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On the development of a direct method of determining the microcrack resistance curve
Engineering Fracture Mechanics Vol. 21, No. 3, pp. 465--472, 1985 Priated ha the U.S.A.
0013-7944,'85 $3.00 + .00 Pergamon Press Ltd.
ON T H E D E V E L O P M E N T OF A D I R E C T M E T H O D OF D E T E R M I N I N G THE M I C R O C R A C K RESISTANCE CURVE L. G. LUO, A. I. QUARRINGTON and J. D. EMBURY Department of Metallurgy and Materials Science, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada Abstract--This report deals with direct observations of microcrack linkage at the crack tip prior to macroscopiccrack initiation. It is shown that this process is directly linked to the inclusion distribution in the material and can be considered in terms of an R curve to describe mierocrack development.
Aa
B0 c
CTOD 6~ 6i
~R li
Is TL
NOTATION average crack extension due to stable crack growth scanned length of crack front sum of the microcrack lengths measured in the direction of B0 crack tip opening displacement microcrack initiation toughness-the start of irreversible damage macrocrack initiation toughness-reached when C = B0 the crack tip opening displacement at maximum load CTOD after the condition C = B0 has been reached, i.e. 8R ~>8,ith contour line matching the contour of the failed part of the stretched zone contour line corresponding to the stable crack front crack orientation with respect to original plates. The first direction is the crack plane normal, the second is the crack propagation direction where T is the transverse and L is the longitudinal direction.
1. I N T R O D U C T I O N THE CURRENT design philosophy, with respect to the fracture resistance of steels for offshore applications is to prevent any initial flaws from developing into a critical size[l]. This critical size can be determined from the initiation fracture toughness of the material. The definition o f the crack tip opening displacement, ~, required for the macroscopic initiation toughness is not exact. This is due in part to the inability o f existing methods to accurately measure 6~ over the entire crack front. Some previous work has considered data points associated with crack extensions o f less than 0.15 mm to be invalid [2], and extrapolated maerocrack data through the microcrack regime. Others have based conclusions on ~,~[3], the crack tip opening displacement reached at maximum load. The fracture process around a flaw in a fracture mechanics specimen is in some senses analagous to the ductile fracture process in a simple tensile specimen. In many cases the failure mechanism is one in which cumulative microstructural damage preceeds macroscopic crack propagation and failure. In the current study, direct observation of the microstructural damage during progressive loading enables microcrack development to be studied for crack extensions o f less than 0.15 mm. These results can be used to establish a more precise definition for 6~ which can then be used to determine a critical flaw size. 2. E X P E R I M E N T A L P R O C E D U R E Notched bar samples 10 x 10 x 65 mm were machined from plates with the compositions given in Table 1.0.5 mm deep notches with notch tip radii o f I00/z, were cut by spark machining in the bottom of the machined 2 mm deep notches. The specimens were fatigued in a strain controlled three point bend rig. The fatigue cracking load was varied from 100 kg to 1400 kg and was applied at 30 hz. The fatigue crack growth was continued until the uncraeked ligament was between 5.5 and 6.5 ram.
466
L. G . L U O
et aL
T a b l e 1. Steel
C %
Mn %
P %
S %
Si %
Cu %
Ni %
Mo %
168
0.044 1.99
0.002
0.005
0.21
328
0.07
1.36
0.000
0.005
0.31
0.013
0.013 0.25 0.15
Desulphurlzed
0.091 1.43
0.009
0.001
0.31
0.17
0.15
STEEL
168
V %
Nb 96
-
Ti %
N %
ASA
-
Cr %
av 5fPa
0.26 0.26
-
17u MPa
0.00S
0.007
NA
310
550
328
0.0S4 0.052 0 . 0 1 0
0.009
0.028
4"/7
619
Desulphur|zed
0.044 0.024
0.038
526
592
-
-
The specimen was then placed in a loading device for three point bending (Fig. 1). The loaded samples could be placed in a scanning electron microscope. Tilting the specimen within the SEM allows direct observation both of the crack tip opening and of the notch root contraction. The specimen can also, if necessary, be rotated so that both the electron gun and the electron detector are coplanar with the fatigue crack. The depth of field of an SEM is sufficient to view the entire stretched zone at magnifications up to 10,000 X. During each of the incremental loading steps, the entire crack front was scanned at 320 X and the total lengths of the microeracks and microvoids were measured along the crack front. For this specimen geometry B0 is between 7 and 8 mm. When the entire crack front is initiated, the specimen can be overloaded to extend the macroscopic crack. This crack extension can be measured in one of two ways. The specimen can be heat tinted at 300~ for 40 min or cooled with liquid nitrogen before the final fracture. Heat tinting produces a blue colour on the fatigue crack surface and a yellow-brown colour on the ductile failure region. Using an optical microscope, the width of the ductile crack extension zone can be measured to determine the Aa for the crack. Cooling the specimen to - 196~ and then applying an impact load, with a Charpy machine, will produce a brittle failure. The distance from the stretched zone to the fracture mode boundary can then be measured. This process of direct observation of the initiation process was performed for steels with various compositions and inclusion levels (Table 1). In all cases the inclusion distribution was determined from a section cut parallel to the fracture plane. 3. RESULTS A series of nine photographs were taken during the incremental loading procedure for steel 168. A composite of these photographs in shown in Fig. 2. This series of pictures shows a two stage stable crack growth mechanism of opening and extension [4, 5]. A composite photograph taken along the crack front (Fig. 3) clearly illustrates the highly localized nature of microcrack formation. This composite also shows the uniformity of the CTOD throughout the central portion of the specimen. A plot of ~ vs CIBo(Fig. 4) is given for the TL direction of each steel. The correlation between 6 andC[Bo shows a straight line for C/Bo > 10Yo. Each point on the line for steel 168 corresponds to a picture in the nine photograph series (Fig. 2). It is possible to relate C]Bo to Aa, which is a more common ordinate for crack growth resistance curves. This correlation was done for a specimen of steel 168. A magnified picture of the fracture surface was taken. To a first approximation, if one assumes that, once initiated, a microcrack or void grows at a constant rate relative to the CTOD and to the growth in the B0 direction, then the shape of the stable crack front will not change during the macrocrack initiation process. A series of lines, 1,-,are drawn on a tracing of a photograph. These lines intersect line Is at several places.
On the development of a direct method of determining the microcrack resistance curve
?
467
.
t,%~.,:- ~..
Fig. 1. The pre-cracked CTOD specimen in the three point bend rig.
i/roll illll Bill ,
:
.,]
9
----
ltJ
Jt
N
I
;::;1! ~ m
I f r!
:,![
!
.':
I
.
:.
,.~Mimm:.,~t'-
-- ": ';'-
--
r;. 2~-i
Fig. 2. A series of micrographs, of the same area of the crack tip, taken at each stage of the incremental loading procedure.
Fig. 3. A composite micrograph of a larger portion of the crack front at the same CTOD as the eighth picture in Fig. 2.
468
L G. LUO et al.
Fig. 7. The inclusion distribution in the desulphurised steel.
Fig. 8. The inclusion distribution in steel 168.
m]
_i
Fig. 9. The inclusion distribution in steel 328.
On the development of a direct method of determining the microcrack resistance curve
469
Fig. 10. The fracture surface in the area o f / h e stretched zone o f steel 168 showing the distinctive change in fracture mechanisms.
.../..,--.? ,
! ~":.?:-/
.~..~L~"-'~.
....
Z''~'"
-" ~
"/
Fig. I 1. An overview, at lower magnification, of the area surrounding the stretched zone.
i' ' .~-.:~
Fig. 12. A typical micrograph of the stretched zone in a desulphurized steel.
~:,
x,
:?
Lr
9149
Fig. 13. T h e same area o f the crack front at a larger C T O D .
L . G . L U O e t al.
470 0.6
I
i
i
i
+ DESULPHURIZED 0.~
0.4
E
E
0.5 0 pc.) 0.2
0.1
I
I
I
I
20
40
60
80
I00
C/Bo(%)
Fig. 4. The relationship between the CTOD and the percentage of the crack front that has initiated is shown for various steels.
The area enclosed between Is and the/,?s represent the area in which microcracks are initiated. The lengths, measured along the li's corresponding to the above areas represent the amount of the crack front in which microcracks are initiated. Dividing the area initiated by the amount initiated will give a length, Aa. This correlation (Fig. 5) will allow the replotting of Fig. 4 into the more familiar R-curve format (Fig. 6). This Figure 6 is a composite R curve containing both mierocrack and macrocrack data. It clearly illustrates the problems in extrapolating macrocrack data through the microcrack region. Mierographs showing the inclusion distributions for the desulphurised steel and for steels 168 and 328 are shown in Figs. 7-9 respectively. A qualitative comparison of Figs. 7-9 with Fig. 4 shows that a reduction in inclusion level leads to an increase i n / i i.
0.08 0.07
'
+
i
I
40
60
I
168
E 0.06 o
z 0.05 _o (/)
z 0.04
x w ' 9~. 0.03
u= o.ozI o.ol j 20
80
I00
PERCENT INITIATED-C/B. (%) Fig. 5. The relationship between the percentage of the crack front that has initiated and the crack extension.
On the developmentof a direct method of determiningthe microcrackresistance curve
471
0.4
+
168
AO.3 E E v t'7,LU tl.I (..) <[ 0.2 _I
_~ 8 1 - 0 Z Z (3_ 0 0.1 13-
U e,-
o
I
o2
o14
o18
,o
C R A C K E X T E N S I O N (ram)
9 Fig. 6. An overall R-curve for steel 168. 4. D I S C U S S I O N The concept of the conventional resistance curve is already well established. The concept of the microcrack resistance curve is presented here as a method of considering a material's resistance to crack initiation. The extension o f R-curves into the microcrack regime requires precise definitions relating to initiation. Microcrack initiation, occuring at 6~0, occurs when the first microcracks or mierovoids are nucleated, macroscopic crack initiation occurs when these microcracks have linked along the crack front so that 100~o o f the crack front has initiated. The microcrack initiation toughness is important to the fracture process because it marks the beginning of the irreversible damage accumulation process. The macroscopic initiation toughness is important because it corresponds to a change in the materials resistance to fracture (Fig. 6). The microcrack resistance curve o f a material can be considered in two ways. Firstly, 6R can be plotted against the average extension, da, and secondly, 6R can be plotted against the percentage of the crack front that has initiated, C/Bo. The former is easily extended to the macriscopic crack regime to create an overall fracture resistance curve. This allows a simple comparison of the two fracture processes. The resistance to fracture is obviously different in the two regimes o f crack growth (Fig. 6). In the microcrack regime, fracture is independent o f specimen geometry but is highly dependent on local conditions, for example the inclusion distribution. More specifically in steel 168, it is the larger inclusions that appear to control the fracture process (Figs. 10, 11). As the incIusion content falls, 6~ increases and the mode o f failure changes to one o f localised shear in which the central portion o f the stretched zone appears to be displaced perpendicular to the crack tip (Figs. 12, 13). In this large CTOD, the shear bands in the slip line field are developed before inclusion interface decohesion can cause failure. REFERENCES [1] Transport Canada Researchand DevelopmentCentre. TechnicalPublication 2717 A Reviewof Steel Propertiesat Low Temperatures, Oct. 1980. [2] ASTM E813-81 Standard Test for Jn,, A measure of Fracture Toughness. 1981Annual Book of ASTM Standards, Part 10, pp. 810-828. [3] G. H. Eide, K. O. Vilpponen et al. "Review of Steels Used in Construction of Offshore Structures". Technical Report of Def. Norske Veritas, April 1982.
472
L.G. LUO et al.
[4] P. Brozzo and G. Buzzichelli, On the metallurgical design of steels with high fracture toughness. Conf. Proc. of Analytical and Experimental Fracture Mech. IV-5, pp. 45-79, Sizthoff & Noordhoff, 1981. [5] M. Ogasawara and H. Okamura, The crack tip opening angle (CTDA) of the plane stress moving crack. Engng Fracture Mech. 18(4), 839-850 (1983). (Receired 21 December 1983)
0013-7944,'85 $3.00 + .00 Pergamon Press Ltd.
ON T H E D E V E L O P M E N T OF A D I R E C T M E T H O D OF D E T E R M I N I N G THE M I C R O C R A C K RESISTANCE CURVE L. G. LUO, A. I. QUARRINGTON and J. D. EMBURY Department of Metallurgy and Materials Science, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada Abstract--This report deals with direct observations of microcrack linkage at the crack tip prior to macroscopiccrack initiation. It is shown that this process is directly linked to the inclusion distribution in the material and can be considered in terms of an R curve to describe mierocrack development.
Aa
B0 c
CTOD 6~ 6i
~R li
Is TL
NOTATION average crack extension due to stable crack growth scanned length of crack front sum of the microcrack lengths measured in the direction of B0 crack tip opening displacement microcrack initiation toughness-the start of irreversible damage macrocrack initiation toughness-reached when C = B0 the crack tip opening displacement at maximum load CTOD after the condition C = B0 has been reached, i.e. 8R ~>8,ith contour line matching the contour of the failed part of the stretched zone contour line corresponding to the stable crack front crack orientation with respect to original plates. The first direction is the crack plane normal, the second is the crack propagation direction where T is the transverse and L is the longitudinal direction.
1. I N T R O D U C T I O N THE CURRENT design philosophy, with respect to the fracture resistance of steels for offshore applications is to prevent any initial flaws from developing into a critical size[l]. This critical size can be determined from the initiation fracture toughness of the material. The definition o f the crack tip opening displacement, ~, required for the macroscopic initiation toughness is not exact. This is due in part to the inability o f existing methods to accurately measure 6~ over the entire crack front. Some previous work has considered data points associated with crack extensions o f less than 0.15 mm to be invalid [2], and extrapolated maerocrack data through the microcrack regime. Others have based conclusions on ~,~[3], the crack tip opening displacement reached at maximum load. The fracture process around a flaw in a fracture mechanics specimen is in some senses analagous to the ductile fracture process in a simple tensile specimen. In many cases the failure mechanism is one in which cumulative microstructural damage preceeds macroscopic crack propagation and failure. In the current study, direct observation of the microstructural damage during progressive loading enables microcrack development to be studied for crack extensions o f less than 0.15 mm. These results can be used to establish a more precise definition for 6~ which can then be used to determine a critical flaw size. 2. E X P E R I M E N T A L P R O C E D U R E Notched bar samples 10 x 10 x 65 mm were machined from plates with the compositions given in Table 1.0.5 mm deep notches with notch tip radii o f I00/z, were cut by spark machining in the bottom of the machined 2 mm deep notches. The specimens were fatigued in a strain controlled three point bend rig. The fatigue cracking load was varied from 100 kg to 1400 kg and was applied at 30 hz. The fatigue crack growth was continued until the uncraeked ligament was between 5.5 and 6.5 ram.
466
L. G . L U O
et aL
T a b l e 1. Steel
C %
Mn %
P %
S %
Si %
Cu %
Ni %
Mo %
168
0.044 1.99
0.002
0.005
0.21
328
0.07
1.36
0.000
0.005
0.31
0.013
0.013 0.25 0.15
Desulphurlzed
0.091 1.43
0.009
0.001
0.31
0.17
0.15
STEEL
168
V %
Nb 96
-
Ti %
N %
ASA
-
Cr %
av 5fPa
0.26 0.26
-
17u MPa
0.00S
0.007
NA
310
550
328
0.0S4 0.052 0 . 0 1 0
0.009
0.028
4"/7
619
Desulphur|zed
0.044 0.024
0.038
526
592
-
-
The specimen was then placed in a loading device for three point bending (Fig. 1). The loaded samples could be placed in a scanning electron microscope. Tilting the specimen within the SEM allows direct observation both of the crack tip opening and of the notch root contraction. The specimen can also, if necessary, be rotated so that both the electron gun and the electron detector are coplanar with the fatigue crack. The depth of field of an SEM is sufficient to view the entire stretched zone at magnifications up to 10,000 X. During each of the incremental loading steps, the entire crack front was scanned at 320 X and the total lengths of the microeracks and microvoids were measured along the crack front. For this specimen geometry B0 is between 7 and 8 mm. When the entire crack front is initiated, the specimen can be overloaded to extend the macroscopic crack. This crack extension can be measured in one of two ways. The specimen can be heat tinted at 300~ for 40 min or cooled with liquid nitrogen before the final fracture. Heat tinting produces a blue colour on the fatigue crack surface and a yellow-brown colour on the ductile failure region. Using an optical microscope, the width of the ductile crack extension zone can be measured to determine the Aa for the crack. Cooling the specimen to - 196~ and then applying an impact load, with a Charpy machine, will produce a brittle failure. The distance from the stretched zone to the fracture mode boundary can then be measured. This process of direct observation of the initiation process was performed for steels with various compositions and inclusion levels (Table 1). In all cases the inclusion distribution was determined from a section cut parallel to the fracture plane. 3. RESULTS A series of nine photographs were taken during the incremental loading procedure for steel 168. A composite of these photographs in shown in Fig. 2. This series of pictures shows a two stage stable crack growth mechanism of opening and extension [4, 5]. A composite photograph taken along the crack front (Fig. 3) clearly illustrates the highly localized nature of microcrack formation. This composite also shows the uniformity of the CTOD throughout the central portion of the specimen. A plot of ~ vs CIBo(Fig. 4) is given for the TL direction of each steel. The correlation between 6 andC[Bo shows a straight line for C/Bo > 10Yo. Each point on the line for steel 168 corresponds to a picture in the nine photograph series (Fig. 2). It is possible to relate C]Bo to Aa, which is a more common ordinate for crack growth resistance curves. This correlation was done for a specimen of steel 168. A magnified picture of the fracture surface was taken. To a first approximation, if one assumes that, once initiated, a microcrack or void grows at a constant rate relative to the CTOD and to the growth in the B0 direction, then the shape of the stable crack front will not change during the macrocrack initiation process. A series of lines, 1,-,are drawn on a tracing of a photograph. These lines intersect line Is at several places.
On the development of a direct method of determining the microcrack resistance curve
?
467
.
t,%~.,:- ~..
Fig. 1. The pre-cracked CTOD specimen in the three point bend rig.
i/roll illll Bill ,
:
.,]
9
----
ltJ
Jt
N
I
;::;1! ~ m
I f r!
:,![
!
.':
I
.
:.
,.~Mimm:.,~t'-
-- ": ';'-
--
r;. 2~-i
Fig. 2. A series of micrographs, of the same area of the crack tip, taken at each stage of the incremental loading procedure.
Fig. 3. A composite micrograph of a larger portion of the crack front at the same CTOD as the eighth picture in Fig. 2.
468
L G. LUO et al.
Fig. 7. The inclusion distribution in the desulphurised steel.
Fig. 8. The inclusion distribution in steel 168.
m]
_i
Fig. 9. The inclusion distribution in steel 328.
On the development of a direct method of determining the microcrack resistance curve
469
Fig. 10. The fracture surface in the area o f / h e stretched zone o f steel 168 showing the distinctive change in fracture mechanisms.
.../..,--.? ,
! ~":.?:-/
.~..~L~"-'~.
....
Z''~'"
-" ~
"/
Fig. I 1. An overview, at lower magnification, of the area surrounding the stretched zone.
i' ' .~-.:~
Fig. 12. A typical micrograph of the stretched zone in a desulphurized steel.
~:,
x,
:?
Lr
9149
Fig. 13. T h e same area o f the crack front at a larger C T O D .
L . G . L U O e t al.
470 0.6
I
i
i
i
+ DESULPHURIZED 0.~
0.4
E
E
0.5 0 pc.) 0.2
0.1
I
I
I
I
20
40
60
80
I00
C/Bo(%)
Fig. 4. The relationship between the CTOD and the percentage of the crack front that has initiated is shown for various steels.
The area enclosed between Is and the/,?s represent the area in which microcracks are initiated. The lengths, measured along the li's corresponding to the above areas represent the amount of the crack front in which microcracks are initiated. Dividing the area initiated by the amount initiated will give a length, Aa. This correlation (Fig. 5) will allow the replotting of Fig. 4 into the more familiar R-curve format (Fig. 6). This Figure 6 is a composite R curve containing both mierocrack and macrocrack data. It clearly illustrates the problems in extrapolating macrocrack data through the microcrack region. Mierographs showing the inclusion distributions for the desulphurised steel and for steels 168 and 328 are shown in Figs. 7-9 respectively. A qualitative comparison of Figs. 7-9 with Fig. 4 shows that a reduction in inclusion level leads to an increase i n / i i.
0.08 0.07
'
+
i
I
40
60
I
168
E 0.06 o
z 0.05 _o (/)
z 0.04
x w ' 9~. 0.03
u= o.ozI o.ol j 20
80
I00
PERCENT INITIATED-C/B. (%) Fig. 5. The relationship between the percentage of the crack front that has initiated and the crack extension.
On the developmentof a direct method of determiningthe microcrackresistance curve
471
0.4
+
168
AO.3 E E v t'7,LU tl.I (..) <[ 0.2 _I
_~ 8 1 - 0 Z Z (3_ 0 0.1 13-
U e,-
o
I
o2
o14
o18
,o
C R A C K E X T E N S I O N (ram)
9 Fig. 6. An overall R-curve for steel 168. 4. D I S C U S S I O N The concept of the conventional resistance curve is already well established. The concept of the microcrack resistance curve is presented here as a method of considering a material's resistance to crack initiation. The extension o f R-curves into the microcrack regime requires precise definitions relating to initiation. Microcrack initiation, occuring at 6~0, occurs when the first microcracks or mierovoids are nucleated, macroscopic crack initiation occurs when these microcracks have linked along the crack front so that 100~o o f the crack front has initiated. The microcrack initiation toughness is important to the fracture process because it marks the beginning of the irreversible damage accumulation process. The macroscopic initiation toughness is important because it corresponds to a change in the materials resistance to fracture (Fig. 6). The microcrack resistance curve o f a material can be considered in two ways. Firstly, 6R can be plotted against the average extension, da, and secondly, 6R can be plotted against the percentage of the crack front that has initiated, C/Bo. The former is easily extended to the macriscopic crack regime to create an overall fracture resistance curve. This allows a simple comparison of the two fracture processes. The resistance to fracture is obviously different in the two regimes o f crack growth (Fig. 6). In the microcrack regime, fracture is independent o f specimen geometry but is highly dependent on local conditions, for example the inclusion distribution. More specifically in steel 168, it is the larger inclusions that appear to control the fracture process (Figs. 10, 11). As the incIusion content falls, 6~ increases and the mode o f failure changes to one o f localised shear in which the central portion o f the stretched zone appears to be displaced perpendicular to the crack tip (Figs. 12, 13). In this large CTOD, the shear bands in the slip line field are developed before inclusion interface decohesion can cause failure. REFERENCES [1] Transport Canada Researchand DevelopmentCentre. TechnicalPublication 2717 A Reviewof Steel Propertiesat Low Temperatures, Oct. 1980. [2] ASTM E813-81 Standard Test for Jn,, A measure of Fracture Toughness. 1981Annual Book of ASTM Standards, Part 10, pp. 810-828. [3] G. H. Eide, K. O. Vilpponen et al. "Review of Steels Used in Construction of Offshore Structures". Technical Report of Def. Norske Veritas, April 1982.
472
L.G. LUO et al.
[4] P. Brozzo and G. Buzzichelli, On the metallurgical design of steels with high fracture toughness. Conf. Proc. of Analytical and Experimental Fracture Mech. IV-5, pp. 45-79, Sizthoff & Noordhoff, 1981. [5] M. Ogasawara and H. Okamura, The crack tip opening angle (CTDA) of the plane stress moving crack. Engng Fracture Mech. 18(4), 839-850 (1983). (Receired 21 December 1983)