**2**. **Discussion**

Table 1

Composition of the alloy (used by Hayes et al. [8])

El. | Ti | Al | Nb | Fe | H | O | N | C |

at. % | 45.9 | 52.9 | 0.91 | 0.048 | 0.0219 | 0.1523 | 0.0026 | 0.0555 |

Table 1. shows the composition of single phase γ-TiAl alloy, forged, heat treated and finally subjected to tensile creep testing, as discussed in the work of Hayes et al [8]. As discussed earlier, that only constructing strain vs time plot to determine “min. strain rate” and designating the same to be the “steady state strain rate”, may be highly misleading for a number of materials, which do not exhibit steady-state creep [18]. Ti-53Nb-1Al, for instance, whether tested to rupture or terminated at mid-strains of 0.18% and 0.5% at 832⁰C, exhibited a very less amount of steady-state creep. In the case of creep test till rupture, significant primary creep is exhibited whereas, in the case of creep test terminated at 0.18% strain, there is no primary creep regime and for the creep test till 0.5% strain, the primary creep regime is in between the two aforementioned extremes. In all cases, there is a very early onset of tertiary creep, However, the rate of tertiary creep in all the three samples is significantly different, as indicated by slopes of plots in Figs. 3 (a) and (b). Besides, from Figs. 1(a) and (b), the strain rate as well as strain for initiation of tertiary creep in three samples, also vary, to a small extent, with the sample having terminating strain of 0.5% showing tertiary creep initiated at the lowest strain rate and the highest strain.

## 2.1 Determination of Activation energies between 760–1000⁰C at 69.4 and 103.4 MPa

**2.1.1** At 69.4 MPa

From Fig. 2(a), the apparent creep activation energies (determined from slope of black curve representing ln(strain rate, in h) vs 1/T at 69.4 MPa) vary from 423.92 kJ/mol in regime 1 to 409.82 kJ/mol in regime 2. Regimes 1 and 2 although seem to be independent [35], but the values of activation energies in two regimes, are found to be within experimental error. Moreover, the ZH (Zener Hollomon) parameter is obtained (from y-intercept of Fig. 2(a)) as 1.23e(14). Besides, Fig. 2(a) also shows rupture time vs 1/T plot (marked red) where SD parameter (determined from the y-intercept) is found to be 4.93e-14 and apparent creep activation energy is determined (from slope of Fig. 2) as 329.03 kJ/mol. The transition temperature from Regime 1 to 2 is ~ 838.11°C.

**2.1.2** At 103.4 MPa

From the ln(strain rate, in h) vs 1/T (per K) plot (marked as red in Fig. 2(b)), ZH parameter (determined from y-intercept) is 1.11e(14) and apparent creep activation energies (determined from slope of ln(strain rate, in h) vs 1/T plot) vary from 364.77 kJ/mol in regime 1 to 377.68 kJ/mol in regime 2. Regimes 1 and 2 are sequential [36].

Besides, Fig. 2(b) also shows rupture time vs 1/T plot (marked as black) where S-D parameter (Sherby- Dorn parameter, determined from y-intercept) is found to be 1.99e(-15) and Apparent Creep activation Energy (determined from slope) is found to be 345.65 kJ/mol. The transition temperature is decreased

to ~ 825.90⁰C about 14⁰C less than that at 69.4 MPa.

Table 2

Grain boundary and lattice diffusion activation energies (Qgb and QL (in kJ/mol), respectively) at different test temperatures between 760 and 900⁰C and creep stresses of 69.4 and 103.4MPa following the work of Hayes et al [8]. Qgb and QL have been calculated using Ashby’s approach [9], [37].

Temperature (⁰C) | Stress (MPa) | Q (kJ/mol) | Qgb (kJ/mol) | QL(kJ/mol) |

760 | 69.4 | 192 | 72 | 120 |

760 | 103.4 | 304 | 114 | 190 |

832 | 69.4 | 560 | 210 | 350 |

832 | 103.4 | 405 | 151.88 | 253.13 |

900 | 69.4 | 624 | 234 | 390 |

900 | 103.4 | 519 | 194.63 | 324.38 |

It is observed that at 832 and 900⁰C, with increase in stress level from 69.4 to 103.4 MPa, there is a decrease in apparent creep activation energy, but the reverse trend is observed at 760⁰C. This is subject to further investigations using microstructural investigation at 760⁰C, but is beyond the scope of discussion of the present work.

## 2.2 Plots for determining stress exponent at 760, 832 and 900⁰C

The plot (Fig. 3) for 760⁰C (black curve) shows that processes in 2 regimes must be independent. At Tr1: 244.69 MPa, the plot suggests that there is transition from dislocation glide controlled creep to dislocation climb controlled creep [36], [38]–[43], suggesting a minor microstructural change leading to a change in creep deformation behaviour.

Based on the red coloured plot at 832°C (Fig. 3): (i) regime 1 (from beginning to point Tr2) Stress exponent (from slope): 3; (ii) regime 2 (from points Tr2 to Tr3), Stress exponent: 4; (iii) regime 3 (from point Tr3 to end), Stress exponent: 4. Moreover, the red plot(in Fig. 3) also suggests that the cree mechanisms operating at 3 aforementioned regimes are independent. At Tr 2: 66.68 MPa there is transition from dislocation glide controlled creep to dislocation climb controlled which again suggests that there is change in mechanism in Dislocation creep due to minor microstructural changes.

Based on the blue coloured plot at 900°C (Fig. 3): (i) regime 1 (from beginning to Tr4): stress exponent: 5 and (ii) regime 2 (from Tr4 to end): stress exponent: 4. This suggests that power law creep [44] is continued but with a different slope (stress exponent) which again suggests transition from dislocation climb to dislocation glide controlled creep and thus, no major microstructural change.

**2.3 Prediction of creep life using Larson-Miller (L-M)** [45] **and Manson-Haferd (M-H)** [46] **parameters**

From Fig. 4, it may be inferred that creep life of the alloy decreases, due to onset of creep rupture [45]–[47], with increase in stress between 69.4-103.4 MPa and temperatures between 760–900⁰C. Table. 3 shows Larson-Miller (L-M) constants and parameters at 69.4, 100 and 103.4 MPa between 760–900⁰C. It may be observed from Table 2. that with increase in stress levels from 69.4-103.4 MPa, both L-M constants and parameters increase between 760–900⁰C.

Table 3

Larson-Miller constants and parameters at 69.4, 100 and 103.4 MPa between 760–900⁰C.

Stress (MPa) | L-M constant (K) | L-M Parameter |

69.4 | 1.74 | 14.05 |

100 | 3.96 | 30.64 |

103.4 | 4.15 | 34.02 |

Based on linear interpolation from Fig. 5, the M-H parameter at Stresses: 69.4 MPa, 100 MPa and 103.4 MPa may be calculated to be equal to -0.033, -0.031 and − 0.014, respectively.

**2.4 Prediction of creep life using modified Monkman-Grant (M-G) parameter** [9], [48]–[52]

Table 4

M-G plot vs modified M-G plot (considering linear fit throughout entire creep life) at 760, 832 and 900⁰C. where p, C and R2 abbreviate for M-G exponent; M-G intercept and Goodness of fit, respectively.

T (⁰C) | P (M-G) | C (M-G) | R2 (M-G) | P (modified M-G) | C (modified M-G) | R2 (modified M-G) |

760 | -1.4 | 1.43 | 0.96 | -1.56 | 1.61 | 0.97 |

832 | -1.3 | 1.31 | 0.93 | -1.33 | 1.40 | 0.98 |

900 | -0.4 | 0.52 | 0.99 | -0.68 | 0.69 | 0.99 |

From Fig. 6 and Table. 4, it may be observed that predominant creep rupture mechanism is power law breakdown [18] at 760 and 832⁰C, due to p being greater than − 1.4 but at 900⁰C, owing to p equal to -0.4, the predominant creep rupture mechanism requires further microstructural investigation and detailed analysis which is beyond the scope of the present study [53]–[55]. Besides, it may also be observed that using modified M-G plots, the goodness of fit is much improved than using the original M-G plots, implying that use of modified M-G plots improves data reliability [56].