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Modelling of the Charpy test as a basis for toughness evaluation
From Charpy to Present Impact Testing D. Franqois and A. Pineau (Eds.) 9 2002 ElsevierScience Ltd. and ESIS. All rights reserved
45
MODELLING OF THE CHARPY TEST AS A BASIS FOR TOUGHNESS EVALUATION W. SCHMI'Iq', I. VARFOLOMEYEV, W. BOHME Fraunhofer-lnstitut for Werkstoffmechanik, Freiburg, Germany
ABSTRACT Micro-mechanical material models are applied for the evaluation of fracture toughness properties from results of instrumented Charpy tests. In the first example the ductile fracture resistance of a weld material from the irradiation surveillance of a nuclear pressure vessel is determined. The initiation values were converted into pseudo plane strain fracture toughness values and used to adjust the ASME reference fracture toughness curve. The second example summarises modelling efforts towards the description of the cleavage-toductile transition region of a ferritic steel. Here, the Beremin model revealed substantial deficiencies concerning the transferability of the results between different specimen types and temperatures. Modifications of the failure models considering the failure mechanisms observed seem to improve the situation. In order to give some additional insight into stress and strain fields in Charpy and fracture mechanics specimens, preliminary results of a study with irradiated weld material will be presented. This study aims at the assessment of upper shelf toughness curves, however the existing numerical models are also applicable for the determination of the stress and strain fields in Charpy specimens tested in the transition temperature regime.
KEYWORDS Charpy V-Notch specimen, instrumented Charpy test, numerical simulation, GTN model, cleavage fracture, ductile fracture
INTRODUCTION Ferritic steels show cleavage fracture with low fracture toughness at low temperatures and ductile tearing with higher toughness values at higher temperatures. In the transition temperature region both failure modes co-exist and compete. The transition temperature is characteristic for the material, but it depends strongly on the testing conditions. For about a century the Charpy impact test [ 1] has been used as an acceptance criterion to determine the transition temperature of different materials. In its original and later standardised
46
w. SCHMITT, I. VARFOLOMEYEV AND W. BOHME
form the basic result of the test is the consumed energy. In a pendulum test equipment this energy is easily evaluated from the difference of the pendulum angles before and after impact. Testing specimens at different temperatures and plotting the consumed energy versus temperature yields a KV(T)-curve from which the transition temperature can be determined. For materials relevant for nuclear installations a fracture toughness curve Kxc(T- RTr,mx) was introduced as a lower bound of many valid fracture mechanics tests. The curve has a unique shape. The position of the curve with respect to the temperature axis is defined by the nilductility reference temperature RTr~D-r,which is determined from drop weight (Pellini) and Charpy tests. The shift of the reference temperature, ARTNDx, due to embrittlement, e.g. by irradiation, is monitored by the respective shift in the Charpy energy vs. temperature curve, KV(T), taken at a certain level of energy. Although fundamental differences exist between the Charpy impact test and fracture mechanics tests many efforts have been undertaken to correlate Charpy energy or the KV(T)-curve with the fracture toughness KIc (e.g., [2,3,4]). These empirical co-relations require large efforts in comparative testing and have, in principle, only limited applicability for a small group of materials. The most frequent application of the Charpy test for the assessment of pressure vessels is that the Charpy transition temperature is used to adjust the fracture toughness reference curve KIR(T). By applying calibrated strain gauges onto the impacting tub it has later become possible to measure force vs. time curves, thus providing more quantitative information about the test. Now it became not only possible to estimate the dynamic yield stress [5]. Under certain conditions it was also possible to estimate the fracture stress [5,6,7,8] analytically. Above all, results of instrumented Charpy tests provide an excellent basis for numerical simulations. Those numerical simulations started with Norris [9] as early as 1979 and have since become more and more elaborate.
EVALUATION OF UPPER SHELF TOUGHNESS VALUES The material under investigation in this study [10] was a weld material out of the irradiation surveillance. The goal of the study was the assessment of a ductile J-resistance curve through the application of the Gurson-Tvergaard-Needleman (GTN) model [11,12,13,14]. From the surveillance programme the load vs. time records of a series of Charpy tests were available. The Charpy energies of these tests are plotted versus temperature in Fig. 1. One test at 100~ (see circle mark) was selected for the evaluation. To complement the data base a sub-sized smooth tensile specimen (diameter 2.6 mm) and four side-grooved SE(B)-specimens (4.9x4.9x24.5 mm 3) were fabricated from broken halves of Charpy specimens and tested at 100~ in the DAP accredited testing laboratory Hot Cell Erlangen of SIEMENS. Figure 2 shows the comparison of experiment and simulation of the tensile test. From the analysis the static stress-strain curve and the GTN parameters are determined. These parameters were now used to simulate the Charpy test. To describe the strain rate dependency of the flow stress, cra (~r the following equation was used
_=
:_e_
~
g0
(1)
47
Modelling of the Charpy Test as a Basis fi~r 7bughness Evaluation
Here a 0 is the flow stress measured at the reference strain rate t~0 . The strain rate sensitivity factor, m = 0.013, was determined by simulating the Charpy test with a combined planestrain/plane-stress model and adjusting the strain rate exponent until a satisfactory agreement between simulated and calculated load levels is achieved (Fig. 3). 120
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Charpy energy as a function of temperature for irradiated weld material.
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Fig. 2.
Measured and calculated force versus diameter change curves of the tensile specimen (irradiated weld material).
48
W. SCtlMITT. 1. VARFOLOMEYEV AND W. BOItME
24 2o 16 12 8 4
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Simulation
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Time [ms]
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Measured and calculated force versus time curves of the (irradiated) Charpy specimen.
The characteristic length parameter, Ir was determined from the simulation of an impact test with one of the SE(B)-specimens. With this now complete set of deformation and damage parameters the SE(B)-test was once more simulated, and a (dynamic) J-resistance curve was determined (Fig. 4). To confirm the consistency of the result, three additional tests with the remaining SE(B)-specimens were performed with different impact energies resulting in different amounts of ductile crack extension between 0.2 and 2 mm. These tests define an experimental J-resistance curve also shown in Fig. 4. Especially the first two data points are in excellent agreement with the calculated curve. Finally, the so validated set of parameters was used to simulate a fictitious static experiment with a compact C(T)20 specimen. The resulting J-resistance curve is also shown in Fig. 4.
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Measured and calculated dynamic, calculated static J-resistance curves.
Modelling of the Charpy Test as a Basis for Toughness Evaluation
49
Here it was demonstrated that the application of numerical simulation employing micromechanical material models describing ductile tearing in combination with advanced experimental techniques is a powerful tool for the assessment of transferable toughness properties even if only small quantities of the material are available and if the testing has to be done under difficult (hot cell) conditions.
MODELLING OF CLEAVAGE FRACTURE The dominant brittle failure mechanism of ferritic steels is trans-crystalline cleavage. Three stages of the cleavage fracture process have been identified: A "hard" particle (e.g., carbide) breaks, thus forming a micro-crack. This requires a certain amount of plastic deformation. The micro-crack overcomes the boundary between particle and ferrite. This is dependent on the particle size, the specific energy for forming new surfaces, and the opening stress. The micro-crack overcomes the adjacent ferrite-ferrite grain boundary. This is dependent on the ferrite grain size, the specific energy for forming new surfaces, and the opening stress.
For a given material, the relative importance of these stages varies with temperature and, according to some authors, also with stress tri-axiality. In contrast to ductile fracture by void nucleation and growth, cleavage fracture is essentially stress controlled. For the assessment of cleavage fracture Ritchie, Knott and Rice [ 15] suggested that the local stress ahead of a crack tip must exceed a critical fracture stress crf over a characteristic distance X0 (RKR-model). The fracture stress crf can be determined from notched specimens. The statistical nature of cleavage fracture has led to the development of the "Local Approach to Cleavage Fracture", or the Beremin model, [16,17]. The failure probability of a structure with or without a crack is given by
with the loading parameter "Weibull stress" V
I
which is defined via the sum of the maximum principal stress over all elements within the plastic zone. The scaling or material parameter, try, is determined from the statistical evaluation of a sufficiently large number of experiments. The Weibull exponent m characterises the scatter of the material properties, the characteristic volume V0 is related to the characteristic distance X0 in the RKR-model.
50
W. SCIIMITT. !. VARFOI.OMEYEV AND W. BOHME
Bemauer et al. [18,19] examined a ferritic pressure vessel steel, German designation 22 NiMoCr 3 7, in the transition temperature regime. They analysed a great number of tests with laboratory specimens tested under a variety of conditions: different temperatures, static and dynamic loading, tensile and bending configurations, notched and pre-cracked specimens. The stress distributions in all specimens were calculated using a visco-plastic GTN-model which allows for the interaction between the elastic-plastic stress and strain fields and the softening effects due to ductile damage and crack growth. The investigations showed that a straightforward transfer of the Beremin model parameters from one test situation to another was not possible. Since no unique trends in the dependencies of the model parameters were found, simple corrections like the introduction of temperature dependent parameters were not successful. Therefore, modifications of the model taking into account micro-structural processes were introduced and examined. Among those modifications, the void modified Beremin model which couples the process of cleavage fracture initiation with ductile void formation produced an improvement with respect to transferability of the model parameters between different test series. It is based on the assumption that voids are also formed around carbide particles which are as a consequence no longer available for cleavage initiation. Together with modifications of the parameter evaluation procedure this model predicted a realistic temperature dependence of cleavage fracture toughness. Nevertheless, many questions remained still to be answered. Maybe in view of the forthcoming centenary of the Charpy test and certainly fostered by the nuclear industry new research efforts have been undertaken towards a better understanding of the Charpy test, employing state-of-the-art simulation techniques and investigations into the failure mechanisms [20,21,22,23]. A project currently under way at Fraunhofer IWM aiming at the assessment of upper shelf toughness of an irradiated weld material gives us the chance to use the available numerical models and to a certain extent also the experimental data base. With this, we want to contribute to the clarification of some aspects of the test. 200
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Charpy energy versus temperature for irradiated weld material.
300
Modelling of the Charpy Test as a Basis for Toughness Evaluation
The experimental basis includes force vs. time records of instrumented Charpy impact tests (the resulting Charpy energies versus temperature are plotted in Fig. 5) and one tensile test at an upper shelf temperature (150~ in which the cross section of the specimens was monitored during necking. All tests were performed by SIEMENS in their hot cell facilities. The parameters of the modified Gurson model (except the characteristic length, It) were determined from the simulation of the tensile test. In the subsequent analysis of a Charpy V-notch specimen test, a three-dimensional finiteelement model was used with a notch root element size of 0.2 mm. The results obtained using this model and the optimised material parameters representative for an upper shelf temperature are found to be in good agreement with the experimental measurements (Fig. 6). The complete set of the GTN parameters is to be applied in a future study to simulate a fictitious test with a compact C(T)25 specimen and, hence, to calculate the J-resistance curve. In the material description the strain rate dependency of the yield stress is taken into account.
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Charpy test, measured and calculated force versus time curves (upper shelf).
The three-dimensional model of the Charpy specimen was also used to simulate tests at lower temperatures. The force versus time records for seven specimens tested in the temperature range between-50~ and 50~ are given in Fig. 7, together with the numerically calculated curve with material parameters representative for a temperature of 0~ In view of the fact that all specimens considered here showed brittle fracture, an analysis of the maximum principal stress and its development with time (i.e. with crack extension) is of particular interest. This maximum stress can be then correlated to individual tests. Figure 8 shows the stress profiles ahead of the notch (crack) tip in the middle cross-section of the specimen at different times. One can see that the maximum principal stress (i.e. the opening stress at the notch root) slightly increases with time, and hence with ductile crack growth.
W. SCItMITF, !. VARFOLOMEYEV AND W. BOHME
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Force versus time records of Charpy tests at different temperatures (-50~ and results of numerical simulation (solid line).
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Fig. 8.
Development of the maximum principal stress with time.
In order to estimate the fracture toughness Kic at 0~ a three-dimensional analysis of a (fictitious) compact tension specimen C(T)25 is performed using the same set of material parameters as was used for the Charpy specimen. For every load increment the stress intensity factor, K~, is calculated and the distribution of maximum principal stress ahead of the crack tip is evaluated. As can be seen from Fig. 7 the calculated force versus time curve is in good agreement with the experimental curve for 0~ especially at the onset of cleavage. Hence, the
Modelling of the Charpy Test as a Basis for Toughness Evaluation
53
real stress distribution in the Charpy specimen at the time of failure is equal to the calculated stress distribution at this time. Figure 9 shows the corresponding distributions of the maximum principal stress for the Charpy specimen at the onset of cleavage (after 278 #s), and for the compact specimen at two load levels with stress maxima slightly below and above the maximum in the Charpy curve corresponding to stress intensity factors KI of 71.3 and 88.8 MPa.m~C~. Interpolation with respect to the maximum stress in the Charpy specimen yields KI = 81.7 MPa.m 1/2. Under the assumption that cleavage failure in both the Charpy and the compact specimen occurs at the same local stress level one may regard this value as a reasonable estimate for the cleavage fracture toughness Kic. 2O0O ....... a_
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~
C(T)25, K=71.3
%'~176176176176176176176176 ~176 .............. 500
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Distance from crack tip [mm]
Fig. 9.
Maximum principal stress ahead of the crack tip and notch root, C(T)25 and Charpy specimens.
There are no real fracture mechanics tests available for this material condition, only a reference temperature RTr,rDT has been determined. Figure 10 shows the fracture toughness reference curve according to ASME together with the "synthetic toughness" obtained from the simulation of the Charpy specimen. One can state that this value is in a reasonable relation with the reference curve. Effects of stress tri-axiality, characteristic volumes etc. have been neglected in this study. The stress tri-axiality plays an important role in the transferability of results between different specimen types. An impression of the three-dimensional distribution of the tri-axiality (defined as ratio of the hydrostatic stress to the equivalent yon Mises stress, orb~ere) in the Charpy specimen can be gained from Fig. l 1. Here, the deformed model of a quarter of the specimen (due to symmetry) is presented. The maximum of the tri-axiality factor, h, is observed some distance ahead of the notch correlating with the position of the maximum principal stress.
54
W. SCHMITI; !. VARFOLOMEYEV AND W. B O t i M E
120 100
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ASME Reference Curve 9 from Charpy
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Temperature [~
Fig. 10. Toughness estimate from Charpy and ASME reference curve.
Stress tri-axialitv: h = c&/o'e
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Time [ms]
Fig. 11. Contour plot of the stress tri-axiality factor for a Charpy specimen.
Also of interest is the development of the strains in the notch root. The calculated opening strain at several integration points of elements next to the notch root is shown as a function of time in Fig. 12. One can conclude from this plot that the local strain rates are of the order of 1000/s - 1500/s. This means that the strain rate sensitivity of the material data must be properly modelled, as has been the case in this analysis.
55
Modelling of the Charpy Test as a Basis fi~r Toughness Evaluation
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Fig. 12.
Strain history in the notch root (different curves correspond to different integration points of the finite-element model).
CONCLUSIONS For about a century, the Charpy test has successfully been used as an acceptance test characterising the brittle-to-ductile transition temperature. Attempts to correlate Charpy energy and transition temperature with fracture toughness were moderately successful within certain classes of steel utilised in nuclear installations. The appearance of numerical techniques like the finite element method and, in particular local approach concepts, together with the rapid increase in computer power have opened new possibilities for the evaluation of the test. However, while the treatment of ductile failure has brought quite promising results from the beginning, modelling of cleavage fracture still poses some difficulties to be resolved in future research. This concerns not only the understanding of all relevant failure mechanisms, and their variation with temperature, loading rate and more, but also the interaction of ductile and cleavage failure, and the appropriate modelling of these effects. For example, state-of-the-art finite element techniques in combination with local approach concepts yield mesh dependent results. This intrinsically negative aspect offers so far the only viable chance to include characteristic distances in the models. Unfortunately, the characteristic distance for ductile failure (assumed to correlate with the average spacing of large inclusions) is in general different from that for cleavage (assumed to correlate with grain size in many cases). Thus, the combined treatment of ductile and cleavage failure in one finite element model will always be a compromise, until new concepts to overcome this mesh dependency will be available.
56
w. SCHMITT,I. VARFOLOMEYEVAND W. BOHME
Nevertheless, significant progress has been made in the last two decades, and, in this study it had even been possible to establish a reasonable estimation of the material fracture toughness. The positive interplay of experimental and numerical techniques will certainly help to resolve most of the open questions of today. Modelling and simulation may be seen as instruments to look into the specimen and disclose essential quantities, maybe not all of them at the same time, though.
ACKNOWLEGEMENT The authors are grateful to EON Kernkraft for supporting part of this work.
REFERENCES 1. Charpy, G. (1901) M~moires et Comptes Rendus de la Soci~t~ des Ing~nieurs Civils de France, 848-877. 2. Barsom, J. and Rolfe, S. (1970). In: Impact Testing of Metals, ASTM STP 466, American Society for Testing and Materials, Philadelphia, USA, 281-302. 3. Sailors, R. and Corton, H. (1972). In: Fracture Toughness, Proceedings of the 1971 National Symposium on Fracture Mechanics, Part 11, ASTM STP 514, American Society for Testing and Materials, Philadelphia, USA, 164-191. 4. Marandet, B. and Sanz, G. (1977). In: Flaw Growth and Fracture, ASTM STP 631, American Society for Testing and Materials, Philadelphia, USA, 72-95. 5. Fearnehough, G. and Hoy, C. (1964) Journal of the Iron and Steel Institute, 912-920. 6. Wilshaw, T. and Pratt, P. (1966) Journal of the Mechanics and Physics of Solids 14, 7-21. 7. Knott, J. (1967) Journal of the Mechanics and Physics of Solids 15, 97-103. 8. Wullaert, R. (1970). In: Impact Testing of Metals, ASTM STP 466, American Society for Testing and Materials, Philadelphia, USA, 148-164. 9. Norris, D. M., Jr. (1979) Engineering Fracture Mechanics 11, 261-274. 10. Schmitt, W., Sun, D.-Z., Bi3hme, W. and Nagel, G. (1994) International Journal of Pressure Vessels and Piping 59, 21-29. 11. Gurson, A. (1977) Journal of Engineering Materials and Technology, 2-15. 12. Tvergaard, V. (1981) International Journal of Fracture 17, 381-388. 13. Tvergaard, V. (1982) International Journal of Fracture 18, 237-252. 14. Tvergaard, V. and Needleman, A. (1984) International Journal of Fracture 32, 157-169. 15. Ritchie, R.O., Knott, J.F. and Rice, J.R. (1973) Journal of the Mechanics and Physics of Solids 21,395-410. 16. Beremin, F.M (1983) Metallurgical Transactions 14A, 2277-2287. 17. Mudry, F. (1987) Nucl. Engng. & Design 105, 65-76. 18. Bernauer, G., Brocks, W. and Schmitt, W. (1999) Engineering Fracture Mechanics 64, 305-325. 19. Brhme, W., Bernauer, G. and Schmitt, W. (1999) Nucl. Engng. & Design 188, 149-154. 20. Rossol, A. (1998). Ph. D. Thesis, Ecole Centrale des Arts et Manufactures, ChatenayMalabry, France. 21. Rossol, A. (2001), private communication. 22. Tanguy, B. (2001). Ph. D. Thesis, Ecole des Mines de Paris, France. 23. Tanguy, B., Besson, J., Piques, R. and Pineau, A. (2001). In: Charpy Centenary Conference CCC2001 (to be published).
45
MODELLING OF THE CHARPY TEST AS A BASIS FOR TOUGHNESS EVALUATION W. SCHMI'Iq', I. VARFOLOMEYEV, W. BOHME Fraunhofer-lnstitut for Werkstoffmechanik, Freiburg, Germany
ABSTRACT Micro-mechanical material models are applied for the evaluation of fracture toughness properties from results of instrumented Charpy tests. In the first example the ductile fracture resistance of a weld material from the irradiation surveillance of a nuclear pressure vessel is determined. The initiation values were converted into pseudo plane strain fracture toughness values and used to adjust the ASME reference fracture toughness curve. The second example summarises modelling efforts towards the description of the cleavage-toductile transition region of a ferritic steel. Here, the Beremin model revealed substantial deficiencies concerning the transferability of the results between different specimen types and temperatures. Modifications of the failure models considering the failure mechanisms observed seem to improve the situation. In order to give some additional insight into stress and strain fields in Charpy and fracture mechanics specimens, preliminary results of a study with irradiated weld material will be presented. This study aims at the assessment of upper shelf toughness curves, however the existing numerical models are also applicable for the determination of the stress and strain fields in Charpy specimens tested in the transition temperature regime.
KEYWORDS Charpy V-Notch specimen, instrumented Charpy test, numerical simulation, GTN model, cleavage fracture, ductile fracture
INTRODUCTION Ferritic steels show cleavage fracture with low fracture toughness at low temperatures and ductile tearing with higher toughness values at higher temperatures. In the transition temperature region both failure modes co-exist and compete. The transition temperature is characteristic for the material, but it depends strongly on the testing conditions. For about a century the Charpy impact test [ 1] has been used as an acceptance criterion to determine the transition temperature of different materials. In its original and later standardised
46
w. SCHMITT, I. VARFOLOMEYEV AND W. BOHME
form the basic result of the test is the consumed energy. In a pendulum test equipment this energy is easily evaluated from the difference of the pendulum angles before and after impact. Testing specimens at different temperatures and plotting the consumed energy versus temperature yields a KV(T)-curve from which the transition temperature can be determined. For materials relevant for nuclear installations a fracture toughness curve Kxc(T- RTr,mx) was introduced as a lower bound of many valid fracture mechanics tests. The curve has a unique shape. The position of the curve with respect to the temperature axis is defined by the nilductility reference temperature RTr~D-r,which is determined from drop weight (Pellini) and Charpy tests. The shift of the reference temperature, ARTNDx, due to embrittlement, e.g. by irradiation, is monitored by the respective shift in the Charpy energy vs. temperature curve, KV(T), taken at a certain level of energy. Although fundamental differences exist between the Charpy impact test and fracture mechanics tests many efforts have been undertaken to correlate Charpy energy or the KV(T)-curve with the fracture toughness KIc (e.g., [2,3,4]). These empirical co-relations require large efforts in comparative testing and have, in principle, only limited applicability for a small group of materials. The most frequent application of the Charpy test for the assessment of pressure vessels is that the Charpy transition temperature is used to adjust the fracture toughness reference curve KIR(T). By applying calibrated strain gauges onto the impacting tub it has later become possible to measure force vs. time curves, thus providing more quantitative information about the test. Now it became not only possible to estimate the dynamic yield stress [5]. Under certain conditions it was also possible to estimate the fracture stress [5,6,7,8] analytically. Above all, results of instrumented Charpy tests provide an excellent basis for numerical simulations. Those numerical simulations started with Norris [9] as early as 1979 and have since become more and more elaborate.
EVALUATION OF UPPER SHELF TOUGHNESS VALUES The material under investigation in this study [10] was a weld material out of the irradiation surveillance. The goal of the study was the assessment of a ductile J-resistance curve through the application of the Gurson-Tvergaard-Needleman (GTN) model [11,12,13,14]. From the surveillance programme the load vs. time records of a series of Charpy tests were available. The Charpy energies of these tests are plotted versus temperature in Fig. 1. One test at 100~ (see circle mark) was selected for the evaluation. To complement the data base a sub-sized smooth tensile specimen (diameter 2.6 mm) and four side-grooved SE(B)-specimens (4.9x4.9x24.5 mm 3) were fabricated from broken halves of Charpy specimens and tested at 100~ in the DAP accredited testing laboratory Hot Cell Erlangen of SIEMENS. Figure 2 shows the comparison of experiment and simulation of the tensile test. From the analysis the static stress-strain curve and the GTN parameters are determined. These parameters were now used to simulate the Charpy test. To describe the strain rate dependency of the flow stress, cra (~r the following equation was used
_=
:_e_
~
g0
(1)
47
Modelling of the Charpy Test as a Basis fi~r 7bughness Evaluation
Here a 0 is the flow stress measured at the reference strain rate t~0 . The strain rate sensitivity factor, m = 0.013, was determined by simulating the Charpy test with a combined planestrain/plane-stress model and adjusting the strain rate exponent until a satisfactory agreement between simulated and calculated load levels is achieved (Fig. 3). 120
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Temperature [~
Fig. I.
Charpy energy as a function of temperature for irradiated weld material.
~'3 v (D k.J i,,_
o 2
ii
9
Experiment Simulation
0
0.2
0.4
0.6
0.8
1
Diameter change [mm]
Fig. 2.
Measured and calculated force versus diameter change curves of the tensile specimen (irradiated weld material).
48
W. SCtlMITT. 1. VARFOLOMEYEV AND W. BOItME
24 2o 16 12 8 4
-,,,._
Simulation
x..
O. 0
0.2
0.4
0.6
0.8
1
Time [ms]
Fig. 3.
Measured and calculated force versus time curves of the (irradiated) Charpy specimen.
The characteristic length parameter, Ir was determined from the simulation of an impact test with one of the SE(B)-specimens. With this now complete set of deformation and damage parameters the SE(B)-test was once more simulated, and a (dynamic) J-resistance curve was determined (Fig. 4). To confirm the consistency of the result, three additional tests with the remaining SE(B)-specimens were performed with different impact energies resulting in different amounts of ductile crack extension between 0.2 and 2 mm. These tests define an experimental J-resistance curve also shown in Fig. 4. Especially the first two data points are in excellent agreement with the calculated curve. Finally, the so validated set of parameters was used to simulate a fictitious static experiment with a compact C(T)20 specimen. The resulting J-resistance curve is also shown in Fig. 4.
Irradiated weld material
-"J r r r" r J
f
E
fa
E~ Z ,,,g L-.
r j..,r-
o
o
I" fJ o~
O f
r~
~
o Dynamic tests SENBI0
..r2_F-r"
o
!
O. O0
i
O. ~,0
Simulation Simulation CT20 T
i
O. 80
i
i
I . 20
l
i
I . 60
1
i
i
2. O0
i
2.40
i
|
2.80
Crack extension Aa [mm] Fig. 4.
Measured and calculated dynamic, calculated static J-resistance curves.
Modelling of the Charpy Test as a Basis for Toughness Evaluation
49
Here it was demonstrated that the application of numerical simulation employing micromechanical material models describing ductile tearing in combination with advanced experimental techniques is a powerful tool for the assessment of transferable toughness properties even if only small quantities of the material are available and if the testing has to be done under difficult (hot cell) conditions.
MODELLING OF CLEAVAGE FRACTURE The dominant brittle failure mechanism of ferritic steels is trans-crystalline cleavage. Three stages of the cleavage fracture process have been identified: A "hard" particle (e.g., carbide) breaks, thus forming a micro-crack. This requires a certain amount of plastic deformation. The micro-crack overcomes the boundary between particle and ferrite. This is dependent on the particle size, the specific energy for forming new surfaces, and the opening stress. The micro-crack overcomes the adjacent ferrite-ferrite grain boundary. This is dependent on the ferrite grain size, the specific energy for forming new surfaces, and the opening stress.
For a given material, the relative importance of these stages varies with temperature and, according to some authors, also with stress tri-axiality. In contrast to ductile fracture by void nucleation and growth, cleavage fracture is essentially stress controlled. For the assessment of cleavage fracture Ritchie, Knott and Rice [ 15] suggested that the local stress ahead of a crack tip must exceed a critical fracture stress crf over a characteristic distance X0 (RKR-model). The fracture stress crf can be determined from notched specimens. The statistical nature of cleavage fracture has led to the development of the "Local Approach to Cleavage Fracture", or the Beremin model, [16,17]. The failure probability of a structure with or without a crack is given by
with the loading parameter "Weibull stress" V
I
which is defined via the sum of the maximum principal stress over all elements within the plastic zone. The scaling or material parameter, try, is determined from the statistical evaluation of a sufficiently large number of experiments. The Weibull exponent m characterises the scatter of the material properties, the characteristic volume V0 is related to the characteristic distance X0 in the RKR-model.
50
W. SCIIMITT. !. VARFOI.OMEYEV AND W. BOHME
Bemauer et al. [18,19] examined a ferritic pressure vessel steel, German designation 22 NiMoCr 3 7, in the transition temperature regime. They analysed a great number of tests with laboratory specimens tested under a variety of conditions: different temperatures, static and dynamic loading, tensile and bending configurations, notched and pre-cracked specimens. The stress distributions in all specimens were calculated using a visco-plastic GTN-model which allows for the interaction between the elastic-plastic stress and strain fields and the softening effects due to ductile damage and crack growth. The investigations showed that a straightforward transfer of the Beremin model parameters from one test situation to another was not possible. Since no unique trends in the dependencies of the model parameters were found, simple corrections like the introduction of temperature dependent parameters were not successful. Therefore, modifications of the model taking into account micro-structural processes were introduced and examined. Among those modifications, the void modified Beremin model which couples the process of cleavage fracture initiation with ductile void formation produced an improvement with respect to transferability of the model parameters between different test series. It is based on the assumption that voids are also formed around carbide particles which are as a consequence no longer available for cleavage initiation. Together with modifications of the parameter evaluation procedure this model predicted a realistic temperature dependence of cleavage fracture toughness. Nevertheless, many questions remained still to be answered. Maybe in view of the forthcoming centenary of the Charpy test and certainly fostered by the nuclear industry new research efforts have been undertaken towards a better understanding of the Charpy test, employing state-of-the-art simulation techniques and investigations into the failure mechanisms [20,21,22,23]. A project currently under way at Fraunhofer IWM aiming at the assessment of upper shelf toughness of an irradiated weld material gives us the chance to use the available numerical models and to a certain extent also the experimental data base. With this, we want to contribute to the clarification of some aspects of the test. 200
I
El-....
160
[] . i . ,
~ 120 I
f-
I
a.
__EL
80
....
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rU
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[] []
- 10t3
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. . . . .
.
.
L.
.
,
0
100
[ 200
Temperature [~ Fig. 5.
.
i
r-i 40
.
F
Charpy energy versus temperature for irradiated weld material.
300
Modelling of the Charpy Test as a Basis for Toughness Evaluation
The experimental basis includes force vs. time records of instrumented Charpy impact tests (the resulting Charpy energies versus temperature are plotted in Fig. 5) and one tensile test at an upper shelf temperature (150~ in which the cross section of the specimens was monitored during necking. All tests were performed by SIEMENS in their hot cell facilities. The parameters of the modified Gurson model (except the characteristic length, It) were determined from the simulation of the tensile test. In the subsequent analysis of a Charpy V-notch specimen test, a three-dimensional finiteelement model was used with a notch root element size of 0.2 mm. The results obtained using this model and the optimised material parameters representative for an upper shelf temperature are found to be in good agreement with the experimental measurements (Fig. 6). The complete set of the GTN parameters is to be applied in a future study to simulate a fictitious test with a compact C(T)25 specimen and, hence, to calculate the J-resistance curve. In the material description the strain rate dependency of the yield stress is taken into account.
2~ I
a
8
, .....
,, '
'%,
I~l~
0- Experiment
i
v'k/' .w "
X~
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time [ms]
Fig. 6.
Charpy test, measured and calculated force versus time curves (upper shelf).
The three-dimensional model of the Charpy specimen was also used to simulate tests at lower temperatures. The force versus time records for seven specimens tested in the temperature range between-50~ and 50~ are given in Fig. 7, together with the numerically calculated curve with material parameters representative for a temperature of 0~ In view of the fact that all specimens considered here showed brittle fracture, an analysis of the maximum principal stress and its development with time (i.e. with crack extension) is of particular interest. This maximum stress can be then correlated to individual tests. Figure 8 shows the stress profiles ahead of the notch (crack) tip in the middle cross-section of the specimen at different times. One can see that the maximum principal stress (i.e. the opening stress at the notch root) slightly increases with time, and hence with ductile crack growth.
W. SCItMITF, !. VARFOLOMEYEV AND W. BOHME
52
16
~ "~
Z ,,1
i
0
u,.
J il~l~; ,
8
i! ' ! o~ .so~ ,
.~
4
U\
2soc i
i
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~
i~, ; :
'
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/
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:
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,'.,,ii,.,
,
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0
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'.
i
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,
'.
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,~
I
200
'~ ".'.
V
.',
V
\ ~
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~J
~
~,/ ,
,
600
800
" ',.r.\
""~-~: ,_/-.
,~
~,~
400
. ;~ ~'~/~ ,.
,~
'
1000
Time [psi
Fig. 7.
Force versus time records of Charpy tests at different temperatures (-50~ and results of numerical simulation (solid line).
to 50~
2000
~'
1600
~ /
~
0.278 ms
,/
1200 I/1 r~
e
Q. ._
u
C" o_
r~
:~
800
4OO
0
1
2
3
4
5
Distance from notch [mm]
Fig. 8.
Development of the maximum principal stress with time.
In order to estimate the fracture toughness Kic at 0~ a three-dimensional analysis of a (fictitious) compact tension specimen C(T)25 is performed using the same set of material parameters as was used for the Charpy specimen. For every load increment the stress intensity factor, K~, is calculated and the distribution of maximum principal stress ahead of the crack tip is evaluated. As can be seen from Fig. 7 the calculated force versus time curve is in good agreement with the experimental curve for 0~ especially at the onset of cleavage. Hence, the
Modelling of the Charpy Test as a Basis for Toughness Evaluation
53
real stress distribution in the Charpy specimen at the time of failure is equal to the calculated stress distribution at this time. Figure 9 shows the corresponding distributions of the maximum principal stress for the Charpy specimen at the onset of cleavage (after 278 #s), and for the compact specimen at two load levels with stress maxima slightly below and above the maximum in the Charpy curve corresponding to stress intensity factors KI of 71.3 and 88.8 MPa.m~C~. Interpolation with respect to the maximum stress in the Charpy specimen yields KI = 81.7 MPa.m 1/2. Under the assumption that cleavage failure in both the Charpy and the compact specimen occurs at the same local stress level one may regard this value as a reasonable estimate for the cleavage fracture toughness Kic. 2O0O ....... a_
1500
m
1000
~
C(T)25, K=71.3
%'~176176176176176176176176 ~176 .............. 500
0
1
2
3
4
5
Distance from crack tip [mm]
Fig. 9.
Maximum principal stress ahead of the crack tip and notch root, C(T)25 and Charpy specimens.
There are no real fracture mechanics tests available for this material condition, only a reference temperature RTr,rDT has been determined. Figure 10 shows the fracture toughness reference curve according to ASME together with the "synthetic toughness" obtained from the simulation of the Charpy specimen. One can state that this value is in a reasonable relation with the reference curve. Effects of stress tri-axiality, characteristic volumes etc. have been neglected in this study. The stress tri-axiality plays an important role in the transferability of results between different specimen types. An impression of the three-dimensional distribution of the tri-axiality (defined as ratio of the hydrostatic stress to the equivalent yon Mises stress, orb~ere) in the Charpy specimen can be gained from Fig. l 1. Here, the deformed model of a quarter of the specimen (due to symmetry) is presented. The maximum of the tri-axiality factor, h, is observed some distance ahead of the notch correlating with the position of the maximum principal stress.
54
W. SCHMITI; !. VARFOLOMEYEV AND W. B O t i M E
120 100
E
80 60
..M
v
40
ASME Reference Curve 9 from Charpy
20
-10
0
10
20
30
40
50
60
Temperature [~
Fig. 10. Toughness estimate from Charpy and ASME reference curve.
Stress tri-axialitv: h = c&/o'e
2 15 0
-2
u..
5 I
~
Experiment Simulation
/ i~ IL
2
L3
0
0.2
0.4
0.6
0.8
Time [ms]
Fig. 11. Contour plot of the stress tri-axiality factor for a Charpy specimen.
Also of interest is the development of the strains in the notch root. The calculated opening strain at several integration points of elements next to the notch root is shown as a function of time in Fig. 12. One can conclude from this plot that the local strain rates are of the order of 1000/s - 1500/s. This means that the strain rate sensitivity of the material data must be properly modelled, as has been the case in this analysis.
55
Modelling of the Charpy Test as a Basis fi~r Toughness Evaluation
2.4 -T I
2.0-E t. E ! ~ 16-1E "
e
.c
i
1.2
i,,.
t:n
i
c 0.8 ,-
. ~
~
o
.
o.4 t i
0.0,
I
0.0
. . . .
I
0.3
. . . . . . . . .
. . . * - - -
l. . . .
* . . . . .
0.6
'
,.
0.9
1.2
1.5
Time [ms]
Fig. 12.
Strain history in the notch root (different curves correspond to different integration points of the finite-element model).
CONCLUSIONS For about a century, the Charpy test has successfully been used as an acceptance test characterising the brittle-to-ductile transition temperature. Attempts to correlate Charpy energy and transition temperature with fracture toughness were moderately successful within certain classes of steel utilised in nuclear installations. The appearance of numerical techniques like the finite element method and, in particular local approach concepts, together with the rapid increase in computer power have opened new possibilities for the evaluation of the test. However, while the treatment of ductile failure has brought quite promising results from the beginning, modelling of cleavage fracture still poses some difficulties to be resolved in future research. This concerns not only the understanding of all relevant failure mechanisms, and their variation with temperature, loading rate and more, but also the interaction of ductile and cleavage failure, and the appropriate modelling of these effects. For example, state-of-the-art finite element techniques in combination with local approach concepts yield mesh dependent results. This intrinsically negative aspect offers so far the only viable chance to include characteristic distances in the models. Unfortunately, the characteristic distance for ductile failure (assumed to correlate with the average spacing of large inclusions) is in general different from that for cleavage (assumed to correlate with grain size in many cases). Thus, the combined treatment of ductile and cleavage failure in one finite element model will always be a compromise, until new concepts to overcome this mesh dependency will be available.
56
w. SCHMITT,I. VARFOLOMEYEVAND W. BOHME
Nevertheless, significant progress has been made in the last two decades, and, in this study it had even been possible to establish a reasonable estimation of the material fracture toughness. The positive interplay of experimental and numerical techniques will certainly help to resolve most of the open questions of today. Modelling and simulation may be seen as instruments to look into the specimen and disclose essential quantities, maybe not all of them at the same time, though.
ACKNOWLEGEMENT The authors are grateful to EON Kernkraft for supporting part of this work.
REFERENCES 1. Charpy, G. (1901) M~moires et Comptes Rendus de la Soci~t~ des Ing~nieurs Civils de France, 848-877. 2. Barsom, J. and Rolfe, S. (1970). In: Impact Testing of Metals, ASTM STP 466, American Society for Testing and Materials, Philadelphia, USA, 281-302. 3. Sailors, R. and Corton, H. (1972). In: Fracture Toughness, Proceedings of the 1971 National Symposium on Fracture Mechanics, Part 11, ASTM STP 514, American Society for Testing and Materials, Philadelphia, USA, 164-191. 4. Marandet, B. and Sanz, G. (1977). In: Flaw Growth and Fracture, ASTM STP 631, American Society for Testing and Materials, Philadelphia, USA, 72-95. 5. Fearnehough, G. and Hoy, C. (1964) Journal of the Iron and Steel Institute, 912-920. 6. Wilshaw, T. and Pratt, P. (1966) Journal of the Mechanics and Physics of Solids 14, 7-21. 7. Knott, J. (1967) Journal of the Mechanics and Physics of Solids 15, 97-103. 8. Wullaert, R. (1970). In: Impact Testing of Metals, ASTM STP 466, American Society for Testing and Materials, Philadelphia, USA, 148-164. 9. Norris, D. M., Jr. (1979) Engineering Fracture Mechanics 11, 261-274. 10. Schmitt, W., Sun, D.-Z., Bi3hme, W. and Nagel, G. (1994) International Journal of Pressure Vessels and Piping 59, 21-29. 11. Gurson, A. (1977) Journal of Engineering Materials and Technology, 2-15. 12. Tvergaard, V. (1981) International Journal of Fracture 17, 381-388. 13. Tvergaard, V. (1982) International Journal of Fracture 18, 237-252. 14. Tvergaard, V. and Needleman, A. (1984) International Journal of Fracture 32, 157-169. 15. Ritchie, R.O., Knott, J.F. and Rice, J.R. (1973) Journal of the Mechanics and Physics of Solids 21,395-410. 16. Beremin, F.M (1983) Metallurgical Transactions 14A, 2277-2287. 17. Mudry, F. (1987) Nucl. Engng. & Design 105, 65-76. 18. Bernauer, G., Brocks, W. and Schmitt, W. (1999) Engineering Fracture Mechanics 64, 305-325. 19. Brhme, W., Bernauer, G. and Schmitt, W. (1999) Nucl. Engng. & Design 188, 149-154. 20. Rossol, A. (1998). Ph. D. Thesis, Ecole Centrale des Arts et Manufactures, ChatenayMalabry, France. 21. Rossol, A. (2001), private communication. 22. Tanguy, B. (2001). Ph. D. Thesis, Ecole des Mines de Paris, France. 23. Tanguy, B., Besson, J., Piques, R. and Pineau, A. (2001). In: Charpy Centenary Conference CCC2001 (to be published).