PSI - Issue 71

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

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m SENBmod . The computed values of m for SENB with a/W = 0.2, 0.5, and 0.8, from Equations (2) and (6) are plotted in Fig. 8. The proposed Equation (6) of constraint parameter, m, computed for the change in S yt /S ut seems perfect, as witnessed through the smooth overlapping of lines. Further, the error analysis of the proposed modified constraint parameter, m SENB mod was carried out and the error of less than 1% was evidenced for all a/W and S yt /S ut considered in this study. Hence, the proposed new equation of first order polynomial is adequate to measure the constraint parameter in the SENB specimen. 0 = 2.48 + 0.14 ( ) (7) 1 = 1.22 − 0.63 ( ) (8) 4.2. Comparison between CTOD estimated from BS 7448 and ASTM 1820 Here, the CTOD will be estimated for different S yt /S ut using both standards. The elastic-plastic fracture analysis is carried out, and verified with the experimentally obtained load vs. CMOD curves. J -integral was extracted directly from the software for CT specimen and used to compute the CTOD as per ASTM 1820. Similarly, the CTOD as per BS 7448 were estimated using Equation (4) with acquired data from numerical analysis. Fig. 9 shows the CTOD vs. J/S Y plot for both standards at different S yt /S ut . The CTOD obtained from BS 7448 are higher in magnitude compared to ASTM 1820. For all the S yt /S ut considered, the ASTM 1820 obtained CTOD values are around 70% lower to the CTOD of BS 7448. The variation of CTOD for J/S Y , initially linear followed by non-linearity for BS 7448. However, ASTM 1820 showed the linear variation as represented through Equation (1). BS 7448 computed CTOD were preferred in crack characterization owing to the similarity with experimental CTOD magnitude. The under-estimation of CTOD in ASTM 1820, reflects the non-usage of this standard for CTOD based fracture assessment.

Fig. 8: Comparison between ASTM 1820 and modified m for SENB specimen.

Recently, N Ekabote, (2024) reviewed the ASTM 1820 based CTOD estimation vulnerability in CT specimen and proposed the correction in constraint factor, m , based on comprehensive finite element analysis. FE origin method was proposed to improve the CTOD estimation from J -integral. Thus, a comparison between δ BS 7448 ( δ as per BS 7448) and FE origin is shown in Fig. 10. FE origin values are around 40% lower than the δ BS 7448 , indicating the J -based CTOD computation is inaccurate and unreliable. Though the δ BS 7448 magnitudes are higher compared to FE origin , the difference between them is reduced compared to δ ASTM 1820 ( δ as per ASTM 1820). Also, the relation between J/S Y and CTOD found to be non-linear for both FE origin and δ BS 7448 . Hence, an effort in redefining the J-CTOD relation for BS 7448 estimated CTOD values may help to achieve better results. In linear elastic fracture analysis, stress intensity factor ( K ) and Energy release rate ( G ) were both related and the relation among these two parameters are widely accepted by all standards. However, in elastic-plastic fracture analysis, a unique and well accepted J-CTOD relationship among the standards is missing. Although both J -integral and CTOD are nonlinear measures of a material's fracture toughness, non-ASTM standards have not been able to establish a relationship between them. BS 7448, is exclusively to measure the CTOD of the material and the relationship with J is not defined. Practitioners in crack assessment fields definitely need the interchangeability between non-linear parameters for wider penetration among engineering applications.