PSI - Issue 71

Nagaraj Ekabote et al. / Procedia Structural Integrity 71 (2025) 58–65

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4. Results and Discussions Firstly, a detailed re-examination of constraint parameter, m , is carried out for CT, DCT, and SENB specimens as specified in ASTM 1820. The necessary modifications in the m equations will be introduced and verified. Further, the load vs. CMOD curves were used to determine the J and CTOD as per ASTM 1820 and BS 7448. A comparison between CTOD estimated by both standards for the various S yt /S ut is carried out. Finally, a relation among both standard’s CTOD will be established. 4.1. Constraint parameter (m) evaluation 4.1.1 Variation of m in CT and DCT CT and DCT specimens, both possess the identical geometry dependent constants A 0 = 3.62, A 1 = 4.21 , A 2 = 4.33, and A 3 = 2.00. Since, m is independent of a/W, only S yt /S ut is varied between 0.5 and 1. Also, as recommended by ASTM 1820, the Equation (2) is valid for all materials having S yt /S ut between 0.5 and 1. The variation of m for the change in S yt /S ut is estimated using Equation (2) and plotted as shown in Fig. 4. In Fig. 4, as the S yt /S ut increased, the magnitude of m decreased. Hence, m is inversely proportional to S yt /S ut . However, almost a linear variation of m is witnessed instead of the hyperbolic curve as represented using 3 rd order polynomial in ASTM 1820. The over-estimation of the curve is witnessed and should be corrected by modifying the m . The nature of the curve is almost linear (as similar to straight line) and can be modelled mathematically, using the first order polynomial in the form of a straight-line equation. The curve fitting of the line yielded the Equation (5) and represented as m CT mod (for DCT as m DCT mod ). Further, the comparison between the Equation (2) and Equation (5) results are shown in Fig. 5. In Fig. 5, both polynomials resulted in identical nature with least variation of m for the change in S yt /S ut . The error of less than 1% between both polynomials, confirmed the correction in estimating the m through Equation (5) is successful.

Fig. 4: m variation in CT and DCT. = = 2.934 − 1.179 ∗ ( )

Fig. 5: Verification of m CT mod and m DCT mod .

(5)

4.1.2 Variation of m in SENB The m equation for SENB is identical to CT and DCT, but the geometry dependent constants are a/W dependent. The geometry dependent constants, A 0 , A 1 , A 2 , and A 3 are estimated for the wide range of a/W, and are varied between 0.2 and 0.8. For the considered a/W, the estimated A 0 , A 1 , A 2 , and A 3 constants in SENB are shown in Table 2. As the a/W increased, the constants decreased linearly as witnessed through Table 2. Further, these constants were utilized to determine the constraint parameter, m. The estimated m values for different a/W and S yt /S ut in case of SENB specimen are plotted in Fig. 6. Table 2. Geometry dependent constants for variation of a/W in SENB a/W A 0 A 1 A 2 A 3 0.2 3.136 3.874 3.982 1.838 0.3 3.114 3.651 3.753 1.732