Relation between various fracture transition temperatures and the k1c fracture toughness transition curve

Engineering

Fracture

Mechanics

Vol. 23. No. 2. pp. 455-465.

$3.00 + .c!d 0013-7944/86 Q 1986 Pergamon Press Ltd.

1986

Printed in Great Britain.

RELATION BETWEEN VARIOUS FRACTURE TRANSITION TEMPERATURES AND THE KIc FRACTURE TOUGHNESS TRANSITION CURVE D. FRANCOIS Ecole Centrale des Arts et Manufactures, Grande Voie des Vignes, F 92290 Chatenay Malabry, France and A. KRASOWSKY Institute for the Problems of Strength, Ukranian Academy of Sciences, Kiev, UKSSR Abstract-A plane strain transition temperature for a given specimen thickness is defined for ferritic steels as the temperature along the K,c transition curve where the ASTM validity limit is reached. It corresponds to a ratio p of the thickness to (K&T,)* proportional to the plastic zone size, equal to 2.5. An empirical formula describing the K,c transition curve yields a relation between the plane strain transition temperature, yield point and the thickness, which depends upon the chosen value of p. For a given steel transition temperatures deduced from other tests such as the temperature corresponding to the initiation of stable tearing, the Charpy FATT, the NDT, the DWTT-FATT, were found to correspond to various characteristic values of the p ratio. This was checked using results found in the literature for different steels. This relation between a particular transition temperature and the thickness, which depends upon the shape of the K,c transition curve, the yield stress and the corresponding value of the p ratio, is useful to make predictions about the thickness and the strain rate effects. It can be used to deduce transition temperatures of various tests from the knowledge of either the K,c transition curve or from two other transition temperatures. It could provide a method to decide when the stress relief is needed after welding plates of a given thickness. It should also find its use in studying irradiation effects.

INTRODUCTION

ductile transition temperature has long been used in the design of steel constructions. The material must be chosen so that its transition temperature is low enough with respect to the minimum service temperature, the difference being a function of the degree of safety which is tolerated. Such an approach is typical of the Pellini[l] fracture analysis diagram and of a number of construction codes[2, 31. Many different tests were devised to find the transition temperature. The Charpy test is possibly the most widely used, but the drop weight tear test (DWTT)[4] and the Pellini test are also well developed. It is well known that the transition temperatures given by these various tests do not coincide. Moreover, in some cases, there is not a single definition of the transition temperature; for instance, in a Charpy test it can be the temperature for a given level of absorbed energy, or the fracture appearance transition, among others. These tests are only qualitative and they do not provide a possibility to predict the fracture of a given structure. Fracture mechanics, on the other hand, lead to a quantitative relation between the loading, the size of a defect and the material fracture toughness which allows to make such a calculation. Of course, conducting a Klc test is more complicated and costly than doing a Charpy test, and in many instances the size requirements cannot be met. The elastoplastic fracture mechanics tests such as the Jlc test or the COD tests are not so well established and they suffer anyway from the same cost drawback. For this reason various authors tried to find the Klc transition curve from other transitions curves, such as the one obtained with Charpy tests[5, 61. The relations which they proposed were established from correlations. They were often based on a comparison between the critical strain energy release rate and the absorbed energy in the other fracture tests. The main reason why there is a brittle-ductile transition is the lowering of the elastic limit a, when the temperature is increased. It leads to a large increase of the plastic zone size at the tip of a crack or at the root of a notch and to a loss of constraint. For a given test the

THE BRITTLE

455

456

D. FRANCOIS and A. KRASOWSKY

transition temperature should thus be related to the ratio between the thickness B and the plastic zone size which is proportional to (&la,)*. The aim of the present paper is to check this idea by comparing results obtained on various steels which could be gathered in the literature.

KK TRANSITION TEMPERATURE For ferritic steels Z& is an increasing function of the temperature. At low temperatures the fracture is by cleavage, whereas at elevated temperatures fracture is by shifts to ductile modes with dimples on the fracture surface. The same behavior is observed in dynamic tests and the Kid transition curve displays the same variation but is shifted to higher temperatures. The transition temperature along these curves can be defined as the temperature corresponding to a given level of Klc, 100 MPa/dm for instance, or to a specilied change in the fracture appearance. However, as we wish to find a relation between the transition temperature and the thickness it seems more appropriate to base the definition on the plastic zone size[7]. A rigorous formula gives the plastic zone size in plane strain at fracture as proportional to ( K,c/u,)*. As a, decreases when the temperature is raised, the plastic zone size becomes larger and larger. We define a parameter l3 which is the ratio between the thickness B of the specimen and (KJ ,I2 B = f3(K&J2.

(1)

Given a thickness B, for a chosen value of S we find a particular temperature on the Klc transition curve which we can define as the transition temperature (Fig. 1). For instance, we can decide to take p as equal to 2.5, which corresponds to the ASTM limit of validity for the thickness of KIc specimens. For a certain thickness B, we can find a plane strain transition temperature T&7], below which the plastic zone size is small enough for plane strain conditions to predominate and for tests to be valid. The transition temperature thus defined is a function of both the thickness B and of the chosen value of the l3 ratio. Quite similarly the same can be done along the dynamic Kid transition curve, obviously giving a higher transition temperature for the same thickness and the same l3 ratio as the Klc transition curve. The Klc transition curve can be approximated by various empirical formulae. For instance,

Fig. 1. Schematic representation

of the K,ctransition curve and the definition of the plane strain transition temperature Tps.

Fracture transition temperatures

4.57

and iu,, curve

300

B,mm

I ’ “8, 5 10 Fig. 2. Plot of the plane strain transition temperature

5

$2

c

5

T~3 versus log B for various steels[Y].

the following formula usu~ly[8] gives a good representation of the expe~ment~ data (see Table 1): Klc = A exp(Z’/TO).

(2)

Eliminating K;c between this formula and formula (l), B = ~~(KK/u,,)~leads to the transition tempe~ture ~TPsITo = Ln[(B/13)(uY/A)Zf.

(3)

This can be checked by plotting TPS against log B. Figure 2 shows that a linear relation is indeed observed in such a diagram. Choosing another value of l3 will simply shift the straight line keeping the slope constant. This slope To12is characteristic of a particular steel, and for another material it has no reason to remain the same. Figure 2 shows that this linear relation between the transition temperature and log B is also well verified in the dynamic case. The slope To/2 has no particular reason to be the same as in the static case. However, it is found that the two slopes differ but little for a given steel. Of course this approach has some limitations because it would be absurd to conclude from formula (3) that the transition temperature disappears when B becomes smaller than @(A/u,,)~ or that it increases to infinity when B becomes very big. It is valid only as far as the approximate formula (2) yields a meaningful representation of the & transition curve which was verified for thicknesses of practical interest in the range S-500 mm. It is known also that p = 2.5 is a very stringent requirement and that a smaller figure could be used in our case if so desired. Formulae other than the approximate formula (2) might be preferred. This would simply change formula (3) but the method described could still be used, and similar results would be obtained. OTHER TRANSITION TEMPERATURES The same diagram T versus log B can be used to plot various data which we could obtain in the literature. It must be pointed out that there are not many publications which give Krc

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1. Comparison

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References

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s-

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for k, = 0.8 x Id MPat/m

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Statics

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D. FRANCOIS

460

and A. KRASOWSKY

transition curves and transition temperatures from other tests together with the variation of u,, with temperature and strain rate. If they existed, we first drew the baseline for the TPStransition temperature against log B for the steel under consideration (Fig. 3). For each value of p a line parallel to this baseline could be drawn. We then plotted on the same diagram the data points corresponding to various other transition temperatures. Each one of them fell on a particular p line. In some instances we could obtain for a particular type of test the transition temperatures for various thicknesses. This allowed us to assign a l3 value to each type of transition, meaning that each one would correspond to a specific ratio of the thickness to the plastic zone size, whatever the phenomenon used to estimate the transition temperature (plastic zone evolution, crack initiation or propagation). We first defined Ti as the transition temperature in a Klc test corresponding to the initiation of some stable tearing[7]. This could be detected by observing, for instance, the fracture surface near the precrack tip. The advantage of this technique is that it can be used in dynamic as well as static tests. It is expected that this transition temperature Tj should correspond to a p ratio smaller than 2.5, because stable tearing occurs when there is sufficient plasticity. As the experiments were performed only at a few definite temperatures, there remained some margin of uncertainty about Ti. We then plotted the fracture appearance transition temperature (FATT) in a Charpy test. It is natural to think that 50% of crystallinity should correspond to some l3 ratio of the thickness to the plane strain plastic zone size. In this respect it may be less legitimate to use a transition connected to some value of the absorbed energy which could not be so directly related to the plastic zone size because of differences in fracture toughness for different steels. The NDT temperature is another type of transition temperature which is often used. In a Pellini test, which value of the thickness should enter the formula was in question. As the standard specimen has a ligament which is smaller than the thickness, we decided to use the characteristic dimension, as it is the one which first leads to a loss of constraint of the plastic zone.

.c K

,

Transition temperature TS NpOT TdOWTT)

4oc

Tsy( f=ATT f TAO

300

200

l_TSO(~WTT) +_ NOT u _T50

(Charpy)

1oc Fig. 3. Plot of dynamic transition tempemtures versus log B for a Soviet low alloy pressure vessel steel.

Fracture transition temperatures

and K/c curve

461

The transition temperature from DWTT is again related to 50% of crystallinity. However, this was quoted only in one publication[71. We also plotted the transition temperature TD, which in smooth tensile tests corresponds to the point where the a, and the cru curves versus the temperature join together, and so corresponds to the disappearance of the ductility. In that kind of test the diameter of the specimen was taken as the parameter B. Lastly, in some instances we used J Ic or Jld tests results. In that case we plotted the transition temperature points corresponding to the limit of validity B 2 50(Jlc/uy). RESULTS Figure 3 puts together the results which were obtained in dynamic tests on a particular steel, a Soviet low alloy pressure vessel steel[7]. The Tps baseline is drawn from tests made in the thickness range 5-40 mm, and it once more display the good approximation given by formula (3). The Pellini NDT corresponds to a lower l3 ratio, about 1.5, which means that in that case the ligament length needs not reach the ASTM limit to provide a sufficient plastic constraint. The DWTT tests were performed with several thicknesses, and it is very interesting to note that the data points all fall on the l3 line corresponding to p = 0.6. This makes plausible the hypothesis that the 50% FATT in this kind of test corresponds to a given ratio of the thickness to the plane strain plastic zone size. The Ti data points, taking into account the above-mentioned uncertainty, fall along the same line and would correspond to a l3 ratio somewhere between 0.3 and 0.7. As expected from the small size of the specimens the FATT from the Charpy curve corresponds to a lower l3 ratio equal to 0.4. Lastly, some JId results could also be plotted. They fall on a low p ratio line somewhere between l3 = 0.1 to 0.2. These l3 values could now be taken as the characteristic ones for the various transition temperatures and various steels. Figure 4 shows the data points obtained for the same steel in static tests. There are somewhat fewer points than on the previous figure. However, the Ti

300

200.

l-h

1OCl

o -Tps o--To

0 Fig. 4. Plot of static transition temperatures

versus log B for a Soviet low alloy pressure vessel steel.

462

D. FRANCOIS and A. KRASOWSKY

points are in the same range as before and so are the Jrc transition points. It is interesting to note that if Klc = mc/(l - u’)) then the p ratio for these transition points would be equal to (1 - v*)5Ou,/E, where E is the Young’s modulus. This ratio m,,/E is equal to 3 x 10s3 as an average, yielding l3 = 0.15, which is what was obtained, However, it is temperature dependent and it is the reason why p is not constant for the transition so defined. If our approach is correct formula (3) should be good for all the steels. Each one would be characterized by a particular set of To and A values and by its yield stress, and each particular transition temperature by the thickness of the specimen and the l3 ratio. Caution must be taken, however, to include the materials parameters TO, A and a, taken at the strain rate induced by the test under consideration. On Fig. 5 we plotted all the points which we could find in publications where sufficient data were given to calculate the transition temperature with formula (3). This formula is in fact an implicit expression to calculate the transition temperature because Us is temperature dependent. Successive approximations proved to converge quickly. We used the p ratio values deduced from Fig. 3. In many instances we could not start from a single Krc transition curve but rather from two envelopes. Figure 5 is a comparison between the calculated and the observed transition temperatures. It shows that a very reasonable one-to-one correlation is obtained. The dotted lines are drawn through the most extreme results. It seems that this correlation is good to -r5o”C. It might be argued that this not a good enough approximation to be of any practical use. In all our calculations we used actual experimental data which we found in literature. But it is necessary to say that it is usually impossible to find there the data which correspond exactly to the same conditions in the tensile and the fracture toughness tests (for instance, the same strain rate). However, in some cases it is not difficult to predict the direction in which the calculated transition temperature should be moved if a correction was made. For example, in the case of both unirradiated and irradiated A508 cl.3 steels from the work by Soulat and Petrequin[l8] we used the yield point temperature dependence for the same steel from Ref. [19], where this dependence is given for a strain rate equal to 17.6 s-‘. The yield points at room temperature for unirradiated material also corresponds well to each other in these two works. But conditions at the crack tip in the Charpy tests correspond to much higher strain rates and to higher yield points.

Fig. 5.. Comparison between observed transition temperatures and the corresponding culated from formula (31, ZT,IT, = Ln(~/~~~u,/A 1’.

ones cai-

Fracture transition temperatures

and K,c curve

463

This strain rate effect correction would move the calculated transition temperature to the right. In such cases we pointed out this possible shift by the arrows at experimental points of Fig. 5. This shows the possibility of a significant reduction of the scatter band. Now we would like to show that this method can be of some value in spite of this uncertainty .

POSSIBLES USES OF THE TRANSITION TEMPERATURE CORRELATION We obtained an expression [eqn (3)] which relates the various transition temperatures to material parameters To, A and uY. This provides us with the possibility of predicting the effect of different variables. Thickness effect

The transition by the expression

temperatures

T, are simply related to the logarithm

T,, - Tt2 = (T0/2) Ln(Bi/&).

of the thickness

ratio

(4)

It is easy to show that in the thickness and temperature range of practical use the variation of the yield stress with temperature is sufficiently small so that Ln(uYi/uYz) is negligible. This relation is well displayed in Fig. 3. The knowledge of To, deduced from the Klc transition curve, is not needed, if the transition temperatures can be determined for two different thicknesses B, and Bz. Then

Tr - T,I Tr2

Loading

-

T,I

=

Ln BIB, Ln B21B1

rate effects

These effects are more complicated to predict because TO, A and a, are all strain rate dependent. However, it was found that, in the instances where it could be checked, TOand A varied only slightly with the strain rate. If this variation is neglected it follows that the transition temperature is inversely proportional to the logarithm of the stress intensity factor rate &, a relation which was indeed found in some cases[ 19, 71. Transition temperature

from different tests

For a given steel the formula (3) yields

T,I - T,2 = (TO/~)Ln[(B~~&MMP~)I.

(6)

In this way it is possible to predict a particular transition temperature from the knowledge of another one. Or again, when the Klc transition curve is missing one could use

LnWBI )(I%43

T, - T,I Tt2

-

T’,I

=

Ln(Bd& )(P1/Pd

(7)

to deduce the transition temperature from the knowledge of two other ones, for instance the Charpy FATT and the NDT, in which case pi would be equal to 0.4 and pZ to 1.5. This kind of consideration might have some bearing on stress relieving practices: When residual stresses are present in a structure, their elimination by a thermal treatment is not needed if there is sufficient plastic deformation before fracture to swamp them out. For a certain thickness this would imply a large enough plastic zone size at fracture, that is to say, a certain l3 ratio. The formula (7) could then be used to estimate, according to the minimum service temperature of a structure, the thickness below which stress relieving could be avoided from the knowledge, for instance, of the Charpy FATT and of the Pellini NDT.

En4 23:2-r

464 Deducing

D. FRANCOIS and A. KRASOWSKY the KIc transition curve from other tests

From formula (3) it appears that the parameters A and To can be calculated when two transition temperatures are known corresponding either to two different thicknesses or to two different kinds of tests (i.e. of l3) or both. It is of course also assumed that the temperature variation of a, is also known. This can be very useful when Klc tests to assess critical defects sizes are difficult or impossible to perform. A somewhat similar proposal was put forward by Sanz and Marandet, who correlated the KIc transition curve with the Charpy one, using a different procedure based on fracture energy considerations. Our method appears to be based on more direct relations with the plastic zone size and seems to be much more flexible, since it can use types of tests other than the Charpy. Conversely, of course, formula (3) provides a way to estimate any transition temperature from the knowledge of the Klc transition curve. Prediction of irradiation effects

Irradiation effects will change To, A and cry. It is not feasible to measure Krc transition curves on irradiated steels for nuclear pressure vessels. However, it is quite possible to obtain the Charpy FATT in that case. Another transition temperature would be needed, to deduce To and A for irradiated steels. The To temperature could be measured because it requires only small specimens. It could also be determined on notched cylindrical specimens with the advantage that the transition temperature would then be higher and thus more easily obtained, It remains to show that they would give a l3 ratio sufficiently different from the Charpy FATT to yield a good enough precision in the calculation of A and To.

CONCLUSION From the analysis of published results on various steels, it appears that the transition temperatures for different tests and for different thickness B are given by the formula T, = (TO/~) LnWP)(uy/A)21, where a,, is the yield stress taken at the strain rate for the test under consideration and A and To are parameters which approximate the Klc transition curve through the formula KIc = A exp(T/Td.

l3 is the ratio of the thickness to the plastic zone size, which takes the value 2.5 for the ASTM plane strain transition, 1.5 for the NDT, 0.6 for the 50% DWTT-FATT, 0.4 for the Charpy FATT, 0.3 to 0.7 for the initiation of stable tearing and 0.1 to 0.2 for the limit of validity of the Jlc test. In spite of the fact that from the published data it was not possible to ascertain the above formula with very good accuracy, it was found to be helpful in making various predictions. Thickness and strain rates effects can thus be found with a minimum number of tests, and the various transition temperatures can be deduced from one another. In particular, the K,c transition curve can be approximately deduced from a knowledge of two transition temperatures obtained with either two thicknesses or two different kinds of tests. REFERENCES [l] W. S. Pellini, Evolution of engineering principles of fracture safe design of steel structures. Naval Research Laboratory, report 6957 (1969). [2] Reglement pour la construction et la classification des plates-formes marines-caracteristiques et contr6le des materiaux. Bureau Vtritas Paris (1980, mise a jour 1982) et normes NF A 36-205, NF A 35-501, NF 36 201, BS 4360. [3] Code of practice for fixed off-shore structures. British Standards Institution BS 6235 (1982); Rules for the design, construction and inspection of off-shore structures. Den Norske Veritas (1977). [4] Standard methods for drop-weight tear test of ferritic steels. Annual Book ofA.STM Standard, part IO, E-436-74 (1980) pp. 602407. [5] R. Hertzberg, Deformation and Fracture Mechanics of Engineering Marerials. Plenum Press, New York (1976).

Fracture transition temperatures

161F. J. Witt, Fracture Parameters

Obtainedfrom

Precracked

and Ktc curve

Charpy Tests: State of the Art and Beyond.

465 C.S.N.I.

Specialist Meeting on Instrumented Precracked Charpy Testing. NP 2102-LD. Res. Proj. 1757-l. CSNI No. 67, Prof. (Nov. 1981). Palo Alto, CA, Dec. 1-3 (1980) pp. 4-131. 171 A. J. Krasowsky, Y. A. Kashtalyan and V. N. Krasiko, Brittle to ductile transition in steels and the critical transition temperature. Int. J. Fracture 23, 297-315 (1983). 181 K. Ikeda and H. Kihara, Proc. 2nd Int. Conf. on Fracture (Edited by P. L. Pratt et al.). pp. 851-867. Chapman & Hall, London (1969). [91 Practical Fracture Mechanics for Structural Steel. London, U.K. Atomic Energy Authority (1969). [lOI J. M. Benson and S. T. Rolfe, Ku transition temperature behavior of a 517-F steel. J. Engng Fracture Mech. 2, 341 (1971).

[III T. G. Heberling and E. Selby, Impact Testing of Metals. ASTM STP 466, pp. 224-240 (1970). [121 T. Iwadat;, Y. Tanaka, S. Ono and J. Watanabe, An analysis of elastic-plastic fracture toughness behavior for J/C measurement in the transition region, Elasto-Plastic Fracture Mechanics. ASTM STP 803, pp. 531-561 (1983). [I31 H. Tsukuda, T. Iwadata, Y. Tanaka and S. Ono, Static and dynamic fracture toughness behavior of heavy section steels for nuclear pressure vessels. J. Mech. Engng 369-374 (1980). iI41 B. Marandet, G. Philippeau and G. Sanz, Influence of loading rate on the fracture toughness of some structural steels in the transition regime. IRSID, RE 908 (juillet 1982). pour cuves de [ISI A. Menard and G. Rousselier, Etude de I’acier faiblement allie au manganese-nickel-molybdene reacteurs a eau ordinaire sous pression approvisionnt sous la forme d’une plaque forgee de 250 mm d’epaisseur aupres de la societt Creusot-Loire- 2eme partie: essais de mecanique de la rupture Km et Jic. HT/PV D.464 MAT/T.43-Electricite de France, Departement Etudes des Materiaux (fevrier 1981). H. Kotilainen, The micromechanisms of cleavage fracture and their relationship to fracture toughness in a bainitic low alloy steel. Techn. Res. Centre of Finland, Mat. a Proc. Technology 23, VTT ESPOO (1980). B. Marandet and G. Pluvinage, Influence de la vitesse de chargement sur la tenacite a rupture d’un acier SA 508 cl. I dans le domaine de transition. Rep. 81-P-0721, Materiaux, Univ. de Metz et IRSID (avril 1984). P. Soulat and P. Petrequin, The effect of irradiation on the toughness of pressurized water reactor vessel steels in different service conditions. Department of Techn., Applied Metallurgical Research Service, Mechanical Metallurgy Service, C.E.A., Saclay, France (May 1983). [I91 G. S. Pisarenko and A. J. Krasowsky, Proceedings of 1971 International Conference on Mechanical Behavior of Materials, Society of Material Science Japan, Kyoto (1972) pp. 421-432. (Received

7 January

1985)