Inverse of Wallin's relation for the effect of strain rate on the ASTM E-1921 reference temperature and its application to reference temperature estimation from Charpy tests
Research highlights
▶ An inverse relation for the Wallin strain rate equation (WSRE), that is, IWSRE, has been derived for predicting the static reference temperature from dynamic results. ▶ Using the IWSRE and some other correlations, a procedure, called IGCAR-procedure, has been developed for conservative estimation of the ASTM E-1921 reference temperature, T0-est, from Charpy V-notch ductile-brittle transition tests alone. The T0-est by the IGCAR-procedure is termed Tq-IGC to distinguish it from other estimates. ▶ Tq-IGC is neither too conservative nor unacceptably non-conservative. ▶ The Tq-IGC along with the conservative Master Curve procedure helps provide assuredly conservative lower-bound fracture toughness curve.
Introduction
By analogy to the well-known Zener–Hollomon strain rate parameter for temperature dependence of yield stress in ferritic steels and based on a simple pattern recognition procedure for determining the form of equation and the relevant properties involved, Wallin (1997) and Wallin and Planman (2001) had derived an empirical relation for the effect of loading rate on the ASTM E-1921 reference temperature, T0 (ASTM E1921-97, 1998), for ferritic steels. This enables the estimation of reference temperature at larger loading rates (expressed in terms of stress-intensity factor – SIF-rates) from room temperature yield stress and (quasi-)static reference temperature, T0. Wallin's expression will be referred as Wallin strain rate equation (WSRE). One of the aims of this paper is to derive an inverse relation to WSRE using the same dataset as used by Wallin (1997) and Wallin and Planman (2001) so that the quasi-static reference temperature can be estimated from a knowledge of room temperature yield stress and dynamic reference temperature, i.e., reference temperature corresponding to faster loading or SIF rates, say, determined from instrumented precracked Charpy tests (Moitra et al., 2005). The new relation will be referred as the inverse Wallin strain rate equation (IWSRE). For further comparison and validation, some different dataset of dynamic and static reference temperatures reported in the literature will be used. In fact, Lucon and Chaouadi (2001), while applying the WSRE, had commented on the desirability and usefulness of an inverse type equation and had advocated a similar procedure as outlined above for deriving such an inverse equation.
Some previous results obtained by the author and co-workers indicate that the estimate of dynamic reference temperature obtained by applying the modified Schindler procedure (MSP) to Charpy data, i.e., (here this is designated as described later), probably gives a close or conservative estimate of dynamic reference temperature (Moitra et al., 2005, Sreenivasan et al., 2004) at a SIF rate of 106 MPa √m s−1. Then, this can be plugged into the IWSRE to give an estimate of T0 that is likely to be a conservative or close estimate of the actual T0. Thus the second objective of this paper is to verify the above proposition. Recently, based on data taken from the literature, the author had examined some of the older (Sreenivasan et al., 2003, Sreenivasan et al., 2004, Sreenivasan, 2008) and newer (Sreenivasan, 2009) Charpy energy-fracture toughness correlations along with some newly derived correlations for their effectiveness in accurately or conservatively estimating the ASTM E-1921 reference temperature, T0 (ASTM E1921-97, 1998). Hence, a third objective of the paper will be to compare the results from the IWSRE method with those from the most promising correlations presented in (Sreenivasan et al., 2003, Sreenivasan et al., 2004, Sreenivasan, 2008, Sreenivasan, 2009) for the dataset presented in those references.
In addition, some recent researches report that older correlations applicable to older steels do not necessarily hold for the new clean steels produced by advanced processes and for the highly alloyed ferritic–martensitic or reduced activation ferritic–martensitic (RAFM) steels (Nevasmaa and Wallin, 1997, Chaouadi, 2005). Nevasmaa and Wallin (1997) have given a comprehensive review of correlations available at the time of their report and have pointed out the need for verifying, augmenting and updating the correlations for newer steels, product forms and embrittlement conditions. They have also stated that the temperature based correlations seem to be the most successful for predicting the reference temperature. Hence the objectives of this paper are commensurate with the observations in Nevasmaa and Wallin (1997). Also, the comprehensive fracture toughness master curve and Charpy data for four 9-12Cr–Mo-type and RAFM steels presented in Chaouadi (2005) provide a firmer basis for comparing and contrasting the various correlations. More importantly, the methodology suggested in this paper, when further validated, would prove very useful in ageing management and life-extension of present power reactors by helping reevaluation of surveillance specimen test results and assuring structural integrity in an assuredly conservative fashion based on Charpy-transition tests alone.
Section snippets
Wallin's relation for the effect of strain rate on the fracture toughness reference temperature T0 for ferritic steels and its inverse relation
Wallin's strain rate shift equation for estimating the dynamic reference temperature from room temperature yield stress and quasi-static (ASTM E-1921) reference temperature (T0) is as given below (Wallin, 1997, Wallin and Planman, 2001):andwhere T0 is the quasi-static (stress intensity factor – SIF-rate ∼1 MPa √m s−1) reference temperature in K and the SIF-rate in Eq. (1b), , is the dynamic rate (MPa √m s−1) and σys-RT is the room temperature
Materials and data
For developing the IWSRE, the data from Table 1 as described above is used (Wallin, 1997, Wallin and Planman, 2001). For further comparing the predictions from the IWSRE, a complete data set of both static and dynamic T0 presented in Table 3 is used (Yoon et al., 2001). The other steels for which T0 values are estimated using the IWSRE procedure are presented in Table 4a, Table 4b, Table 4c and are the same as detailed in Sreenivasan et al., 2003, Sreenivasan et al., 2004 and Sreenivasan, 2008,
Inverse Wallin strain rate equation – IWSRE
As discussed in Section 2.1, the data in Table 1 were fitted to Eq. (3) to determine the constants A, B, C, D and E. The resulting IWSRE is as given below.andCorrelation coefficient, R = 0.8801; standard error of estimate, SEE = 20 °C.where, as in the case of Eq. (1), the temperatures are in K, YS is in MPa and SIF rate is in MPa √m s−1. The fit was done using a commercial technical graphing programme using its nonlinear regression
Conclusions
An inverse relation to that of Wallin's strain rate equation has been obtained for predicting the static reference temperature from dynamic results. An additive factor of 10–15 °C to the estimates would provide results that are more conservative or closer to the actual values mostly within 20 °C.
Wallin strain rate equation (WSRE) predicts the reference temperature at faster loading rates (expressed as stress intensity factor (SIF) rates) from room temperature yield strength (RT-YS) and
Acknowledgements
The author acknowledges with thanks the excellent support and encouragement received from Dr. Baldev Raj, Director, IGCAR, Kalpakkam, India.
References (29)
Estimation of ASTM E-1921 reference temperature from Charpy tests: Charpy energy-fracture toughness correlation method
Eng. Fract. Mech.
(2008)On the (in)adequacy of the Charpy impact test to monitor irradiation effects of ferritic/martensitic steels
J. Nucl. Mater.
(2007)- et al.
Upper shelf temperature dependence of fracture toughness for four low to intermediate strength ferritic steels
Eng. Fract. Mech.
(1977) - et al.
Fracture toughness evaluation of a H.S.L.A. steel
Eng. Fract. Mech.
(2004) - et al.
Dynamic fracture toughness properties of a 9Cr–1Mo weld from instrumented impact and drop-weight tests
Int. J. Pres. Ves. Pip.
(1996) Effect of strain rate on the fracture toughness reference temperature T0 for ferritic steels
- Wallin, K., Planman, T., 2001. Effect of strain rate on the fracture toughness of ferritic steels. IAEA Specialists...
Standard test method for determination of reference temperature, T0, for ferritic steels in the transition range
- et al.
Ductile-brittle transition temperatures and dynamic fracture toughness of 9Cr–1Mo steel
Metall. Mater. Trans.
(2005) - et al.
Radiation damage assessment by the use of dynamic toughness measurements on pre-cracked Charpy-V specimens
Predicting reference temperature from instrumented Charpy V-notch impact tests using modified Schindler procedure for computing dynamic fracture toughness
Int. J. Fract.
Dynamic fracture toughness and Charpy transition properties of a service exposed 2.25Cr–1Mo reheater header pipe
J. Eng. Mater. Tech. (Trans. ASME)
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