Transactions, SMiRT 16, Washington DC, August 2001 Paper # 2062
D Y N A M I C FRACTURE TOUGHNESS OF CAST STEEL USED F O R
N U C L E A R WASTE CONTAINERS WITH NOTCHED CHARPY SPECIMEN
Aberkane M. 1), Lenkey G. 2), Pluvinage G. 1)
1) Laboratoire de Fiabilit6 M6eanique. Universitd de Metz France
2) Bay Zoltan Institute for logistics and production systems. Miskoletapolea Igloi u. 2. H 3 519 Hungary.
Design of nuclear waste containers against the risk of brittle fracture by shock requires dynamic fracture
toughness values. A fast and cheap method consists is to use Charpy specimen with notch preferably to preeraeked
specimen. Fracture toughness increases with notch radius below a critical value. Below this value, fracture toughness is
constant. Dynamic fracture toughness has been measured by instrumented Charpy impact testing in the upper shelf and
transition region. It has been found, using J - Aa approach, that in the upper shelf region at + 20 o C the critical notch
radius is about 1.3 mm and Jo value is about 200 kJ/m2. In the transition regime, using essential work for fracture,
toughness is about 250 kJ/m2 a t - 20 ° C. For the prescribed transition temperature- 40 ° C, the fracture toughness value
is high enough to ensure ductile crack initiation.
Transport and storage containers for spent nuclear fuel have to ensure the safe enclosure of a radioactive
material and must meet stringent requirements on safety. For the safe enclosure of the radioactive material during
transportation, it must be proved that the extension of non-detected cracks alter fabrication will not occur even in the
ease of most severe accident loading. According to the Intemational Atomic Agency Energy (IAEA) , fracture
toughness transition temperature is required to be higher t h a n - 4 0 ° . Above this temperature, fracture occurs in the
transition region by ductile initiation followed by brittle propagation. In the upper shelf plateau, fracture initiates and
propagates in a ductile manner. The control of the required fracture toughness needs to take into account the ductile
behavior of materials using a rapid and cheap procedure. Choice of energetic fracture criteria determined from notched
specimens has been made to full fill these requirements.
The critical energetic parameter J0 at initiation is defined according to Tumer  as proportional to the specific
energy for initiation U.]Bb0
jo= r/.U~ (1)
Where rl is a parameter, B is the specimen thickness and b0 is the initial ligament size.
According to Cotterell and Reddel , the essential work of fracture and the dissipated plastic work per
ligament area W~ are the two components of the specific energy for initiation:
U', =G+Wk.bo (2)
Essential work of fracture is applicable for fracture initiated after complete ligament plastiflcation. Fracture
toughness is sensitive to notch radius when measured on notched specimen. Fig. 1 shows that generally beyond a critical
value, fracture toughness increases linearly with notch radius. Under this value, J0,2 is constant. This fact allows to use
cheap notched specimen because it has been seen that for several materials Pc is in the range of (0,2 - 1 mm) . The
slope of the linear part called oq can be considered as a notch sensitivity index.
In this paper, fracture toughness of east ferritic steel has been measured in the transition region using the
essential work of fracture and in the upper shelf plateau using the concept of J-Aa fracture resistance curve. Influence of
notch radius on these values is discussed.
Fig, 1 Evolution of fracture toughness J0a versus notch radius,
Dermition of critical notch radius Pc and notch semitivity index ~s.
INFLUENCE OF N O T C H RADIUS ON vl FACTOR
rl is defined from the formula of the energetic parameter J according to Eq.(1). It is considered as equivalent of
J integral and consequently:
j= lv~ (3)
Then 11 can be written as follows:
rl=~U =(~a ) Oa (4)
rl has been computed by finite element using stress strain behavior as described by Ludwik law. Fig. 2 shows the
evolution of 11 for a eonstant notch radius equal to 0.7 mm versus the relative notch depth a/W. Fig .3 shows the evolution
of ri for constant relative notch depth a/W= 0.5 versus notch radius. We can notice that 13 differs from the deep notch
solution for elastic ease (11 =2) and is sensitive to notch radius. These solutions for rl have been used for detemaination of
Jic fracture toughness.
Deep n~)tch solution
0.2 0.3 0.4 0.5 0.6 0.7
Fig, 2 Evolution of 11versus relative notch depth (a/W) for comtant notch radius p =7mm
(Charpy U_notched specimen)
We notice that 11 increases with the relative depth a/W. The evolution of rl as a function of notch root radius shows an
absolute minimum whose abscissa called Pc is ranging between 0.75 and 1 mm (Fig. 3). Similarly, we notice that for
radius values below Pc, rl decreases linearly with the increase of O. Beyond this critical abscissa; rl increases with p and
becomes approximately constant for a radius ranging between 1.54 and 2 mm. The difference between 1] got for crack
and that got for notch with the same length can reach 36% of the last one, which is relatively important and justifies the
I i- = :
.... i i ................
1.0 ................................................................. .~
0.5 .....................,,.......................................... ".....................
0.0 0.5 1.0 1.5 2.0
oo o (mm)
Fig. 3 Evolution of 11versus notch radius for constant relative notch depth a/W=0.50
(Charpy U__notched specimen)
M A T E R I A L AND S P E C I M E N S
The investigated steel material is a cast ferritic steel used for nuclear waste containers. The chemical
composition and the mechanical properties are given in Table 1 and in Table 2 respectively.
Table 1. Chemical composition of the investigated steel
Weigth % C Si Mn Cr Mo Ni Cu
Cast Steel 0, 09 0,37 1, 18 0,12 0,03 0,29 0,29
Table 2. Mechanical properties of the investigated steel
Yield stress Ultimate strength A% KCV +20°C
(MPa) (MPa) daJ / em 2
375 478 31,7 8
We assume that the material is strain hardening and obeys the following stress-strain law:
Where K is the strain-hardening coefficient and n the strain-hardening exponent (I( = 737 MPa; n =0.12). Charpy
U_notehed specimens were used in the experiments with constant notch radius and different notch depthes as given in
Table 3 and with constant relative notch depth and different notch radii given in Table 4.
Table 3. Geometry of the different Charpy U_notehed specimens with a constant notch radius p = 0.7ram
bo=W-a(mm) 8 716151413
Table 4. Geometry of the different charpy U._notched specimens with a eomtmut relative notch deptht a/W =0.5
o(mm) 0.13 10.25 10.4 10.7111212.5
Test temperatures have been chosen in the upper shelf region (+20°C) and in the lower transition region (-20°C) as it is
shown in Fig. 4.
t I u
J0,2 Evaluation I ~ upper
T1 -20°C =
160 I [ upper I
T2 20°C =
I transition A
I I region I
transition [ gk
I region I
I I I
lower shelf I
A [ I
40 I I A I
t . [ . !
O0 -80 -60 -40 -20 0 20 40
Fig, 4 Charpy impact energy versus temperature for cast steel indicating
the different mode of fracture
FRACTURE TOUGHNESS FROM CHARPY IMPACT TEST IN THE UPPER SHELF PLATEAU.
Typical load-time diagram of ductile fracture obtained in the upper shelf plateau is presented in Fig. 5a. Load
increases until a maximum value and decreases slowly. Initiation takes place just before the maximum load and is
followed by ductile tearing.
.15 -- - - - . . . . "'- ....... =" " • . , .. =. . . . . . . . . ,..
l a lil 10
i Ib I i m
! ii!iiiiii :ii ! ....... ...... "i
•:.:.:-:-:: : : : : : : : : : : : : : : : : : : : : : : 0
o ! 2 .3 ~ S. :0 : 0 1 2 3 4 5 6. 7
Fig 5a and 5b. Instrumented Charpy impact test force-time curve; Definition of energy for initiation, non-
stable and stable tearing (Cast steel, Test temperature +20°C).
In the following diagram total fracture energy Ut can be separated into two parts one for initiation Ui and one
for tearing UTe=
U,=U,+Ur, or (6)
Tearing process can be also separated into two parts: transient tearing process from initiation to maximum load
Ux,Nst and stable tearing Ux, st (Fig.5b). Stable tearing is governed by the faet that crack opening angle (COA) is assumed
to be constant. Eq. (6) can be written as"
UTear'--UT, N~-[-UT, st (7)
Only the absorbed energy at maximum load Um and Lit are required as experimental input data, which can be
obtained very easily and unambiguously from the force-time curve (Fig. 6). And then Eq. (8) can be rewrite:
--- . . . . . . . . . . . . ... , . . . . . . . .~..
0 I 2 S 4 6 5
Fig. 6 Instrumented Charpy impact test force-time curve; Def'mition of total energy at maximum load and energy
at stable tearing.
These different mechanisms on ductile failure can be represented on a J-A~ fracture resistance curve, Fig. 7. The
energertie parameter J is plotted versus the crack extension Aa.
0,2 mm ~a
Fig. 7 J-Aa curve
The J-Aa curve can be divided into 3 parts:
Part I: initiation (actually a conventional crack extension of Aa0 = 0,2 mm is considered as initiation). The J
values reach initiation value J0,2.
J(Aa)=m For Aa<Aa0 (11)
m is a parameter and R~ is the flow stress.
part H: transient tearing process where energetic parameter J is a power function of crack extension
J(Aa)=R(Aa) For Z~lo<Aa<Z~ m (12)
Aam is crack extension at maximum load
Pi~"t HI: stable tearing process.
INnSng this process the following assumptions are used to compute the energy for stable tearing UT,S, Crack
opening angle is constant, crack opening displacement is obtained assuming a fixed rotational center position;
and bending moment is computed from an elastic-plastic material behavior strain hardening is taken into
account using the flow stress R~. This model has been proposed by Sehindler  and leads to:
For z~a>/~l m (13)
This model of fracture resistance curve leads to a three parameters model with parameters: p, R and Z~am.
Obtention of these three parameters is be done only through values of the absorbed energy at maximum load Um and total
energy for fracture Ut. Detection of initiation is not necessary using this procedure. However a large scatter on maximum
and total energy, an average value of p = 0.85 and Aam = 0.79 mm has been found. Evolution of J0,2 versus notch radius
is plotted in Fig.8. We can notice that for notch radius below pc=lmm the initiation toughness J0,2i has a constant value
equal to 0.2 MJ/m ~-.Notch sensitivity has been found to be equal to cq = 100 MJ/m3.
Jo,2 (K Jim 2)
............. . ............. ~........................... ~ . . . . . . . . . ~ ............
i i i m i
nllm II i
..,..*..*.. ............... i ......................................... ~.............
0 1 2 3
p ( ~ )
Fig. 8 Jo~ versus different values of Notch radius.
FRACTURE TOUGHNESS IN THE TRANSITION REGION
We can distinguish the upper transition range and the lower transition range. In the upper transition region,
unstable cleavage fracture occurs after some amount (larger than 0,2mm) of stable tearing. In this range, we observe that
the total fracture energy U¢ is lower than the one in upper shelf. In the lower transition region where less than 0,2mm
ductile crack propagation precedes the onset of the unstable cleavage, the essential work of fracture Fe can be determined
by the following relation ship;
U, =Fe+kbo (15)
Where Fe is the essential work of fracture, k is the slope of the linear firing curve and b0 is the ligament size in mm. A
typical load displacement diagram is presented in Fig. 9 and the initiation energy for is defined as shown.
. ...... @ . . . . . ! ................
1 : 2 . ...... - ui
o 1 2 3-
Fig. 9 Example of recorded force-time of Charpy impact test in transition region
Plot of specific energy versus ligament size bo is presented in Fig. 10. Extrapolation to origin gives the value of
the essential work for fracture, which is equal to 0.25 MJ/m 2.
U/Bb (MJ/m 2)
: m l=
i. . . . . . . . . .. . . . ~i. . . . . . . . . . . . . . . . . •i. . . . . . . ~ ~. . . .
• .. .. ~. . . . . . . . . . . .
. i  ~ i 
0.2 ........... .:. . . . . . . = . . . . . . . ! . . . . . . . i = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 2 4 6 8 10
Fig. 10 Determination of the essential work of fracture in the transition region
Influence of notch radius on fracture toughness has been studied by several authors as mentioned in .
Literature survey showed that:
,t, Below a critical notch radius pc fracture toughness is constant;
o:- Beyond this value, Jic increases linearly with notch radius;
However some disagreement appears about the size of the critical notch radius. Some authors in  using rl
values obtained for cracked specimens, the critical notch radius is of the same order of magnitude than grain size or
microstrueture units. For other  using rl values, which take into account the influence of notch radius, Po is about
lmm. Using the same approach we have found a critical notch radius of about lmm. This value allows the use of
notched specimen, which is cheaper and faster to prepare than precraeked specimens. For this reason, a probabilistie
approach of safe design against brittle fracture is also possible. Sehindler  has proposed than in the case of small scale
yielding, J integral for a notched specimen, called -In c a n be divided into two parts:
J.(a)=dzc(a)+ z ~ (16)
AJ is considered as proportional to the notch radius.
zSd=Cp=cpW*f = (17)
where e and C are material constants, and W*fis the strain energy density of fracture.
combining Eq. (5) and Eq. (18);
. K e f +' (19)
W*f = K = 1080 M J / m 3, n = 227 ~¢IJ/m 3 with 0,12 and ef =Ln (1+A)=0.275. Values of c following Eq. (17) has been
found equal to 0.63, with c~ = 100MJ/m 3. Which is close to the value found by Schindler (c = 0,88 for high strength steel
and e = 0,77 for mild steel). However, the possibilities of using a large notch radius leads to an increasing scattering.
This introduces a limitation to this method.
Dynamic fracture toughness of east steel has been measured with instrumented Charpy impact testing using the
U_notehed Charpy specimens. Tests have been done in the upper transition region (-20°C) and upper shelf plateau. In
the upper shelf region, toughness has been detemained using J-Aa fracture resistance curve (20°C). In the upper transition
(-20°C) region, fracture toughness has been detemained using the essential work of fracture. In both cases, ductile
initiation leads to the same fracture resistance at initiation [200-250 KJ/m2].
1. Guidelines for safe design of shipping packages against brittle fracture, IAEA-TECDOC-717, 1993.
2. Tumer,CE., "Methods for post-yield fracture safety assessment," Post-Yield Fracture safety, 1979, pp. 23-210.
3. Cotterell, B., and Reddel, J.K, "The essential work of plane stress ductile fracture," International Joumal of Fracture,
Vol. 13, N°3, 1977, pp. 267-270.
4. Akourri, O., Louah, M., Kifani, A., Gilgert, G. and Pluvinage, G.,"The effect of notch radius on fracture toughness
Jic," Engineering Fracture Mechanics, Vol. 65, Issue. 4, 2000, pp. 491-505.
5. Sehindler, H.J., and Veidt, M., "Fracture toughness evaluation from instrumented sub-size Charpy-type tests,"
Small Specimen Test Techniques, ASTM STP 1329, 1998, pp. 48-61.
6. Veldt, M. and Sehindler, H. J., "On the effect of notch radius and local friction on mode I and mode II fracture
toughness of a high strength steel," Engineering Fracture Mechanics, Vo158, N°3, 1997, pp. 223-231.