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

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Abstract

An inverse relation to that of Wallin's strain rate equation has been obtained for predicting the static reference temperature from dynamic results. 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 quasi-static reference temperature, T0. The inverse WSRE (IWSRE) predicts T0 from T0dy, that is, T0 at dynamic loading rates as obtained in impact and other dynamic tests. For this purpose, the same dataset that was used by Wallin for deriving the original WSRE has been used. It has also been found that the dynamic reference temperature obtained by applying the modified Schindler procedure (MSP) to Charpy V-notch (CVN) impact tests, that is, TQSchdy, provides a conservative or close estimate of reference temperature corresponding to a loading rate of ∼106 MPa √m s−1. Then using the TQSchdy in the IWSRE along with RT-YS and SIF rate of 106 MPa √m s−1, results in an estimate of quasi-static T0, namely, TQMSP-IW, the subscript indicating use of both the MSP and IWSRE. An equation directly correlating TQSchdy to T0 has also been obtained. The estimates of T0 from this direct correlation are referred as TQMSP, the subscript indicating the use of MSP. It has been shown that the larger of the two estimates, TQMSP-IW and TQMSP, provides a reasonably accurate, but conservative estimate of T0 and is termed – TQSchW, to indicate the use of both the MSP and IWSRE procedures. TQSchW is a promising estimate for steels with TQSchdy less than 60 °C – termed TQ-est, to indicate the estimated reference temperature value; for steels with TQSchdy>60°C, TQ-est is the larger of the two estimates, namely, TQM2 and TQSchW. The equation reported in the literature correlating the brittleness transition temperature, TD (obtained from instrumented Charpy V-notch – CVN – impact tests), though has a tendency to accuracy and ease of estimation, is not suitable for making conservative reference temperature estimates, because of excessive scatter and lack of robustness in TD estimation. The shifts in TQ-est, namely, ΔTQ-est, are acceptably conservative even for the highly irradiated steel. For the high reference temperature steels and low upper shelf inhomogeneous steels, the anomaly of TQ-est being larger than RTNDT indicates that the conservatism of even the RTNDT approach is not much for such steels. A very useful application of the procedures in this paper is that the TQ-est or (TQ-est – 20 °C) can provide a convenient test temperature for performing the tests as per ASTM E-1921 test standard for determining T0. The whole procedure or methodology detailed in this paper for obtaining the conservatively estimated reference temperature, TQ-est, is designated as IGCAR-procedure, IGCAR being the acronym for the author's organization.

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., T0Schdy (here this is designated TQSchdy 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):Γ= 9.9expT01901.66+σys-RT7221.09andT0dy=T0Γ(ΓlnK˙)where 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), K˙, 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.Γ=41.54expT0dy72.86125.98+σys-RT0.1420.409andT0=T0dyΓ(ΓlnK˙)Correlation 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.

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