Liu and H. Kobayashi, Scr. Metall., 14 (1980) 525. H. Kobayashi, K. Hirano, H. Nakamura and H. Nakazawa, in D. M. R. Taplin (ed.), Fracture
22 23 24 25 26 27 28
29
30
1977, Proc. 4th Int. Conf. on Fracture, Waterloo, Ontario, June 19-24, 1977, Pergamon, Oxford, 1977, p. 583. P. N. Duy and S. Bayard, J. Eng. Mater. Technol., 103 (1981) 55. K. F. Amouzouvi and M. N. Bassim, Mater. Sci. Eng., 55 (1982) 257. H. Fujita, O. Kamiya and M. Tanan, J. Mater. Sci., 17 (1982) 3541. P. Doig, R. F. Smith and P. E. J. Flewitt, Eng. Fract. Mech., 19 (1984) 653. W. D. Dover, Eng. Fract. Mech., 5 (1973) 11. L. A. Simpson, J. Eng. Mater. Technol., 22 (1980) 97. D. Hamis and D. Elliot, Proc. Conf. on the Mechanics and Physics o f Fracture, Metals Society, London, 1976, p. 107. P. Hopkins and G. Jolley, Proc. 4th Eur. Colloq. on Fracture, Leoben, 1982, Verein Deutscher Ingenieure, Di]sseldorf, 1982, p. 3. D. Munz and H. P. Kelley, Proc. 3rd Eur. Colloq. on Fracture, 1980, Verein Deutscher Ingenieure, Di~sseldorf, 1980, p. 105.
111
Influence of S p e c i m e n Size on the Crack-opening Stretch Zone S. K. PUTATUNDA and J. M. RIGSBEE
Department of Metallurgy and Mining Engineering, University of Illinois, Urbana, IL 61801 (U.S.A.) (Received May 11, 1984)
ABSTRACT
An investigation has been carried out to find the influence o f specimen size (thickness and width) on the blunting line in the Jxc test procedure (where Jic is the critical value o f the elastic-plastic toughness parameter). Compact tension specimens prepared from aircraft quality A I S I 4340 steel heat treated to a yield strength level o f 1000 MPa were used. The Jic values were determined by two different methods, i.e. (i) multiple-specimen resistance curve and (ii) by measurement o f the critical stretch zone width on the fracture surface. This investigation shows that the stretch zone size ahead o f the crack tip during blunting as well as the post-crack-initiation stage is independent o f specimen size. The slope o f the blunting line was f o u n d to be 1.2, compared with 2. 0 (eqn. (2)) in the standard Ji¢ test procedure. Ji¢ values obtained by measurement o f the critical stretch zone size were found to be in good agreement with the Jxc value obtained by the multiple-specimen resistance curve method. J, the crack-opening displacement COD and the stretch zone size (Aa)sz were f o u n d to be related by the expressions J = 0.6o0(COD) and COD ~ 1.86(Aa)~z (where Oo is the flow stress).
J where the crack advance line intersects the blunting line (Fig. 1). During the initial loading of a precracked specimen, crack tip blunting causes formation of a stretched zone prior to material separation (Fig. 2). Landes and Begley [2] reported that the apparent crack extension (Aa)sz associated with this stretch zone can be approximated by assuming the stretch zone size to be equal to half the crack-opening displacement COD. This can be expressed as (Aa)s: ~
I-w Z
½(COD)
(I)
STEP 3
~
"~
tO
~'~ST EP 2
"r
~STEPI
. ~
~STEP
4
/START
(a)
CRACK EXTENSION
~
Ao
LE TEARING
J V,~KCRA~KBLUNTING 1. INTRODUCTION
--0~
I
,
~
INITIAL
SHARP CRACK
;~4..(,,,o},:z I , ~,
~
BLUNTING TEARING
I
~
S T A B L E TEARING
i
The J integral is increasingly used as a fracture parameter for characterization of elasticplastic behavior of engineering materials. The value Jic [ 1 ], which is the critical value of the elastic-plastic fracture toughness parameter, is usually determined by a resistance curve technique (Ja curve) where the J values are plotted as a function of crack extension. The Jic fracture toughness is taken as the value of 0025-5416/85/$3.30
PRIOR TO
(b) ~z~o~.i Fig. 1. (a) Four steps of ductile fracture process on a resistance curve: start, sharp crack, no loading; step 1, crack tip blunting; step 2, initiation of stable crack growth, JIc; step 3, stable crack growth; step 4, ductile instability. (b) Schematic diagram of a JR curve. © Elsevier Sequoia/Printed in The Netherlands
112 Crack
growth
direction
0
T
Fatigue -
//
//
precracked region
Fig. 2. Schematic section profile of the stretch zone:
CTOD, crack-tip-opening displacement.
The crack-opening displacement is then related to J by the following relation: J = may(COD)
(2)
where ay is the yield strength of the material and m is a constraint factor. The flow stress a0 customarily is substituted for the yield strength o~ in this equation to take into account the strain-hardening effect [ 3 ]. Combining eqns. (1) and (2) results in a blunting line equation given by J = 2mao(Aa)sz
(3)
In the standard Ji~ test procedure [4] the value of m is assumed to be equal to unity. However, it has been recently reported that the value of m depends on the material [ 5 - 7 ] , the state of stress [8] and the specimen size [9]. Thus an assumption of a uniform m value of about unity may not be valid for all classes of materials and all specimen sizes. Since evaluation of a proper blunting line is essential for determination of the Jic fracture toughness parameter, this aspect needs closer and systematic examination and is a main objective of this paper. Blunting at the crack tip is caused by the plastic deformation ahead of the crack tip. The specimen size parameters, thickness and width [ 10, 11 ] have been reported to influence the plastic zone size and therefore could affect the blunting process and consequently the size of the stretch zone. However, in very few investigations has the effect of the specimen size on the stretch zone been examined, and those in which this has been done are not conclusive [9, 12]. This aspect was therefore examined in the present investigation. The multiple-specimen J a curve technique has its own limitations since several specimens identical in all respects are required to obtain
a single J1c value. Therefore, emphasis is now on the determination of Jic by a single-specimen technique. The most difficult part of such a method is the identification of the crack initiation point and this problem has not yet been satisfactorily resolved. Recently, several workers [ 1 2 - 1 4 ] have att e m p t e d to correlate the Jic fracture toughness with the critical stretch zone size (Aa)szc as measured on the fracture surface of the specimens (post-crack-initiation stage). Several empirical relationships [ 1 2 - 1 4 ] have been proposed relating Jic to the critical stretch zone size. However, such a correlation, although very important and useful, has so far not been clearly established and needs further investigation. In the present investigation the critical stretch zone size was measured in the specimens which had stable crack extensions to determine whether sufficient correlation exists between the critical stretch zone size and Jic to allow this procedure to be used to estimate the Ji¢ fracture toughness. The objectives of the present investigation were as follows: first, to find out the effect of specimen thickness and width on stretch zone size; second, to determine a valid size-independent blunting line equation; lastly, to examine whether the Ji¢ fracture toughness can be determined through the measurement of the critical stretch zone size. Compact tension specimens {with TL orientation, i.e. the load was applied in the transverse direction and the crack propagated in the longitudinal direction) prepared from aircraft quality AISI 4340 steel and heat treated to a yield strength level of 1000 MPa were used in the present investigation. The multiple-specimen JR curve method was used to determine unambiguous JI~ values for specimens of three different thicknesses and three different widths. In addition, several specimens of each size (thickness and width) were loaded to different levels of blunting (without any stable crack extension) and were used to evaluate the blunting line from measurements of their stretch zone.
2. EXPERIMENTAL PROCEDURE 2.1. Material
The aircraft quality AISI 4340 steel plate was available in the form of a hot-rolled plate 12.5 mm thick with an identifiable rolling
113 TABLE 1 Chemical composition Element Amount (wt.%) of element
C 0.43
Cr 0.81
S 0.10
Mn 0.73
Ni
P
Si
1.81
0.006
0.36
TABLE 2
TABLE 3
Mechanical properties
Specimen designation
Ultimate tensile strength Yield strength Elongation Reduction in area Brinell hardness
1070 MN m-2 1014 MN m-2 11.5% 50.8% 320-+ 20 HB
direction. The chemical composition of the material and its mechanical properties after heat t r e a t m e n t are given in Tables 1 and 2 respectively. 2.2. Specimen preparation Modified c o m p a c t tension specimens with TL orientation were prepared as described in A S T M Standard E 813-81 [4]. Six series of specimens were investigated. In the first three series the specimen_ width was held constant (W ~ 100 mm) and three thicknesses were studied (B ~ 12 mm, B ~ 6 nlm and B ~ 4 mm). In the n e x t three series the thickness was held constant (B ~ 12 mm) but the width was varied (W ~ 150 mm, W ~ 100 mm and W ~ 62.5 mm). The dimensions of the specimens are given in Table 3 together with the scheme for classification. After fabrication, the specimens were austenitized at 816 °C for 1 h and t he n quenched in oil. I m m edi at el y after quenching, t h e y were t e m p e r e d at 649 °C for 1 h and then air cooled to r o o m temperature. All the specimens were heat treated in an identical manner. The specimens were then ground on b o t h surfaces. 2.3. Fracture toughness measurements A multiple-specimen JR curve m e t h o d was e m p l o y e d to determine the Jic fracture toughness. Measurement of fracture toughness involves simultaneous m e a s u r e m e n t of load, load-line displacement and crack extensions. F r o m these measurements, J values were calculated using the standard relationship [4].
Mo 0.222
A1 0.050
Group Series
Width (mm)
Thickness (mm)
Number of specimens
1 1 1
601-609 401-410 251-259
150 100 62.5
12 12 12
9 10 9
2 2
411-419 421-429
100 100
6 4
9 9
The specimens were initially precracked in fatigue up to an a~ W value of a b o u t 0.55 f r o m the initial n o t c h a/W value of a b o u t 0.30. The last 2 m m of fatigue cracking were carried out at a AK level of 25 MN m -3/2, which conf o r m e d to the standard specification [4]. T hen the specimens were m o n o t o n i c a l l y loaded t o different amounts of load displacem e n t (which correspond to different amounts of crack extension) and unloaded. After the specimens had been unloaded, t h e y were again cracked in fatigue and finally fractured in liquid nitrogen. This was done t o retain fractographic features for subsequent analysis by scanning electron m i croscopy (SEM). On the fracture surface the physical crack extension Aa and the original crack length a0 were measured with the help of a traveling microscope. An average of nine readings across the specimen thickness was taken to obtain a0 and Aa (physical) for subsequent c o m p u t a t i o n of J values. The J values were calculated from the area under the load displacement curve and appropriately corrected using the Merkle and Corten [15] relationship. On a J versus Aa diagram a least-squares fit straight line was obtained. This was ext e n d e d to the blunting line given by J = 2Uo Aa and the J~c values were det erm i ned for the three thickness series and the three width series.
(3a)
114
2.4. Measurement o f stretch zone size In order to measure the stretch zone size on the fracture surface, a fractographic sample of the fracture surface area was cut from each of the specimens: the fracture surface included the crack front, the stretch zone, the stable crack growth region and the post-fatigue crack growth region. The samples were then cleaned in acetone and the fracture surfaces were examined by SEM. It should be noted that because of lack of clarity the boundaries of the respective fracture surface regions could not be identified and measured on all the specimens. The specimen data for measurements which were carried out with confidence are given in Figs. 5 and 6. These samples showed the following regions on the fractured surface: (1) fatigue-precracked region, (2) stretch zone, (3) stable crack extension, (4) post-fatigue crack and (5) liquid nitrogen fracture stage. These features are schematically shown in Fig. 3. The stretch zone at the start of crack extension is referred to as the critical stretch zone (Aa)szc. (Aa)szc is expected to depend only on the J value at the start of crack extension, i.e. Ji~ does not increase with subsequent loading. The crack extension starts at the mid-thickness region at JIc and then spreads toward the surfaces at progressively higher J values. When the stretch zone is interpreted, it must be remembered that the stretch zone at the mid-thickness and near the specimen surface forms at two different J levels in the specimen. Thus the stretch zone values measured only near the mid-thickness of t h e specimen are expected to correlate with Jxc.
Secondly, to check for consistency, the stretch zone size needs to be measured on both halves of the specimen. The formation of stretch zones at two different J levels in the midthickness and surface of the specimen will contribute to scatter in these measurements. On the basis of the above considerations a number of specimens of different sizes (thickness and widths) were examined and the stretch zone size was measured at 20-25 points near the mid-thickness region of each half of the specimen. An initial statistical analysis of the stretch zone size measurement showed that a minimum of 25 readings is necessary for the measurement of the stretch zone with a 95% confidence limit. The size of the stretch zone in each specimen was determined by holding the specimen at 45 ° to the incident SEM beam. In this position the stretch zone could be clearly seen and the measurements were carried out in the mid-thickness portion of the crack front with confidence. The measured stretch zone values had to be multiplied by a factor sec 45 ° to convert to actual values. The stretch zone was clearly demarcated by a featureless region bounded by a fatigue precrack on one side and a stable crack extension region on the other side. The stretch zone region appeared as a dark band against a white background, the width of which could be measured sufficiently accurately. This is shown in Fig. 4. The stable crack extension region was characterized by the presence of microvoid coalescence, which enables it to be distinguished from the stretch zone.
3. R E S U L T S A N D D I S C U S S I O N -FATIGUE- PRECRACKED PORTION
- - S T A B L E CRACK EXTENSION
ST ETN CH ZR O E~~IItL IQ I UD IN TIROGE FR NACTURE POS FT A-TG IUC ERACK Fig. 3. V a r i o u s f r a c t o g r a p h i c f e a t u r e s o n t h e specim e n surface.
The results of the present investigation will be presented and discussed in the following order: first, the effect of the size parameters B and W on the stretch zone size; next, the relationship between the stretch zone and the blunting line; finally, the correlation between Jic and the critical stretch zone size (Aa)szc. Various fractographic features will also be discussed. 3.1. E f f ect o f thickness and width on stretch zone size As was mentioned in Section 2.2, the stretch zone was measured in specimens with
115
T STABLE CRACK EXTENStON
L STRETCH ZONE
FATIGUE PRECRACK
,t
l
STABLE CRACK EXTENSION
STRETCH ZONE
T FATIGUE ~ C R AC~
Fig. 4. Microfractographs of (a) a s p e c i m e n 12 m m thick and (b) a s p e c i m e n 4 m m thick, showing the stretch zone, stable crack e x t e n s i o n and fatigue precrack. (Magnification, 400×.)
116 O.15 l
r
r
i
i
BLUNTING LIN E_~ SLOPE 2 I =
"•
O.10
~J
~~/~
I
'
I
'
I
~,?.
.\~
MEAN VALUE= +
+
0
~_~:
. . . . . . .
•
__
g
<3
+&
• e-~_
o+
• ° O
o
= _-~_
•
o
_,
. . . . . . .
o
O.O5
/
/ I
O 80
-
/ ..../.~..,,~o m
'-
i
~
t
I
80
~
I
t
160
I
240
i
I
320
J (kJ m -2)
!
/. 0
I
i CONVE]NTIONA L
320
--" 'E240
i
H/
0.05
J O.10
(AO)sz
Fig. 6. E f f e c t o f the s p e c i m e n size on the critical s t r e t c h zone.
....
,
I O. 15
(mm -I)
Fig. 5. E f f e c t o f the s p e c i m e n size o n t h e s t r e t c h zone.
Symbol
W (ram)
B (ram)
o • +
~62.5 ~100 >`150
~12 ~12 ~12
•
~100
>-4
[]
=100
>`6
different thicknesses B of a b o u t 12, 6 and 4 mm. All these specimens had a c ons t ant width W of a b o u t 100 mm. Figures 5 and 6 show plots of stretch zone size v e r s u s J and critical stretch zone size v e r s u s J respectively for three specimen thicknesses and three specimen widths. It is evident f r om these figures that the specimen thickness has no apparent influence on the stretch zone size. The reason for the observed scatter in the stretch zone values has already been m e n t i o n e d in Section 2. The thickness effect on stretch zone size has been studied by earlier workers [9, 12, 16 ]. However, the results r e p o r t e d in the literature are o f t e n c o n t r a d i c t o r y and conflicting. Gilmore e t al. [9] r e p o r t a larger value o f stretch zone size in 12.7 m m specimens prepared f r om martensitic stainless steel H T8 0 than for 2.5 m m specimens of the same material. In contrast, Ohji e t al. [16] and Kobayashi e t al. [12] f o u n d the stretch zone
Symbol o
W (mm) ~62.5
B (mm) ~12
•
>`100
~-12
+
>`150
~.12
•
>`100
~4
[]
~100
~6
width to be virtually i n d e p e n d e n t of specimen thickness. The results of the present investigation also show that the specimen thickness has little influence on the stretch zone, which is in agreement with the results report ed by Ohji e t al. and Kobayashi e t al. Figures 5 and 6 also show the effect of the specimen width on the stretch zone size. All these specimens had a constant thickness B of a b o u t 12 mm. The stretch zone sizes as measured on these specimens are comparable with the measured values on specimens with different thicknesses. It is clear from Figs. 5 and 6 that specimen width also has little or virtually no effect on the stretch zone size when loaded t o comparative J values. However, the scatter in the measured stretch zone values is somewhat lower than was f o u n d for the specimens with varying thicknesses. Very few studies have been c o n d u c t e d to date to study the influence of the specimen width on the stretch zone size. One of the present authors and coworkers [17] in a previous publication found that the width had no effect on the stretch zone size in a material that undergoes simultaneous pop-in and stable crack extension. Our results also show t hat
117 the specimen width has no apparent influence on the stretch zone size, although this material did not undergo any pop-in type of crack extension.
The JR curves of these specimens with different thicknesses and widths have been determined by the multiple-specimen technique and have been reported in another publication [18]. Figures 7 and 8 show the multiplespecimen JR curves for these specimens. It is clear that with the conventional blunting line (J -- 2(Aa)szOo) the Jic value for different thicknesses varies from 62 kJ m -2 for specimens 4 m m thick to 78 kJ m -2 for specimens 12 mm thick. However, if the blunting line J = 1.2(Aa)szOo obtained by the stretch zone size measurement were to be used, the scatter in the Jic values is reduced. (The Jic values vary between 68 and 80 kJ m-e.) The blunting line obtained by stretch zone size measurements when used in the plot of JR curves for three different widths W of about 150, 100 and 62.5 mm gives J~c values within -+10% of the mean value of 76 kJ m -e. It is imperative to note that all these specimens had a constant thickness (B ~ 12 ram) and had square or flat fracture present on them. None of these specimens (constant thickness B ~ 12 mm) had any shear lips. Thus it appears that the blunting line obtained by stretch zone measurements is more appropriate in determining the Ji~ values for specimens instead of
3.2. Stretch zone size and blunting line The stretch zone values obtained from direct measurements on the specimen surfaces are compared with the conventional blunting line in Fig. 5. As was mentioned earlier, these specimens were loaded to different levels of blunting such that no stable crack extensions were present on them. The data points plotted in Fig. 5 are an average of 2 0 - 2 5 measurements taken on each specimen in the midthickness region. The conventional blunting line represented by eqn. (3) has a slope of J/oo(Aa)sz = 2. The (Aa)~ values measured on the specimen surfaces, however, fall within the two limits shown as broken lines in Fig. 5. These data points lie between a line of slope 1.5 and a line of slope 1.0, and the mean value of the slope of the line passing through these points is about 1.2 compared with a slope of 2 for the conventional blunting line used in the standard J1~ test procedure.
I
'
I
I
'
I
'
I '
VBLUNTING LINE J= 2O'oAa
32O
r /
I,
I
/
I /!NEWBLUNTiNOL,NE //joe,~o
L Ill
240
L.-o.m
e~
m,',
OFFSETLINE
FII:
~/
32.0 ~-
' -
,
~l~,;'i
~',/
l
k
-
I
7 ° /
:
-
I/i"J;> ~
0
;i
l
'
I
! 1.5 m m
o /
°~oo~""
"
I
I
ov ~
I
o
i
I
~ OFFSET
Ill I II/ !I
I
,
I
,
0.8
I 1.2
i
I 1.6
Ao (mm)
Fig. 7. Multiple-specimen JR curve for three different thicknesses (constant width W = 100 ram): I, B ~4mm;o,B~ 6mm;A,B ~ 12ram.
0
I
I 0 1 C~-~I (9' .
-
I
I OFFSET
0.4
'
,J=2°oAa
///
i
0[
I
i.....--BLUNTING LINE
I-I I ;
! III
~
I l / I~O-15mm I I I #OFFSET LINE 240 F I /--~-NEW I BLUNTING LINE
'E
~^I I I ~ . ,
I
r LINE I I 0.4
0.8 a o (mm)
1.2
1.6
Fig. 8. M u l t i p l e - s p e c i m e n JR c u r v e f o r t h r e e d i f f e r e n t w i d t h s ( c o n s t a n t t h i c k n e s s B = 12 r a m ) : o, W 6 2 . 5 r a m ; i , W ~ 1 0 0 m m ; +, W ~- 1 5 0 r a m .
118
using a standard blunting line with a slope of 2 for all materials. The slope of the blunting line has previously been studied by several workers [5-7, 9]. Mills [5] has reported that the value of the constraint factor m depends on the material. For a low strain-hardening material the value of m is reported to be equal to u n i t y [5, 6], whereas for a material with a high strain-hardening coefficient the value of m lies between 2 and 3 [5]. Gilmore et al. [9] reported a size-dependent value for the constraint factor m. For specimens 12.7 m m thick prepared from a martensitic stainless steel, they reported an m value in the range 0.8-0.95, but for specimens of the same material with a smaller thickness (B ~ 2.5 mm) they f o u n d a higher m value of about 2.6-2.8. Broek [19] found an m value of the order of 1.1 for all aluminum alloys. Liu and Kobayashi [20] reported a value for the constraint factor in the range 1.1-1.5. Others have found an m value in the range 0.79-3.0. The results of Kobayashi et al. [21], however, show a constraint factor of the order of 0.60. A two-dimensional analysis by Shih [8] correlating J and the crack-opening displacem e n t predicts the value of the constraint factor m to equal about 1.4 for a low strainhardening material. The material used in the present investigation had a very low strainhardening coefficient (n ~ 0.03). Our results, however, indicate that the constraint factor m is independent of size and has a value of approximately 0.6 and is thus in agreement with the results reported by Kobayashi et al. [211. 3.3. Critical stretch z o n e size and J~¢
The stretch zone forms during the loading of the precracked specimens and attains a critical value at the initiation of fracture. This critical value of the stretch zone size remains unaffected by continued stable crack growth [12] and is defined as (Aa)sze. The critical stretch zone size was measured in the mid-thickness region in all the specimens which had stable crack extension present on them. Figure 6 shows a diagram of these (Aa)szc values against J for different thicknesses and widths. As was mentioned earlier, these (Aa)szc values were f o u n d to be independent of specimen size (thickness and width). The mean value of (Aa)szc when used
TABLE 4 Comparison of fracture toughness values obtained by various methods
Method
Mean value of fracture toughness JIc (kJ m -2)
KIc (MPa m 1/2)
Multiple-specimen resistance 68 curve with conventional blunting line
124
Multiple-specimen resistance 76 curve wtih new blunting line J = 1.2o0(Aa)sz
132
Stretch zone measurements
143
90
in Fig. 5 and extrapolated to the new blunting line with slope 1.2 (the blunting line obtained by direct measurements on the specimen surfaces on the specimens without any stable crack growth as reported in Section 3.2) gives a Jic value of 90 kJ m -2, which is about 18% higher than the mean value 76 kJ m -2 obtained by the multiple-specimen resistance curve m e t h o d (Table 4). However, in terms of Kic the fracture toughness value is only 10% higher than the mean value of 132 MPa m 1/2. It is evident from Fig. 5 that, when this mean critical stretch zone size value is extrapolated to the conventional blunting line represented by J = 2o0(Aa)sz, it gives a considerably higher Jic value and consequently a higher value of Kic (Jie ~ 150 kJ m -2) than the value obtained by the multiple-specimen resistance curve methods. It therefore appears that the critical stretch zone size measurements can be used for this class of materials for a determination of the KI~ fracture toughness provided that the correct blunting line is used in J1e tests. Several other workers [22-25] have found reasonable agreement between the critical stretch zone size and Kic. Our results also show that a good estimation of Kic is possible by proper and elaborate measurements of critical stretch zone sizes. Several empirical relationships have been proposed by some workers [13, 14, 24] for Kie and (Aa)sze. Two of these models, namely those of Fujita et al. [24] and Yin et al. [13], were examined for our test data. However,
119
when the measured (Aa)szc values were used in these equations, the Kxc values estimated were found to be much higher (200 and 180 MPa m 1/2) than those obtained from Ji¢ by the multiple-specimen resistance curve method.
=0.50 [
3.4. J versus crack-opening displacement relationship
r :0.45
The crack-opening displacements were calculated using Dover's equation [26] for compact tension specimens. In all these calculations the value of the rotational factor r used depended on the extent of stable crack growth on the specimens. For specimens loaded to a high crack extension (Aa >~ 1.50 mm) or high levels of load-line displacement, the value of the rotational factor r was taken as 0.50. Similarly, for specimens loaded to crack extensions of approximately 1.0-1.5 mm, the r value was taken as 0.45. For specimens loaded to crack extensions of between 0.5 and 1.0 mm the r value was taken as 0.40. This is illustrated in Fig. 9. This m e t h o d was
r --0.40
/
L 0.5
1.0 AO (mm)
J
1.50
Fig. 9. R o t a t i o n a l f a c t o r r vs. stable crack e x t e n s i o n .
0.50
E
o.2o
C
+
0.10
/
0 0
'-~MEAN SLOPE = 0.60
I
I 0. I0
I
I 0.20
I
I 0.30
J
1 0.40
COD (ram) Fig. 10. I n t e r r e l a t i o n b e t w e e n J a n d t h e c r a c k - o p e n i n g d i s p l a c e m e n t COD. Symbol
W (mm)
B (mm)
© • + • []
~-62.5 ~100 ~150 ~100 ~100
~12 ~12 ~12 ~4 ~-6
120
adopted since there is no standard relationship for the determination of the crack-opening displacement for c o m p a c t tension specimens and the value of the rotational factor r has been reported to be in the range 0 . 3 2 0.50 [26]. The crack-opening displacement values calculated by the above m e t h o d are plotted in Fig. 10 against J/oo. J values were calculated for each specimen from the load displacement area and corrected appropriately using the Merkle and Corten relationship [15]. The slope of the least-squares fit line joining these data points was found to be about 0.60 and the J versus crack-opening displacement relationship was found to be expressed as J = 0.6a0(COD) for this material. As was mentioned earlier, the value for m has
'
I
'
I
'
I
1
0.40
(1)
z
+
E E a o
been reported to be in the range 0 . 7 - 3 . 0 for different materials. Simpson [27] reported an m value of about 1.08 for Zr-2.5wt.%Nb. Our results show that there is a good correlation between J and crack-opening displacement. The constraint factor m has a value of 0.6 for this material. Figure 11 is a plot of the crack-opening displacement versus stretch zone size. It is evident from this figure that a good correlation exists between the crack-opening displacement and (Aa)sz; the slope of the line of leastsquares fit was found to be a b o u t 1.86, which is slightly lower than the analytical value of 2 predicted by Landes and Begley [2]. Similar patterns of results have been reported by other workers [28, 29]. The good correlation between J, crack-opening displacement and
o 0
0.30
GO T Z t-- UJ
+
I.U
o
z
v
+
0
+
0
113
0.20
+o
°
+
0
0
SPECIMENS LOADED UP TO BLUNTING
0. I0
,,,~MEAN 0
l
0
SLOPE= 1.86 I
0.05
~
=f
(Aa)szc I
0.10
~
I
0.15
(Ao)sz (mm) Fig. 11. C r a c k - o p e n i n g d i s p l a c e m e n t C O D vs. s t r e t c h z o n e size.
Symbol
W (mm)
B (ram)
O • + • Q
~62.5 ~100 ~150 ~100 ~100
~12 ~12 ~12 ~4 ~6
121
(Aa)~ confirms the fact that the stretch zone measurements in the present investigation are reliable and can be related directly to the toughness parameters J and crack-opening displacement.
3.5. Fractographic features The various regions present on the fractured surface were described earlier and are illustrated in Fig. 4. In general, the fractographic features which define a given region of the fracture surface were the same for all specimens. In the fatigue-precracked region the striation markings were not very clearly visible. This is probably because the last 2 m m of the fatigue cracking were carried out at a low AK level of 25 MN m -312. At such low AK levels, striations are difficult to observe because of their fine spacing. At high magnifications (3600X), however, sometimes microvoids and striation markings were observed. The stretched zone could be clearly seen as a wide dark band in a bright background as shown in Fig. 4. The stretch zone has been reported either to be characterized by glide markings or to have a featureless appearance [30]. In the present investigation, examination of the stretch zone at a high magnification revealed the presence of microvoids. The stable cracked region is characterized by the presence of very fine equiaxed dimples: These are clearly visible as shown in Fig. 4. In between a few of the voids, some inclusions could be seen. Parallel ridges perpendicular to the crack front were also observed. The ridges were typical of a TL orientation where the crack propagation takes place along the axes of stringer-type inclusions.
4. CONCLUSIONS
Specimen size (thickness and width) has virtually no influence on the stretch zone size obtained by direct measurements on the specimen fracture surface. The blunting line is best represented by the relation J = 1.2(Aa)szo0 for AISI 4340 steel heat treated to a yield strength of 1000 MPa. A good correlation exists between the critical value of the stretch zone and Kic, and computation of/{ic is possible by measurements
of the critical stretch zone size for this material. The crack-opening displacement and (Aa)sz are related by COD = 1.86(Aa)sz for compact tension specimens in the thickness and width ranges investigated in this investigation. The new blunting line obtained by measurement of the stretch zone size in this investigation can give a size-independent Jic value. The Jic value obtained by measurement of the stretch zone size is about 18% higher than the Jic value obtained by the multiple-specimen resistance curve method.
ACKNOWLEDGMENTS
The authors would like to thank Professor H. T. Corten for many helpful discussions concerning this work. One of the authors (S.K.P.) acknowledges the help and support of the Department of Metallurgy, University of Illinois at Urbana-Champaign, for completion of this work and the Materials Engineering Research Laboratory for the mechanical testing facilities. Part of the support for this work was provided by the Council for International Exchange of Scholars, Washington, DC, which is gratefully acknowledged.
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