Ductile-brittle fracture transition due to increasing crack length in a medium carbon steel

Acta metall, mater. Vol. 39, No. 1I, pp. 2527-2532, 1991 Printed in Great Britain. All rights reserved

0956-7151/91 $3.00 + 0.00 Copyright L~ 1991 Pergamon Press pie

DUCTILE-BRITTLE FRACTURE TRANSITION DUE TO INCREASING CRACK LENGTH IN A MEDIUM CARBON STEEL S H A N G - X I A N WU, Y I U - W I N G M A I , B. C O T I ' E R E L L and C U O N G V I E T LE Center for Advanced Materials Technology, Department of Mechanical Engineering, University of Sydney, Sydney, N.S.W. 2006, Australia (Received 24 September 1990; m revised form 8 May 1991) Abstract--A phenomenon of ductile-brittle fracture transition with increasing normalized crack length

in CSI030 steel has been observed in notch bend specimens. It is found that for stationary cracks in threeand four-point bend specimens the transition occurs at about a/W = 0.2. For propagating cracks in four-point bend specimens, this transition occurs at larger a/W ratios in some specimens but there is no transition in three-point bending. The Ritchie-Knott-Rice (RKR) critical stress model for cleavage fracture, in combination with finite element analyses of crack tip stress fields, successfully explains the ductile-brittle transition with relative crack length. The model also successfully predicts critical values of the CTOD for cleavage fracture. Ri~um~--On observe un phrnomene de transition de rupture ductile--fragile avec une augmentation de la Iongueur normalisre de fissure dans un acier CS1030 sur des 6chantillons de flexion entaillrs. On trouve que, pour des fissures stationnaires, dans des 6chantillons de flexion sur trois ou quatre points, la transition se produit/t environ a/W = 0,2. Avec des fissures qui se propagent, dans les 6chantillons de flexion sur quatre points, cette transition se produit pour des rapports a/W plus grands dans certains 6chantilons, mais il n'y pas de transition dans les 6chantillons en flexion sur trois points. Le modrle de contrainte critique de Ritchie, Knott et Rice pour la rupture par clivage, combin6 avec l'analyse par 616ments finis des champs de contraintes sur les 16vres de la fissure, expliquent avec succrs la transition ductile--fragile avec une longueur relative de fissure. Le modrle prevoit aussi avec succ~s les valeurs critiques du CTOD pour la rupture par clivage. Zusammenfagsang--Die Erscheinung eines duktil-sprrden Bruchiibergangs mit zunehmender normalisierter RiBl:inge wurde in gekerbten Proben des Stables CS1030 beobachtet. Ffir station/ire Risse in Dreiund Vierpunktbiegeproben ergibt sich, dab der Obergang bei etwa a/W = 0,2 auftritt. Bei wandernden Rissen in Vierpunktbiegeproben tritt der Obergang in einigen Proben bei hrheren Verh/iltnissen a~ W auf, in Dreipunktbiegeproben findet sich kein Obergang. Das Ritchie--Knott-Rice-Modell der kritischen Spannung fiir Spaltbruch erkl/irt in Kombination mit Finit-Element-Analysen des Spannungsfeldes an der RiBspitze den duktil-spr6den ~bergang mit der relativen RiBl/inge. Das Modell sagt auch kritische Werte des CTOD fiir Spaltbru.ch erfolgreich voraus.

1. INTRODUCTION The phenomenon of ductile-brittle fracture transition is observed in many engineering materials [1]. In the case of ferritic steels such as the low and medium carbon structural steels [2, 3], the fracture toughness is found to decrease with decreasing temperature and increasing loading rate. Thus changes in test temperature and loading rate may cause a ductile-brittle fracture transition which can be explained in terms of the elevated yield stress of the material. Another well-known cause for a ductile-brittle transition is associated with the change of stress-strain state ahead of a crack tip due to a transition from plane stress fracture for a thin plate where the toughness is high to plane strain fracture for a thick plate where the toughness is low. In plane strain the stress triaxiality produces a high hydrostatic stress and a

high elevation of normal tensile stress ahead of the crack tip hence promoting brittle fracture. The ductile-brittle fracture transitions described above can be explained by the critical stress model for cleavage fracture. Cleavage fracture causes the creation of new free surfaces by the rupture of atomic bonds across well-defined low index crystallographic planes. For structural metals, and in particular ferritic steels, evidence suggests that cleavage fracture is controlled by stress. Early investigations [4,5] suggested that unstable cleavage fracture occurs when the local tensile stress (trry) ahead of a stress concentrator exceeds a critical stress (err) which is relatively independent of temperature and strain rate. This model can qualitatively explain the ductile--brittle fracture transition in a notched bar of mild steel due to decreasing temperature and increasing strain rate. As temperature decreases or strain rate increases, the

2527

2528

SHANG-XIAN WU et al.: DUCTILE-BRI'I~rLE FRACTURE TRANSITION

Table 1. Mechanical properties of CS1030 plain carbon steel

Condition

0.2% Proof stress (MPa)

As-received

460

Ultimate Critical tensile Reduction fracture strength Elongation in area stress (MPa) (%) (%) (MPa) 587

17

57

1522

yield stress try of mild steel increases, but the critical stress af remains largely unchanged. Finally, when the maximum local tensile stress ahead of a stress concentrator t r . exceeds at, the fracture mechanism changes from ductile to brittle. Ritchie et al. [6], using the temperature-dependent /(1¢ data for a high nitrogen mild steel, showed that at the initiation of cleavage fracture the tensile stress a~ exceeded a critical stress ar over a characteristic distance/0. Ritchie et al. [7] later also used the R K R critical stress model to predict temperature and strain rate variations of fracture toughness of SA533B-I and SA302B steels at the lower shelf. Other workers have since demonstrated the applicability of this model to failure in low alloy steels [8], high carbon steels [9], mild steels over a range of grain sizes [10], and titanium alloys [11]. Slip-line field analyses [12] show that the maximum hydrostatic stresses ahead of a deep crack and a shallow crack are quite different. It is therefore expected that crack length variations may cause a transition of fracture mechanism from ductile tearing to brittle cleavage in some structural steels. In Section 2 experimental results of brittle--ductile transition with relative crack length in a CS1030 steel are reported. In order to use the R K R critical stress model to predict the ductile--brittle fracture transition the detailed distributions of stresses ahead of the crack tip are needed. Finite element analyses of stress fields ahead of deep and shallow crack tips are presented in Section 3. The results of finite element analyses are used to establish a theory for the ductile--brittle fracture transition due to increasing crack length and given in Section 4.

same thickness B = 25 mm and the same ligament size ( W - a ) = 12.5mm, but different normalized crack lengths a/W. CTOD measurements were performed at room temperature under three-point bending with span S ( = 4 W) and four-point bending with external span S~(=190mm) and internal span $2 = (85 mm) in an Instron 1195 testing machine with a constant displacement rate of 0.1 mm/min. The crack mouth displacement V was measured with a clip gauge and a P - V plot was recorded on each specimen, where P is the applied load. The CTOD values were calculated from K2(I - v 2) = - + 6v 2ay E

(1)

where ay is yield strength, E Young's modulus, v Poisson's ratio and K nominal stress-intensity factor. K-factor for three-point bend geometry was calculated from the formula given in ASTM E399 and for the four-point bend geometry was calculated by [14] 3PL K = ~-~--i x / ~

[1.122-1.121a/W

+ 3.740(a/W) 2 + 3.873(a/W) 3 - 19.05(a/W) 4 + 22.55(a/W) 5]

(2)

where

L

=

(s, - so~2.

For specimens with deep notches, in which unstable brittle crack extension occurred, the plastic component 6p of CTOD in equation (l) was calculated from

(3)

rp(W - a ) V p 6P=rp(W-a)+a

+z

where Vp is the plastic component of the crack mouth opening displacement at the unstable point on the 0.25

,po,otb.o t: ::

2. EXPERIMENTS AND RESULTS 0.20

2.1. Experimental details The test material was a CS1030 (carbon content ~0.3%) plain carbon steel bar of diameter 42 mm in the as-received condition and its mechanical properties are given in Table 1. The mean size of the ferrite grains and the pearlite colonies were measured by quantitative metallography [13] and was about 25/am. Three-point bend specimens 25 mm by 25 mm by 110mm and four-point bend specimens 25 mm by 25 mm by 200 mm were machined from the steel bar. On each specimen a notch was cut and then a fatigue precrack was developed such that the total length of notch plus precrack (a) was 12.5 mm. The specimen width (W) was then reduced to predetermined normalized a / W values. Hence all specimens have the

0.15

t._

Theory

t-.-

Theory

E 0.10 t] o

0.05

~

~

o~ o

ol.1

0!2

I

0.3

I

0.4

015

0.6

a/w Fig. 1. Results o f C T O D tests for four-point and three-point bend specimens with deep and shallow cracks for CS1030 steel (6, for cleavage fracture; /ii for ductile tearing).

SHANG-XIAN

W U et al.:

DUCTILE-BRITI'LE

FRACTURE

TRANSITION

2529

Table 3. Details of finite element meshes of various specimen geometries Speomen 3-point bend

4-point bend

Fig. 2. Fracture path of shallow cracks in a CSI030 steel in three-point bending. P - V record, z the distance of knife edge measurement point from the front face of specimen, and rp the plastic rotation factor which is taken as 0.45 for the three-point bend [15, 16] and 0.37 for the four-point bend [17] geometries. The critical 6~ value was calculated from the maximum applied load Pc using equations (I) and (2). Fracture initiated as a stable tear from the shallow notched specimens and the CTOD at initiation was obtained by the multiple specimen technique where the CTOD is measured after a range of crack extensions. The CTOD at initiation was then obtained from the intersection of a linear regression line with the theoretical blunting line 6 = 2Aa. Because the plastic deformation extends to the notched surface of specimens with shallow notches, the standard method of measuring 6p cannot be used, and the plastic component 60 of the CTOD was measured from the relative displacement of two indentations at the crack tip on both sides of the specimens. The specimens were then broken open at the temperature of liquid nitrogen so that the crack extension could be measured. Previous work [18] has shown that the CTOD measured by a similar method for deep notched specimens, where the specimen was sectioned and the CTOD was measured at the crack tip, does agree with the values obtained by the standard method. In the present measurements the CTOD was measured on the surface, but since the contraction at the notch root was only about 1.5% the error induced from using a surface measurement should be slight. To study the ductile-brittle fracture transition for a propagating crack some specimens with a/W=O,05-O.l were loaded under three- or fourpoint bending until unstable brittle fracture occurred. Table 2. Experimental results for propagating cracks in four-point bending Specimen number

W (mm)

a0 (mm)

ao/W

a, (mm)

at:W

1 2 3 4 5 6

12.73 12.80 14.05 12.51 12.52 12.14

1.22 1.12 2.54 1.05 1.72 1.74

0.096 0.086 0.181 0.084 0.137 0.143

2.51 2.73 4.22 5.12 5.32 5.34

0.197 0.213 0.300 0.409 0.425 0.440

a/W

Number of element

Number of node

l/c

0.1 0.2 0.5 0.1 0.2 0.5

164 164 180 172 172 188

551 551 599 579 579 627

0.25;360 0.25/360 0.25;200 0.25;360 0.25/360 0.25;200

In these specimens a ductile tear preceded the unstable cleavage fracture. The total crack length at the ductile--brittle fracture transition including the original crack length and the slow stable crack extension was measured on the fracture surface. To determine the critical fracture stress of o f the material, tensile and slow four-point bend tests with 12.7mm by 12.7mm bars with a 45 :~ V-notch of depth 4.23mm and root radius of 0.25 mm were performed at temperatures of - 196 and - 100~:C [7]. The yield stress ay and nominal bending stress at the onset of catastrophic failure were measured from these tests. Using the Griftiths and Owen [19] finite element stress analyses for the above specimen geometry, the critical values of the maximum principal stress at the notch tip (Oymyax=af) were calculated.

2.2. Experimental results The critical fracture stress at is given in Table 1 and the CTOD results are presented in Fig. 1. The CTOD test results show that when the non-dimensional crack length a/W > 0.2 fracture in both three- and four-point bend specimens is both brittle and unstable without any prior stable ductile crack extension; the fracture toughness ~¢ is low. However, when a/W is less than 0.2, the fracture initiates by slow stable ductile crack extension and the CTOD ~, is large. SEM fractographic examinations of fracture surfaces reveal different micromechanisms of fracture for deep and shallow crack specimens. The micromechanism of fracture for deep crack specimens is brittle cleavage fracture with no slow tearing between the precrack and the unstable cleavage fracture, whereas for shallow crack specimens a SEM fractograph reveals the void coalescence characteristics of slow stable crack extension. The experimental results on propagating cracks showed quite different crack paths and behaviour for shallow notches under three-point and four-point bending. In three-point bending shallow cracks initiated in a stable ductile tear, but after a small normal crack propagation the fracture deviated along the slip-line direction, in the direction of the band of intense strong shear strain, and grew stably at approximately 45 ° to the original crack direction. These fractures did not show a transition from ductile to cleavage fracture. Figure 2 shows the crack path of a shallow crack in three-point bending. In four-point bending shallow cracks initiated in a ductile tear which continued to grow normally to the surface

SHANG-XIAN WU et al.: DUCTILE-BRITTLE FRACTURE TRANSITION

2530 1000

The material modelled in the analyses is the CS1030 plain carbon steel with Poisson's ratio v = 0.3, Young's modulus E = 206 GPa and yield stress oy = 460 MPa. The stress-strain relationship in Fig. 3 obtained experimentally is used in the analyses. An incremental initial stiffness solution procedure was used in the analyses and 200 load increments were taken to reach the load level of about 1.2 PL, where PL is the limit load given by slip-line field analyses. The values of J-integral were calculated along 10 concentric circular contour paths around the crack tip and an average J value was obtained from the 10 values.

.J

I 5

.

.

.

.

,

,

,

,

110 Strain

15

(%)

Fig. 3. Stress-strain relationship of the modelled material CS1030 steel. until a transition to unstable cleavage fracture occurred. Table 2 shows the initial non-dimensional crack length ao/W and the crack length at the ductile-brittle fracture transition a,/W for the six specimens tested. The ductile--brittle fracture transition occurred at about the same value of a/W as the stationary crack in two specimens, but at greater values in the other four specimens. The experimental results for growing cracks seem to suggest that the crack length at the ductile-brittle fracture transition for growing cracks is greater than for stationary cracks. 3. FINITE E L E M E N T ANALYSES O F T H R E E AND F O U R - P O I N T BEND S P E C I M E N S W I T H D E E P AND S H A L L O W CRACKS

3.1. The finite element model Since there was little contraction at the notch of specimens tested, it is considered that a plane strain finite element analysis should give the stresses and strains reasonably accurately at the mid thickness of the specimens. The finite element analyses are based on small strain theory and employ ,/2 flow theory of plasticity. Eight-noded isoparametric elements with 2 by 2 Gauss quadrature are employed, as suggested by Owen and Fawkes [20]. The specimen geometries considered are three-point bend with a/W = 0.1, 0.2 and 0.5 and four-point bend with a/W = 0.1, 0.2 and 0.5. Because of symmetry only half the beam needs to be calculated. Twelve wedge-shaped collapsed eightnoded parametric elements surround the crack tip and 25 nodes, initially sharing the same location at the crack tip, are allowed to displace independently. These crack tip elements give a displacement gradient with a 1~r-singularity [21 ]. Eight rings of eight-noded isoparametric quadrilateral elements are placed outside the special crack tip elements. The ratio between the length of the crack tip element 1 to the ligament c = (W - a) and other details of the finite element meshes of various specimen geometries are given in Table 3.

3.2. Stress and strain fields ahead of deep and shallow crcIc~S The stress and strain fields obtained from the finite element calculations for three- and four-point bend specimens with deep and shallow cracks can be compared at various levels of plastic deformation. From the relationships between J, 6 . K and the plastic zone radius r~ we have

J/try =

m 6 t ~ (6 tray/E)ry

(4)

where for plane strain m is approximately 2. Hence

J/try can be taken as an indicator of the extention of plastic deformation and c/(J/try) can be used to assess the extention of plastic deformation relative to the ligament size c. There are differences in the stress and strain fields of deep and shallow cracks under large scale yielding condition c/(J/try) = 120 as is shown in Figs 4 and 5. At this level of plastic deformation the specimens are generally yielded and, if the notches are shallow, the plastic deformation has spread to both free surfaces. For large plastic strain [c/(J/trv)= 120], the normal stress ahead of a shallow crack is smaller than that ahead of a deep crack (see Fig. 4). Slip line analyses [12] show that the stress ahead of a shallow crack is 6.0

o a/w=0.5 5.0

o

a a/W=0.2

~0

o a/W=0.1 4.0

•

o

0 4

000

0 o

-~3.0

0

o

0

°o~,~,,., o 000

0

0 0 0

0

0

0

2.0

1.0

0

I 1

I 2

I 3

I 4

X/(2/o,) Fig, 4. Normalized tensile stress ahead of crack under large

scale yielding condition c/(J/oy) = 120 for three-point bend specimens with deep and shallow cracks.

SHANG-XIAN WU et al.: DUCTILE-BRIT1"LE FRACTURE TRANSITION 12.0

2531

60 O

ca a/W=0.5

&

a/W=0.2

I0.0

5.0

O

o a/W=0.1 8.0

/ "' 0

6.0

&

0

.0

0 n

4.0 u

position of maximum stress

~

0

0 A

0

o

o,/o,

I "//,_/

~

~

//

~

./w_- 0.

.......................

0

2.or/

0

2,0

n

I

&

o 0

(3 l

l

1

9

o

l

I

3

4

Xl(Jlo,)

Fig. 5. Equivalent plastic strain along plane at 45° from plane of crack under large scale yielding condition c/(J/a~)= 120 for three-point bend specimens with deep and shallow cracks. limited because the plastic deformation spreads to the notched surface of the beam. On the other hand the plastic strain is larger for shallow notches (see Fig. 5). Cleavage and ductile tearing are competing fracture mechanisms in ferritic steels. Cleavage fractures are stress critical whereas, though ductile fractures do in part depend on stress, they are mainly strain critical. If the crack is physically large so that the critical stress for cleavage can be obtained with only small scale yielding then cleavage fracture will occur from both deep and shallow notches. However, with small specimens cleavage fracture are more likely to initiate at deep cracks. 6,0

,5.0

i' 4.0 "J ' , ,

~/

position of maximum stre~ according to slip-line theory

3,0

2.0

1.0

I

I 2

I

I 4

I

I 6

I

I 8

I 10

.Vl(al~)

Fig. 6. Truncated finite element analyses of normalized tensile stress ar~/a~ ahead of crack tip of three-point bend specimens with various crack lengths.

10[ 0

I

I 2

I

I 4

I

1 6

I

I 8

I 10

XI( Jl,.r~j Fig. 7. Truncated finite element analyses of normalized tensile s t r e s s g~/O'y ahead of crack tip of four-point bend slx~clmens with various crack lengths. 4. DUCTILE-BRI'Iq'LE TRANSITION The finite element analyses of three- and four-point bend specimens of CSl030 steel in Section 3 are based on small strain formulation. Because these analyses did not consider crack blunting there was a stress singularity at the crack tip. The slip-line field analysis of Rice and Johnson [22] and the finite strain finite element analysis of McMeeking [23] show that crack tip blunting produces a large strain zone ahead of the crack tip and limits the maximum tensile stress achievable there. The analyses of Rice and Johnson and McMeeking show that the extension of the large strain zone for the case of small scale yielding is (2-3)~, ahead of the crack tip. McMeeking [23] shows that beyond this distance the results given by finite strain analysis agree with the results given by small strain analysis. In the large strain zone the tensile stress O'yyalso decreases with decreasing distance from the blunted crack tip because of the lack of plastic constraint. Our slip-line field analysis [12] shows that the size of the large strain zone in three-point bend specimens is 0.753 t for a / W = O . 1 and 0.93 t for a/W=0.5. Because brittle cleavage fracture in CSI030 steel occurred at a load level of (0.9-0.95) times the limit load, the specimens were close to general yielding. Hence we take the size of the large strain zone as X/(J/cry) ~ 1.5 for a / W = 0.1 and 1.8 for a / W = 0.5. This estimation of size of large strain agrees with the results of finite element analyses of Sun et al. [24]. Their results show that the tensile stress ahead of the crack tip in four specimen geometries starts to decrease at a distance of X / ( J / % ) ~ 1.5-2. Therefore, the stress distributions given by small strain finite element analyses, for a

2532

SHANG-XIAN WU eta/.:

DUCTILE-BRrVrLE FRACTURE TRANSITION

J-level that corresponds to a load of 0.95 times the limit load, have been truncated as shown in Figs 6 and 7. There is very little change in the stress distributions for higher loads. According to the R K R critical stress model for cleavage fracture [6], brittle cleavage fracture occurs when the local tensile stress tryy exceeds the critical stress trf of the material over a characteristic distance 10. The critical stress at of CS1030 steel is 1522 MPa as given in Table 1. The of/ay = 3.31 line is given in Figs 6 and 7. It can be seen for shallow crack specimens with a / W < 0.2 loaded essentially to the limit load that the local tensile stress ayy is less than the critical fracture stress of due to the lower in-plane plastic constraint. Hence for shallow notches cleavage fracture does not occur and crack growth takes place by ductile tearing. For deeper notches the maximum tensile stress ayy reaches the critical stress of and cleavage fracture ensues. Note that Figs 6 and 7 indicate that the transition from cleavage to ductile initiation takes place at a slightly larger value of a / W for three-point bend specimens than for the fourpoint bend specimens; such a difference exists in experimental data (see Fig. 1). F r o m Fig. 7 it is seen that the critical cleavage stress for a four-point bend specimen with a relative crack depth a / W = 0.5 is exceeded over a distance X / ( J / o y ) = 4.7 from the crack tip, which corresponds to a distance equal to X = 9.4~ t if it is assumed that m in the equation (4) is 2. The experimental value of the critical C T O D 6c for the four-point bend specimen with a relative crack depth a / W = 0 . 5 is 0.025 mm. Hence the characteristic distance 10 over which the critical stress is exceeded is 0.23 mm, which is about 9 times the mean size of the ferrite grains. This characteristic distance has then been used with the aid of Figs 6 and 7 to predict the critical C T O D 6c for the other values o f a / W for the four-point bend specimens and all the values for the three-point bend specimens; these predicted values are shown in Fig. 1. The predicted values agree well with the experimental ones. Note that the predicted critical C T O D do not depend on the value assumed for m providing the same value applies for all crack depths. 5. CONCLUSIONS Notch bend experiments with a medium carbon steel have shown that whereas a cleavage fracture initiates if the notch is deep a ductile tear will initiate if the notch is shallow. For shallow notched fourpoint bend specimens the ductile tear propagates normal to the surface and transition to a cleavage fracture occurs at a crack depth somewhat larger than the initiation transition. In three-point bend specimens with shallow notches, though the initial ductile tear propagates for a short distance normal to the surface, it quickly turns to propagate at about 45 ° to the surface and does not transform into a cleavage fracture.

Finite element analyses show that the distribution of the stress and strain ahead of a shallow crack differ from that ahead of a deep notch for large plastic deformation when the deformation spreads to the notched surface. The stress distributions show that for shallow cracks the stress is less than the critical stress needed to initiate a cleavage fracture explaining the cleavage-ductile transition that occurs for shallow cracks. The stress distributions also enable the R K R characteristic distance over which the critical stress must be exceeded to the estimated. Predictions from this estimation of the critical C T O D for cleavage fracture agree well with experimental data. Acknowledgements--The authors wish to thank the Australian Research Council (ARC) and the Australian Welding Research Association (AWRA) for the continuing support of this work. One of us (S.-X. Wu) gratefully acknowledges the support of an ARC Research Fellowship. We also wish to thank Professor R. O. Ritchie of the University of California at Berkeley for the helpful discussions and suggestions when he visited the Department of Mechanical Engineering, University of Sydney. REFERENCES

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