A modified normalization method for determining fracture toughness of steel

Abstract

Normalization method (NM) is a practical method for determining the J–R curves and fracture toughness of steels. There is some concern, however, about the performance of this method on steels with small strain hardening exponent and yield strength owing mainly to the assumption of infinite strain hardening exponent. This paper intends to analytically modify the NM by removing this assumption and incorporating the strain hardening in calculating the blunting corrected crack length. This modification enables the NM to be applied to steels with small strain hardening exponent and yield strength. Experiments are undertaken to verify the modified NM (CNM). A comparison of fracture toughness determined by CNM with that by the unloading compliance method and NM corroborates the improved accuracy of the developed CNM. The paper concludes that the developed CNM overcomes the deficiency of the NM for steels with small strain hardening exponent and yield strength.

A new method for determining the accurate J‐R curves of steels

“…For the UC method, the estimated crack (extension) length is underestimated, while for the NM, the estimated crack (extension) length is overestimated as previously proved in Gao et al 29,30 The crack extension underestimation by the UC method is because of the thickening of the specimen during test, 30 while the crack extension overestimation by NM is because that the strain hardening exponent is assumed to be infinity in the calculation of blunted initial crack length 28,29 . The detailed analytical and experimental evidence can be found in Gao et al 28–30 Thus, for an arbitrary point on the P‐V curve, the J ‐integral determined by the three methods is almost the same, but different crack extensions can be obtained for one specimen using different methods, which is the root reason for different J ‐R curves of one specimen obtained using different methods. Intuitively, if there is a method that can determine the crack (extension) length accurately, an accurate J ‐R curve can be determined and so is the fracture toughness.…”

“…Based on this procedure, a number of examples were given to accurately establish the J-R curves using data taken from Gao et al [28][29][30] as presented in Table 1. The results of the J-R curves determined by AJR are shown in Figure 3, together with those from the UC method and NM.…”

“…Table 1 presents results from the tests by Gao et al [28][29][30] for three types of steel with six 10-mm CT specimens, six 10-mm SE(B) specimens, and six 16-mm SE(B) specimens. The sketches of these specimens can be seen in Figure 1.…”

“…As it is known, J-R curves are derived from P-V curves which are raw load and displacement records and hence should be the same for all methods used. Results from the tests with different specimens and materials conducted by Gao et al [28][29][30] proved that, for an arbitrary point on the P-V curve, the J-integral determined by UC and NM is almost the same. 28 Wallin and Laukkanen 31 also proved that the J-integral calculated in the BT method is identical to the J-integral calculated using the single-specimen test, such as UC.…”

“…For instance, the average difference in the tested J Ic between W700-S-10-01 and 02 is only 8.93%, but the average difference in the tested J Ic between W700-S-16 specimens and W700-C-10 is over 18.14%. [28][29][30] Clearly, the geometry and configuration play a significant role in UC method and NM. Gao et al 30 also found that the largest disagreement between UC and NM is from thicker CT specimens with shallower initial crack length.…”