Minimum number of specimens to characterize fracture toughness in the ductile-to-brittle transition region

Minimum number of specimens to characterize fracture toughness in the ductile-to-brittle transition region

EmgheerbtgFractureMetics Vol.41,No. 3,pp.451-%3, 1994 Copyright 0 1994Elsevierscieace Ltd. Printed in Great Britain. All rights reserved 001E7944/94...

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Vol.41,No. 3,pp.451-%3, 1994

Copyright 0 1994Elsevierscieace Ltd. Printed in Great Britain. All rights reserved 001E7944/94 1.00 + 0.00

TECHNICAL NOTE MINIMUM NUMBER OF SPECIMENS TO CHARACTERIZE FRACTURE TOUGHNESS IN THE DUCTILE-TO-BRITTLE TRANSITION REGION J. E. PEREZ IPIfiA and S. M. C. CENTURION Fracture Mechanics Croup, School of Engineering, U.N. Comahue, Buenos Aires 1400, ZC8300, Neuquen, Argentina E. P. AS-I-A UTN Reg. Haedo, Paris 543, Haedo. Argentina Ahatraet-A study of the quantity of specimens necemary to evahtate the fracture toughness in the dutile-to-brittle transition region is presented in this work. An analysis of Iwadate cr ul.‘s proposal is made from a dimensional point of view to fulill the Ka- mquirements. A verification of Wallin’s proposals is also made. An experimental validation of the different proposals is made using series of up to 36 specimens. Finally, a reinterpretation of the ductile-to-brittle transition curve is proposed, considering a better understanding of the different phenomena that occur and their close correction.

INTRODUCTION FRACTURE TOUCWNES in metals and alloys with body-centered cubic (bee) structures, such as ferrite steels, exhibits a transition region. This region is confined by a cleavage fracture lower shelf at low temperature and a ductile tearing upper shelf at higher ones. The transition region phenomenon is directIy related to yield stress, increasing when the temperature decmams, making tensile stresses reach suiBcient values to start the brittle fracture process near the crack tip. A larger strain hardening to set in motion the cleavage mechanisms in the superior transition region than in the inferior one will be necemary. This means a bigger plastic deformation, which may include some stable crack growth. In the transient region, a specimen test will show a typical nonlinear load-displacement record due to plasticity followed, in some cases, by stable crack growth before the cleavage failure abruptly interrupts the test (Fig. 1). The area below the test curve can be evaluated by means of the J-integral, using Jc or the cleavage J parameter. Cleavage and ductile fracture seem to be in some way independent events, so that either before or after Jlc, cleavage may occur at some point of the R-curve. Paris et al. [l] defme the cleavage fracture on a microscopic scale as a material local instability phenomenon, while ductile instability is associated with the global conditions of the system, such as compliance and geometry. In Fig. 2, the categories of transition fracture toughness behavior can be observed 12). The transition xone verifies a sixe effect so that average fracture toughness values of small specimensarehigherthan those of other, larger specimens of the same material [2]. The transition phenomenon is intended to be interpreted by two theories. One of them explains this behavior due to a reduced constraint in small specimens, showing consequently higher fracture toughness average values [3]. This theory just&s the British Standard Institution method for crack opening displacement testing [4], where it is suggested that constraint conditions are completely simulated on the specimen when the same servioe thickness is used. The second theory was introduced by Landes and Shaffer [2]. They proposed a statistical model based on the large scatter of small thickness fracture tests. According to these authors, fracture toughness along the crack front is not constant, so the instability will not be represented by the average value but by the minimum toughness point. Largespecimens would have a higher probability of finding low toughness points than small ones, therefore less experimental scatter would be obtained. The lower extreme scatter would deal with different specimen sixes. La&es and Schatfer [2] apphed a two-parameter Weibull distribution function to Jc results from small specimen tests. They have predicted the fracture. toughness distribution for large specimens by means of calculated parameters. Unfortunately, Jc mean values tend to xero for very large sizes when the two-parameter model is applied. It is evident that a fracture toughness lower bound occurs, although the specimen size grows inddinitely. This lower bound limit may be taken into account through the third W&bull parameter [5]: (1)

where f3= J,, + C, C = scale factor, b = Weibull slope, Jo = threshold parameter and N = sia factor. 451


Technical Note





Fig. 1. Typical nonlinear load-displacement


Fig. 2. Categories of transition fracture toughness behavior.

Then, after determining the C, b and J,, Weibull parameters according to eq. (1) using small test specimen values, we can calculate the statistical distribution of results given by tests on N size ratio specimens by means of eq. (2). Therefore, by testing small specimens the fracture toughness in larger specimens can be found (Fig. 3). On the other hand, Wallin [6] proposed the following function: P, = 1 - exp[ - const B Kfl


which corresponds to a Weibull distribution with a fixed shape parameter. Then, and through the inclusion of a third parameter, K,,, we get (4) in conjunction with a stable crack growth and a large scale yielding correction. The statistical theory seems more adequate for experimental values than the one based on a constraint criterion, although there are still some aspects unsolved concerning the minimum number of specimens and size effect when there is no geometrical similarity. Iwadate et al. [7] stated that a 4T-Cf specimen has on its crack front four times the properties corresponding to a IT-CT specimen. Therefore if the total crack front length corresponding to all small fracture fronts is equivalent to the specimen length that makes K,= valid, the minimum fracture toughness value, KJ,,,s,, would be consistent with the valid K,c. They sought the specimen number to assure a minimum Jc value (KJ,,) equivalent to K,= and with a suitable scatter grade. They divided the transition zone into two regions (I and II), which are shown in Fig. 4. The following relationships were defined for each one: Region I

NB 2 3000 J&S,


Region II

NB 2 1000 Jcmin/Su.


According to these authors, these expressions assure a crack front between four and five times the value corresponding to a K,= valid test. A study on the minimum necessary quantity of specimens to characterize the fracture toughness in the transition region is done in this work.

Fig. 3. Distribution of Jc instabilities for small and large specimens.

Fig. 4. Transition region characterization a/.‘~ proposal [7].

from Iwadate et


Technical Note Tahle 1. ADN42.

36 soecimens

Group 1

Group 2

Group 3

Group 4

Group 5

Group 6

6.12 86.77 72.64 14.27 69.89 9.34

13.2 128.41 327 46.85 256.18 186.24

174.35 416.81 55.02 333.21 22.4 133.58

168.57 360.79 20.2 264.17 19.24 91.31

219.52 339.08 236.76 276.64 50.31 13.36

92.13 147.92 320.44 30.8 35.48 49.09

MATERIALS AND METHODS Thirty-six tests have been made using I/ZT-CT specimens on ADN42 steel with annealing heat treatment at 780°C for 2; hr followed by furnace cooling. This treatment was performed in order to increase the material fracture toughness at room temperature, because before the heat treatment it showed K,, valid values [8]. The specimens were obtained by cutting bar segments 44 mm in diameter according to ASTM E-8 13. The tests were performed on a 100 kN Amsler screw machine with displacement control. The testing results were evaluated by means of a Weibull distribution of three parameters for groups of six, 12, 18. 24, 30 and 36 specimens with 63 determinations. Previous results obtained on 20MnMoNi55 and ADN42 (without heat treatment) steels [8,9] and others taken from several authors m were also evaluated. Our results and the ones from the literature were plotted in order to find the convergence of threshold values (I,,) and minimum Jchin values for the different parameters under analysis. The sets of data of ADN42, A470, A508 and 2OMnMoNiSS steels were also analyxed following Wallin’s proposal [6]. Many combinations verifying stable growth corrected sets of data and sets of data without stable crack growth were done.

RESULTS Table 1 shows ADN42 testing results. These were separated in six groups of six tests each. These groups were established according to the testing order. Figutes 5-9 show the following graphs: J c-mm vs J or,,” vs Jo vs Jo vs

NBs,IJ,, NBS;lEJ,, NBS,/J,, NBS;@&,,

Jo vs


for annealed ADN42 steel results. Similar estimations and graphs for other material series were made. Convergence values were found using a &20% criterion according to Iwadate ef af. [7]. Table 2 shows these values, the serial specimen numbers and the minimum test number required by eq. (4). indicating those series where the convergence is fully fitted for larger specimen numbers than the one given by eq. (4). Figure 10 shows the graph belonging to Wallin’s proposal for the ADN42 set of data with stable crack growth correction.


0, 0


Fig. 5. Convergena


of I,,


related to NBS,/J,,



for ADN42 steel.

Technical Note

Fig. 6. Convcrgcnce of Jchi. related to NB(S,>2/EJ,for ADN42 steel.

Fig. 7. Convcrgcncc of JO related to NBS,//,,for ADN42 steel.

DISCUSSION Onthephciple of the statistical model, the microawpic heterogeneity hypothesis of fracture toughnus along the crack front takes place. Iwadatc cr al. [7j cxphined that due to the expcrimcotal scatter they found that the thickness corresponding to the &valid test was enough, and they prow cqs (5) and (6) to guarantee a crack front between four





A0 = =. 10












Fig. 8. Convergence of Je rclatod to NB(S,y/'Iu,for ADN42 steel.


Technical Note

Fig. 9. Convergence of J, related to the specimen number for ADN42 steel. Table 2 Material ZOMnMoN,SS, ADN42, series ADN42, series ASDB, 20°C A479, 100°C ADN42, series

6B, C 2 1

Test number

Jcminvs NBS, /Jw

:: 19

22$& 12,ooot

3u3E 15:OOO

557 30


12% 14:OOOt

5WO 15,000 18,000




Nd for Iwadate

N, for J,, f 20%

65 I1 30

252 4

25 18 15


14 45

E 30


tDoes not agree with eq. (6). and five times that necesmry to obtain a &-valid test. It is supposed that the microscopic heterogeneity in fracture properties is represented on this crack front kngth. In the first place, the consistency of the hypothesis must be analyzed. The minimum thickness condition for i& is: B > 2.5 (K,&)z.


It is given in order to obtain a small scale plasticity and predominant plane strain state. The reason for low scatter in the lower shelf zone is probably not due to the microscopic heterogeneity represented by the crack front, but to a smaller competition between the ductile and brittle mechanisms. If this hypothesis, that “the crack front length has to be larger than the necessary crack front kngth to obtain a valid K,c” is true, the following will have to occur: NB b B 2 2.5(K,,/S,)’


K2=U (9)

Fig. 10. ADN42 with stable crack growth correction (Wallin’s proposal).


Technical Note


Fig. 11. Crack fronts that really contribute to brittle fracture.

which is different from Iwadate et al.‘s proposal. Taking E/S, values between 1000 and 210, it is found that iVE(Iwadate) obtained from eq. (6) is: 0.4 E, < NB, < 1.9 B,,


where B, is the minimum thickness for a &-valid value and NE, is Iwadate’s equivalent crack front length. For relatively low yield stress materials, eq. (6) is not conservative. Furthermore, if we consider that the crack front that really contributes to the brittle fracture is that corresponding to the thickness minus the shear lips, we have NB,,, < 8, (Fig. 11). Landes and McCabe [5] suggested a transition region evaluation by means of a three-parameter Weibull function, defining a lower bound fracture toughness value called the threshold parameter, J,,. Its use is more reliable than the minimum values of each specimen series. To establish the reliability grade of the threshold value, it is necessary to guarantee, for the adopted distribution function, that the scatter values of the fracture toughness on the tested series must be representative of microscopic heterogeneity. This condition will only be satisfied by a minimum specimen number. It can be observed in Figs 5-9 that the scatter of threshold values, J,, is a consequence of small representative samples and insufficient specimen numbers. When the test number is increased, not only does the J, scatter decrease, but also the average value. One column of Table 2 shows NBS,,/J,, values for which the Jmi, scatter is less than 20%. In the three series of ADN42 and A470 to IOO’C, these values are beyond the 1000 limit given by eq. (6). On the other hand, Jo vs NBS:/EJ,,, graphs also present an important scatter for convergence values to J,, + 20%. This indicates that scatter in the characterization of the threshold parameter cannot be represented by performing a number of tests corresponding to the equivalent crack front for valid K,,. The convergence verifies the summaries of crack fronts between four and 26 times that necessary to obtain a valid Klc. Observing the column corresponding to specimen number, from which the scatter of J, values is less than 20%, it presents similar values for different materials, between 15 and 30 specimens. Therefore, this indicates that scatter is not controlled by the same variables as K,=. In Iwadate et al.‘s work [7] and ours, the data convergence method was used to represent the Jo value, for instance, Jo vs the number of specimens. This method is inconvenient in that for many sets of data we are forcing the convergence towards a determined value. For example, we can say that if 100 specimens are analyzed in groups and all the possible combinations are studied, as we increase the number of specimens in each group we will be increasing the data average as well. This will force the convergence in a determined way, taking the dispersion to zero when analyzing the 100 specimens. On the other hand, when proving Wallin’s proposal [6] with our and other authors’ sets of data, an inconsistency or Ji values were negative. This is physically impossible. appears some

d Fig. 12. Ductile-to-brittte

transition curve reinterpretation.


Technical Note



According to experimental evidence, we can reinterpret the ductile-to-brittle curve, which allows us to consider the scatter of the results and the occurrence of the different fracture modes at the same temperature. We do not propose one curve but the area covered by two curves (Fig. 12). One of them, the “lower bound”, which is a material characteristic, corresponds to the different J, threshold values that the material presents at the different transition temperatures. The second curve, the “upper bound”, corresponds to the scatter’s upper end and it is as a function of the thickness. Large specimens will give a thin transition area, while small ones will widen the scatter band. For this transition region, and according to Fig. 12, we can define several temperatures which establish the sub-zones that are described below: for T < T, for TA < T occur after for T, < T growth. In for Tc i T load point for T > T,

there will be brittle fracture without stable crack growth. < Ts there will be brittle fracture without stable crack growth in some specimens. On others brittle fracture will

some crack growth. < Tc some specimens will present cleavage without crack growth. Others will give cleavage after some crack

other specimens the maximum load point will be exceeded without brittle fracture. < T, there will be brittle fracture in some tests, but always with stable crack growth. In others the maximum

will be exceeded without cleavage. there will be no cleavage before maximum load for any specimen.

As the upper bound Jc curve is a thickness function, due to the fact that it represents the maximum values of scatter temperatures, T,, T, and Tc will also be functions of thickness. They will be close to T, for larger thickness. The lower bound curve is a material property, being thickness independent.

CONCLUSIONS On the basis of the analyzed results, there is no direct relationship between crack front length, corresponding to a valid test, and the statistical characterization of fracture toughness in the ductile-to-brittle transition zone. In several cases, the minimum number of specimens predicted by Iwadate er al., eq. (6), is lower than that necessary to have a representative Weibull distribution of experimental scatter values. A quantity between 15 and 30 specimens Seems to be necessary, independent of material characteristic values such as toughness and yielding. More research work on this subject to extend these conclusions over a larger range of materials, sizes and temperatures should be performed. More research should also be done in order to see to what extent that quantity between 15 and 30 specimens is enough or if it is a result of the forced convergence on 20-36 specimens. However, it is not practical to perform many tests in order to obtain only one point on the ductile-to-brittle transition curve. On the other hand, using many sets of data, Wallin’s proposal is not physically consistent in some cases. Finally, a reinterpretation of the transition curve was made, where an upper curve (thickness dependent) was introduced so that it represents the maximum scatter values, explaining how either cleavage with stable crack growth or maximum load values without fracture can occur at the same temperature. &

REFERENCES [1] P. C. Paris, H. Tada, A. Zahoor and H. Ernst, The theory of instability of the tearing mode of elastic-plastic crack growth. ASTM STP 668, 5-36 (1979). [2] J. D. Landes and D. H. Schaffer, Statistical characterization in transition region. ASTM STP 700, 368-382 (1980). [3] M. G. Dawes, Developments in Fracture Mechanics I, pp. 368-382. Applied Science, London (1979). [4] B.S. 5762, Methods for crack opening displacement (COD) testing. British Standard Institution (1979). [S] J. D. Landes and D. E. McCabe, The effect of section size on the transition temperature of structural steels. Scientific Paper 82-ID-Metal-P2, Westinghouse RD Center (1982). (61 K. Wallin, Statistical modeling of fracture in the ductile to brittle transition region. European Symp. on Elastic-Plastic Fracture Mechanics: Elements of Defect Assessment, Freiburg, Germany (9-12 October 1989). [7] T. Iwadate, Y. Tanaka, S. Ono and J. Watanabe, An analysis of elastic-plastic fracture toughness behavior for J,, measurement in the transition region. ASTM STP 803, 531-561 (1983). [8] E. P. Asta, J. E. Perez Ipitia and M. Zalazar, Tenacidad a la fractura en barras de acero dureza natural. Proc. Jornudas Metaltkgicus, SAM, La Plata, pp. 318-321 (16-20 May 1988). [9] J. E. Perez Ipiiia, E. P. Asta and H. L. Toloy, Funcion estadistica de Weibull en tres pammetros aplicada a resultados de ensayos de tenacidad a la fractura elastoplastica en la region de transition ductil-fragil. &gun& Coloquio Lutionoamericano en Meccinica y Micromecanismos de Fractura, Santiago, Chile (20-24 October 1986). (Received

24 February