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Larson–Miller fit of the simulated creep-rupture sample of MIL-HDBK-5J: optimum constant, life at 30 ksi and 1800 °F, stress for 100 hours
| Tool | Creep Life |
| Source | U.S. Department of Defense (2003). Metallic Materials and Elements for Aerospace Vehicle Structures. MIL-HDBK-5J, 31 January 2003. Section 9.9.4.1, pp. 9-235 to 9-240 (Table 9.9.4.1, Figures 9.9.4.1(c) and (d)); equation forms of section 9.6.4.2, p. 9-138. |
| Level | Professional |
Problem
The handbook's creep-rupture example plans a test program for a modified Alloy 325 between 1600 and 1900 °F and prints a simulated sample: 22 tests at 1600, 1750 and 1900 °F and 19 specification tests at 30 ksi and 1800 °F. It reports a Larson–Miller analysis with the constant C = 19 on its master-curve figure. Fit the 41 tests by least squares, then find the mean and lower-bound rupture life at 30 ksi and 1800 °F and the stress that gives 100 hours at 1800 °F.
Inputs to Enter
- Rupture model: Alloy 325 (MOD), 41 simulated tests (MIL-HDBK-5J Table 9.9.4.1), stresses 10 to 63 ksi, lives 8.8 to 2,912 h
- Parameter Larson–Miller, quadratic master curve in log(stress), optimum constant; temperatures in °F (T + 459.67 °R)
- Service stress 30 ksi, service temperature 1800 °F, required life 100 h, no design factor, confidence 95 %
Answers
- log t = c + (b1 + b2 X + b3 X²)/T with c = −19.382, b1 = 50,916, b2 = 8,972.5, b3 = −7,683.5 (T in °R, X = log ksi): C = 19.38 (the handbook's figure is labelled C = 19)
- Sum of squares of log t 1.277, standard error 0.1857 with 37 degrees of freedom (the handbook names 0.1 to 0.2 as typical), R² 0.896
- The 19 specification lives: mean of the logarithms 37.4 h, s(log) = 0.150 (book the same)
- Mean life at 30 ksi, 1800 °F: log t = −19.382 + 47,405/2,259.67 = 1.596, t = 39.5 h (specification mean 37.4 h)
- Lower bound, 95 % one-sided prediction for one more test: log t − 1.687 × 0.1857 × √(1 + 0.037) = 1.277, t = 18.9 h
- Stress for 100 h at 1800 °F: 25.6 ksi on the mean curve, 22.3 ksi on the lower-bound curve; 30 ksi reaches 100 h at 1,757 °F
- Other parameters on the same tests: Orr–Sherby–Dorn S = 1.314, Manson–Succop S = 1.291; the Manson–Haferd search runs to its edge (no convergence temperature in these data)
Notes
The tool's default inputs are this case; press Submit. The handbook prints the data, the constant C = 19 and curves, not the coefficients of its master curve, so the coefficients and lives are the tool's own least-squares values; with C held at 19 the fitted master curve passes the figure's curve within reading accuracy. The same dropdown loads the handbook's printed equations for Inconel 718 forging and HAYNES HR-120 and the two data sets of NASA Memorandum 3-10-59E, whose printed constants (C = 23.8 and 15.3) the fit reproduces.