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FIG. 7--J and J~ versus temperature for A533B steel [19].

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FIG. 8--Min J for cleavage with max and rain JLB, A533B steel [13].

180 F R A C T U R E M E C H A N I C S : T W E N T Y - F O U R T H V O L U M E

A second example of an A533B steel [14] shows that the JLB analysis works well in the middle transition region. Here, the toughness values were far away from the valid Kic region and were at a temperature where the data had high upward scatter in the maximum toughness values. The maximum toughness values in a group were often of the order of 20 times the minimum values. The JLB estimate used here worked very well (Fig. 9). For example, the group of B = 12.5 and 0% side grooving had very high Jec values; the range went from 1106 to 860 kJ/mL The JLB estimated from these were 40.3 and 36.3 kJ/mL These JLB estimates were both in the range of the lowest toughness measured at that temperature of 54 kJ/m 2 and on the conservative side. This shows that small specimens with high toughness are able to make a more conservative estimate of the lower-bound toughness and are more useful than the large specimens. Also, the estimate is often not overly conservative. The second A533B steel at - 30~ is used to illustrate this. The JLB estimates range from 18.6 to 52.6 kJ/m 2 with the lowest measured toughness being 54 kJ/m 2. The lowest J estimate is one third of the lowest measured toughness.

To evaluate the JLB method, individual sets of test results from the seven sources were evaluated to see how often the JLB estimate was conservative. A total of 68 sets with more than 700 toughness values were evaluated. The criterion for conservatism was that all JLB estimates were below the minimum measured value of toughness in that set. Of the 68 sets evaluated, 42 sets fit this criterion for being conservative and 26 did not. Of the 26 that did not, 17 were in the region of valid K~c toughness. This is by far the most difficult region for the single-

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1000

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FIG. 9--Max and min J for cleavage with max and min Jz~ A533B steel [14].

LANDES ET AL. ON DETERMINING LOWER-BOUND TOUGHNESS 181 specimen JLB estimate. For the remaining 9 sets that were not in the Kic region and had toughness results that were not conservative by the JLB estimate, 8 of the 9 had only one point that fell in the nonconservative region. The ninth set was the PVS at - 9 0 ~ that was illustrated in Figs.

3 and 5 a s b e i n g a difficult set of data that needed a different value of slope m. The 17 that were near the valid Kxc region were reevaluated using the const = 3000 assumption. This made the toughness values conservative in only 9 more of the 17 cases; 5 of these were from the A533B steel as discussed previously. Another heat of A533B steel had 6 cases that were near or at the valid K~c region for the bottom of the scatterband. For all 6 cases, using const = 3000 did not make all of the predictions conservative.

Comparison with Multiple-Specimen Lower Bounds

The usefulness of the single-specimen JLB estimate can be assessed by comparing the JLB

with other multiple-specimen methods for estimating a lower bound to a set of transition toughness data. This analysis was conducted by Zerbst [18] and is summarized here for information purposes. A full description of these results will be reported by Zerbst. His multiple-specimen lower-bound estimates included four approaches:

9 an A S T M approach from McCabe [19] in which the [3ic and Weibull plot were used to get a lower bound at 5% probability,

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182 FRACTURE MECHANICS: -I-WENTY-FOURTH VOLUME

9 a proposal of Stienstra et al. [11 ], which could predict a 5% lower bound with three or more specimens,

9 a proposal from Iwadate et al. [6] in which the lowest toughness value was taken as the lower bound when the data set met a criterion for a minimum number of tests, and 9 a simple two-parameter Weibull model with the lower bound taken at 5% probability.

The lower-bound estimates from these four multiple-specimen methods were compared with the proposed single-specimen model in Figs. 10 through 12. The difficult group for the PVS at - 9 0 ~ is presented first in Fig. 10. Here, the single-specimen method bounds all of the other methods; unfortunately, this includes the actual minimum toughness in the group. Note that the Iwadate method uses the minimum toughness to set the JLB" When enough specimens are available, it always corresponds to the minimum toughness in a set of specimens. In Fig. 11, the other difficult case of the PVS at - 6 0 ~ is presented. Here, the result is nearly the same except that the two-parameter Weibull model gave a higher estimate than the others. The final example is for a second PVS set at - 9 0 ~ (B = 25 mm, W = 50 mm; Fig. 12). Here, the single-specimen method is conservative relative to the minimum measured toughness in the set as are all of the multiple-specimen methods except for Iwadates, which corresponds to the minimum toughness in the set. The single-specimen method again bounds the others.

One important feature illustrated in these examples is that the single-specimen method is not

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LANDES ET AL. ON DETERMINING LOWER-BOUND TOUGHNESS 183

Minimum Toughness in G r n u n

9 PVS -90 -2 min [ ] PVS -90-2 max

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F I G . 12--JLB estimates f r o m Zerbst with single-specimen method, PVS 3 -90~

out of line with the multiple-specimen methods. Usually the minimum and maximum JLB from the single-specimen method bound the other methods. In eight example groups from PVS analyzed by Zerbst, the single-specimen method always bounded the ASTM estimate [18].

None of the multiple-specimen methods could get a JLB for every data set. They sometimes failed because a requirement important for the method could not be met. The single-specimen JLa always worked because it requires only one cleavage toughness result and eliminates no data due to validity requirements. More of the specimen sets are being evaluated by Zerbst who is also conducting a statistical confidence study on the single-specimen JLB method [20].

These will be reported separately.

Discussion

The single-specimen JLa estimate gives a good method for assessing the lower bound to a large scatterband of data from one or a few toughness test results. With it, an assessment of the transition lower bound could be made from the test of only one specimen at each temperature of interest. The method seems to give the best estimate for small specimens, which have high scatter. It performs worst for large specimens and toughness values in the Kic range. As a rough guideline, any test that results in a value of N = 1 Eq 1 is in the Kic range. Any result that is N = 3 or less is in the low-toughness area in which the estimate may not be good.

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184 FRACTURE MECHANICS: TWENTY-FOURTH VOLUME

seems to give about the same estimate of a lower-bound toughness. However, the single- specimen method can always be applied because it requires only one value, whereas the multiple-specimen methods may not have enough data to work. It is never certain from a finite set of data what the lowest toughness value could be at a given temperature. Even the multiple- specimen lower-bound estimates cannot guarantee that an additional test would be above the lower-bound estimate. These estimates merely give a reasonable method for finding a lower bound. Although the JLB has no sound technical basis and is always empirically evaluated, the fact that it compares well with the multiple-specimen estimates lends confidence to its use.

One question that can be addressed is whether the method may predict JLB values that are too low to be useful, thus exerting a penalty for using them. An examination of all 68 sets was not made for this; however, the general trend showed that the JLB gave estimates from 25 to 100% of the lowest toughness at a given temperature. Where the JLB estimate was always conservative with respect to the minimum toughness, the chance for its being undesirably low was greatest. The example of the CrMoV is the best; here the estimate Of JLB from the minimum toughness in a group tended to give values that were 25 to 50% of the actual minimum toughness. For the PVS, the minimum JLB was about 60% of the minimum measured toughness. On the other hand, for the first A533B steel [13 ] the minimum JLB and measured toughness always coincided.

One practice that should be reconsidered based on these results is that of eliminating high toughness results as a result of size or other validity criteria. By using the method discussed here, a reasonable estimate of the lower-bound toughness can be made from any fracture toughness test that fails in cleavage. The high scattered results give better estimates than some of the lower toughness data, which meet validity criteria. In particular, having a valid K~o result does not appear to guarantee any confidence in the attainment of a lower bound. These valid Kxc results have a fairly large scatter. The highest to lowest toughness values sometimes differ by a factor of five, and the Weibull slope is of the same order as it would be for toughness values higher in the transition. Therefore, individual Kxc toughness values must be treated with care.

Summary

The single-specimen lower-bound toughness estimate proposed in this paper can be used with a fair degree of confidence to estimate a lower bound to the transition toughness data. It gave a conservative estimate of the lower-bound toughness for more than 95% of the transition toughness data evaluated and more than 60% of the data sets analyzed. It is consistent with other multiple-specimen lower-bound estimates and predicts correctly the relatively fiat vari- ation of the lower bound to the toughness transition with temperature for the steels studied even while the upper bound was showing high upward scatter. This method for estimating a lower bound can make use of all transition toughness values that result from a cleavage fracture even though the value did not meet a size or other validity criterion. It is simple to apply and is therefore recommended to the reader to apply to his or her own transition toughness data to get further evaluation of its usefulness.

References

[1 ] Milne, I. and Chell, G. G., "Effect of Size on the J Fracture Criterion," in Elastic-Plastic Fracture, ASTM STP 668, J. D. Landes, J. A. Begley, and G. A. Clarke, Eds., American Society for Testing and Materials, Philadelphia, 1979, pp. 358-377.

[2 ] Milne, I. and Curry, D. A., "The Effect of Triaxiality on Ductile Cleavage Transitions in a Pressure Vessel Steel," in Fracture and Fatigue, Proceedings of the Third European Colloquium on Fracture, ECF-3, J. C. Radon, Ed., London, 1980.

LANDES ET AL. ON DETERMINING LOWER-BOUND TOUGHNESS 185 [3] Pisarski, H. G., "Influence of Thickness on Critical Crack Opening Displacement (COD) and J

Values," International Journal of Fracture, Vol. 17, No. 4, Aug. 1981, pp. 427-440.

[4 ] Landes, J. D. and Shaffer, D. H., "Statistical Characterization of Fracture in the Transition Region,"

in Fracture Mechanics: Twelfth Conference, ASTM STP 700, American Society for Testing and Materials, Philadelphia, 1980, pp. 368-382.

[5] Landes, J. D. and McCabe, D. E., "Effect of Section Size on Transition Temperature Behavior of Steels," in Fracture Mechanics: Fifteenth Symposium, ASTM STP 883, R. J. Sanford, Ed., American Society for Testing and Materials, Philadelphia, 1984, pp. 378-392.

[6] Iwadate, T., Tanaka, Y., Ono, S., and Watanabe, J., '~An Analysis of Elastic-Plastic Fracture Tough- ness Behavior of J~c Measurement in the Transition' Region," in Elastic-Plastic, Fracture: Second Symposium, Volume 11 Fracture Resistance Curves and Engineering Applications, ASTM STP 803, C. F. Shih and J. P. Gudas, Eds., American Society for Testing and Materials, Philadelphia, 1983, pp. II-531-II-561.

[7] Wallin, K., Saario, T., and T6rrOnen, K., " A Statistical Model for Carbide Induced Brittle Fracture in Steels," Metal Science, Vol. 18, 1984, pp. 13-16.

[8] Wallin, K., "Statistical Modeling of Fracture in the Ductile to Brittle Transition Region," in Defect Assessment in Components--Fundamentals and Applications, ESIS]EGF9, J. G. Blauel and K. H.

Schwalbe, Eds., Mechanical Engineering Publications Ltd., London, 1991, pp, 1-31.

[9] Anderson, T. L. and Stienstra, D., " A Model to Predict the Sources and Magnitude of Scatter in Toughness Data in the Transition Region," Journal of Testing and Evaluation, Vol, 17, 1989, pp.

46--53.

[10] Lin, T., Evans, E. G., and Ritchie, R. O., " A Statistical Model of Brittle Fracture by Transgranular Cleavage," Journal of the Mechanics and Physics of Solids, Vol. ~4, 1986, pp. 477-497.

[11] Stienstra, D., Anderson, T. L., and Ringer, L. J., "Statistical Inferences on Cleavage Fracture Tough- ness Data," Journal of Engineering Material Technology, Vol. 112, 1990, pp. 31-37.

[12 ] Miyata, T., Otsuka, A., and Katayama, T., "Probabilistic Analysis of Cleavage Fracture and Fracture Toughness of Steels," Journal of the Society of Material Science in Japan, Vol. 37, 1988, pp. 1191- 1196.

[13] Morland, E., Ingham, T., and Swan, D., "The Effect of Specimen Geometry on Fracture Toughness (K~c) in the Lower Shelf Regime," NRL-R-1002(R), NRL Risley, United Kingdom Atomic Energy Authority, Warrington, Jan. 1989.

[14] Modand, E., "The Effect of Side-Grooving on the Fracture Tou.ghness of A533B-1 Steel in the Transition Regime," NRL-R-10068(R), NRL Risley, United Kingdom Atomic Energy Authority, Warrington, Nov. 1988.

[15] McCabe, D. E., " A Comparison of Weibull and ~3tc Analysis of Transition Range Data," in Fracture Mechanics: Twenty-Third Symposium, ASTM STP 1189, R. Chona, Ed., American Society for Testing and Materials, Philadelphia, 1993, pp. 80-94.

[16] JSPS/MPC Round Robin on Fracture Toughness in the Transition Region, presented to the Japan Society for Promotion of Science and Materials Properties Council Task Group Meeting, Indianap- olis, IN, May 1991.

[17] Ingham, T., Knee, N., Milne, I., and Morland, E., "Fracture Toughness in the Transition Regime for A533B-1 Steel: Prediction of Large Specimen Results from Specimen Tests," ND-R-1354(R), United Kingdom Atomic Energy Authority, Risley, July 1987.

[18] Zerbst, U., Heerens, J., and Petrovski, B., "Estimation of Lower Bound Fracture Resistance of a Pressure Vessel Steel Based on Different Proposals," in Fatigue and Fracture of Engineering Mate- rials, Vol. 11, No. 11, Nov. 1993, pp. 1147-1160.

[19] McCabe, D. E. and Merkle, J. G., "Proposed Test Practice (Method) for Fracture Toughness in the Transition Range," presented to the ASTM Task Group E24.08.08, Nov. 1991.

[20] Zerbst, U., "Modification of the Single Specimen Model for Lower Bound Fracture Analysis,"

(submitted for publication, 1992).

Ted L. Anderson, 1 David Stienstra, 2 and Robert H. Dodds, Jr. 3

A Theoretical Framework for Addressing Fracture in the Ductile-Brittle Transition Region

REFERENCE: Anderson, T. L., Stienstra, D., and Dodds, R. H., Jr., " A Theoretical Frame- work for Addressing Fracture in the Ductile-Brittle Transition Region," Fracture Mechan- ics: Twenty-Fourth Volume, ASTM STP 1207, John D. Landes, Donald E. McCabe, and J. A. M.

Boulet, Eds., American Society for Testing and Materials, Philadelphia, 1994, pp. 186-214.

ABSTRACT: Fracture in the ductile-brittle transition region of ferritic steels is complicated by scatter, produced by local sampling effects, and specimen geometry dependence, which results from relaxation in crack tip constraint. Scatter and constraint are interrelated in that each influences the magnitude of the other. This article summarizes recent research on fracture in the transition region and presents 'a unified framework for addressing size effects and scatter.

A stress volume model for quantifying constraint effects is described briefly, and a comparison between theory and experiment is presented. This model has been applied only to stationary cracks in plane strain, but methods to account for ductile crack growth and three-dimensional effects are described.

The inadequacies of the weakest link model for cleavage fracture are discussed, and an improved statistical model is introduced. This new model considers the probability of propagation and arrest of cleavage microcracks.

A number of recommendations for analyzing cleavage fracture toughness data are presented.

Transition region data for a given material should be viewed as a statistical distribution rather than a single value. However, these data should be corrected for constraint effects and ductile crack growth before applying statistical analysis. One of several statistical distributions may be applied to cleavage data; each of the proposed distribution functions has advantages and disad- vantages. One of the unknowns in transition region fracture is the threshold toughness of the material, that is, the absolute lower bound.

KEYWORDS: ductile-brittle transition, elastic-plastic fracture, constraint, scatter, size effects on toughness, cleavage

Many ferritic steel structures operate in or near the ductile-brittle transition region, in which unstable cleavage fracture is a possibility. Consequently, it is necessary to quantify the fracture toughness of steels in this region. Obtaining meaningful data in the transition region is extremely difficult, however, because cleavage fracture toughness values are often highly scattered and are sensitive to the size and geometry of the test specimen. Thus the transferability o f laboratory toughness measurements to structures is dubious at best.

The scatter in transition region data is a direct result of the m i c r o m e c h a n i s m of fracture.

Cleavage in ferritic steels initiates f r o m microstructural features such as inclusions and grain 1 Associate professor, Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843.

2 Assistant professor, Department of Mechanical Engineering, Rose-Hullman Institute of Technology, 5500 Wabash Ave., Terre Haute, IN 47803.

3 Professor, Department of Civil Engineering, University of Illinois, 3140 Newmark Lab., Champaign, IL 61801.

Copyright9 by ASTM International

186 Www.astIII.0F~

ANDERSON ET AL. ON DUCTILE-BRITTLE TRANSITION REGION 1 8 7

FIG. 1---Relationship between cleavage fracture toughness and the distance between the crack tip and the cleavage trigger [1].

boundary carbides. The largest or most favorably oriented particle ahead of the crack tip often controls overall failure of the sample. The location of this cleavage trigger relative to the crack tip dictates toughness. If the critical particle is near the crack tip, the toughness is low, whereas a significantly higher toughness can be measured if the cleavage trigger is relatively remote from the crack tip; in some cases, a crack will grow by ductile tearing until it reaches a microstructural feature that is capable of triggering cleavage. Figure 1 illustrates this effect with data obtained by Hereens and Read [1]. The scatter in this data set is significant, with the highest and lowest toughness value differing by an order of magnitude. Note, however, that toughness correlates very well with the distance from the original crack tip to the cleavage trigger.

Size and geometry effects on transition region toughness often stem from a relaxation in stress triaxiality at the crack tip. Although cleavage is often referred to as "brittle" fracture, it can be preceded by large-scale yielding and ductile crack growth. This plastic flow relaxes the constraint at the crack tip, particularly in specimens with shallow notches and in geometries loaded in tension. Constraint loss can result in a significant (factor of 3 to 6) elevation of the apparent fracture toughness of the material.

Both problems associated with the transition region (that is, size effects and scatter) are interrelated in that each influences the magnitude of the other. For example, loss of crack tip constraint in finite specimens magnifies data scatter that originates from material variability.

Moreover, the crack tip sampling effects that produce scatter can lead to a statistical thickness effect in which a large specimen tends to exhibit lower toughness than a small specimen because the crack tip in the large specimen is more likely to sample a critical microstmctural feature.

In previous studies [2-6], the authors have addressed constraint effects and scatter separately.

The present article reviews this recent work and outlines a unified framework for treating transition region fracture.

Analysis of Constraint Effects

Anderson and Dodds [2-4] have developed a method for quantifying the effect of specimen size and geometry on cleavage fracture toughness. This approach involves detailed elastic- plastic finite element analysis, which resolves crack tip stress fields, combined with a local Copyright by ASTM Int'l (all rights reserved); Sat Dec 19 20:01:40 EST 2015

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LANDES ET AL. ON DETERMINING LOWER-BOUND TOUGHNESS 179