PSI - Issue 71

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

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However, ASTM preferred and defined the CTOD estimation through J -integral. ASTM 1820 seems to be emphasizing on determination of J rather than CTOD . J-CTOD relation was established as similar to linear fracture mechanics parameters, stress intensity factor ( K ) and energy release rate ( G ). However, CTOD estimation by J involves the constraint parameter, m and material property (yield stress ( S yt ) and ultimate stress ( S ut )) of the specimen. ASTM 1820, basically explains the J or J -Resistance curve determination for metallic materials and also CTOD estimation by J . The J -based CTOD, results in conservative estimation of CTOD . Although CTOD is the oldest fracture toughness parameter, its determination relies on J value in ASTM 1820. An exclusive CTOD standard for the determination of CTOD in ASTM is missing. Hence, ASTM 1820 usage in CTOD based fracture assessment is limited and practitioners often depend on non-ASTM standards. However, other standards use PHM for the determination of CTOD and are widely accepted for fracture toughness assessments. A reliable and efficient relationship between J and CTOD may ensure ASTM 1820 wider applicability for CTOD based fracture assessments. In ASTM 1820, CTOD estimation is carried out by using Equation (1) and is based on comprehensive finite element analysis, valid for S yt / S ut ≥ 0.5. In Equation (1), S Y is the effective yield stress and is calculated by S yt and S ut of the material. The constraint factor, m (shown in Equation (2)) is defined by a polynomial of 3 rd order and is dependent on crack length to width ( a/W ) along with geometry dependent constants, A 0 , A 1 , A 2 , and A 3 . The CT and DCT specimen have the identical constants values. While, the constants for SENB specimens are in-plane dimension dependent. The primary concern related to J-CTOD relation is the under-estimation of actual CTOD . The under-estimation may be related to the improper constraint measurement represented through m . 1820 = (1) = + 2 = 0 − 1 ∗ ( )+ 2 ∗ ( ) 2 − 3 ∗ ( ) 3 (2) For CT and DCT, 0 =3.62, 1 = 4.21, 2 =4.33, 4 =2.00 For SENB , 0 = 3.18 − (0.22 ∗ ( ) ) Earlier literature reported the m dependency on type of specimen, dimensions of the specimen (crack length and thickness), and material properties (N Ekabote 2024). Although, the Equation (2) imbibes these constraint effects, the estimated CTOD resulted in lesser magnitude than the actual CTOD measured experimentally for both SENB and CT specimens (Khor W et al., 2016). The critical CTOD is higher in CT compared to SENB, owing to the high constraint at crack in SENB (Ranganath et al. 1990). Kudari, S. K., and K. G. Kodancha., (2008) reported the d n (=1/ m ) variation for both SENB and CT specimens by varying the a/W . For a/W > 0.5, the d n in CT specimen was almost independent of the a/W , while for SENB, d n was gradually increased with increase in a/W for 0.4 and 0.6. In ASTM 1820, the geometry dependent constants A 0 , A 1 , A 2 , and A 3 are independent of the a/W for CT and dependent in case of SENB. The inconsistency in understanding the constraint parameter, m, and insufficient justification in usage of the cubic polynomial equations in ASTM 1820, makes the m susceptible. A thorough analysis of m , may be helpful in understanding its dependency on various factors as defined in ASTM 1820. Similarly , CTOD evaluation based on BS 7448 involves the PHM and is defined as shown in Equation (3). First part of Equation (3) represents the elastic part of CTOD and the latter, plastic CTOD derived from PHM. In Equation (3), ν is the Poisson’s ratio, E is Young’s modulus, r p is the rotational factor, b is the un-cracked ligament length (= W a ), and z is the distance of knife edge from specimen. In the present case, the knife edges were grooved within CT specimen only, making the value of z as zero in Equation (3). The rotational factor, r p , depends on a/W and strain hardening of the material (Tagawa, Tetsuya, et al., 2010). However, in earlier studies the r p value was considered as 0.46 for CT specimens. Hence, the Equation (3) can be rewritten in the form of Equation (4) by substituting the r p and 1 = 4.32 − (2.23 ∗ ( ) ) 2 = 4.44 − (2.29 ∗ ( ) ) 3 = 2.05 − (1.06 ∗ ( ) )