Creep Rupture

Creep and Stress Rupture (structures/materials/creep-rupture)

Use when the task is the time-dependent creep and stress rupture life of an aerospace metallic part at elevated temperature: the steady-state creep strain rate from the Norton power law, the rupture life from the Larson-Miller parameter, the Monkman-Grant cross-check from the minimum creep rate, the creep strain accumulated over the service time, and the design-life margin check. This leaf implements the classic parametric methods in pure Python, stdlib only. It pairs with structures/materials/ramberg-osgood for the room-temperature elastic-plastic curve, structures/materials/fracture-toughness for the crack-driven failure mode, structures/materials/material-selection for the temperature limits in the alloy trade, and structures/thermal- structures/thermal-stress-analysis for the load side of the same elevated-temperature environment. This leaf does NOT cover cyclic endurance (the structures/fatigue pack owns cyclic life methods), constrained-expansion thermal stress, or statistically based tensile design values (structures/materials/mmpsd-allowables).

Domain quick reference

• Norton steady-state creep rate: eps_dot_c = A * sigma^n * exp(-Q / (R * T)), with A in 1/s per Pa^n, n the stress exponent, Q the activation energy in J/mol, R = 8.314 J/mol/K and T in K. The default module material is a representative nickel superalloy (Inconel-718 class) with reference-only typicals A = 2.0e-47, n = 7.0, Q = 360000 J/mol; any of A, n, Q and the LMP/MG constants can be overridden with a dict.
• Larson-Miller parameter: LMP = T * (C + log10(t_r)), with t_r the rupture life in hours, T in K, C a material constant (about 20). The stress-LMP master curve is taken linear in log10 stress: LMP = lm_a - lm_b * log10(sigma_pa / 1e6), lm_a = 35552, lm_b = 6000 for the default alloy.
• Rupture life from the LMP: t_r = 10 ** (LMP / T - C), hours.
• Monkman-Grant: log10(t_r) + m * log10(eps_dot_min) = C_mg with the creep rate in 1/h (m = 1.0, C_mg = -1.645 default); gives a rupture life from the minimum creep rate that cross-checks the LMP estimate.
• Accumulated creep strain: eps_c(t) = eps_dot_c * t over the service time (steady-state only; primary creep is neglected in this leaf, a documented conservative assumption for the design check).
• Time to a target creep strain: t = target / eps_dot_c; the 1 percent creep design point is t_1pct = 0.01 / eps_dot_c.
• Margins against the required life t_req: margin_rupture = t_r / t_req - 1 and margin_creep = t_1pct / t_req - 1; the lower margin governs and the verdict is PASS when it is >= 0.
• Units: stress in Pa, temperature in K, time in seconds (rupture lives reported in hours where noted). All functions raise ValueError on non-positive stress, temperature, time, target strain or creep rate, a negative stress exponent, or an unknown material name.

Workflow

1. Fix the operating point: the sustained stress sigma in Pa (convert MPa by multiplying by 1e6) and the metal temperature T in K (Celsius plus 273.15).
2. Compute the steady-state creep rate with norton_creep_rate(sigma, temp_k, material); pass a registered material name or a dict of constant overrides on top of the default alloy.
3. Get the Larson-Miller parameter at the stress with larson_miller_parameter(sigma, material) and the rupture life with rupture_life_hours(sigma, temp_k, material); the raw conversion rupture_life_from_lmp(lmp, temp_k, c_const) exposes the formula.
4. Cross-check with the Monkman-Grant route: monkman_grant_life( eps_dot_min, material) from the Norton rate; the two rupture lives should agree within the scatter band of the material data.
5. Accumulate the damage over the service time with creep_strain_accumulated(eps_dot, time_s), and read the 1 percent design point from time_to_creep_strain(0.01, eps_dot).
6. Run the design check with creep_margin(time_required_s, sigma, temp_k, material): it returns the rupture life, the time to 1 percent strain, both margins, the governing mode and the PASS/FAIL verdict for the required life.
7. Confirm the deterministic checks with the contract test scripts/test_creep_rupture.py.

Worked example

A turbine disk rim material at 300 MPa and 600 C (873.15 K), 1000 h required life, default alloy constants:

• Norton creep rate: eps_dot = 2.0e-47 * (3.0e8)^7 * exp(-360000 / (8.314 * 873.15)) = 1.2698e-9 1/s.
• Larson-Miller parameter: LMP = 35552 - 6000 * log10(300) = 20689.27.
• Rupture life (LMP route): t_r = 10 ** (20689.27 / 873.15 - 20) = 4954.3 h, well above the 1000 h requirement.
• Rupture life (Monkman-Grant route): with eps_dot per hour = 4.5714e-6, log10(t_r) = -1.645 - log10(4.5714e-6) = 3.695, so t_r = 4954.0 h, matching the LMP estimate within 0.01 percent.
• Time to 1 percent creep strain: t_1pct = 0.01 / 1.2698e-9 = 7875105.5 s = 2187.5 h.
• Accumulated strain over the 1000 h service time: 1.2698e-9 * 3600000 = 0.00457, below the 1 percent design point.
• Margin check: margin_rupture = 4954.3 / 1000 - 1 = 3.954 and margin_creep = 2187.5 / 1000 - 1 = 1.188. The lower margin is the creep margin, so creep governs the design and the verdict is PASS.
• Sensitivity: raise the temperature to 650 C (923.15 K) at the same stress and the rupture life collapses to 258.0 h while t_1pct falls to 149.1 h; against the 1000 h requirement both margins go negative and the verdict is FAIL, showing why the creep check lives at the hot operating point.

Pitfalls

• Forgetting creep is time at temperature: the Norton rate is exponentially sensitive to T (the rupture life collapses from 4954 h at 600 C to 258 h at 650 C in the worked example), so a room-temperature check or a small temperature slip misses the whole failure mode.
• Neglecting the primary-creep assumption: the accumulated strain eps_c = eps_dot * t is steady-state only; primary creep is neglected by design as a conservative assumption, and the margin should be read with that in mind.
• Checking only one margin: creep_margin returns BOTH the rupture margin (3.954) and the 1-percent-strain margin (1.188) in the worked example, and the LOWER one governs - the time to 1 percent strain can gate before rupture.
• Trusting one rupture-life route: the LMP and Monkman-Grant estimates should agree within the material scatter band (they match within 0.01 percent in the worked example); a large discrepancy signals a bad input or a material outside the master curve.
• Mixing units in the input chain: stress enters in Pa (convert MPa by 1e6), temperature in K (Celsius plus 273.15), time in seconds for the margin check while rupture lives come back in hours; a seconds-versus-hours slip misreads the life by 3600x.
• Treating the module material as an alloy database: the Inconel-718 class constants are reference-only typicals and any of A, n, Q and the LMP/MG constants can be overridden with a dict; quoting the defaults for another alloy is a material-data error.

Verification

• Confirm norton_creep_rate(3.0e8, 873.15) returns 1.2698e-9 1/s and that the rate rises monotonically over 5 stress points and with temperature.
• Confirm rupture_life_hours(3.0e8, 873.15) returns 4954.3 h, that the life falls monotonically over 5 stress points and as the temperature rises, and that monkman_grant_life at the Norton rate agrees with the LMP life within 0.1 percent.
• Confirm creep_margin(3600000.0, 3.0e8, 873.15) returns margins 3.954 and 1.188 with governing "creep" and verdict "PASS", and that the 20000 h and 650 C cases return "FAIL".
• Confirm the round trip: rupture_life_from_lmp of the module LMP recovers the rupture life, and time_to_creep_strain scales inversely with the creep rate.
• Confirm every non-positive stress, temperature, time, target strain and creep rate, every negative stress exponent, and every unknown material name raises ValueError.
• Run the contract test offline: python3 scripts/test_creep_rupture.py (34 tests, deterministic).

Related leaves

• structures/materials/ramberg-osgood: the room-temperature elastic-plastic stress-strain curve beneath the creep regime.
• structures/materials/fracture-toughness: the crack-driven failure mode that competes with creep rupture in hot-section parts.
• structures/materials/material-selection: temperature limits and alloy family screening before the creep check.
• structures/thermal-structures/thermal-stress-analysis: the constrained-expansion load side of the same elevated-temperature environment (owned by that leaf, not here).
• structures/fatigue/stress-life-curve and structures/fatigue/strain- life-fatigue: cyclic life methods, the non-creep route for the same part.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_creep_rupture.py

The test covers the worked-example anchors (Norton rate 1.2698e-9 1/s, LMP 20689.27, rupture life 4954.3 h, time to 1 percent strain 2187.5 h, 1000 h margin verdict PASS), the monotonicity of the creep rate with stress and temperature and of the rupture life with stress and temperature, the Monkman-Grant vs LMP cross-check, the accumulated strain and time-to-strain scalings, the margin verdicts at long and hot operating points, material dict overrides, and ValueError rejection of non-physical inputs and unknown materials.

Compliance

• Standards referenced, not reproduced: MMPDS documents creep and creep-rupture design practice for metallic airframe materials; FAR-25 frames the elevated-temperature part and its strength demonstration. The equations above are standard engineering methodology, summary-only per standards-map.yaml, and the material constants are reference-only typicals, not a reproduced data table.
• compliance: STANDARDS-REF, gated: false.