PSI - Issue 23

Ayan Ray et al. / Procedia Structural Integrity 23 (2019) 299–304 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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characteristic normalized crack lengths for CVRNB specimens. The value of Y c ( α 0, α 1 ) was estimated using the expression suggested by Shang-Xian (1984) considering W / B as 1.5 and chevron notch angle ( θ ) as 60 0. . The estimated magnitudes of K Icv for the alloys are shown in Fig. 2(c) and (d). Consideration of the thickness criterion indicated the estimated values of K Icv to be under plane strain states.

Fig. 2: Histograms showing estimated fracture toughness values of: (a) HEA-B using SENB specimen, (b) HEA-F using SENB specimen, (c) HEA-B using CVRNB specimen, and (d) HEA-F using CVRNB specimens.

Thermal activation analyses have been carried out on the recorded results of stress relaxation (SR) and strain rate change (SRC) tests in order to determine the activation volume ( V ), effective activation volume ( V *) and athermal stress (   ), the analyses being carried out following an earlier report by some of the present authors (Kumari and Ray, 2016). In order to estimate V , the variations of relaxed stress with time at the different strains/stresses are recorded (Fig. 3a) and the magnitude of V is estimated for each strain level using Feltham’s (1961) and Conrad’s (1970) approaches. The expressions used to calculate V by these approaches are (Kumari and Ray, 2016): ∆ = − ( ) ln (1 + ) Feltham’s approach (3) V = kT(∂lnγ̇⁄∂τ) Conrad’s approach (4) where k =Boltzmann's constant, T =absolute temperature, t =time,  = shear stress on the dislocation, ̇ =plastic strain rate and a =constant. The magnitude of  is calculated from normal stress using the value of the Taylor factor (  ). In Feltham’s analysis, linear fit is made between Δ σ and ln (1+ t / a ) by iterating the value of a to achieve the maximum magnitude of linear regression co-efficient ( R 2 ). The magnitude of V is then calculated from the slope of the best fit line with maximum R 2 between Δ σ and ln (1+ t/a ) following Eqn. 3 (Fig. 3b). In the other approach, linear regression analysis is carried out between ln( ̇) and  , the slope of the plot yields the magnitude of V from the knowledge of kT (Fig. 3c). The maximum deviation between the magnitudes of V estimated using Feltham’s and Conrad’s analyses for any specific strain is ≤ 4%.

Fig. 3: Method of analyzing activation volume from stress relaxation tests (a) typical raw data from the test for HEA-F, and the method of analyzing using (b) Feltham’s procedu re and (c) Conrad’s procedure. The value of V is estimated from the results of the strain rate change tests using the expression (Huang et al., 2014): = [( ln ̇ 1 ln ̇ 2 ) /Ψ( 1 − 2 )] (5)