Prediction of KIc in a high strength bainitic steel
L. Rancel, M. Gómez, J.M. Amo, S.F. Medina,
National Centre for Metallurgical Research (CENIM-CSIC), Av. Gregorio del Amo 8;
28040-Madrid
smedina@cenim.csic.es; lucia.rancel@cenim.csic.es; mgomez@cenim.csic.es;
amoortega@cenim.csic.es;
Abstract
In the present work the stress intensity factor (KIc) has been determined for a high
strength bainitic steel. Reference has been made to ASTM E 399 standard, which
involves the use of complex geometry specimens. An experimental value of 1627 Nmm3/2
was obtained for KIc, which is equivalent to a value of 51.4 MPam1/2. It has been
verified that Lescovsek’s expression, which predicts KIc as a function of hardness (HRc)
and the CVN Charpy impact test value, can be applied to steels with a bainitic
microstructure, as the CVN value is more influential than HRc. The acceptable
prediction of Lescovsek's expression shows the way to improve the KIc value in bainitic
steels.
Keywords: fracture, stress intensity factor, Charpy impact, model
Introduction
The stress intensity factor (K) characterises crack tip conditions in a linear elastic
material. A crack can experience three types of loading: mode I, where the main load is
applied normal to the crack plane, tending to open the crack; mode II, corresponding to
in-plane shear loading, where one crack face tends to slide over the other; and mode III,
which refers to out-of-plane shear loading [1]. The stress intensity factor normally refers
to mode I and is determined using the American Society for Testing and Materials
(ASTM) standard for KIc [2].
The quantitative relationship of KIc to features of a material's microstructure and the
micromechanisms of fracture has developed over the last forty years [3].
It is assumed that a material fails locally at some critical combination of stress and
strain, so the fracture must occur at a critical stress intensity, KIc. Thus KIc is an
alternative measure of fracture toughness. The critical stress intensity factor is only a
material constant when certain conditions are met. Fracture toughness decreases with
specimen thickness until a plateau is reached, and further increases in thickness have
little or no effect on toughness [1]. The critical value of stress intensity factor at the
plateau is defined as KIc, the plane strain fracture toughness.
For low toughness materials, brittle fracture is the governing failure mechanism, and
critical stress varies lineally with KIc. At very high toughness values, linear elastic
fracture mechanics (LEFM) ceases to be valid, and failure is governed by the flow
properties of the material; a simple limit load analysis is all that is required to predict
failure stress in a material with very high fracture toughness [1]. There is another
alternative approach to fracture analysis: the energy criterion. Griffith [4] was the first
to propose the energy criterion for fracture. Several researchers have modified Griffith’s
equation in order to correct for yielding at the crack tip [5-7].
KIc test values are not widely used in toughness specifications. This is surprising, since
KIc values are more useful to the designer than Charpy V-notch (CVN) impact test
values, since the strength and toughness of materials needs to be taken into account in
the design of tools and dies made from high strength steels in order to prevent the
possibility of rapid and brittle fracture. KIc values can be used in design applications
because they are measured in terms of the allowable stress level for a given flaw size.
However, due to the difficulty of KIc testing, in terms of both specimen machining and
the actual performance of the tests, especially at low temperature, KIc values are not
widely used in toughness specifications for tool and high-speed steels.
Lescovsek [8] found a correlation between KIc, hardness (HRc) and CVN impact test
values for tool steels. This correlation can be used to estimate KIc values from CVN and
HRc test results. Conversely, fracture-mechanics concepts can be used to develop
stress-flaw-size relations for various work applications and then use the correlation to
select the best toughness level at the working hardness for a work tool.
On the other hand, the bainitic packet appears to be the microstructural unit controlling
the cleavage resistance of low carbon bainitic steels, since its size is slightly smaller
than the average unit crack path (UCP), and the critical stage in the fracture process
appears to be the propagation of a Griffith crack from one packet to another [9,10]. For
other authors, the lath width or effective plate width controls cleavage fracture in high
carbon steels [11]. Finally, Yang et al. reported that cleavage fracture is more influenced
by coarse carbides at the crack tip than other microstructure parameters [12].
In this work, the results of fracture mechanics testing of a high strength bainitic steel are
reported and it is verified whether Lescovsek’s expression can predict the KIc value.
Furthermore, a study is made of the microstructural unit controlling cleavage resistance.
Materials and Procedure
The steel has been manufactured using electroslag remelting (ESR) equipment and its
chemical composition is shown in Table 1.
Table 1. Chemical composition (wt.%) of the steel used. Base steel 35CrMo4.
C
0.38
Si
0.28
Mn
0.90
Cr
1.01
Mo
0.20
V
0.12
N
0.0214
Three specimens of the studied steel, referred to as CR2, were used to carry out fracture
mechanics tests. The specimens were reheated at 950ºC for 45 min in a vacuum furnace
and subsequently cooled by an argon stream in the furnace at an average cooling rate of
2 K/s. The resulting microstructures were fully bainitic (Fig. 1) with 6.5% retained
austenite, as determined by X-ray diffraction analysis.
The specimens were machined according to ASTM E 399 standard [2]. Their
dimensions were as follows:
Specimen thickness: B=14 mm;
Specimen width: W=2B=28 mm;
Total length=1.25W=35 mm;
Notch width: N<W/10=3 mm;
Notch angle: q<90º; q=60º;
Hole diameter: 0.25W=7 mm
Fig. 2 shows a specimen machined with these dimensions, whose design complexity can
be observed. The tests consist of two stages. The aim of the first step is to create a
crack, and consists of placing the specimen in a clamp and subjecting it to cyclic tensile
loading followed by release, at a load of 5.24 kN and a cycle frequency of 12 kHz. In
accordance with ASTM standard E 399, the fatigue crack length on each specimen
containing a straight-through notch must be at least 0.025W.
Fig. 3 shows a cyclically loaded specimen after 24 hours of testing. A small crack is
observed in the notch tip. The second stage of the test starts when the crack has been
initiated, and consists of subjecting the specimen to continuous tensile loading until the
crack propagates and fracture of the specimen occurs. Three specimens were tested.
Charpy impact testing verifies the amount of energy absorbed during the high strain rate
fracture of a material and is a measure of a material’s resistance to brittle fracture. The
test specimens are notched, and the size of specimens are set forth by ASTM standard
E23. Charpy test specimens are 10mm x 10mm x 55mm with a V shaped notch 2 mm
deep. The notch opening is 45°. Three specimens were tested for each austenitisation
temperature.
Tensile tests were performed in accordance with standard EN-1002-1. The specimens
for tensile tests were treated at 950ºC for 45 min and cooled at a rate of approximately 2
Ks-1. Two specimens were tested for each austenitisation temperature.
Results and Discussion: Fracture Mechanics Testing
Crack Length
The first measurement of the tested specimens was the length of the crack generated in
the first stage. Measurements were made at three different points (a1, a2, a3) and the
values obtained were then averaged (Table 2). In order for the measurements to be
valid, i.e. to generate a crack that allows the second stage of tensile loading until
fracture to be performed, the deviation of measurements from the average value should
not be higher than 15%. This criterion was fulfilled in all cases. Figs. 4 (a-c) show the
fracture surface of the three specimens tested until fracture. The initial crack (smooth
surface) and fracture surface (rough surface) can be distinguished.
Table 2. Measurement of crack length in specimens tested at 950ºCx45 min with
bainitic final microstructure.
Steelspecimen
CR2-1
CR2-2
CR2-3
a1 (mm)
a2 (mm)
a3 (mm)
a (mm)
14.95
13.23
13.23
15.14
13.29
13.36
13.87
13.03
12.98
14.65
13.18
13.19
Calculation and Interpretation of Results
The KIc property determined by the test method characterises a material’s fracture
resistance in a neutral environment in the presence of a sharp crack under severe tensile
constraint. The state of stress near the crack front approaches triaxial plane strain and
the crack-tip plastic region is small compared to the crack size and specimen
dimensions in the constraint direction. The KIc value is believed to represent a lower
limiting value of fracture toughness. This value may be used to estimate the relation
between failure stress and defect size for a material in service where in the conditions of
high constraint would be expected.
In order to establish whether a valid KIc has been determined, it is first necessary to
calculate a conditional result, KQ, which involves a construction on the test record, and
then to determine whether this result is consistent with the size and yield strength of the
specimen according to standard E 399, point 7.1 [2].
The test record consists of an autographic plot of the load-sensing transducer output
versus the displacement gage output. After the test, the load-displacement curve is
compared with the three types included in standard E 399 and matched with one of
them. Fig. 5 shows the load-displacement curve for specimen CR2-1. This curve
corresponds to type II. The load PQ is subsequently determined according to the
instructions set out in the standard and its relationship to KQ will be studied later. To
determine PQ a straight line is drawn from the origin. The slope is equal to 95% of the
slope of the lineal part of the load-displacement curve (Fig. 5). This line intersects the
curve at a point where the load is smaller than the preceding maximum. The maximum
is the value taken for PQ and is 11470 N for this particular case. On the other hand,
Pmax/PQ should be smaller than 1.10. Fig. 5 shows that this criterion has been followed:
Pmax 11600

 1.01  1.10
PQ
11470
(1)
For the compact specimen used, KQ is calculated in accordance with the following
expression:
KQ 
PQ
B W
Where:
PQ =load as determined above
B=specimen thickness
W=specimen width
a=crack length as determined above
f(
a
) ……………..(2)
W
The following values were calculated:
a 14.65

 0.523
W
28
(3)
To facilitate the calculation of KQ, values of f (
a
) are tabulated in standard E 399 [2].
W
In the present case, the value found was:
f(
a
)  10.386
W
(4)
Finally, the value found for KQ in accordance with expression (2) was:
KQ 
PQ
B W
3
f(
a
11470
)
10.386  1608 N / mm 2
W
14 28
(5)
The parameters in the rest of the tests were calculated applying the same methodology.
Each load-displacement curve (Figs. 6,7) was classified according to the three types
established in standard E 399. The values found are shown in Table 3.
Table 3. Determination of KQ parameter.
Steelspecimen
CR2-1
CR2-2
CR2-3
Curve type
a/W
f(a/W)
PQ, (N)
II
I*
II
0.523
0.471
0.471
10.386
8.86
8.86
11470
13304
14070
KQ,
(N/mm3/2)
1608
1591
1683
* The Pmax/PQ=1.15 relationship was slightly larger than 1.10.
Calculation of KIc
Once the load KQ has been calculated for each tested specimen, a new expression must
be calculated:
 KQ
2.5
  YS



2
(6)
Where YS is the 0.2% offset yield strength in tension. If this amount is less than both
the specimen thickness (B) and the crack length (a), then KQ is equal to KIc. Otherwise,
the test is not a valid KIc test. Table 4 shows the experimental values of a, B, KQ, YS
and equation (6) for the tested specimens.
Table 4. Values of a, B, KQ, YS and expression (2).
Steelspecimen
CR2-1
CR2-2
CR2-3
a (mm)
B (mm)
14.7
13.2
13.2
14
14
14
KQ,
(Nmm-3/2)
1608
1591
1683
YS
(MPa)
731
731
731
Expres. (6)
(mm)
12.9
11.8
13.2
In all cases, except for specimen CR2-3, the values of equation (6) are smaller than the
crack length and specimen width. Therefore, KIc coincides with KQ. In specimen CR2-3
the value of equation (6) was smaller than “B” and equal to “a”, so KIc can be assumed
to be equal to KQ. In other words, the test is valid in all cases. Therefore, the value of
KIc will be the average of the values obtained for KQ (Table 4), which yields a value of
1627 Nmm-3/2, equivalent to 51.4 MPam1/2.
The KIc values obtained will serve to determine the critical sizes of acceptable cracks in
parts and pieces as a function of the initial tensile solicitation state. As critical values of
KIc are considered, the results will be independent of the employed material thickness.
This fact allows a wide range of possibilities to evaluate real situations in the presence
of defects resulting from both the manufacturing process and subsequent use.
Prediction of KIc
The expression given by Lescovsek is [8]:
K Ic  A  CVN 1.11  HRc 0.135
(7)
where, CVN is expressed in J and KIc in MPam1/2. The value of A may be 5.68,
deduced from a combination of experimental values, or 4.53, obtained by fitting the
correlation between KIc and HRc.
The empirical equation (7) was constructed using results obtained in high strength steels
with a tempered martensitic microstructure with similar carbon contents to the steel
used in the present work. Tempering was performed at temperatures of between 540ºC
and 620ºC and the obtained hardness values were between 40 and 55 HRc.
The average value of Charpy impact tests for an austenitisation temperature of 950ºC is
shown in Table 5. Fig. 8 shows a SEM-fractograph of the fracture surface in the Charpy
impact test at a testing temperature of 22ºC. The low absorbed impact energy value of
12 J indicates a brittle fracture. This is a cleavage fracture and an absence of “voids” is
observed. As the fracture advances, the number of active cleavage planes decreases by a
joining process that forms progressively higher cleavage steps.
The hardness of the Charpy specimens was measured at several different points, and the
result shown in Table 5 is an average value.
Table 5. Charpy impact test and hardness values.
Charpy impact absorbed
energy (J)
12
Hardness (HRC)
35
Inserting the values of Table 5 in equation (7), and bearing in mind the possible values
of the coefficient A, KIc values of 44.2 MPam1/2 and 55.4 MPam1/2, respectively, were
obtained (Table 6).
Table 6. Predicted and experimental values of KIc according to equation (7).
A
5.68
4.53
Predicted KIc
(MPam1/2)
55.4
44.2
Experimental KIc
(MPam1/2)
51.4
51.4
Difference (MPam1/2):
Predicted-Experimental
+4
-7.2
The experimental value of KIc is closer to the value predicted by equation (7) when
coefficient A takes a value of 5.68. Nevertheless, whatever the value taken for
coefficient A, equation (7) acceptably predicts the value of KIc in the bainitic steel used
in this work. This is the case despite the fact that equation (7) was formulated for
quenched and tempered steels with a martensitic microstructure. It is well known that a
martensitic microstructure tempered at a certain hardness yields a higher CVN value
than the bainitic microstructure of the same hardness, especially in the case of upper
bainite, as here. The explanation why equation (7) can predict the value of KIc depends
more on the CVN value than on HRc. In this expression the KIc intensity factor
maintains an almost linear dependence on CVN, an exponent of 1.11, and a very small
dependence on HRc, exponent of -0.135.
If the experimental values of CVN, HRC and KIc are replaced in equation (7), a value of
5.27 is deduced for coefficient A, which is between the two values given by Lescovsek
[8].
Therefore, given that CVN is the "variable" that most influences KIc, the way to
increase the latter’s value is to achieve a finer bainitic microstructure, which is done by
reducing the austenitic grain size prior to the bainitic transformation [13] or by the
obtainment of lower bainites through isothermic treatments carried out in very strict
temperature conditions (both austenitisation temperature and bainitic transformation
temperature) and transformation times [14].
Finally, Fig. 9 displays a fractograph at less magnification, where the typical river
marking of cleavage fracture can be seen. Comparison of this micrograph with those
presented in Fig. 4 shows a similar appearance, indicating that both are “cleavage
fractures”.
Conclusions
The expression given by Lescovsek acceptably predicts the value of KIc, especially
when the coefficient A is taken as 5.68. Fitting the equation to the values found for KIc,
CVN and HRc yields a coefficient A value of 5.27, which is very close to the predicted
value.
The value of CVN has more of an influence on KIc than HRc. This makes it possible to
establish the way to increase the KIc value, which according to the literature would be
possible by reducing the bainitic packet size prior to the bainitic transformation or by
the obtainment of lower bainites by means of isothermic treatments.
References
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Fig. 1. Bainite microstructure of steel used. Austenitisation
temperature=950ºC. Cooling rate=2 K. s-1.
Fig. 2. Machined specimen for fracture mechanics testing.
Fig. 3. Crack generated in notch tip.
(a)
(b)
(c)
Fig. 4. Fracture surfaces of steel used: a) specimen 1; b) specimen 2; c) specimen 3;
Heat treatment: 950ºCx45 min and cooling in furnace.
Sample CR2-1
12
11.47
11.60
10
Load (kN)
8
6
4
2
0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
Displacement (mm)
Fig. 5. Load-displacement curve for specimen CR2-1.
Sample CR2-2
16
15.35
14.36
14
12
Load (kN)
10
8
6
4
2
0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
Displacement (mm)
Fig. 6. Load-displacement curve for specimen CR2-2.
Sample CR2-3
16
14.07
14
13.93
12
Load (kN)
10
8
6
4
2
0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
Displacement (mm)
Fig. 7. Load-displacement curve for specimen CR2-3.
Fig. 8. Fracture surface of Charpy-V-notch specimen of steel tested at 22ºC.
Fig. 9. Fractures of V-notch specimen of steel tested at 22ºC. Magnification 6x