**Transactions of the 17th _{International Conference on }**

**Structural Mechanics in Reactor Technology (**

**SMiRT 17)****Prague, Czech Republic, August 17 –22, 2003**

** Paper # G04-5**

**Evaluation of Strain Rate Effects on Transition Behaviour Applying the Master**

**Curve Methodology **

Ivo Dlouhy1)*)_{, Jan Kohout}2)_{, Vladislav Jurasek}3)_{, Miloslav Holzmann}1)

1) _{Institute of Physics of Materials, Academy of Sciences of the Czech Republic Brno, Czech Republic }
2) _{Military Academy Brno, Department of Physics, Czech Republic}

3) _{University of Technology, Brno, Faculty of Mechanical Engineering, Czech Republic}
*) _{Corresponding author: idlouhy@ipm.cz}

**ABSTRACT**

Master curve methodology has been used for an evaluation of strain rate effects on transition behaviour of wrought CrMo and cast ferritic C Mn steel. The physical aspects of strain rate effect on reference temperature has been analysed as a base for the prediction of this dependence. Statistical aspects of the strain rate effects on the master curve have been discussed showing capability of the method for the prediction of strain rate susceptibility of steel fracture behaviour.

It has been experimentally proved that the master curve shape does not depend on the loading rate. The
relationship between reference temperature T0 (or the shift of T0 with respect to quasi-static loading rate) and loading
rate can be described with linear dependence if logarithmic scale of temporal change of stress intensity factor is
considered. For experimental establishing of the dependence of reference temperature on loading rates only two *T0*
values as determined at different loading rates are sufficient. However, it is useful to achieve the comparable accuracy
of both T0 determinations that may demand larger number of specimens for the measurement of T0 at the higher loading
rate. Standard quasistatic fracture toughness has been predicted from small pre-cracked Charpy type specimens tested
dynamically applying the reference temperature shift obtained experimentally. The predicted fracture toughness
temperature diagram has been proved experimentally.

**KEY WORDS:** ferritic steel, cast ferritic steel, pressure vessel steel, fracture toughness, transition behaviour, master
curve, reference temperature, strain rate effect, statistical aspects

**INTRODUCTION**

Master curve (MC) concept is currently widely used for the evaluation of temperature dependence of fracture
toughness in lower shelf and transition region [1-8]. Fracture toughness values applied for the master curve
determination have to be obtained at small scale yielding conditions at a crack tip at the moment of unstable fracture
initiation. The MC concept includes the weakest link theory describing distribution of fracture toughness values at a
given temperature [1,2], methodology for statistical size effects accounting [3] and, in addition, different crack length
effect on fracture toughness level [4,5]. Based on data obtained for low alloy steels with ferritic microstructure and
yield stress ranging from 275 to 825 MPa, the MC has been verified and the independence of the MC shape itself on
different alloying, heat treatment, and radiation embrittlement has been shown. These variables cause only a shift of
MC along temperature axis. Master curve localisation on temperature axis is then expressed by reference temperature,
*T0, which is a temperature corresponding to fracture toughness value (50 % probability) of 100 MPa m*1/2_{.}

For determining the reference temperature standard large (1T) specimens are usually required. But there are structures under operation for which the transition behaviour of fracture toughness is of great interest (reactor pressure vessels, rotors of steam generators etc.) and application of MC concept would be very useful. For these components only small specimens (e.g. pre-cracked Charpy type specimens, P-CVN) can be used for assessment of degradation, however. It has been shown [2,11] that the P-CVN specimens can be used in determining the reference temperature T0 and thereby making possible to apply the MC concept for the integrity assessment procedure of these components. Specimen size and loading rate effects on brittle fracture of ferritic steels tested in the ductile to brittle transition region thus remain key topic for the application of P-CVN specimens. As proved by Dodds et al. and others [17-19] these specimens lose constraint well before the onset of unstable fracture. The test results obtained thus could provide nonconservative and invalid estimate of conditions required for the onset of unstable fracture in full-scale component. It has been found however, that if the P-CVN specimens were loaded in impact the additional constraint would be present at the crack tip allowing to predict correctly the unstable fracture initiation from the P-CVN data [11] (tested dynamically). This allows the factor in the size-deformation limit to be reduced from the range of 50 to 100 to between 25 and 30 and the P-CVN results to be qualified for prediction of unstable fracture initiation in 1T specimens or full-scale components [20] without any adjustment for crack tip constraint loss.

The aim of the present contribution has been to verify the character of the dependence of the reference temperature on loading rate based on some physical considerations. Additionally fracture data from small pre-cracked Charpy type specimens tested dynamically will be used for prediction of temperature dependence of static fracture toughness for standard (1T) specimens.

**THEORETICAL BACKGROUND**

As the main mechanism preceding to fracture, the dislocation movement through microstructural obstacles, i.e. plastic deformation, is considered. In order to move over the obstacle, minimum activation energy is necessary to reach for the dislocation. Kirk et al. [6] shown that shape of master curve is affected only by the obstacles producing short-range stress fields. Frequency of successful jumps over the obstacle can be described by known Arrhenius eq. and comparing it to Orowan eq. (quantification of relation between deformation and dislocation velocities) the equation for strain rate determined by temperature activated dislocation velocity can be obtained [21,22].

∆_{−}
=
*kT*
*G*
exp
0
ε

ε& & (1)

This eq. (1) can be also written in forms

*Z*
*kT*
*G*_{≡}
∆
= exp
0 ε

ε& & and *T* *È*

*k*
*G* _{≡}
=
∆
ε
ε
&
&0
ln (2)

where Z is temperature-compensated strain rate, usually called as Zener-Hollomon parameter, see e.g. Roberts [23], and
Θ is rate-compensated temperature, sometimes also called as Zener-Hollomon parameter, e.g. Wallin and Planman [14].
Meaning of the parameters consists in possibility to replace the couple of quantities ε&*,T* by single quantity Z (or Θ).

The value of parameter *Z (or parameterΘ) is deciding for the obstacles overcoming by the stress fields of short*
range. The overcoming of other obstacles has to be covered by increasing applied stress. The Zener-Hollomon
parameter may be used for description of temperature and strain rate effects on yield stress. It can be also used for
description of these effects on fracture toughness transition behaviour.

The master curve shape itself is not affected by the strain rate effects, for steel followed here see [21,24]. The strain rate effect is thus possible to describe by temperature shift of the master curve.

Generally, fracture toughness is a function of both temperature and strain rate as external factors. Both factors can be replaced by single Zener-Hollomon parameter. Fracture toughness can be written as a function of this parameter (in this case parameter Θ is used)

=
=
ε
ε
ε
&
&
&_{)} _{ln} 0

,

(*T* *K* *T*

*K*

*K* . (3)

The extent of the temperature shift can be expressed from the difference of reference temperatures at the stipulated
value of fracture toughness (100 MPa m1/2_{). The dependence of the reference temperature on the loading rate can be}
expressed [21] as

*I*
*K*
*K*
*K*
*T*
*K*
*K*
*C*
*K*
*T*
*T*
&
&
&
&
&
&
ln
ln
ln
ln
ln
)

( 01 0

0 0 − = − =

The same equation was derived by Wallin and Planman [14] where designation *Ã*=ln*K*&_{0} was applied.

For the case of ln*K*&*I* <<ln*K*&0, which is very often valid, an approximate simplification of Eq. (4) can be obtained

01 0

01 0

0 1

0 0

0 ln

ln ln

ln 1 ln ln

ln 1

ln *K* *K* *T*

*T*
*K*
*K*
*K*

*C*
*K*

*K*
*K*

*C*

*T* *I* *I* _{}= * _{I}* +

+ ≈

− =

−

& & &

& &

& &

& (5)

whereby the linear dependence between reference temperature and logarithm of time variation of stress intensity factor
is obtained. The slope of this straight line is *T*01 ln*K*0 and the value for *KI* =1MPam1/2s−1is T01.

Eqs. (4) or (5) describing reference temperature dependence on time variation of stress intensity factor contain two
basic parameters *T01 and K*_{0} (or *Ã*=ln*K*_{0} in Wallin’s approach). The former determines the position of the master

curve (reference temperature for _{=}_{1}_{MPa}_{m}1/2_{s}−1

*I*

*K* ), the latter determines the shift of MC with changing loading rate.
Unfortunately, physical meaning of *K*_{0} is rather unclear. Using parameter Z instead of parameter Θ, see Eq. (2), and (5)

can be rewritten in form

_{01}

2 01

0 * _{G}* ln

*K*

*T*

*kT*

*T* * _{I}* +

∆

≈ & . (6)

The shift of transition curve due to loading rate can thus be determined by activation enthalpy ∆G that is well defined physical quantity and it can be measured by mechanical tests [24]. Having the transition curve for defined value of loading rate, its shift for different loading rates can be predicted.

**EXPERIMENTAL DETAILS**

Experimental investigations of the loading rate effect on the transition behaviour of fracture toughness consisted of two parts: (i) verification of the linearity of the reference temperature dependence on loading rate and (ii) application of the known reference temperature shift (due to different loading rate) on prediction of quasistatic standard fracture toughness from dynamically loaded P-CVN specimens.

For the first part, a 2.25Cr-1Mo steel, often applied for pressure vessels, was selected. The basic mechanical
characteristics of the steel at room temperature were as follows: *Re = 308 MPa, Rm = 495 MPa, impact energy KV =*
192 J. Two sets of test specimens for fracture toughness determination were manufactured and followed:

**Set (a)** Specimens for static three-point bending test with dimensions of *B = 25 mm, W = 50 mm and L = 240 mm*
(support span *S = 4 W = 200 mm), crack length to specimens width ratio a/W *≈ 0.5. The specimens were tested in
temperature range from –180 to 20 °C. Loading rate expressed by stress intensity factor rate *K*I determined from

linear-elastic part of the measured dependence was 2 MPa m1/2 s–1_{. Fracture mechanical characteristics KIC, KJC or KC}
were determined in agreement with [26].

**Set (b)** Specimens for three point bending test having dimensions of B = W = 15 mm and L = 75 mm in length (support
span S = 4 W = 60 mm), crack length a/W ≈ 0.5 were used for the fracture toughness measurements at different loading
rate. Servo-hydraulic test machine ZWICK Rel was used for the tests applying temperatures ranging from –140 to
20 °C. The piston speeds used at tests are given in Table 1 together with corresponding temporal change of stress
intensity factor *K*I. The quasi-static approach was used for fracture toughness determination, for details [21].

Table 1*. Loading rates (piston speeds) and corresponding values of K*&* _{I}*used in fracture toughness measurements

piston speed [mm.s–1_{]} _{5⋅10}–2 _{5⋅10}–1 _{5} _{5⋅10} _{5⋅10}2

*I*

*K*& [MPa m1/2_{ s}–1_{]} _{6.2} _{64} _{640} _{6.4⋅10}3 _{1.0⋅10}5

For the other part of experiments and considerations, a cast C-Mn steel [8,26], predetermined for containers of
spent nuclear fuel, was used. The basic mechanical characteristics of the steel at room temperature were as follows: Re =
270 MPa, *Rm = 435 MPa, impact energyKV = 181 J. The experimental data have been generated when investigating*
problems of fracture resistance of this steel for containers of spent nuclear fuel [26]. The following data sets have been
applied for purposes of this investigation:

tested at one temperature in lower (30 specimens at -130 °C) and higher part (10 specimens at 100 °C) of transition
region. Data for the surface locations of thick walled plate have been selected for purposes of this paper, details in [26].
**Set (d)** Pre-cracked Charpy type specimens (10x10x55 mm) with support span 40 mm were tested on instrumented
impact tester by low blow method. The test conditions corresponded to standard [27]. Loading rate (about 1 m.s-1_{)}
expressed by stress intensity factor rate *K*I was of the order 105 MPa m1/2 s–1. The temperature range for the test was so

selected to cover the lower shelf and transition region of fracture toughness values. Note, that the data from this P-CVN set have been compared to standard 1T SENB specimens tested dynamically [8,15] with very good correlation

**RESULTS AND DISCUSSION**

**Reference Temperature vs. Loading Rate Dependence (2.25Cr-1Mo steel)**

Based on temperature dependences of fracture toughness values two procedures of reference temperature and master curve determination were applied both based on multitemperature approach:

(i) Iteration method based on the approach derived by Wallin [28] exploiting maximum likelihood method (MLM), and (ii) Regression method (by least square method - LSM) of fracture data in transition region applying general equation

) exp(

min

JC *K* *A* *BT*

*K* = + . (7)

Both mentioned procedures were directly used only when the experimental data *KJC were measured on test*
specimens having 1T with thickness (25 mm).

For specimens having thickness *Bx different from standard one (set (b) of specimens), 1T, it was necessary to*
adjust fracture toughness values to 1T equivalent values. Standard equation was used for these purposes

## [

## ]

4 / 1

1T )

( JC

JC(1T) 20 20

− +

=

*B*
*B*
*K*

*K* *x*

*x* . (8)

This correction for statistical size effect applied for fracture toughness values *KJC greater than 40 up to*
50 MPa m1/2_{ (the weakest link theory is not valid for smaller ones). Estimated reference temperatures, T0, for particular}
loading rates are shown in Table 2. At quasi-static loading (i.e. for *K _{I}* = 2 MPa m1/2

_{ s}–1

_{) a value of reference}temperature T0 = –87°C was established. Following conclusion could be drawn from the results:

- The reference temperature is shifted to higher value with increasing strain rate. For loading rate *K*&*I* = 105 MPa m1/2 s–1

temperature shift ∆T0 is approximately 60 °C according to both methods of T0 evaluation.

- The difference among T0 values estimated according to method (i) and (ii) is not large, maximally 9 °C. The T0 values determined using maximum likelihood method are always higher than those from regression (except one value); the maximum likelihood method seems to be more conservative.

Table 2. The reference temperatures T0 determined using maximum likelihood method (i), and

using least square method (ii), respectively

*I*

*K*& [MPa m1/2_{ s}–1_{]} _{2} _{62} _{64} _{640} _{6.4⋅10}3 _{1.0⋅10}5

*T0 [°C] *(i) _{–87} _{–83} _{–62} _{–47} _{–38} _{–26}

*T0 [°C] *(ii) _{–91} _{–74} _{–67} _{–51} _{–44} _{–35}

Known value of reference temperature T0 allows the master curve on temperature axis to localise for given loading
rate *KI*. As the MC keeps the shape independent of loading rate, all fracture toughness data measured at different

loading rates *KI* will align into one scatter band in KJC vs. (T–T0) coordinates. The scatter band is specified by tolerance

limits defined by equations [3]:

)] ( 019 . 0 exp[ 8 . 37 4 .

25 0

JC(0.05) *T* *T*

*K* = + − (9)

)] ( 019 . 0 exp[ 2 . 102 6 .

34 _{0}

JC(0.95) *T* *T*

*K* = + − (10)

- Very good agreement of the experimental data with master curve shape including the tolerance bands that can be taken as a good evidence of validity of master curve concept at dynamic loading conditions.

- Despite differences in reference temperature *T0 caused by different methods of its determination good agreement*
between master curve and experimental data has been observed for both methods followed.

- The conservative nature of maximum likelihood method has been confirmed as it has been noted when comparing the
*T0 values in *Table 2.

Fig. 1* Fracture toughness temperature diagram for the highest loading rate used*

In Figure 2 the fracture toughness diagram versus temperature difference *T–T0 is shown. It confirms *

above-mentioned assumption that the master curve shape itself is not dependent on loading rate. It is worthy of notice that
valid fracture toughness values less than 50 MPa m1/2_{ are localized also in 90 % confidence interval though for these}
fracture toughness values the master curve concept is not valid. In Fig. 2, the filledsymbols represent original fracture
toughness values of measured on specimens having thickness B = 15 mm that didn’t need any corrections (according to
Eq. (8)). Also fracture data for standard specimens having thickness *B = 25 mm are without any adjustments. Empty*
symbols represent values corrected for statistical size effects using equation (8).

Fig. 2 Fracture toughness at different loading rates as a function of temperature difference T-T*0*

-200 -150 -100 -50 0

temperature [ °C ]

0 50 100 150 200 250

frac

tu

re

toug

hn

es

s

K , KIC

JC

[

M

Pa

.m

1/

2 ]

KJC(0,95)

KJC(med)

KJC(0,05)
dK/dt = 105_{ MPa.m}1/2_{.s}-1

iterations / MLM regression / LSM corrected to 1T valid values

-200 -150 -100 -50 0 50

temperature difference T - T_{0} [ °C ]

0 50 100 150 200 250 300

fra

ctu

re

to

ug

hn

es

s

KIC , KJC

[

M

Pa

.m

1/

2 ]

KJC(0,95)

KJC(0,05)

dK/dt = 2 MPa.m1/2_{.s}-1

dK/dt = 6.2 MPa.m1/2_{.s}-1

dK/dt = 6.4 ∗10 MPa.m1/2_{.s}-1

dK/dt = 6.4 ∗102 MPa.m1/2.s-1
dK/dt = 5.1 ∗103 MPa.m1/2.s-1
dK/dt = 105_{ MPa.m}1/2_{.s}-1

In Figure 3, the dependence between reference temperature shift ∆T0 and logarithm of loading rate *K*&* _{I}* is shown.
There are data dependences for a number of weld materials originally published by Yoon [16]. There are also
experimental points for SA 515 steel followed by Joyce [11]. Finally, there are included ∆T0 values calculated from

*T0*values shown in Table 2 (filled rhombi and full line). The temperature shift is given by difference between

*T0 for*selected loading rate

*K*and

_{I}*T0*corresponding to quasi-static tests. All these experimental results confirm that the dependence of reference temperature T0 or temperature shift ∆T0 against ln

*K*can be approximated by the straight line in semi-logarithmic coordinates. This empirical finding well supports the theoretical considerations that lead to Eq. (5) [21,24].

_{I}Having included data of different steels in Fig. 3 it follows from their comparison that slope of linear dependences
of reference temperature shift, ∆T0, against temporal change of stress intensity factor in logarithmic scale, ln *K _{I}*,
appears to be material susceptible (i.e. it is different for different steels).

Fig. 3 Dependence of temperature difference T-T0 on loading rate represented in terms of *K*&*I*

The prediction of the fracture toughness temperature dependences for different loading rates is also affected by the
accuracy of the reference temperature *T0 estimation procedure. The fracture toughness values exhibit large inherent*
scatter in the transition region and this fact has significant influences on the accuracy of the reference temperature *T0*
determination and, hence, the effect on the temperature shift ∆T0. The accuracy of T0 determination increases with the
number of specimens used for the toughness determination but a noticeable increase of the accuracy cannot be expected
when test temperatures lie deep below temperature T0 [21,25]. Similar situation can be expected for higher loading rates
when step (discontinuous [13,15]) increase of fracture toughness values occurs from lower to upper shelf level. Then
only the values from lower shelf region can be used and further course of the master curve has to be extrapolated. To
obtain comparable accuracy in this case, the number of fracture toughness data is necessary to increase.

1x10-1 _{1x10}0 _{1x10}1 _{1x10}2 _{1x10}3 _{1x10}4 _{1x10}5 _{1x10}6

dK_{I} /dt [ MPa.m1/2_{ .s}-1_{ ]}

0 20 40 60 80 100

∆

T0

[

°C

]

Cr-Mo SA5151 (Joyce) WF-25 WF-25(9) 5JRQ45 WF-182-1 WF-193

-100 -80 -60 -40 -20 0

T0

[

°

Fig. 4 Confidence intervals for reference temperatures at different loading rates

For the experimental data investigated here the effect of specimen number used for reference temperature
determination on confidence limit has been followed [25]. Based on these analyses the 95% confidence limits (bars) of
*T0 are plotted in *Figure 4 showing the temperature T0 as a function of ln (*KI*). Straight line dependence is theoretically

supported by Eq. (5) and regression calculations allow to determine the values of regression parameters Ts and ∆G (or

0

ln*K*

*Ã*= ) together with their standard deviations: Ts = (–90±3) °C = (183±3) K, ∆G = (0.49±0.05) eV = (47±5) kJ/mol,
Γ = 31±3. The confidence limits are comparable because approximately the same number of specimens was used for
determining T0 and the master curve had not be extrapolated even for the highest loading rates. These conditions have
not been apparently met in measurements of T0 for steel SA 515 performed by Joyce as a large scatter of dT0 values can
be observed already at *KI*=104 MPa m1/2 s–1.

**Fracture Toughness Prediction from Dynamically Loaded P-CVN Specimens (cast C-Mn steel)**

In principle, only two T0 values determined at two different loading rates are sufficient to establish experimentally
the dependence of reference temperature *T0 on the loading rateKI*. However, it is useful to achieve the comparable

accuracy of *T0 determination in both cases, which may need larger number of specimens in the case of the higher*
loading rate.

As example, the dependence of reference temperature *T0 against loading rateK*&* _{I}* is shown in Figure 5 for cast
ferritic steel investigated extensively in other our work [24]. This plot has been obtained when following the fracture
behaviour of standard 1T specimens [27] for quasistatic loading conditions as set (c) of data, and for dynamic loading as
data generated by means of instrumented drop weight tower in work of Lenkey [8,24]. Two locations of thick walled
segment for container of spent nuclear fuel were followed, central plane of the plate, C, and surface region, E. The
characteristics of both are represented in Fig. 5. For comparison the data for 2.25Cr 1Mo steel are replotted from Fig. 3

into this figure. For the cast ferritic steel the shift of reference temperature is represented here by dotted arrow.

From the material point of view one of the main findings is that steel is strongly susceptible to loading rate.
Remarkable shift of reference temperature (and/or other transition temperatures in corresponding way) is observed
being on level of 133 °C for location E when comparing these temperatures with values obtained at static loading (dK/dt
about 105 _{MPam}0.5_{s}-1_{ against 1 MPam}0.5_{s}-1_{). }

Fig. 5 Effect of loading rate stressed in terms of *K*&* _{I}* on shift of reference temperature

The generation of *T0 vs.K*&*I* dependence by this way is naturally not too effective. As it has been indicated in

theoretical background some possibility of this dependence prediction is open based eq. (6) and tensile data obtaining. The different aspects of the procedure are under investigation now [24].

As mentioned in introduction pre-cracked Charpy type specimen (P-CVN) is the most suitable geometry for the assessment of radiation and elevated temperature ageing of container cask and RPV steels, as well as for analysis of strain rate effect. The importance of the above mentioned dependence can be seen in possibility to transfer the fracture

1x100 _{1x10}1 _{1x10}2 _{1x10}3 _{1x10}4 _{1x10}5 _{1x10}6 _{1x10}7

dKI/dt [ MPa.m1/2 s-1 ] -150

-100 -50 0 50

re

fe

re

nc

e

te

m

per

at

ur

e,

T0

[ °

C

] **2.25Cr 1Mo **
**cast C-Mn**
loc C
loc E

0 50 100 150

∆

T [

°

C ]

characteristics received at given loading conditions (most frequently pre-cracked Charpy specimen tested dynamically, often not meeting the EPLM conditions for standard specimens) to other test specimen type and/or real components. For known shift of reference temperature the master curve approach can be successfully used in this case.

To test this possibility the data set (d) of fracture toughness values from P-CVN specimens tested dynamically have been used. The data from P-CVN specimens tested dynamically that met the size deformation validity limit

2 / 1 d e )

it (lim

Jd [(EbR )/50]

K = (11)

have been corrected for statistical size effects according to eq. (8). The reference temperature have been obtained by multitemperature method supplying the value T0 = -5 ºC (see Table 3).

For the data from dynamically loaded P-CVN specimens and corrected additionally for statistical size effect (for the cast ferritic steel investigated, surface location E) the predicted master curve and 90 % probability scatter band corresponding to standard specimens thickness is shown in Figure 6.

Fig. 6 Temperature dependence of fracture toughness for P-CVN specimens

To prove the reliability of these data for further analyses the mentioned probability scatter band for P-CVN specimens can be compared to standard SENB specimen data tested by instrumented drop weight tower. As it has been shown in other our work [14] the master curve and 90 % probability scatter band obtained for standard specimen was lying slightly in conservative side of experimental fracture toughness data from P-CVN specimens; nevertheless still very good correlation both data sets was observed. The median values corresponding to the standard geometry loaded dynamically is represented by dashed curve in Figure 6, the reference temperature can be compared based on data shown in Table 3.

Table 3. Comparison of reference temperatures T0 (in ºC) for different testing conditions

Having the valid data from P-CVN specimens tested by low blow method a prediction for standard 1T SENB
specimens behaviour at static loading could be carried out. The reference temperature t0PCVNd _{from P-CVN data can be}
determined according to standard procedure as above shown. Than the shift of reference temperature ∆T0 can be read
from Figure 5 and reference temperature for static fracture behaviour *t0*PCVNp_{ can be obtained subtracting from t0}PCVNd

SENB dynamically

P-CVN dynamically

1T SENB PREDICTED

1T SENB statically

P-CVN statically

- 8 - 5 -138 -144 -144

-80 -60 -40 -20 0

temperature [ °C ]

0 100 200 300 400 500

dy

na

m

ic

fr

ac

tu

re

to

ug

hn

es

s [

M

Pa

.m

1/

2 ]

KJd (limit)

**K _{Jd}**

**K _{Jdm}**

t_{DBL}PCVN

t_{0}PCVN
**C-Mn steel (E)**

PCVN low blow

t_{0}SENB

the transition behaviour for static fracture toughness (corresponding master curve with 90 % probability scatter band) could be predicted.

To test validity of this prediction really measured fracture toughness values are shown in Fig. 7 represented by open (for transition region) and filled rhombi (for upper shelf region). These data (median values) are in figure also

represented by thin dashed line. Good correlation can be stated, the prediction is slightly on conservative side of really measured values.

Fig. 7 Predicted transition behaviour of standard 1T SENB specimens based on data

generated from PCVN specimens tested dynamically

**CONCLUSIONS**

The effect of loading rate on the change of reference temperature has been followed taking into account physical basis of the experimentally determined dependence. Main findings can be summarised as follows:

It has been experimentally proved that the master curve shape does not depend on the loading rate.

The relationship between reference temperature T0 (or the shift of T0 with respect to quasi-static loading rate) and loading rate may be based on theory of thermally activated processes and dislocation mechanics. It can be described with linear dependence if logarithmic scale of loading rate is considered.

For experimental establishing of the dependence of reference temperature on loading rates only two T0 values as determined at different loading rates are sufficient. However, it is useful to achieve the comparable accuracy of both T0 determinations that may demand larger number of specimens for the measurement of T0 at the higher loading rate.

From the engineering point of view, for evaluation of the influence of loading rates on the temperature behaviour of fracture toughness the dependence between reference temperature and loading rate is fully sufficient which can be determined by the values of two parameters.

Shift of reference temperatures determined experimentally has been applied when predicting the quasistatic fracture toughness for 1T SENB specimens from P-CVN specimens tested dynamically. Very good correlation predicted values with reference set has been found.

**ACKNOWLEDGEMENTS**

The research was financially supported by grant No. A2041003 of the Grant Agency of the Academy of Sciences and project No. 106/01/0342 of the Grant Agency of the Czech Republic.

-150 -100 -50 0

temperature [ °C ]

0 100 200 300 400 500

fra

ctu

re

to

ug

hn

es

s [

M

Pa

.m

1/

2

]

KJc (limit)

**KJi**
**C-Mn steel (E)**
K_{JC }SENB

KJu

KJC(med) PCVN dyn
K_{JC}(mean) SENB

t_{DBL}
t_{0}SENB _{t}

0PCVNp t0PCVNd

**REFERENCES**

1. Wallin K., (1993), Macroscopic Nature of Brittle Fracture, *J. de Physique, Colloq 7, Suppl J. de Physique II, Vol. 3*, pp

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