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A study of COD and crack initiation by a replication technique
l?uginu?ing Fmclun
Mechanics, 1977, Vol. 9. pp. 137446.
Pergamon Press.
Phted
in Great Britain
A STUDY OF COD AND CRACK INITIATION BY A REPLICATION TECHNIQUE B. A. HELIX and K. J. MILLER Engineering Department, University of Cambridge, CambridgeCB2 lPZ, England Abstract-A silicone rubber has been used to infiltrate cracks created during slow bend tests on notched BY 100 and HY 130 steel specimens at room temperature. Crack opening displacements have been measured directly from the hardened rubber replicas of the crack. The growth of the stretch zone is in agreement with that predicted by slip line analysis. Crack initiation is seen to be a nebulous process occurring irregularly along the slot front. The initial growth of a fibrous crack has also been studied.
INTRODUCTION previous work has shown that unstable fracture in precracked specimens of a tough material is preceded by stable fibrous crack growth. Studies by Smith and Knott [ 11and Harrison and Feamehough[2] have shown that the crack opening displacement (COD) at fibrous crack initiation, &, appears to be a material constant, while the COD at maximum load, S,, is dependent on specimen dimensions and machine stiffness. However, in practice S, is easy to measure whereas it is difficult to detect the precise incidence of crack initiation. Previous efforts to determine Si have involved deformation of several specimens to various crack lengths, followed by fracture at liquid nitrogen temperature[l]. The amount of fibrous crack growth is then measured on the surface of the broken specimens and Si is obtained by extrapolation to zero fibrous growth. Recently Robinson[3] has suggested that a hardening silicone rubber can be used to make a replica of a crack while under load. By taking such replicas at increasing stages of deformation it is possible to follow both the initiation and the initial growth of the crack. This paper describes work carried out using the above technique to study the initiation of fibrous cracking in HY 100 and HY 130 steels. In addition a relationship between clip gauge displacement, V, and on-load COD, 6, was obtained. Results indicate that deformation occurs by a simple hinge mechanism about a constant centre of rotation only after general yielding has taken place. MUCH
EXPERIMENTAL DETAILS Tests were carried out on various thickness bend specimens of HY 100 (25 and 38 mm plate) and HY 130 (25 mm plate) at room temperature. Chemical compositions of the materials are shown in Table 1 and the tensile properties listed in Table 2. Test pieces, with dimensions as shown in Fig. 1, were all cut transverse to the rolling direction (T) but were notched either in the rolling (L) or short transverse (ST) directions, Fig. 2, leading to the nomenclature T/L and T/ST. All specimens were tested using three point bending in an Instron 100kN capacity machine at a cross-head displacement rate of 0.5 mm/mm. A few specimens were pre-fatigued cracked using a Mand 60 kN machine but the majority of test pieces were notched with rubber bonded slitting wheels of width 0.16 and 0.23 mm to a nominal notch depth to specimen depth ratio (a I W) of 0.4. The displacement, V, at the open end of the notch was measured using a clip gauge mounted on two knife edges 1 mm above the specimen surface. Records of clip gauge displacement with increasing load were obtained for each test. Direct measurements of the COD at the crack tip were made by infiltrating the notch with Unitek Xantopren Blue dental impression material, a hardening silicone rubber. The liquid rubber was placed in the notch and the specimen loaded to known values of displacement. After about 20 min, with the specimen under load, the rubber had solidified and could be removed with tweezers. The procedure was then repeated for increasing displacements. The replica of the crack front was first examined at a magnification of x 10 under a projection microscope and then a thin section was cut from the rubber at the crack front mid-point. The width of the slot and the nature of any cracking was examined and was recorded on tracings at x50. 137
138
B. 4. FIELDS and K. i. MILLER
100 mm
“.
5
..
IO to 24mm
Fig. I. Testpiece dimensions. Short Transverse
(ST)
Fig. 2. Specimen and notch orientations. Table 1. Chemical compositions
Table 2. Tensile properties
Data
provided
by
NCRE,
Dunfermiine,
Fife.
In order to determine whether any volume change occurred in the rubber during setting, replicas were taken of parallel sided slots, the widths of which were measured with feeler gauges. A comparison of the measurements from replicas and feeler gauges is shown in Fig. 3. The maximum deviation was never greater than 0.01 mm. RESULTS A typical load-displacement curve for HY 100is shown in Fig. 4. Fast fracture did not occur in any specimen but fibrous tearing was found to initiate prior to the achievement of maximum load. Traces of the crack front at the displacements shown in Fig. 4 can be seen in Fig. 5. The development of cracking is extremely non-uniform, appearing first as isolated linking of microvoids with the slot front. It is thus di~cult to define a critical point of crack initiation. However, previous workers[l] have examined the fractured specimen surfaces of several test
139
A study of COD and crack initiation by a replication technique 06r
Feeler
gauge width,
mm
Fig. 3. The accuracy of measurement of slot widths using the plastic replica technique.
Clip gauge displacement
,V,mm
Fig. 4. A displacement curve for HY 100;specimen width 24 mm.
I.Omm
s-
i,
-
h
4 2
I Fig. 5. The appearance of the crack front with increasing deformation corresponding to points shown in Fig. 4.
pieces and measured either the fibrous crack length or the area of fibrous growth and have extrapolated back to zero growth to obtain “initiation” conditions of COD, 6,. By using the rubber infiltration technique the instant of initiation, as defined in this way, can be located fairly accurately from only one specimen; i.e. in this case at point 2 in Fii. 5. Cross-sections through the mid-point of the rubber replica are shown in Fig. 6. It can be seen that the slot length, and the width, have increased before any cracking has occurred. This corresponds to the stretch zone observed on fracture surfaces between the original slot front and
140
B. A. FIELDS and K.
MILLER
6
,
Reference
$05
Fig. 6. The formation of the stretch zone and a crack in HY 100at points corresponding to those show in Fig. 4.
the fibrous crack growth. Similar sections for HY 130 showed exactly the same effect, Fig. 7. Values of COD, see Fig. 8, can be measured directly from the projected image and compared with clip gauge displacements. DISCUSSION (1) Relationship between V and S In order to calculate the opening at the crack tip, 6, from the clip gauge displacement, V, it is usually assumed that the crack faces open using a simple hinge mechanism with a fixed rotation axis at a position defined as the fraction, r, of the remaining ligament width, W - a ; i.e. at a position r( W - a) beyond the crack tip. Geometrical considerations then indicate that
“=((a
+z)lr(VW--a))+1
where z is the height of the clip gauge above the specimen surface. The British Standards Draft for Development for COD testing[4] suggests the use of r = 0.33. However, using the above formula several workers[3,5,6] have observed that in practice r increases from about 0.1 to 0.47 as deformation due to bending increases. These results have been
l-l’ 0
Fig. 7. The formation of cracking in two HY 130specimens of different orientations.
141
A study of COD and crack i~tiatio~ by a replication technique
Before crack initiation
After crock initiation
fib
Fig. 8. Measurement of (a) 6 and x, and (b) &,from the projected image of the replica.
explained by suggesting that the centre of rotation moves away from the crack tip continually during deformation. Etching studies [‘7lhave indicated that when yielding has spread across the ligament (W - a) the centre of rotation is at the ligament mid-point, i.e. r = 0.5. The present results provide a direct calibration between V and on-load 6 values, see Fig. 9. At the start of loading V increases but the width of the notch tip remains unchanged. Thus initially, rotation occurs very close to the notch tip and within experimental accuracy r = 0, For the present geometry if r = 0.5 then 6 = 0.4 V. Hence a line of slope 0.4 is included in Fig. 9 and can be seen to be in good agreement with results for V > 0.25 mm. It was observed that initial crack growth was very slow so that in Fig. 9 even specimens with S = 0.44 showed crack extensions of only 0.2 mm averaged along the crack front. This decrease in the initial sections thickness (a - W) = 12 mm has a ne~i~ble effect on results calculated from eqn (1) thus just~ying the inclusion of points where 6 > &. For V < 0.25 mm r increases from 0 to 0.5 as S increases. A value of V of 0.25 mm can be shown to fall within the range of values calculated for general yield conditions by considering the upper and lower bounds for the bending moment of notched bars at general yield, AfS,, as given in [8], i.e. upper bound
M,, = 0.30~7,(W - a)‘B
(2)
lower bound
MBy= 0.25+( W - a)‘B.
(3)
KEY X 0 + 1) 0 Cl
05
HYl00 HYi00 HYIOO HYl30 HYl30 HY130
B=24mm 0=24mm E=iOmm B-24mm Ba24mm B-24mm
w=0,23mm w=Olbmm w = 0.23 mm w=023mm w=016mm w-0
s = 04vr = 05
0.1
i
o-
/
/
n
-1
0.2
/
I
Q4
0.6 Clip
,
Q8
/
/
I.0
gauge displacement,
I.2
t
I,4
V, mm
Fig. 9. The relationship between ciip gauge displacement and COD.
07
142
B. A. FIELDS and K. J. MlLLER
For HY 100 the upper and lower bound general yield loads were calculated to be 41 and i? kN corresponding to values of V of approx. 0.30 and 0.22 mm, Fig. 6. For HY 130 equivalent values of V of 0.32 and 0.23 mm were found from similar load-clip gauge displacement curves. Thu< the results indicate that deformation occurs by a simple hinge mechanism about a fixed axis itnia after general yielding has taken place. The effect of using a constant r value of 0.33, as suggested in the British Standards Draft flor Development for COD testing [4] (equivalent to 6 = 0.3 V for the present geometry) is also shown in Fig. 9. It can be seen that for small values of V, i.e. ~0.5 mm, an overestimation of COD results. Thus for specimens where crack initiation occurs before general yield the calculation of & from eqn (1) can lead to large errors. (2) Stretch zone measurements Pelloux[9] has shown a simple model for the formation of the stretch zone at the crack tip, Fig. 10. Shear initiates on a plane at 45” to the crack tip, e.g. along AC, until work hardening makes further shear on AI3 more favourable. Thus deformation takes place by incremental shear that alternates between the two planes at 45” to the crack direction, so leading to an extension of the crack, x, (Fig. 8) equal to half the crack flank opening displacement, S. Pelloux refers to work of McClintock [ lo] who has carried out a slip line analysis for a double notched tensile specimen and obtained a blunted crack tip with x = 0.5 6. Rice and Johnson[l l] predict the shape of the blunted crack tip using slip line theory for both small scale yielding and fully plastic cases and obtain values of x = 0.55 S and 0.65 6 respectively. They note that while the analysis, strictly speaking, applies to an initially sharp crack, it is also an approximation to the case of an initially blunt notch, provided the plastic zone size is large compared to the notch root size. In the present work using the rubber infiltration technique direct measurements can be made of the stretch zone formation before cracking begins, see Fig. 8. Values of extension, x, and COD, 6, have been measured from tracings such as those shown in Figs. 6 and 7. The results are given in Fig. 11 and can be seen to be in good agreement with a relationship x = 0.5 6.
Fz ‘5
Fig. 10. Pelloux’s model[9] for the formation of a stretch zone at a crack tip in simple tension
A study of COD and crack initiation by a replication technique
x
WYIOO
l
HYIOO A HY130
Crack Fig.
w - 023mm w = 016mm
w=
0.23mm
0.1
0”
extension
during
143
02 blunting,
x. mm
11. The relations~p between COD and stretch zone Size.
Table 3. Values of b, 6t and 6, for HI’ 100and HY 130parent plate
A number of workers including Broek[l;?] and Elliott[l3] have attempted to relate stretch zone dimensions and COD from measurements of the fracture surface. Elliott obtains a relationship 6 = 1.5~ +0.04, where y is the length of the stretch zone surface measured at 45” to the crack extension, i.e. y = fi, leading to 6 = 2.1~ +0.04. He refers to a “threshold” COD of 0.4 mm for which the stretch zone width is zero. Such a theory cannot be true since the very existence of a COD is due to the presence of crack tip bl~ting, i.e. the fo~tion of the stretch zone. The apparent anomaly can be explained by use of the correct relationship to calculate the COD from the clip gauge displacement. Elliott used eqn (1) with a value of r = 0.33 mm. For the present case a value of COD of 0.04mm would have been obtained from a clip gauge displacement, V, of 0.14 mm. It can be seen from Fig. 9, that this corresponds to an actual value of COD, 8, of 0,005 mm. This latter value confirms within ex~~ent~ error the relations~p S = 2x. The above correction would suggest that the theory of Elliot that the “threshold” COD is
144
B. A. FIELDS and K. J.
MlLI.ER
equrvalent to Klscc, the threshold value of stress intensity below which stress corrmm does not occur, is incorrect.
uacktng
(3) CWical COD Measurements of COD were made directly from projected images of the sectioned replicas as shown in Fig. 8. The increase in COD between successive replicas was, on average, 0.03-0.04 mm, enabling & to be located to within about +0.02 mm. Robinson [3] has pointed out that once the crack has initiated the COD, 6, is made up of two components: (ii that due to initiation, &, and (2) the opening of the propagated crack near to the original crack tip, Z, i.e. & = 6 - Z, see Fig. 8(b). In specimens showing a suitable crack a value of 6, was calculated in this way and for clarity designated 6:. Average values of Si, I?? and 6, (COD at maximum load) are shown in Table 3 for HY 100and HY 130. The results indicate that within the observed scatter there is no significant effect of specimen thickness, orientation or slot width. For 38 and 25 mm thick HY 100 plate and 25 mm thick HY 130 plate respectively the values of & are approx. 0.12, 0.14 and 0.15 mm. However, little useful knowledge is obtained by knowing the toughness which the first stable microcracking occurs. In order to retain the technical usefulness of toughness testing, the critical value of S used to predict the behaviour of large specimens must be that at which significant crack growth takes place in an unstable manner. Hence the COD at maximum load has been used by some authors as an alternative to & in calculations of critical crack size. However, for the present materials the maximum load is limited by plastic collapse of the ligament below the notch. This can be seen for two reasons. (1) Although crack initiation occurs prior to maximum load, stable crack growth is still negligible (between points 4 and 5 in Fig. 4) suggesting that the maximum load is not connected with crack growth. (2) An approximate calculation of the plastic collapse load (substituting tensile strength for yield stress in eqn (2)) gives 48 and 52 kN for 24 mm thick specimens of HY 100 and HY 130 respectively, compared to experimental values of 49 and 61 kN. From either or both of these considerations it is argued that the maximum load attained in small specimens of these materials is not related to 6, for unstable propagation. It is important to realise that the achievement of &, while a necessary criterion for fracture. is not a sufficient one. In so called “brittle” failures initiation of a crack is more difficult than propagation, hence an initiation criterion is valid. In more ductile materials initiation may occur before the critical stress necessary for propagation is achieved. Stable crack growth under increasing load will continue until this critical stress is reached. During this crack growth the COD due to plasticity at the original crack tip does not change. The apparent COD may alter because of a component due to the opening of the crack (Fig. 8) but repeated measurements at the slot tip show & to be unaltered within experimental error during further loading. Thus although ri. may be a material property it is not, in these materials, a valid measure of toughness as it is not related to the point of instability. This will be true for all materials where stable crack growth precedes unstable crack propagation. In the present materials it appears that the critical stress for propagation is above the tensile strength. This implies that for this thickness of material (24 mm) the propagation of a crack cannot take place however large the specimen dimensions. In such cases values of 6: give no practical information and 6, has no meaning. (4) Initial crack growth In addition to locating crack initiation it is possible to follow the initial growth of a crack using the rubber infiltration technique. In this case it was usually necessary to let the rubber set and then strain the specimen further to allow the rubber to be removed without tearing. Examples of crack profiles are shown in Figs. 12 and 13. Figure 12 shows profiles for two orientations of HY 100 specimens. In general in this material cracking was observed to take place directly ahead of the slot. This was also seen in a T/L specimen by sectioning the test piece normal to the plane of cracking, see Fig. 14(a). In HY 130, however, the majority of cracking was seen to be of a zig-zag nature, see Figs. 13 and 14(b). For the T/ST orientation some crack fronts showed a certain amount of delamination along the transverse direction (Fig. i3(c)). That this effect is real and not due to bending of the replica can be seen from a section of the same specimen: see Fig. 14(c). A
Fig. M(a).
. (I
*.I.
**
l”
Fig. M(b).
Fig. 14(c).
A study of COD and crack initiation by a replication technique
145
I.Omm
Fig. 12. The growth of cracking in two HY 100specimens of different orientations in each case 6 = 0.76mm. I,Omm
A ST t
a.
T
b.
Fig. 13. Crack growth at different points along the crack front in an HY 130specimen with 6 = 0.76mm.
comparison of Figs. 13(c) and 14(c) indicates that the rubber infiltration technique provides a reliable method for observing the presence and growth of a fibrous crack. A further observation was that the maximum crack length occurring at a given COD was different for each case considered, i.e. in HY 100 more crack growth occurred in the T/L orientation than for a T/ST specimen although the COD’s at crack initiation were similar. A more detailed analysis of the crack length D COD may prove an interesting way of studying relative crack growth resistances. CONCLUSIONS
(1) A direct calibration can be made between clip gauge displacement and COD, enabling the present inaccuracies in calculating small values of COD to be eliminated. (2) The nature of the stretch zone has been studied, the extension of the crack tip during blunting being equal to half the COD. (3) In HY 100and HY 130plastic collapse takes place without unstable crack propagation for specimens up to 24mm thick. In such cases measurements of COD are irrelevant for design purposes. Acknowledgements-The authors would like to thank Cambridge University Engineering Department for provision of laboratory facilities. This work has been carried out with the support of the Procurement Executive, Ministry of Defence.
REFERENCES [l] R. F. Smith and J. F. Knott, Proc. of the Conj. on Practical Application of Fracture Mechanics to Pressure Vessel Technology, p. 65. A.I.M.E., London (1971). [2] T. C. Harrison and G. D. Feamehough, ht. J. Fracture Me& 5, 348 (1969). [3] J. N. Robinson and A. S. Tetehnan, Measurement of K,C on small specimens using critical crack tip opening displacement. ASTM S’J’P559, 139-158(1974). EFM Vol. 9, No. I-J
146
B. A. FIELDS and K. J. MILLER
[4] British Standards Draft for Development 19, London (1972). [5] C. C. Veerman and T. MuRer, Engng Fracture Mech. 4, 2.5(1972). [6] T. I&am, G. R. Egan, D. Elliott and T. C. Harrison, Proc. of the Conj. on Practical Application of Fracture Mechanics to Pressure Vessel Technology, p. 200. A.I.M.E., London (1971). [7] A. P. Green and B. B. Hundy, J. Mech. Phys. Solids 4, 128(1956). [8] J. F. Knott, Fundamentals of Fracture Mechanics, p. 173. Butterworths, London (1973). [9] R. M. N. Pelloux, Engng Fracture Mech. 1, 697 (1970). [IO] F. A. McClintock, Int. Conj. on Fracture, Kiruna, Sweden (1%7). [l l] J. R. Rice and M. A. Johnson, In Inelastic Behaviour of Solids (Ed. Kanninen et al.), p. 641. McGraw-Hill, New York (1970). [12] D. Broek, Engng Fracture Mech. 6, 173 (1974). [13] D. Elliott, The Practical Implications of Fracture Mechanisms, p. 21. Spring Meeting, Institution of Metallurgists, London (1973). [14] J. F. Knott, Mater. Sci. Engng 7, 1 (1970). [IS] C. G. Chipperlield and J. F. Knott, Internal Report. Cambridge University Metallurgy Dept. (1972). (Received March 1975)
Mechanics, 1977, Vol. 9. pp. 137446.
Pergamon Press.
Phted
in Great Britain
A STUDY OF COD AND CRACK INITIATION BY A REPLICATION TECHNIQUE B. A. HELIX and K. J. MILLER Engineering Department, University of Cambridge, CambridgeCB2 lPZ, England Abstract-A silicone rubber has been used to infiltrate cracks created during slow bend tests on notched BY 100 and HY 130 steel specimens at room temperature. Crack opening displacements have been measured directly from the hardened rubber replicas of the crack. The growth of the stretch zone is in agreement with that predicted by slip line analysis. Crack initiation is seen to be a nebulous process occurring irregularly along the slot front. The initial growth of a fibrous crack has also been studied.
INTRODUCTION previous work has shown that unstable fracture in precracked specimens of a tough material is preceded by stable fibrous crack growth. Studies by Smith and Knott [ 11and Harrison and Feamehough[2] have shown that the crack opening displacement (COD) at fibrous crack initiation, &, appears to be a material constant, while the COD at maximum load, S,, is dependent on specimen dimensions and machine stiffness. However, in practice S, is easy to measure whereas it is difficult to detect the precise incidence of crack initiation. Previous efforts to determine Si have involved deformation of several specimens to various crack lengths, followed by fracture at liquid nitrogen temperature[l]. The amount of fibrous crack growth is then measured on the surface of the broken specimens and Si is obtained by extrapolation to zero fibrous growth. Recently Robinson[3] has suggested that a hardening silicone rubber can be used to make a replica of a crack while under load. By taking such replicas at increasing stages of deformation it is possible to follow both the initiation and the initial growth of the crack. This paper describes work carried out using the above technique to study the initiation of fibrous cracking in HY 100 and HY 130 steels. In addition a relationship between clip gauge displacement, V, and on-load COD, 6, was obtained. Results indicate that deformation occurs by a simple hinge mechanism about a constant centre of rotation only after general yielding has taken place. MUCH
EXPERIMENTAL DETAILS Tests were carried out on various thickness bend specimens of HY 100 (25 and 38 mm plate) and HY 130 (25 mm plate) at room temperature. Chemical compositions of the materials are shown in Table 1 and the tensile properties listed in Table 2. Test pieces, with dimensions as shown in Fig. 1, were all cut transverse to the rolling direction (T) but were notched either in the rolling (L) or short transverse (ST) directions, Fig. 2, leading to the nomenclature T/L and T/ST. All specimens were tested using three point bending in an Instron 100kN capacity machine at a cross-head displacement rate of 0.5 mm/mm. A few specimens were pre-fatigued cracked using a Mand 60 kN machine but the majority of test pieces were notched with rubber bonded slitting wheels of width 0.16 and 0.23 mm to a nominal notch depth to specimen depth ratio (a I W) of 0.4. The displacement, V, at the open end of the notch was measured using a clip gauge mounted on two knife edges 1 mm above the specimen surface. Records of clip gauge displacement with increasing load were obtained for each test. Direct measurements of the COD at the crack tip were made by infiltrating the notch with Unitek Xantopren Blue dental impression material, a hardening silicone rubber. The liquid rubber was placed in the notch and the specimen loaded to known values of displacement. After about 20 min, with the specimen under load, the rubber had solidified and could be removed with tweezers. The procedure was then repeated for increasing displacements. The replica of the crack front was first examined at a magnification of x 10 under a projection microscope and then a thin section was cut from the rubber at the crack front mid-point. The width of the slot and the nature of any cracking was examined and was recorded on tracings at x50. 137
138
B. 4. FIELDS and K. i. MILLER
100 mm
“.
5
..
IO to 24mm
Fig. I. Testpiece dimensions. Short Transverse
(ST)
Fig. 2. Specimen and notch orientations. Table 1. Chemical compositions
Table 2. Tensile properties
Data
provided
by
NCRE,
Dunfermiine,
Fife.
In order to determine whether any volume change occurred in the rubber during setting, replicas were taken of parallel sided slots, the widths of which were measured with feeler gauges. A comparison of the measurements from replicas and feeler gauges is shown in Fig. 3. The maximum deviation was never greater than 0.01 mm. RESULTS A typical load-displacement curve for HY 100is shown in Fig. 4. Fast fracture did not occur in any specimen but fibrous tearing was found to initiate prior to the achievement of maximum load. Traces of the crack front at the displacements shown in Fig. 4 can be seen in Fig. 5. The development of cracking is extremely non-uniform, appearing first as isolated linking of microvoids with the slot front. It is thus di~cult to define a critical point of crack initiation. However, previous workers[l] have examined the fractured specimen surfaces of several test
139
A study of COD and crack initiation by a replication technique 06r
Feeler
gauge width,
mm
Fig. 3. The accuracy of measurement of slot widths using the plastic replica technique.
Clip gauge displacement
,V,mm
Fig. 4. A displacement curve for HY 100;specimen width 24 mm.
I.Omm
s-
i,
-
h
4 2
I Fig. 5. The appearance of the crack front with increasing deformation corresponding to points shown in Fig. 4.
pieces and measured either the fibrous crack length or the area of fibrous growth and have extrapolated back to zero growth to obtain “initiation” conditions of COD, 6,. By using the rubber infiltration technique the instant of initiation, as defined in this way, can be located fairly accurately from only one specimen; i.e. in this case at point 2 in Fii. 5. Cross-sections through the mid-point of the rubber replica are shown in Fig. 6. It can be seen that the slot length, and the width, have increased before any cracking has occurred. This corresponds to the stretch zone observed on fracture surfaces between the original slot front and
140
B. A. FIELDS and K.
MILLER
6
,
Reference
$05
Fig. 6. The formation of the stretch zone and a crack in HY 100at points corresponding to those show in Fig. 4.
the fibrous crack growth. Similar sections for HY 130 showed exactly the same effect, Fig. 7. Values of COD, see Fig. 8, can be measured directly from the projected image and compared with clip gauge displacements. DISCUSSION (1) Relationship between V and S In order to calculate the opening at the crack tip, 6, from the clip gauge displacement, V, it is usually assumed that the crack faces open using a simple hinge mechanism with a fixed rotation axis at a position defined as the fraction, r, of the remaining ligament width, W - a ; i.e. at a position r( W - a) beyond the crack tip. Geometrical considerations then indicate that
“=((a
+z)lr(VW--a))+1
where z is the height of the clip gauge above the specimen surface. The British Standards Draft for Development for COD testing[4] suggests the use of r = 0.33. However, using the above formula several workers[3,5,6] have observed that in practice r increases from about 0.1 to 0.47 as deformation due to bending increases. These results have been
l-l’ 0
Fig. 7. The formation of cracking in two HY 130specimens of different orientations.
141
A study of COD and crack i~tiatio~ by a replication technique
Before crack initiation
After crock initiation
fib
Fig. 8. Measurement of (a) 6 and x, and (b) &,from the projected image of the replica.
explained by suggesting that the centre of rotation moves away from the crack tip continually during deformation. Etching studies [‘7lhave indicated that when yielding has spread across the ligament (W - a) the centre of rotation is at the ligament mid-point, i.e. r = 0.5. The present results provide a direct calibration between V and on-load 6 values, see Fig. 9. At the start of loading V increases but the width of the notch tip remains unchanged. Thus initially, rotation occurs very close to the notch tip and within experimental accuracy r = 0, For the present geometry if r = 0.5 then 6 = 0.4 V. Hence a line of slope 0.4 is included in Fig. 9 and can be seen to be in good agreement with results for V > 0.25 mm. It was observed that initial crack growth was very slow so that in Fig. 9 even specimens with S = 0.44 showed crack extensions of only 0.2 mm averaged along the crack front. This decrease in the initial sections thickness (a - W) = 12 mm has a ne~i~ble effect on results calculated from eqn (1) thus just~ying the inclusion of points where 6 > &. For V < 0.25 mm r increases from 0 to 0.5 as S increases. A value of V of 0.25 mm can be shown to fall within the range of values calculated for general yield conditions by considering the upper and lower bounds for the bending moment of notched bars at general yield, AfS,, as given in [8], i.e. upper bound
M,, = 0.30~7,(W - a)‘B
(2)
lower bound
MBy= 0.25+( W - a)‘B.
(3)
KEY X 0 + 1) 0 Cl
05
HYl00 HYi00 HYIOO HYl30 HYl30 HY130
B=24mm 0=24mm E=iOmm B-24mm Ba24mm B-24mm
w=0,23mm w=Olbmm w = 0.23 mm w=023mm w=016mm w-0
s = 04vr = 05
0.1
i
o-
/
/
n
-1
0.2
/
I
Q4
0.6 Clip
,
Q8
/
/
I.0
gauge displacement,
I.2
t
I,4
V, mm
Fig. 9. The relationship between ciip gauge displacement and COD.
07
142
B. A. FIELDS and K. J. MlLLER
For HY 100 the upper and lower bound general yield loads were calculated to be 41 and i? kN corresponding to values of V of approx. 0.30 and 0.22 mm, Fig. 6. For HY 130 equivalent values of V of 0.32 and 0.23 mm were found from similar load-clip gauge displacement curves. Thu< the results indicate that deformation occurs by a simple hinge mechanism about a fixed axis itnia after general yielding has taken place. The effect of using a constant r value of 0.33, as suggested in the British Standards Draft flor Development for COD testing [4] (equivalent to 6 = 0.3 V for the present geometry) is also shown in Fig. 9. It can be seen that for small values of V, i.e. ~0.5 mm, an overestimation of COD results. Thus for specimens where crack initiation occurs before general yield the calculation of & from eqn (1) can lead to large errors. (2) Stretch zone measurements Pelloux[9] has shown a simple model for the formation of the stretch zone at the crack tip, Fig. 10. Shear initiates on a plane at 45” to the crack tip, e.g. along AC, until work hardening makes further shear on AI3 more favourable. Thus deformation takes place by incremental shear that alternates between the two planes at 45” to the crack direction, so leading to an extension of the crack, x, (Fig. 8) equal to half the crack flank opening displacement, S. Pelloux refers to work of McClintock [ lo] who has carried out a slip line analysis for a double notched tensile specimen and obtained a blunted crack tip with x = 0.5 6. Rice and Johnson[l l] predict the shape of the blunted crack tip using slip line theory for both small scale yielding and fully plastic cases and obtain values of x = 0.55 S and 0.65 6 respectively. They note that while the analysis, strictly speaking, applies to an initially sharp crack, it is also an approximation to the case of an initially blunt notch, provided the plastic zone size is large compared to the notch root size. In the present work using the rubber infiltration technique direct measurements can be made of the stretch zone formation before cracking begins, see Fig. 8. Values of extension, x, and COD, 6, have been measured from tracings such as those shown in Figs. 6 and 7. The results are given in Fig. 11 and can be seen to be in good agreement with a relationship x = 0.5 6.
Fz ‘5
Fig. 10. Pelloux’s model[9] for the formation of a stretch zone at a crack tip in simple tension
A study of COD and crack initiation by a replication technique
x
WYIOO
l
HYIOO A HY130
Crack Fig.
w - 023mm w = 016mm
w=
0.23mm
0.1
0”
extension
during
143
02 blunting,
x. mm
11. The relations~p between COD and stretch zone Size.
Table 3. Values of b, 6t and 6, for HI’ 100and HY 130parent plate
A number of workers including Broek[l;?] and Elliott[l3] have attempted to relate stretch zone dimensions and COD from measurements of the fracture surface. Elliott obtains a relationship 6 = 1.5~ +0.04, where y is the length of the stretch zone surface measured at 45” to the crack extension, i.e. y = fi, leading to 6 = 2.1~ +0.04. He refers to a “threshold” COD of 0.4 mm for which the stretch zone width is zero. Such a theory cannot be true since the very existence of a COD is due to the presence of crack tip bl~ting, i.e. the fo~tion of the stretch zone. The apparent anomaly can be explained by use of the correct relationship to calculate the COD from the clip gauge displacement. Elliott used eqn (1) with a value of r = 0.33 mm. For the present case a value of COD of 0.04mm would have been obtained from a clip gauge displacement, V, of 0.14 mm. It can be seen from Fig. 9, that this corresponds to an actual value of COD, 8, of 0,005 mm. This latter value confirms within ex~~ent~ error the relations~p S = 2x. The above correction would suggest that the theory of Elliot that the “threshold” COD is
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MlLI.ER
equrvalent to Klscc, the threshold value of stress intensity below which stress corrmm does not occur, is incorrect.
uacktng
(3) CWical COD Measurements of COD were made directly from projected images of the sectioned replicas as shown in Fig. 8. The increase in COD between successive replicas was, on average, 0.03-0.04 mm, enabling & to be located to within about +0.02 mm. Robinson [3] has pointed out that once the crack has initiated the COD, 6, is made up of two components: (ii that due to initiation, &, and (2) the opening of the propagated crack near to the original crack tip, Z, i.e. & = 6 - Z, see Fig. 8(b). In specimens showing a suitable crack a value of 6, was calculated in this way and for clarity designated 6:. Average values of Si, I?? and 6, (COD at maximum load) are shown in Table 3 for HY 100and HY 130. The results indicate that within the observed scatter there is no significant effect of specimen thickness, orientation or slot width. For 38 and 25 mm thick HY 100 plate and 25 mm thick HY 130 plate respectively the values of & are approx. 0.12, 0.14 and 0.15 mm. However, little useful knowledge is obtained by knowing the toughness which the first stable microcracking occurs. In order to retain the technical usefulness of toughness testing, the critical value of S used to predict the behaviour of large specimens must be that at which significant crack growth takes place in an unstable manner. Hence the COD at maximum load has been used by some authors as an alternative to & in calculations of critical crack size. However, for the present materials the maximum load is limited by plastic collapse of the ligament below the notch. This can be seen for two reasons. (1) Although crack initiation occurs prior to maximum load, stable crack growth is still negligible (between points 4 and 5 in Fig. 4) suggesting that the maximum load is not connected with crack growth. (2) An approximate calculation of the plastic collapse load (substituting tensile strength for yield stress in eqn (2)) gives 48 and 52 kN for 24 mm thick specimens of HY 100 and HY 130 respectively, compared to experimental values of 49 and 61 kN. From either or both of these considerations it is argued that the maximum load attained in small specimens of these materials is not related to 6, for unstable propagation. It is important to realise that the achievement of &, while a necessary criterion for fracture. is not a sufficient one. In so called “brittle” failures initiation of a crack is more difficult than propagation, hence an initiation criterion is valid. In more ductile materials initiation may occur before the critical stress necessary for propagation is achieved. Stable crack growth under increasing load will continue until this critical stress is reached. During this crack growth the COD due to plasticity at the original crack tip does not change. The apparent COD may alter because of a component due to the opening of the crack (Fig. 8) but repeated measurements at the slot tip show & to be unaltered within experimental error during further loading. Thus although ri. may be a material property it is not, in these materials, a valid measure of toughness as it is not related to the point of instability. This will be true for all materials where stable crack growth precedes unstable crack propagation. In the present materials it appears that the critical stress for propagation is above the tensile strength. This implies that for this thickness of material (24 mm) the propagation of a crack cannot take place however large the specimen dimensions. In such cases values of 6: give no practical information and 6, has no meaning. (4) Initial crack growth In addition to locating crack initiation it is possible to follow the initial growth of a crack using the rubber infiltration technique. In this case it was usually necessary to let the rubber set and then strain the specimen further to allow the rubber to be removed without tearing. Examples of crack profiles are shown in Figs. 12 and 13. Figure 12 shows profiles for two orientations of HY 100 specimens. In general in this material cracking was observed to take place directly ahead of the slot. This was also seen in a T/L specimen by sectioning the test piece normal to the plane of cracking, see Fig. 14(a). In HY 130, however, the majority of cracking was seen to be of a zig-zag nature, see Figs. 13 and 14(b). For the T/ST orientation some crack fronts showed a certain amount of delamination along the transverse direction (Fig. i3(c)). That this effect is real and not due to bending of the replica can be seen from a section of the same specimen: see Fig. 14(c). A
Fig. M(a).
. (I
*.I.
**
l”
Fig. M(b).
Fig. 14(c).
A study of COD and crack initiation by a replication technique
145
I.Omm
Fig. 12. The growth of cracking in two HY 100specimens of different orientations in each case 6 = 0.76mm. I,Omm
A ST t
a.
T
b.
Fig. 13. Crack growth at different points along the crack front in an HY 130specimen with 6 = 0.76mm.
comparison of Figs. 13(c) and 14(c) indicates that the rubber infiltration technique provides a reliable method for observing the presence and growth of a fibrous crack. A further observation was that the maximum crack length occurring at a given COD was different for each case considered, i.e. in HY 100 more crack growth occurred in the T/L orientation than for a T/ST specimen although the COD’s at crack initiation were similar. A more detailed analysis of the crack length D COD may prove an interesting way of studying relative crack growth resistances. CONCLUSIONS
(1) A direct calibration can be made between clip gauge displacement and COD, enabling the present inaccuracies in calculating small values of COD to be eliminated. (2) The nature of the stretch zone has been studied, the extension of the crack tip during blunting being equal to half the COD. (3) In HY 100and HY 130plastic collapse takes place without unstable crack propagation for specimens up to 24mm thick. In such cases measurements of COD are irrelevant for design purposes. Acknowledgements-The authors would like to thank Cambridge University Engineering Department for provision of laboratory facilities. This work has been carried out with the support of the Procurement Executive, Ministry of Defence.
REFERENCES [l] R. F. Smith and J. F. Knott, Proc. of the Conj. on Practical Application of Fracture Mechanics to Pressure Vessel Technology, p. 65. A.I.M.E., London (1971). [2] T. C. Harrison and G. D. Feamehough, ht. J. Fracture Me& 5, 348 (1969). [3] J. N. Robinson and A. S. Tetehnan, Measurement of K,C on small specimens using critical crack tip opening displacement. ASTM S’J’P559, 139-158(1974). EFM Vol. 9, No. I-J
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[4] British Standards Draft for Development 19, London (1972). [5] C. C. Veerman and T. MuRer, Engng Fracture Mech. 4, 2.5(1972). [6] T. I&am, G. R. Egan, D. Elliott and T. C. Harrison, Proc. of the Conj. on Practical Application of Fracture Mechanics to Pressure Vessel Technology, p. 200. A.I.M.E., London (1971). [7] A. P. Green and B. B. Hundy, J. Mech. Phys. Solids 4, 128(1956). [8] J. F. Knott, Fundamentals of Fracture Mechanics, p. 173. Butterworths, London (1973). [9] R. M. N. Pelloux, Engng Fracture Mech. 1, 697 (1970). [IO] F. A. McClintock, Int. Conj. on Fracture, Kiruna, Sweden (1%7). [l l] J. R. Rice and M. A. Johnson, In Inelastic Behaviour of Solids (Ed. Kanninen et al.), p. 641. McGraw-Hill, New York (1970). [12] D. Broek, Engng Fracture Mech. 6, 173 (1974). [13] D. Elliott, The Practical Implications of Fracture Mechanisms, p. 21. Spring Meeting, Institution of Metallurgists, London (1973). [14] J. F. Knott, Mater. Sci. Engng 7, 1 (1970). [IS] C. G. Chipperlield and J. F. Knott, Internal Report. Cambridge University Metallurgy Dept. (1972). (Received March 1975)