Issue 39

S. K. Kudari et alii, Frattura ed Integrità Strutturale, 39 (2017) 216-225; DOI: 10.3221/IGF-ESIS.39.21 224 To evaluate the worthiness of the analytical expressions to estimate K I-max , T 11-max and T 33-max proposed in this analysis, the estimated magnitudes K I-max , T 11-max and T 33-max obtained by Eq.(6), Eq.(11) and Tab.3 are compared with the similar results on the CT specimen presented by Toshiyuki and Tomohiro [12]. The authors [12] have given the variation of T 11- max and T 33-max for the toughness value of the material (0.55% Carbon Steel) K I-max = 66 MPam 1/2 . Fig. 10 shows a typical variation of estimated K I-max , T 11-max and T 33-max at the specimen thickness center against B/W (0.1 -1.0) obtained by proposed analytical expressions (Eq.(6), (11) and Tab.3) for K I-max = 66 MPam 1/2 and results of Toshiyuki and Tomohiro [12]. The authors [12] have computed various parameters for B/W=0.25, 0.4 and 0.5 only. According to Fig. 10, the magnitudes of K I-max were not affected by B/W as expected and are in excellent agreement with Toshiyuki and Tomohiro [12]. T 11 showed visible dependence on B/W, though the variation was less than 20% and it is in good agreement with the earlier reported results [12]. In summary, the in-plane parameters at the specimen thickness center showed small dependence on B, and are in excellent agreement with the earlier results [12] providing validation for the proposed Eq.(6) and (11). On the other hand, out-of-plane constraint factor, T 33 showed strong dependence on B/W. T 33 was found negative and approached zero as B/W increased from 0.1 to 1. Fig. 10 shows that the nature of variation of present results of T 33 (obtained by Tab.3 expressions) is in similar manner to the one presented by Toshiyuki and Tomohiro [12]. However, some difference in the magnitude of T 33 between both the results for B/W=0.25-0.5 is observed. This difference is attributed to the effect of side grooves in the CT specimen used in the work of Toshiyuki and Tomohiro [12]. The side grooves in the specimen affects the strain distribution in the out-of-plane direction and restricts the value of T 33 (Ref. Eq.(12)). To study this effect, we have conducted 3D FEA on CT specimen used by Toshiyuki and Tomohiro [12] without side groove and for the same material properties. These computed results are superimposed in Fig.10 by red colored lines for comparison. This plot show that the results (K I-max , T 11-max and T 33-max ) for the specimen without side groove match with the one computed by the analytical expressions (Eq.(6), (11) and Tab.3) proposed in this work. This exercise infers that the use of side grooves in a specimen controls  33 and improves the out-of-plane constraint (Ref.Fig.10: for a/W=0.5, T 33 is improved from -150 MPa to -84 MPa (44%) by using 10% side groove [12]). The Fig. 10 provides validation to the proposed analytical formulations to estimate K I-max , T 11-max and T 33-max . Figure 10 : A typical variation of K I-max , T 11-max and T 33-max against B/W obtained by proposed analytical expressions and results of Toshiyuki and Tomohiro [12]. S UMMARY n this study, stress intensity factor and T-stress (T 11 and T 33 ) solutions for CT specimens for wide range of specimen thickness and crack lengths were computed using 3D elastic FEA. It is observed that magnitude of T 33 (Ref: Fig.(9)) is highly negative for B/W=0.1 (thin specimens), and almost zero for B/W=1 (thick specimens), indicating that the thick specimens have higher out-of-plane constraint. For B/W=0.5, ASTM requirement for K IC test [15], it is observed I