Creep, fatigue and interaction verification¶
Evidence levels¶
The older hot-wall demonstration now uses standard three-dimensional Mises output, including plane-strain out-of-plane stress. Its former hand-written two-dimensional deviator and associated Golden values are superseded; see the correction and independent checks.
For the current P92 commands, data boundaries and next engineering gates, start with the P92 evidence map.
Keep four decisions separate: (1) constitutive equations and their discrete updates, (2) finite-element equilibrium and refinement, (3) material prediction against independent tests, and (4) acceptance under an explicitly selected design procedure. Passing the first two does not establish the last two. The numerical fixtures below use synthetic coefficients, not a qualified material database. No standard text, licensed design curve or private data is embedded in AgentFEM.
Reference map¶
These references were checked on 2026-10-29. ASTM entries identify test methods and editions from the official public catalogue; their full normative text has not been reviewed here. This is not a declaration of ASTM compliance.
| Question | Reference | Use and limit |
|---|---|---|
| Creep and rupture measurements | ASTM E139-24 | Organize constant-load creep/rupture observations; deformation and rupture are distinct outputs |
| Strain-controlled cyclic tests | ASTM E606/E606M-21 | Select compatible fatigue data; retain amplitude/range, cycle/reversal, temperature and strain-rate conventions |
| Cycles with holds | ASTM E2714-26 | Identify the creep-fatigue test family; does not supply a universal life law or component acceptance |
| Stress integration | MOOSE power-law creep | Independent algorithm reference; not an executed cross-solver comparison |
| Interaction assessment limitations | JRC92093, DOI 10.1115/ICONE22-30640 | Study of 316/P91 assessment methods; relaxation and cyclic response matter, and design margins are not best-estimate life predictions |
| Hold-time and temperature sensitivity | INL, Creep-fatigue behavior of Alloy 617 (2016) | Candidate experimental comparison: reported hold-time effects differ between 850 and 950 degrees C; no Alloy 617 fit is claimed here |
| Loading-order sensitivity | INL experimental verification of Division 5 rules | Candidate variable-amplitude/sequence validation, beyond an order-independent damage sum |
| Traceable material measurements | NIMS creep data sheets | Candidate data source; check sheet revision, usage terms, material heat and condition before extracting or fitting data |
| Independent cycle-counting output | MathWorks rainflow worked examples | Compare numerical count/range/mean triples for nested reversals and residual half-cycles; not an executed MATLAB comparison or full ASTM certification |
| Nonuniform secondary creep | NAFEMS R0027 Test 7 in the Abaqus benchmark manual | Reuse the existing creep_thick_cylinder_benchmark; do not replace it with another project-level solver |
| P91 mechanism selection | JRC94508, DOI 10.2790/49517 | Cyclic softening changes subsequent creep response; the public report summary also identifies limited long-hold/low-strain evidence. Do not present a hardening-only model or linear interaction as universal |
| Elastic follow-up and separated test families | ANL-ART-168 (2019) | Section 2.1 provides a two-bar relaxation reference; Appendix A separates ordinary controlled strain from SMT effective strain and tensile/compressive holds. Do not mix those inputs as interchangeable fatigue samples |
| Traceable Grade 91 material scope | NIMS Grade 91 sheet article, DOI 10.1080/27660400.2025.2588872 | Public landing page identifies tube/plate/pipe grades, temperature/stress scope and CC BY 4.0. Candidate for matched-condition creep validation, not a fit already admitted to core |
Do not conflate the separately published INL/EXT-21-64314 Alloy 709 report with Alloy 617 data. A similar test protocol is not the same material.
Executable analytical references¶
The next experimental source gate is recorded in the Alloy 617 audit. Public parameters are not interchangeable with another constitutive model. Local assessment inputs can now use co-located accepted material histories; this closes a data-lifecycle gap, not the experimental-validation gate.
The executed P92 relaxation comparison uses public digital BAM records: a separate RF calibration and an initially held-out SLR condition, source hashes, physical unit conversions and ordinary FEM time refinement. It reports experimental errors without inventing an acceptance tolerance or qualifying a full cyclic material/lifetime model. The subsequent sinh mechanism screen retains SLR as diagnostic data, not a new blind holdout. Its independent continuous integration and full-path FEM refinement pass numerical checks, but the tested candidates still miss the long low-stress hold.
Run the focused checks in the scientific environment:
python -m pytest -q tests/test_creep_fatigue_references.py tests/test_creep_damage_history.py tests/test_rainflow_references.py tests/test_assessments.py tests/test_strain_life.py
Constant-strain Norton relaxation¶
A homogeneous 3D unit cube has a fixed axial strain and free lateral
contraction. The ordinary model.step solves a uniaxial stress state. For
creep_rate = A (sigma / s_ref)^n, set k = E A / s_ref^n. Independent
continuous solutions are
An instantaneous elastic preload defines sigma_0 at t=0; this fixture checks the subsequent relaxation, not energy balance across that preload. E=200000 MPa, nu=0.3, A=1e-4 /s, s_ref=100 MPa, sigma_0=200 MPa and duration=2 s. Reaction stress, lateral traction-free stress and accumulated creep strain are checked. Maximum errors over the full sampled trajectory are:
| n | Exact final stress (MPa) | 16 increments | 32 increments | 64 increments |
|---|---|---|---|---|
| 1 | 134.064009 | 0.660977 | 0.332805 | 0.166989 |
| 3 | 97.590007 | 3.360815 | 1.754748 | 0.897590 |
The approximately first-order decay checks backward-Euler accuracy against a continuous solution, rather than comparing two copies of the same recurrence. This homogeneous patch is not a nonuniform spatial-convergence claim.
Elastic follow-up through ordinary regional equilibrium¶
tests/test_creep_elastic_followup.py is a shear analogue of the elastic/creep
series-bar mechanism discussed in ANL-ART-168 Section 2.1, not a reproduction
of its axial specimen or Alloy 617 tests. Two equal-area, unit-length slabs
carry equal shear traction. The left slab creeps; the right is elastic.
The ordinary regional power-law Step uses coefficient zero in the elastic
region, not a separate benchmark solver or an empirical follow-up correction.
For fixed total displacement, compatibility gives
(1/G1+1/G2)*d(tau)/dt + d(gamma_creep)/dt = 0. Define
f=1+G1/G2 and use associative Mises shear flow to obtain
The exponential/power-law continuous solutions above apply to tau. G1=100000 MPa, tau_0=100 MPa, A=1e-4 /s, s_ref=100 MPa, duration=2 s. Four Q1 cells resolve the piecewise-affine displacement field; antiplane support supplies the required transverse reactions. Maximum stress-history errors are:
| f / n | Exact final tau (MPa) | 16 increments error (MPa) | 32 | 64 |
|---|---|---|---|---|
| 2 / 1 | 74.08182 | 0.206073 | 0.103603 | 0.0519448 |
| 2 / 3 | 59.76143 | 0.981558 | 0.503437 | 0.255129 |
| 5 / 1 | 88.69204 | 0.0397219 | 0.0199082 | 0.0099660 |
| 5 / 3 | 76.24929 | 0.395441 | 0.200246 | 0.100769 |
Tests check interface traction balance, zero creep in the elastic region, compatibility of the creeping strain and first-order time convergence. Elastic follow-up slows relaxation compared with complete local strain restraint at the same initial stress. This supports an existing regional pure-creep route, not regional admission of the new joint creep/plastic composition. Initial elastic preload work and experimental component qualification are outside this benchmark.
Time-fraction integration through a relaxing history¶
Use a deliberately synthetic rupture relation
t_r(sigma) = 1000 (sigma_0/sigma)^n seconds. Its independent continuous damage
integral is Dc = (sigma_0-sigma_end)/(1000 k sigma_0^n).
The existing result consumer takes the maximum stress per declared dwell
block. Dividing the relaxation into accepted-time intervals gives:
| n | Exact Dc | Absolute error, 16 increments | 32 increments | 64 increments |
|---|---|---|---|---|
| 1 | 0.001648400 | 2.42724e-5 | 1.21809e-5 | 6.10168e-6 |
| 3 | 0.000640062 | 9.43434e-5 | 4.73017e-5 | 2.36819e-5 |
This upper estimate converges for this monotone rupture relation and resolved monotone stress history. A single maximum over a long hold is not the time-resolved integral; a sample mean is not a time-weighted integral. Neither is universally conservative for an arbitrary supplied rupture function or an under-resolved history. This test verifies extraction and quadrature behavior, not physical creep-fatigue interaction.
The time-resolved consumer assessments.creep_damage_from_result now retains
the actual sampled relaxation and integrates the reciprocal rupture time,
instead of assigning each hold a single maximum. Against the same continuous
reference, its absolute damage errors are:
| n | 16 increments | 32 increments | 64 increments |
|---|---|---|---|
| 1 | 3.87400e-6 | 1.93036e-6 | 9.63480e-7 |
| 3 | 3.96548e-5 | 1.98208e-5 | 9.90696e-6 |
These errors remain first-order because the input FE stress is backward-Euler accurate. Separate tests on exact sampled exponential stress and on a synthetic temperature-dependent rate exhibit second-order trapezoidal convergence. Do not infer universal conservatism or material accuracy from either test. Explicit hour/second invariance, mismatched grids, domain failures, nonoverlapping dwells, finite strict JSON and late-failure nonpublication are also tested. Original sampling gaps remain in the assessment evidence. The optional source-gap limit has a recorded 1e-12 relative roundoff allowance so ordinary equal time increments are not rejected by subtraction noise. There is no absolute or time-origin-scaled tolerance; large time offsets and very small intervals cannot conceal a genuinely undersampled history.
Optional quadrature_subdivisions separates quadrature refinement from source
sampling. A synthetic linear stress path with cubic reciprocal rupture time
has an independent polynomial integral: successive 1/2/4/8 subdivisions reduce
trapezoidal error by four while the original source gaps remain unchanged.
Refinement retains every original union-grid knot. It cannot bypass source-gap
limits or recover unrecorded stress transients; unrepresentable time refinements
are rejected rather than silently collapsed.
Independent rainflow counting¶
tests/test_rainflow_references.py checks the nine published count/range/mean
triples in the MathWorks algorithm example, including four full cycles and
five residual half-cycles. Duplicating dwell samples or inserting monotone
samples does not change the cycles. A scale-invariance regression fixes an
old numerical weakness: multiplying neighboring slopes could underflow and
erase a reversal. Direct direction comparisons preserve small-range cycles;
non-real histories and unrepresentable ranges are rejected. These checks
validate counting, not a fatigue-life calibration.
Nonuniform spatial verification in a limiting case¶
tests/test_creep_manufactured_field.py checks the joint material with plastic
yield deliberately unreachable and linear creep active. On a unit cuboid,
choose u_z=s*x*(1-x)*t, u_x=u_y=0, s=0.001. With shear modulus G,
lambda=3GA/s_ref and h(t)=(1-exp(-lambda*t))/lambda, the continuous stress
is sigma_xz=G*s*(1-2x)*h(t). The body force b_z=2G*s*h(t) balances its
divergence. Boundary constraints and tractions are those of this exact field.
At t=1 s, 64 equal physical increments and 2/4/8 Q1 hexahedra across x give relative displacement L2 errors 0.248996, 0.0612490 and 0.0143323. This is approximately second-order spatial decay before the temporal error floor, not merely equality of homogeneous patch solutions. It verifies the nonuniform creep-dominated limit. The existing axisymmetric NAFEMS cylinder checks cover a different, pure-creep route and are not evidence of axisymmetric admission for the joint material.
Active simultaneous plasticity and creep in a nonuniform field¶
The same ordinary Step also solves an independently integrable force-driven
field: tau_xz=S*t*(1-2x), b_z=2S*t, with S=60 MPa, E=200000 MPa,
nu=0.3, yield Y=50 MPa, isotropic hardening H=10000 MPa and
creep_rate=A*(q/s_ref)^3, A=0.001 /s, s_ref=100 MPa. Plane shear gives
q=sqrt(3)*abs(tau). Under this monotonic loading, the exact plastic strain
is p=max(q-Y,0)/H, while equivalent creep is the time integral of that
known cubic stress law. The axial shear displacement follows by spatially
integrating du_z/dx=tau/G+sqrt(3)*sign(tau)*(p+c), with zero displacement
at x=0 and x=1. This reference does not call an AgentFEM material update.
For t=1 s and 128 increments, 4/8/16 Q1 elements give relative displacement
L2 errors 0.128625, 0.0320049, 0.00781042. Plastic and creep variables are both
nonzero, and a central elastic region remains. Peak plastic strain is also
checked against the independent midpoint equilibrium stress. At fixed mesh,
32/64 increments give peak-creep relative errors 0.0634766 and 0.0314941,
matching the independently summed cubic endpoint rule 2/N+1/N^2 relative
to the continuous integral. Thus temporal bias remains visible rather than
being mislabeled as spatial error. This verifies bounded proportional,
isothermal small-strain behavior; it is not experimental validation, spatial
verification of nonproportional cyclic thermal loading, or a life prediction.
Prescribed nonuniform temperature with active plasticity and creep¶
A second version retains the force-driven field above and introduces
Arrhenius dependence, with Q=120000 J/mol, R=8.31446261815324 J/(mol K),
T_ref=800 K and a=2. Prescribe
so the continuous local rate coefficient is exactly
A(x)=A_ref*(1+a*(1-2x)^2). The analytical stress/plastic field remains
as above. Let l=min(x,1-x), y=1-2l; at t=1 the creep part of displacement is
The Q1 temperature field is independently interpolated from this profile. On 4/8/16 cells with 128 increments, relative displacement L2 errors are 0.137992, 0.0346244 and 0.00813975. Both plasticity and creep are active. This checks spatial temperature sampling and its rate effect together with equilibrium. Thermal expansion is deliberately zero to isolate that mechanism; the profile is prescribed, not an independently verified heat-conduction solution. Nonproportional thermal cycling and experimental material accuracy remain separate gates.
Rotating stress, distinct flow directions and thermal cycling¶
tests/test_creep_plasticity_rotating_reference.py constructs a continuous
material path independently of the discrete return map. This follows the
general verification principle of prescribed/manufactured solutions described
by Salari and Knupp, SAND2000-1444;
the particular material fixture here is not a published experimental test.
Two orthonormal deviatoric tensors define a direction
e(t)=e1*cos(pi*t)+e2*sin(pi*t) for 0 <= t <= 1 s. Prescribe accumulated
plastic strain p=beta*t, beta=0.002 /s, with plastic flow
n_p=sqrt(3/2)*e(t). For linear isotropic hardening, stress is
sqrt(2/3)*(Y+H*p)*e(t). For Chaboche, the relative stress has radius
Y+Q*(1-exp(-b*p)); add the exact continuous backstress convolution
alpha_i(t) = sqrt(2/3)*C_i*beta *
[real(z_i)*e1 + imag(z_i)*e2]
z_i = [exp(i*pi*t)-exp(-gamma_i*beta*t)] / (gamma_i*beta+i*pi)
The current stress and relative stress deliberately have different directions, so creep and plastic flow are not coaxial in the Chaboche fixture. Integrate the prescribed continuous creep/plastic rates to construct total strain, then supply only that strain and temperature to the tested material update. No AgentFEM return-map result enters the reference. Independent 64/128-point Gauss integration agrees within 1e-12 relative and 1e-15 absolute tolerance.
Both isothermal and T=800+50*sin(pi*t)^2 K heating/cooling paths are tested;
the latter includes alpha=1e-5 /K thermal expansion and Arrhenius creep with
Q_activation=120000 J/mol. E=200000 MPa, nu=0.3, Y=200 MPa,
A_ref=1e-5 /s, s_ref=100 MPa, n=3. Linear H=2000 MPa, or Chaboche
C=(12000,3000) MPa, gamma=(100,8), Q=60 MPa and b=10. Maximum stress
Frobenius errors over accepted time stations are:
| Plastic branch / temperature | 32 increments (MPa) | 64 | 128 |
|---|---|---|---|
| Linear isotropic / constant | 7.01398 | 3.57182 | 1.80262 |
| Linear isotropic / heating-cooling | 7.07495 | 3.60098 | 1.81684 |
| Chaboche / constant | 6.69018 | 3.40388 | 1.71705 |
| Chaboche / heating-cooling | 6.76379 | 3.43956 | 1.73459 |
Creep/plastic tensors, their accumulated scalars, and all Chaboche backstress branches also show first-order error reduction. This is a nonproportional thermal material-point reference, not nonuniform structural verification or an experimentally calibrated thermomechanical fatigue-life model. The initial elastic preload to yield is prescribed; its work is outside this test.
Perfect-plastic cyclic limit and strain-life conventions¶
The simultaneous material, with zero creep and perfect J2 plasticity, follows
a prescribed uniaxial strain cycle. For E=200000 MPa, sigma_y=200 MPa and
eps_a=0.003, the independent closed-loop work is
4 sigma_y (eps_a - sigma_y/E) = 1.6 MPa (energy per unit volume).
The assembled reaction loop gives 1.6 MPa; reversal stresses are +/-200 MPa.
A synthetic Coffin-Manson-Basquin curve with both exponents -0.5 has a closed form life, not a numerical round-trip reference. This cycle gives N=14168.055556 full cycles and Miner damage 7.05813156e-5. Residual half-cycle counting, amplitude versus range and N versus 2N are tested separately. This does not calibrate fatigue damage from plastic work.
Fail-closed assessment¶
The complete damage point must lie inside the declared interaction-diagram
abscissa range and below its ordinate. In particular, Dc>1 and Df=0 must not
pass the reference Dc+Df=1 diagram. A partial diagram cannot certify values
outside its supplied range. Imported negative/nonfinite damage is rejected.
margin remains the vertical fatigue margin; consult acceptable and
within_interaction_domain together. acceptable only refers to that declared
diagram, not to a regulatory or component-life approval.
Next material-validation gate¶
A first open-data audit inspected the experimental CSV from
Rovinelli et al., Mendeley Data v1, DOI 10.17632/kcbcnywygr.1
(CC BY 4.0, retrieved 2026-10-29). Its 77 records contain three principal
stresses in MPa and rupture time in hours: IN600 (41), SS316 (13), SS304 (23).
The raw file SHA-256 is
f1c187779effc0b8230111f966f4ed885720495488d397c25060904d9f4add9a, matching the
repository file metadata. Experimental and simulation tables were kept
distinct; only the experimental table was inspected. It contains no explicit
temperature, heat, condition, censoring flag or hold-cycle observations.
The landing-page description mentions IN100 while the table says IN600.
Consequently this is a candidate rupture reference, not admitted calibration
or independent creep-fatigue validation data. Resolve identities against
the original papers before fitting; do not infer temperatures or treat the
published correlation coefficients as an independent prediction.
The public JRC P91 assessment recommendations make cyclic softening a mechanism-selection gate, not a cosmetic fit choice. The current Chaboche asset admits nonnegative isotropic saturation and plastic-flow-driven dynamic recovery. It does not evolve static backstress recovery during a hold or represent cyclic softening. A future extension must define physical-time state evolution, consistent tangent, temperature/domain dependence, recoverable storage and dissipation, and joint rollback/restart. Simply allowing a negative saturation parameter or changing a Norton coefficient is not an accepted implementation. A fitted model must predict held-out relaxation/cycling observations before a life assessment is promoted.
The OSTI record 974288 identifies a potentially useful experimental appendix,
but the attempted public PDF retrieval returned a rate-limit HTML page on
2026-10-29. Its tables have not been inspected or admitted. A search snippet
is not enough to establish strain conventions, material identities or reuse
rights, and no missing values were inferred.
A subsequent review obtained the CC BY 4.0 NIMS Grade 91 article linked above and visually checked Tables 7–9. The reported rupture times are in hours, temperatures in degrees C, stress in MPa, and minimum creep rates in percent/hour, not strain/second. Tube, plate and pipe fits and their stress regimes are separate. These are published regression relations/derived strengths, not a held-out raw measurement set; reproducing their tables would verify transcription and units, not independent material prediction. A material card must preserve that distinction and the underlying heat/condition scope before any calibration is admitted.
- Select one material heat/condition and isothermal test temperature; acquire compatible creep, continuous cycling and hold-cycle data with documented rights, revision, units and failure definition.
- Calibrate deformation using creep curves, cyclic loops and relaxation; reserve a different amplitude/hold duration for prediction. Never fit and score on the same curves, or mix design lower bounds with mean test lives.
- Compare full stress relaxation and hysteresis before assessing life. Add static recovery, cyclic softening or temperature-dependent properties only when these comparisons identify the missing mechanism.
- Independently assess fatigue and rupture calibration, then test interaction on held-out hold cycles. Do not double-count hold effects already included in a strain-life calibration. Record scatter and censored tests.
- Only then progress to a nonuniform specimen and component mesh/time checks. Multiaxial and nonisothermal life, global damage feedback and regularization remain separate gates. ASME/RCC-MRx curves and their safety factors require a reviewed, versioned project input; no universal curve is silently supplied.
The P92 full-path diagnostic is an executed example of this ordering: ordinary structural histories converge to an independent reference, while the same frozen high-stress law still misses a low-stress long hold. Numerical verification passes separately from material validation. Retain the failed transfer as evidence rather than changing the parameters against the held-out curve and continuing to label it independent.