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Void growth at ductile crack initiation of a structural steel
Engineering Fracture Mechanics
Vol. 39, No. I, pp. 314, 1991
0013-7944/91 $3.00 + 0.00 0 1991 Pergamon Press pk.
Printed in Great Britain.
VOID GROWTH AT DUCTILE CRACK INITIATION OF A STRUCTURAL STEEL Y. W. SHI,? J. T. BARNBYS and A. S. NADKARNIS tDepartment
of Mechanical Engineering, Xi’an Jiao-tong University, Xi’an, Shaanxi Province, P.R. China
SDepartment of Metallurgy and Materials Engineering, University of Aston, Birmingham, U.K. Abstract-This investigation deals with the critical void growth in a BS4360 Grade 50D structural steel. The tests are carried out on four variations of the Charpy size specimens, namely a standard geometry; side grooved; fatigue cracked; side grooved and fatigue cracked. The geometry variations are intended to vary the level of hydrostatic stress or constraint in the region of fracture initiation. The void growth is measured on mid-sections of specimens at onset of crack growth. It is known that there are two micromechanistic concepts regarding initiation of the ductile failure processes. One is the critical void volume fraction, and the other is the critical void growth rate. The experimental studies indicate that the critical void volume fraction (f,), at onset of crack growth is not a material constant. The volume fraction is dependent on the geometry constraint. However, the critical void growth rate R,/R, is a material constant within a first approximation. Thus, it is probable in engineering to evaluate the crack initiation in a cracked specimen by using the critical void growth rate measured on smooth tensile specimen with lower constraint to take it easy.
1. INTRODUCTION IT IS well-known that the mechanism of ductile fracture is a damage accumulation process and that it involves three main stages of void nucleation, growth, and coalescence. The macroscopic ductility and fracture toughness of materials may be strongly dependent on the void damage processes. Many theoretical and experimental investigations dealing with the understanding of void nucleation and growth have been reviewed[l+. Recently, some workers paid attention to modeling of ductile fracture by microvoid coalescence for the prediction of fracture toughness. In the previous studies circumferential notched round tensile specimens have been largely employed. In these tests, void growth measured on bulk notched specimens is suggested to possibly evaluate the ductile failure initiation[5-81. At the initiation, fall-off in average stress occurs in the plot of average stress at the minimum cross-section against effective plastic strain, and voids can link up on a large scale. However, some difficulties arise if it is attempted to use the experimental results obtained from the notched tensile specimens to model ductile rupture at a crack tip. The main difficulty encountered is associated with the fact that very steep stress and strain gradients are present at the crack tip, and the void coalescence events take place more strongly with the blunted crack tip than do with one another. Moreover, the stress triaxiality ahead of crack tip is more severe than that in the centre of notched tensile specimens. The purpose of this work is to measure the void volume fraction and void growth rate at the initiation CTOD in a structural steel, because these two micromechanistic concepts regarding initiation of the ductile failure processes are generally used at present. Charpy size specimens with geometry variations were tested in three point bending in order to vary the hydrostatic stress or constraint in the regions of fracture initiation. As the crack tip behaviour is usually evaluated by using experimental results obtained from notched tensile specimens, and up to now very few experimental studies have yet been undertaken to study the situation at crack tip, metallographic examination on the sections of cracked specimens in detail would seem to be very useful to assess the applicability of critical conditions of void growth.
2. MATERIAL
AND TESTING
The test material was to the specification BS4360 Grade 50D structural steel widely used in the North Sea offshore structure. The steel was at a thickness of 51 mm at normalizing condition. The chemical composition and mechanical properties are given in Table 1. 37
38
Y. W. SHI et
al.
Table 1. Chemical composition and mechanical properties (a) Chemical composition (wt.%): C Mn Si 0.18 1.42 0.23 (bj \ , Mechanical orooerties: Yield stress a (MPa) 349
S 0.008
Tensile strength (MPa) 542
P 0.007
Al 0.03 Elongation (%) 40
cu 0.11
Ni 0.25
Cr 0.21
MO 0.03
Strain hardening exponent (in Ramberg-Osgood) 4.5
Charpy size specimens were cut out in the L-T direction. In the tests there were four variations of the Charpy specimens, namely a standard geometry; side grooved; fatigue cracked; side grooved and fatigue cracked. The geometry variations were intended to vary the level of constraint in the region of fracture initiation. Pre-fatigue cracking was carried out at a stress ratio of 0.1 and the maximum stress intensity factor Kf of 22 MPa &. The final crack length to width ratio was chosen to be 0.5. The specimens were tested in three point bending at room temperature in a 50 kN Instron testing machine at a cross head speed of 0.2 mm/min. Fracture initiation was determined by using a direct current electrical potential drop method (DCPD). The specimens were unloaded subsequently, then the specimens were sectioned in a plane which was perpendicular to the crack plane and parallel to the longitudinal direction of the specimen at - 196°C. The void volume fractions were estimated by observing the fracture surfaces using a scanning electron microscope (SEM) at a magnification of 1000, and using a statistical point counting technique[9].
3. RESULTS It is known that the combination of plastic strain and stress triaxiality produces a maximum void growth rate at a specific distance ahead of notch or crack tip[lO, 111. The finite element analysis of the Charpy specimen indicates that maximum value of the stress triaxiality develops at about 0.5 mm ahead of the notch root[l2]. Thus, a region between 0.4 and 0.6 mm ahead of the notch root was chosen to investigate the void growth behaviour. In fact this void growth rate represented a critical value since the test was stopped when initiation of failure was detected using DCPD method. The detection of initiation of failure using DCPD involved a measurement of increase in probe potential of 5 /JV when a direct current of 20 A was passed through the specimen. Some of the specimens were fractured along the crack plane at - 190°C after testing, and subsequently examined in SEM to ensure that an increment of 5 PV represented the crack initiation. Point counting was carried out directly on the screen SEM in order to establish the void volume fractions. The void volume fraction for each specimen was an average value of 100 random fields, because of large measured scatter in the relative void volume at failure initiation. If a ratio of mean stress cr, to effective stress 5 is characterized as a stress triaxiality, the stress triaxiality distribution ahead of the notch in the Charpy specimen has been calculated, and the maximum value of stress triaxiality is 2.2 and its location is 0.5 mm ahead of the notch tip[l2]. Moreover, the stress triaxiality distribution ahead of a blunted crack in the side-grooved and fatigue-cracked Charpy specimen may be estimated from the analysis of McMeeking[l3] since his calculation refers to a material of similar tensile properties and work hardening characteristics to the material tested here. Thus, the maximum triaxiality was estimated at 4.13, and its location was at 1.33 times the critical CTOD, which for the steel tested is 0.52 mm. It is resonable to assume that the stress triaxialities in the other two specimen types will be present within these two extremities, Higher constraints will be present in the fatigue cracked CVN specimen than in the side-grooved CVN specimen. As seen in Fig. l(a) the critical void volume fractions at the location of the maximum stress triaxiality increase significantly with increasing the stress triaxiality.
Void growth at ductile crack initiation
39
12-
(a)
. . .
a-
n” b
4-
G i
,_ u.b -c s b
0
I I
I 4
, 3
I 2
Stress triaxiality
I 5
(~~15)
,P
. . .
l
.
. . .
.
I
I
I
1
1.25
I.30
I .35
1.40
Constraint factor (C) Fig. I. Strong variation of critical void volume fraction as a function of geometry constraint of specimens. (a) Critical void volume fraction (f,)i vs stress triaxiality ~,,,/a. (b) Critical void volume fraction (f,), vs constraint factor C.
Moreover, the stress state in the specimens with geometry variations may be estimated by a constraint factor on general yielding. The constraint factor (C) for the specimens tested is given byLl41 C =4P,,
W/a,B(W-a)’
where PGy is the general yield load; a is the crack length; B is the specimen thickness; W is the specimen width; cry is the yield stress of steel. In general the C value is changed from 0.1 in plane stress to 1.4 in plane strain condition. It should be emphasized that the estimative constraints are only approximations for real materials since slip-line field solutions treat the material as being rigid-plastic. Based on the experimental record of load versus deflection, the C values are calculated and the influence of constraint factor on void volume fraction (fv)i in Charpy specimens at onset of ductile crack growth is shown in Fig. l(b). As mentioned earlier, statistical point counting was carried out directly on the SEM screen. The statistics were such that many fields did not have voids and other fields had very few voids. In the standard CVN specimen 80% of the fields resulted in zero void counts, whereas in the side-grooved and fatigue-cracked CVN specimen only 40% of the fields had a zero void count. This is also reflected in the results presented in Fig. 1. At the same time, the void growth rates were carefully determined. SEM observations of the fracture surfaces showed the inclusions in their associated voids surrounded by cleavage fracture. The mean radius of the inclusions and that of the voids were measured on photographs which were randomly taken at the same locations as the point counting. A typical SEM photograph is shown in Fig. 2. About 20 particles were observed for each specimen. Figure 3 shows the variation of void growth rate Ri/& at the onset of crack growth as a function of specimen constraint, where Ri and R. are the void radius at CTOD initiation and the initial void radius, respectively. The initial size of the voids is taken as the size of the associated inclusions. It is clear that the void growth rates
40
Y. W. SHI ef al.
Constraint
factor (C)
Fig. 3. Weak variation of critical void growth rate RI/& as a function of geometry constraint.
R,/R, at the onset of crack growth determined by this test are not sensitive to the constraint of the specimens. 4. DISCUSSION 4.1. Concepts on ductile crack initiation There are two different concepts regarding initiation of the ductile failure process. One concept is that failure initiation in the material occurs at a critical volume fraction (fv)i of large voids[l5]. This critical void fraction is essential to initiate failure process by a mechanism of flow localization. Once small scale voids are initiated the failure process is cooperative. The critical value of void volume is thought to depend upon the inclusion content. It is suggested that in very dirty or highly precipitation-hardened materials at severe stress states, flow localization may occur as soon as the voids are formed. Moreover, in order to determine the critical void volume fraction of large voids for a structural steel A533B, a series of tensile specimens were tested[6]. The large voids were found to nucleate at MnS and Al,O, inclusions and they grew with increase in plastic strain. It was found that nucleation of small voids occurred when the relative void volume of large voids reached a value of 0.01. That is, the initiation of material failure is defined to occur when a void volume fraction of 0.01 is attained. A second concept is that failure initiation is associated with a critical void growth rate RI/R,. Since a critical void growth rate can exist at different void volume fractions, it is possible that this criterion would be related with the work hardening characteristics of the material. The critical void growth rate is usually defined in terms of an average void radius. It has been proposed that the critical void growth rate can be used to model failure initiations, and for a structural steel A508 the value of Ri/& is 1.48, which is associated with a stress triaxiality of 1.80[7]. In addition, it is indicated that the directionality of the wrought steel would affect the critical values of the fracture criterion[8]. This is attributed to the different initial radii or alternatively the different spacing between the inclusions. Moreover, it has been recently reported that the critical void growth rate within a first approximation can be considered to be independent of the stress triaxiality, though sometimes there exists a decrease in the critical void growth rate when the stress triaxiality is increased[7, 8, 161. 4.2. Effect of constraint on critical void growth rate In the present experiments, the results show a weak variation of critical void growth rate Ri/R, as a function of constraint factor. An average value of R,/R, is equal to 1.52 at the onset of crack growth for the constraint factor range from 1.21 to 1.33. For the identical test material a series of smooth tensile specimens were pulled and interrupted at different strain level before neck formation. Void growth rate R/R0 was measured on the longitudinal sections of the strained uniaxial tensile specimens. The average value of R/R, was equal to 1.3 1 for the plastic strain range from 0.006 to 0.21[17]. It is clear that the critical void growth rate 4/R,, at the onset of crack growth is only slightly higher than the void growth R/R,, occurred in the uniaxial tension tests. Moreover, there is a small decrease in the Rx/R, values, when the constraint factors increase from the standard Charpy specimen to the side-grooved and pre-cracked Charpy specimens.
Void growth at ductile crack initiation
Fig. 2. Typical fractograph on mid-section of a side-grooved Charpy size specimen at the onset of crack growth.
41
Void growth at ductile crack initiation
43
It should be noted that the effective plastic strains at failure initiation are lower in specimens with higher constraint. It is the combination of stress triaxiality and effective plastic strain that controls the failure process. The results infer that the increase in critical void growth rate Ri/& for real structural steels is very difficult even though a higher constraint is imposed on the specimens. A possible reason could be the fact that most engineering materials contain at least two populations of particles nucleating voids. Void formation takes place much more easily at large inclusions than at small inclusions or carbide particles, The experiments indicate that void growth from large inclusions in this material does not occur by the simple continue mechanics of individual void growth but by the coalescence with the surrounding smaller voids including the nucleation at carbides or intermetallic precipitates. The second generation small voids can grow rapidly within the stress field of the large voids. Moreover, the presence of the small voids around large voids reduces the local strain hardening rate[l8], which is an important parameter in the continuum mechanics model for void growth. 4.3. Effect of constraint on critical void volume fraction The experiments indicate a strong variation of critical void volume fraction ( fV)i as a function of constraint factor or stress triaxiality. For the identical test material_& = 2.44 x 10e3 was obtained on the longitudinal sections of strained uniaxial tensile specimens[l7]. It was shown that for the standard Charpy and the side-grooved pre-cracked Charpy specimens the critical void volume fractions were respectively about 1 to 3 times the relative void volume in the uniaxial tension test. It was inferred that the value of (s”)i was promoted in a triaxial stress field. In general, that is because in tensile tests large inclusions which have low values of critical stress nucleate voids early in the fracture processes, and small inclusions nucleate voids only after considerable strain due to their very high values of critical stress. However, the situation is different in the CTOD tests of pre-cracked specimens. The high constraint stresses combined with the strain concentration may create interfacial stresses which exceed the critical stress at many of the small inclusions. In this case, the large inclusions as well as some of the small inclusions are attributed to the critical void volume fraction in the crack tip region. As a very small strain is required to initiate voids at the crack tip where the constraint is higher than in the notched specimens, the critical void volume fraction measured in the crack tip region is representative of the sum in the large void growth and the further smaller void nucleation. Therefore, the criticai void volume fraction at the onset of crack growth is not a material constant. The fractions increase obviously when the stress triaxiality or constraint factor increases, and they are strongly dependent on the geometry constraint of the test specimens. However, the critical void growth rate RI/R, may be a material constant in a wide range of constraint factor or stress triaxiality. As the critical void growth rate is not sensitive to the specimen geometry constraint, thus it is probable to evaluate the crack initiation by using experimental results obtained from smooth or notched tensile specimens with lower constraint to take it easy, though the volume of material in the notched and cracked specimens in which failue events take place is different. 5. CONCLUSIONS There are two different micromechanistic concepts regarding initiation of the ductile failure processes. One concept is that failure initiation in material occurs at a critical void volume fraction, and the other concept is that failure initiation is associated with a critical void growth rate. In the present experiments, it is indicated that the critical void volume fraction (fV)i at onset of crack growth is not a material constant. The volume fraction is dependent on the geometry constraint, and the fractions increase obviously when the stress triaxiality or constraint factor increases. However, the critical void growth rate Ri/R, is a material constant within a first approximation, though there is a small decrease in the critical void growth rate at onset of crack growth when the constraint factors increase. It is clear that an individual void growth for real structural steels is very difficult, it may be because the presence of small voids around large voids and local strain softening. Thus, it is probable in engineering to evaluate the crack initiation in a cracked specimen by using the critical void growth rate measured on smooth or notched tensile specimen with lower constraint.
44
Y. W. SHI et al.
Acknowledgements-The
authors wish to gratefully thank the National Natural Science Foundation financial support, and Dr. C. J. Flavell for preparing some of the experiments.
of China for its
REFERENCES S. H. Goods, and L. M. Brown, Acta Merailurgica 27, 1-15 (1979). D. A. Curry and J. F. Knott, Current aspects of crack growth under monotonic loading, Fracture and Fatigue, ECF3. Proc. of 3rd Colloquium on Fracture, London (Edited by J. C. Radon), pp. 209-216. Pergamon Press, Oxford (1980). A. Pineau, Review of fracture micromechanisms and a local approach to predicting crack resistance in low strength steels. Advances in Fracture Research, ICFS, Cannes (Edited by D. Francois et al.), pp. 553-577. Pergamon Press, Oxford (1981). [41 R. C. Bates, Modeling of ductile fracture by microvoid coalescence. Fracture: Inieractions of Microstructure, Mechanisms, Mechanics (Edited by J. M. Wells and J. D. Landes), pp. 117-155. The Metallurgical Society of AIME (1984). PI A. C Mackenzie, J. W. Hancock, and D. K. Brown, Engng Fracfure Mech. 9, 167-188 (1977). 161 D. A. Shockey, K. C. Dao, L. Seaman, R. Burback, and D. R. Curran, Computational modeling of microstructural fracture processes in A533B pressure vessel steel, NP-1398. Electric Power Research Institute, Palo Alto, California (1980). 171 F. M. Beremin, Study of fracture criteria for ductile rupture of A508 steel. Advances in Fracture Research, ICFS, Cannes (Edited by D. Francois et al.), pp. 809-816. Pergamon Press, Oxford (1981). J. C. Lautridou and A. Pineau, Engng Fracture Mech. 15, 55-71 (1981). Y. W. Shi and J. T. Bamby, Int. J. Fracture 25, 143-151 (1984). J. F. Knott, Metal Science 14, 327-336 (1980). J. T. Bamby, Y. W. Shi, and A. S. Nadkarni, Int. J. Fracture 25, 273-283 (1984). D. M. Norris, Engng Fracture Mech. 11, 261-274 (1979). R. M. McMeeking, J. Mech. Physics Solids 25, 357-381 (1977). W. L. Server, J. Engng Mater. Technol. Trans. ASME 100, 183-188 (1978). J. W. Hancock and A. C. Mackenzie, J. Mech. Physics Solids 24, 147-169 (1976). Y. W. Shi, Critical void growth for ductile rupture of steel welds. Engng Fracture Mech. (submitted). Y. W. Shi, Void growth in uniaxial and triaxial stress field for a structural steel. Mater. Science Engng (in press). M. F. Ashby, Philosophical Magazine 14, 1157-I 178 (1966). (Received 15 November 1989)
Vol. 39, No. I, pp. 314, 1991
0013-7944/91 $3.00 + 0.00 0 1991 Pergamon Press pk.
Printed in Great Britain.
VOID GROWTH AT DUCTILE CRACK INITIATION OF A STRUCTURAL STEEL Y. W. SHI,? J. T. BARNBYS and A. S. NADKARNIS tDepartment
of Mechanical Engineering, Xi’an Jiao-tong University, Xi’an, Shaanxi Province, P.R. China
SDepartment of Metallurgy and Materials Engineering, University of Aston, Birmingham, U.K. Abstract-This investigation deals with the critical void growth in a BS4360 Grade 50D structural steel. The tests are carried out on four variations of the Charpy size specimens, namely a standard geometry; side grooved; fatigue cracked; side grooved and fatigue cracked. The geometry variations are intended to vary the level of hydrostatic stress or constraint in the region of fracture initiation. The void growth is measured on mid-sections of specimens at onset of crack growth. It is known that there are two micromechanistic concepts regarding initiation of the ductile failure processes. One is the critical void volume fraction, and the other is the critical void growth rate. The experimental studies indicate that the critical void volume fraction (f,), at onset of crack growth is not a material constant. The volume fraction is dependent on the geometry constraint. However, the critical void growth rate R,/R, is a material constant within a first approximation. Thus, it is probable in engineering to evaluate the crack initiation in a cracked specimen by using the critical void growth rate measured on smooth tensile specimen with lower constraint to take it easy.
1. INTRODUCTION IT IS well-known that the mechanism of ductile fracture is a damage accumulation process and that it involves three main stages of void nucleation, growth, and coalescence. The macroscopic ductility and fracture toughness of materials may be strongly dependent on the void damage processes. Many theoretical and experimental investigations dealing with the understanding of void nucleation and growth have been reviewed[l+. Recently, some workers paid attention to modeling of ductile fracture by microvoid coalescence for the prediction of fracture toughness. In the previous studies circumferential notched round tensile specimens have been largely employed. In these tests, void growth measured on bulk notched specimens is suggested to possibly evaluate the ductile failure initiation[5-81. At the initiation, fall-off in average stress occurs in the plot of average stress at the minimum cross-section against effective plastic strain, and voids can link up on a large scale. However, some difficulties arise if it is attempted to use the experimental results obtained from the notched tensile specimens to model ductile rupture at a crack tip. The main difficulty encountered is associated with the fact that very steep stress and strain gradients are present at the crack tip, and the void coalescence events take place more strongly with the blunted crack tip than do with one another. Moreover, the stress triaxiality ahead of crack tip is more severe than that in the centre of notched tensile specimens. The purpose of this work is to measure the void volume fraction and void growth rate at the initiation CTOD in a structural steel, because these two micromechanistic concepts regarding initiation of the ductile failure processes are generally used at present. Charpy size specimens with geometry variations were tested in three point bending in order to vary the hydrostatic stress or constraint in the regions of fracture initiation. As the crack tip behaviour is usually evaluated by using experimental results obtained from notched tensile specimens, and up to now very few experimental studies have yet been undertaken to study the situation at crack tip, metallographic examination on the sections of cracked specimens in detail would seem to be very useful to assess the applicability of critical conditions of void growth.
2. MATERIAL
AND TESTING
The test material was to the specification BS4360 Grade 50D structural steel widely used in the North Sea offshore structure. The steel was at a thickness of 51 mm at normalizing condition. The chemical composition and mechanical properties are given in Table 1. 37
38
Y. W. SHI et
al.
Table 1. Chemical composition and mechanical properties (a) Chemical composition (wt.%): C Mn Si 0.18 1.42 0.23 (bj \ , Mechanical orooerties: Yield stress a (MPa) 349
S 0.008
Tensile strength (MPa) 542
P 0.007
Al 0.03 Elongation (%) 40
cu 0.11
Ni 0.25
Cr 0.21
MO 0.03
Strain hardening exponent (in Ramberg-Osgood) 4.5
Charpy size specimens were cut out in the L-T direction. In the tests there were four variations of the Charpy specimens, namely a standard geometry; side grooved; fatigue cracked; side grooved and fatigue cracked. The geometry variations were intended to vary the level of constraint in the region of fracture initiation. Pre-fatigue cracking was carried out at a stress ratio of 0.1 and the maximum stress intensity factor Kf of 22 MPa &. The final crack length to width ratio was chosen to be 0.5. The specimens were tested in three point bending at room temperature in a 50 kN Instron testing machine at a cross head speed of 0.2 mm/min. Fracture initiation was determined by using a direct current electrical potential drop method (DCPD). The specimens were unloaded subsequently, then the specimens were sectioned in a plane which was perpendicular to the crack plane and parallel to the longitudinal direction of the specimen at - 196°C. The void volume fractions were estimated by observing the fracture surfaces using a scanning electron microscope (SEM) at a magnification of 1000, and using a statistical point counting technique[9].
3. RESULTS It is known that the combination of plastic strain and stress triaxiality produces a maximum void growth rate at a specific distance ahead of notch or crack tip[lO, 111. The finite element analysis of the Charpy specimen indicates that maximum value of the stress triaxiality develops at about 0.5 mm ahead of the notch root[l2]. Thus, a region between 0.4 and 0.6 mm ahead of the notch root was chosen to investigate the void growth behaviour. In fact this void growth rate represented a critical value since the test was stopped when initiation of failure was detected using DCPD method. The detection of initiation of failure using DCPD involved a measurement of increase in probe potential of 5 /JV when a direct current of 20 A was passed through the specimen. Some of the specimens were fractured along the crack plane at - 190°C after testing, and subsequently examined in SEM to ensure that an increment of 5 PV represented the crack initiation. Point counting was carried out directly on the screen SEM in order to establish the void volume fractions. The void volume fraction for each specimen was an average value of 100 random fields, because of large measured scatter in the relative void volume at failure initiation. If a ratio of mean stress cr, to effective stress 5 is characterized as a stress triaxiality, the stress triaxiality distribution ahead of the notch in the Charpy specimen has been calculated, and the maximum value of stress triaxiality is 2.2 and its location is 0.5 mm ahead of the notch tip[l2]. Moreover, the stress triaxiality distribution ahead of a blunted crack in the side-grooved and fatigue-cracked Charpy specimen may be estimated from the analysis of McMeeking[l3] since his calculation refers to a material of similar tensile properties and work hardening characteristics to the material tested here. Thus, the maximum triaxiality was estimated at 4.13, and its location was at 1.33 times the critical CTOD, which for the steel tested is 0.52 mm. It is resonable to assume that the stress triaxialities in the other two specimen types will be present within these two extremities, Higher constraints will be present in the fatigue cracked CVN specimen than in the side-grooved CVN specimen. As seen in Fig. l(a) the critical void volume fractions at the location of the maximum stress triaxiality increase significantly with increasing the stress triaxiality.
Void growth at ductile crack initiation
39
12-
(a)
. . .
a-
n” b
4-
G i
,_ u.b -c s b
0
I I
I 4
, 3
I 2
Stress triaxiality
I 5
(~~15)
,P
. . .
l
.
. . .
.
I
I
I
1
1.25
I.30
I .35
1.40
Constraint factor (C) Fig. I. Strong variation of critical void volume fraction as a function of geometry constraint of specimens. (a) Critical void volume fraction (f,)i vs stress triaxiality ~,,,/a. (b) Critical void volume fraction (f,), vs constraint factor C.
Moreover, the stress state in the specimens with geometry variations may be estimated by a constraint factor on general yielding. The constraint factor (C) for the specimens tested is given byLl41 C =4P,,
W/a,B(W-a)’
where PGy is the general yield load; a is the crack length; B is the specimen thickness; W is the specimen width; cry is the yield stress of steel. In general the C value is changed from 0.1 in plane stress to 1.4 in plane strain condition. It should be emphasized that the estimative constraints are only approximations for real materials since slip-line field solutions treat the material as being rigid-plastic. Based on the experimental record of load versus deflection, the C values are calculated and the influence of constraint factor on void volume fraction (fv)i in Charpy specimens at onset of ductile crack growth is shown in Fig. l(b). As mentioned earlier, statistical point counting was carried out directly on the SEM screen. The statistics were such that many fields did not have voids and other fields had very few voids. In the standard CVN specimen 80% of the fields resulted in zero void counts, whereas in the side-grooved and fatigue-cracked CVN specimen only 40% of the fields had a zero void count. This is also reflected in the results presented in Fig. 1. At the same time, the void growth rates were carefully determined. SEM observations of the fracture surfaces showed the inclusions in their associated voids surrounded by cleavage fracture. The mean radius of the inclusions and that of the voids were measured on photographs which were randomly taken at the same locations as the point counting. A typical SEM photograph is shown in Fig. 2. About 20 particles were observed for each specimen. Figure 3 shows the variation of void growth rate Ri/& at the onset of crack growth as a function of specimen constraint, where Ri and R. are the void radius at CTOD initiation and the initial void radius, respectively. The initial size of the voids is taken as the size of the associated inclusions. It is clear that the void growth rates
40
Y. W. SHI ef al.
Constraint
factor (C)
Fig. 3. Weak variation of critical void growth rate RI/& as a function of geometry constraint.
R,/R, at the onset of crack growth determined by this test are not sensitive to the constraint of the specimens. 4. DISCUSSION 4.1. Concepts on ductile crack initiation There are two different concepts regarding initiation of the ductile failure process. One concept is that failure initiation in the material occurs at a critical volume fraction (fv)i of large voids[l5]. This critical void fraction is essential to initiate failure process by a mechanism of flow localization. Once small scale voids are initiated the failure process is cooperative. The critical value of void volume is thought to depend upon the inclusion content. It is suggested that in very dirty or highly precipitation-hardened materials at severe stress states, flow localization may occur as soon as the voids are formed. Moreover, in order to determine the critical void volume fraction of large voids for a structural steel A533B, a series of tensile specimens were tested[6]. The large voids were found to nucleate at MnS and Al,O, inclusions and they grew with increase in plastic strain. It was found that nucleation of small voids occurred when the relative void volume of large voids reached a value of 0.01. That is, the initiation of material failure is defined to occur when a void volume fraction of 0.01 is attained. A second concept is that failure initiation is associated with a critical void growth rate RI/R,. Since a critical void growth rate can exist at different void volume fractions, it is possible that this criterion would be related with the work hardening characteristics of the material. The critical void growth rate is usually defined in terms of an average void radius. It has been proposed that the critical void growth rate can be used to model failure initiations, and for a structural steel A508 the value of Ri/& is 1.48, which is associated with a stress triaxiality of 1.80[7]. In addition, it is indicated that the directionality of the wrought steel would affect the critical values of the fracture criterion[8]. This is attributed to the different initial radii or alternatively the different spacing between the inclusions. Moreover, it has been recently reported that the critical void growth rate within a first approximation can be considered to be independent of the stress triaxiality, though sometimes there exists a decrease in the critical void growth rate when the stress triaxiality is increased[7, 8, 161. 4.2. Effect of constraint on critical void growth rate In the present experiments, the results show a weak variation of critical void growth rate Ri/R, as a function of constraint factor. An average value of R,/R, is equal to 1.52 at the onset of crack growth for the constraint factor range from 1.21 to 1.33. For the identical test material a series of smooth tensile specimens were pulled and interrupted at different strain level before neck formation. Void growth rate R/R0 was measured on the longitudinal sections of the strained uniaxial tensile specimens. The average value of R/R, was equal to 1.3 1 for the plastic strain range from 0.006 to 0.21[17]. It is clear that the critical void growth rate 4/R,, at the onset of crack growth is only slightly higher than the void growth R/R,, occurred in the uniaxial tension tests. Moreover, there is a small decrease in the Rx/R, values, when the constraint factors increase from the standard Charpy specimen to the side-grooved and pre-cracked Charpy specimens.
Void growth at ductile crack initiation
Fig. 2. Typical fractograph on mid-section of a side-grooved Charpy size specimen at the onset of crack growth.
41
Void growth at ductile crack initiation
43
It should be noted that the effective plastic strains at failure initiation are lower in specimens with higher constraint. It is the combination of stress triaxiality and effective plastic strain that controls the failure process. The results infer that the increase in critical void growth rate Ri/& for real structural steels is very difficult even though a higher constraint is imposed on the specimens. A possible reason could be the fact that most engineering materials contain at least two populations of particles nucleating voids. Void formation takes place much more easily at large inclusions than at small inclusions or carbide particles, The experiments indicate that void growth from large inclusions in this material does not occur by the simple continue mechanics of individual void growth but by the coalescence with the surrounding smaller voids including the nucleation at carbides or intermetallic precipitates. The second generation small voids can grow rapidly within the stress field of the large voids. Moreover, the presence of the small voids around large voids reduces the local strain hardening rate[l8], which is an important parameter in the continuum mechanics model for void growth. 4.3. Effect of constraint on critical void volume fraction The experiments indicate a strong variation of critical void volume fraction ( fV)i as a function of constraint factor or stress triaxiality. For the identical test material_& = 2.44 x 10e3 was obtained on the longitudinal sections of strained uniaxial tensile specimens[l7]. It was shown that for the standard Charpy and the side-grooved pre-cracked Charpy specimens the critical void volume fractions were respectively about 1 to 3 times the relative void volume in the uniaxial tension test. It was inferred that the value of (s”)i was promoted in a triaxial stress field. In general, that is because in tensile tests large inclusions which have low values of critical stress nucleate voids early in the fracture processes, and small inclusions nucleate voids only after considerable strain due to their very high values of critical stress. However, the situation is different in the CTOD tests of pre-cracked specimens. The high constraint stresses combined with the strain concentration may create interfacial stresses which exceed the critical stress at many of the small inclusions. In this case, the large inclusions as well as some of the small inclusions are attributed to the critical void volume fraction in the crack tip region. As a very small strain is required to initiate voids at the crack tip where the constraint is higher than in the notched specimens, the critical void volume fraction measured in the crack tip region is representative of the sum in the large void growth and the further smaller void nucleation. Therefore, the criticai void volume fraction at the onset of crack growth is not a material constant. The fractions increase obviously when the stress triaxiality or constraint factor increases, and they are strongly dependent on the geometry constraint of the test specimens. However, the critical void growth rate RI/R, may be a material constant in a wide range of constraint factor or stress triaxiality. As the critical void growth rate is not sensitive to the specimen geometry constraint, thus it is probable to evaluate the crack initiation by using experimental results obtained from smooth or notched tensile specimens with lower constraint to take it easy, though the volume of material in the notched and cracked specimens in which failue events take place is different. 5. CONCLUSIONS There are two different micromechanistic concepts regarding initiation of the ductile failure processes. One concept is that failure initiation in material occurs at a critical void volume fraction, and the other concept is that failure initiation is associated with a critical void growth rate. In the present experiments, it is indicated that the critical void volume fraction (fV)i at onset of crack growth is not a material constant. The volume fraction is dependent on the geometry constraint, and the fractions increase obviously when the stress triaxiality or constraint factor increases. However, the critical void growth rate Ri/R, is a material constant within a first approximation, though there is a small decrease in the critical void growth rate at onset of crack growth when the constraint factors increase. It is clear that an individual void growth for real structural steels is very difficult, it may be because the presence of small voids around large voids and local strain softening. Thus, it is probable in engineering to evaluate the crack initiation in a cracked specimen by using the critical void growth rate measured on smooth or notched tensile specimen with lower constraint.
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Y. W. SHI et al.
Acknowledgements-The
authors wish to gratefully thank the National Natural Science Foundation financial support, and Dr. C. J. Flavell for preparing some of the experiments.
of China for its
REFERENCES S. H. Goods, and L. M. Brown, Acta Merailurgica 27, 1-15 (1979). D. A. Curry and J. F. Knott, Current aspects of crack growth under monotonic loading, Fracture and Fatigue, ECF3. Proc. of 3rd Colloquium on Fracture, London (Edited by J. C. Radon), pp. 209-216. Pergamon Press, Oxford (1980). A. Pineau, Review of fracture micromechanisms and a local approach to predicting crack resistance in low strength steels. Advances in Fracture Research, ICFS, Cannes (Edited by D. Francois et al.), pp. 553-577. Pergamon Press, Oxford (1981). [41 R. C. Bates, Modeling of ductile fracture by microvoid coalescence. Fracture: Inieractions of Microstructure, Mechanisms, Mechanics (Edited by J. M. Wells and J. D. Landes), pp. 117-155. The Metallurgical Society of AIME (1984). PI A. C Mackenzie, J. W. Hancock, and D. K. Brown, Engng Fracfure Mech. 9, 167-188 (1977). 161 D. A. Shockey, K. C. Dao, L. Seaman, R. Burback, and D. R. Curran, Computational modeling of microstructural fracture processes in A533B pressure vessel steel, NP-1398. Electric Power Research Institute, Palo Alto, California (1980). 171 F. M. Beremin, Study of fracture criteria for ductile rupture of A508 steel. Advances in Fracture Research, ICFS, Cannes (Edited by D. Francois et al.), pp. 809-816. Pergamon Press, Oxford (1981). J. C. Lautridou and A. Pineau, Engng Fracture Mech. 15, 55-71 (1981). Y. W. Shi and J. T. Bamby, Int. J. Fracture 25, 143-151 (1984). J. F. Knott, Metal Science 14, 327-336 (1980). J. T. Bamby, Y. W. Shi, and A. S. Nadkarni, Int. J. Fracture 25, 273-283 (1984). D. M. Norris, Engng Fracture Mech. 11, 261-274 (1979). R. M. McMeeking, J. Mech. Physics Solids 25, 357-381 (1977). W. L. Server, J. Engng Mater. Technol. Trans. ASME 100, 183-188 (1978). J. W. Hancock and A. C. Mackenzie, J. Mech. Physics Solids 24, 147-169 (1976). Y. W. Shi, Critical void growth for ductile rupture of steel welds. Engng Fracture Mech. (submitted). Y. W. Shi, Void growth in uniaxial and triaxial stress field for a structural steel. Mater. Science Engng (in press). M. F. Ashby, Philosophical Magazine 14, 1157-I 178 (1966). (Received 15 November 1989)