PSI - Issue 14

Amit Singh et al. / Procedia Structural Integrity 14 (2019) 78–88 Amit Singh et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 3. The tensile and strain hardening behavior of IMI 834 alloy: (a) True stress vs. true strain plot, (b) Strain hardenin g rate, θ, vs. true plastic stress (Kocks – Mecking plot) and (c) Plot of logarithmic strain hardening vs logarithmic true stress, modified C-J plot

4.3. Effect of solution treatment temperature on strain hardening and flow stress behavior

The strain hardening rate vs. true stress (well known as Kocks-Mecking plot) plotted as per Equation (8) is shown in Fig.3b. It can be seen that as the ST temperature decreases from β transus temperature 1333 K (i.e. from 0.045% α p phase) the strain hardening rate increases. It is noticeable that, the strain hardening rate is very low for the samples ST near to β transus temperature 1333 K to 1303K (i.e. α p phase fraction up to 14.5%), while for ST temperature 1288 K (i.e. α p 22% phase) an improved strain hardening rate is recorded compared to 1333 K ST temperature. Similar inference can be drawn from the degree of strain hardening (σ UTS /σ 0.2% ) listed in Table 2. This strain hardening rate can be explained by decreasing lamellae thickness with decreasing ST temperature which leads to increased strain hardening. One probability for this is that the accumulation of mobile dislocation at the lamellae boundaries dominates over the annihilation of dislocations due to increase in the boundaries densities. The results obtained here similar to that reported by Andres et al. (1997), in which strain hardening was explained by changing the cooling rate. The results of constitutive modeling using various empirical equations, the goodness of fit represented as correlation coefficient and the parameters of constitutive relation obtained are summarized in Table 3 and 4 respectively. It can be observed that, better fit i.e., R 2 close to 1 was achieved for Hollomon, Swift and Ludwigson equation. Hence, the strain hardening exponent of the Hollomon and Ludwigson equation (n and n 3 in Table 4 )