Creep Model Verification

The need for model verification

Before using a creep model in a full component FEA, the model must be verified. Verification is the process of confirming that the FEA code correctly implements the constitutive model and that the user has correctly entered the material constants and the analysis parameters. Verification is distinct from validation (which confirms that the model represents the real material behaviour). Verification answers the question: is the FEA solving the equations correctly? A creep model that is not verified may produce results with significant numerical error, even if the model form and the constants are correct. Verification is a necessary step before the results can be used for engineering decisions.

Single-element tests

The single-element test is the most basic verification. A single finite element is subjected to a constant stress (or a constant load) and a constant temperature, with the creep model activated. The FEA output (creep strain vs time) is compared to the analytical solution of the creep law for the same conditions. For a Norton secondary creep law, the analytical solution is eps_creep = A * sigma^n * t (linear in time). For a Norton-Bailey law, the analytical solution is eps_creep = A * sigma^n * t^(m+1)/(m+1). The FEA output should match the analytical solution within a small tolerance. If it does not, there is an error in the model setup — the constants, the time stepping or the FEA implementation. The single-element test should be run for each creep law and each set of constants before the full analysis.

Single-element verification (Norton-Bailey):

  Analytical solution (constant sigma, T):
    eps_creep(t) = A * sigma^n * t^(m+1) / (m+1)
                 * exp(-Q/(R*T))

  FEA should reproduce:
    |eps_creep_FEA - eps_creep_analytical| / eps_creep_analytical < tol

  Typical tolerance: tol < 0.01 (1%)

  Also check:
    - Creep strain is monotonic (increases with time)
    - Creep rate matches the analytical rate
    - Stress is constant (for constant-load test)
    - No oscillation or instability

If the FEA does not match the analytical solution,
check:
  - Material constants entered correctly
  - Units consistent (SI vs non-SI)
  - Time stepping adequate
  - Creep law selected correctly in the FEA code

Analytical comparison for stress redistribution

For a structure with stress redistribution (e.g. a thick pressure vessel wall, a two-bar structure), an analytical or semi-analytical solution may be available for the steady-state creep stress distribution. The FEA should reproduce this distribution. For a Norton creep law, the steady-state creep stress in a thick cylinder is known analytically (the stress distribution is proportional to the elastic distribution raised to the power 1/n). The FEA stress distribution at long times should match the analytical steady-state distribution. This verifies that the FEA correctly captures the stress redistribution, not just the creep strain accumulation. The comparison should be made at a time when the steady state is expected to have been reached (which depends on the creep rate and the geometry).

Material data reproduction

The creep model should reproduce the material test data from which it was calibrated. A creep test at a specific stress and temperature should be reproduced by a single-element FEA with the same stress and temperature. The FEA strain-time curve should match the test data within the scatter of the data. If the model does not reproduce the calibration data, the calibration is incorrect or the model form is inadequate. The reproduction should be checked for all the test conditions used in the calibration — at different stresses and temperatures. If the model reproduces some conditions but not others, the model form may be inadequate for the full range (e.g. the stress exponent may change across the stress range). The material data reproduction is a check on the calibration, not just the FEA implementation.

• Creep Model Calibration

Benchmark cases

Benchmark cases are standard problems with known solutions (analytical or from independent FEA codes) that are used to verify the FEA implementation. For creep, benchmark cases include: a thick cylinder under internal pressure with creep (steady-state stress distribution), a beam in bending with creep (stress redistribution from the elastic to the steady-state distribution), a plate with a hole under remote tension with creep (stress concentration relaxation). The FEA results should match the benchmark solutions within a specified tolerance. Benchmark cases verify both the creep model implementation and the overall FEA setup (mesh, boundary conditions, load steps). If the FEA does not match the benchmark, the source of the discrepancy should be identified and resolved before proceeding to the component analysis.

Sensitivity and test correlation

The verified model should be assessed for sensitivity to the constitutive constants, the time step and the mesh. The sensitivity study identifies the parameters that most affect the result and verifies that the analysis settings (time step, mesh) are adequate. Finally, if component-level test data is available (e.g. a creep test of a full-size component or a model component), the FEA should be correlated with the test data. The correlation validates the model at the component level — it confirms that the constitutive model, the boundary conditions and the geometry collectively produce the correct response. The correlation should be documented as part of the analysis. If the correlation is poor, the source of the discrepancy should be investigated — it may be the material data, the boundary conditions, the mesh or the model form.

• Sensitivity Analysis in Creep Assessment
• Creep Analysis Verification & Validation
• Verification & Validation — Model Quality

A verification hierarchy for production models

Verification is strongest when it progresses from the simplest possible problem to the production model. Begin with unit and dimensional checks on the material constants, then reproduce constant-stress and constant-temperature element tests. Add controlled problems that exercise temperature dependence, multiaxial stress, stress relaxation and redistribution separately. Only after those checks pass should the full geometry, contact and service history be introduced. This hierarchy makes faults diagnosable: if a component result is unexpected, the analyst can distinguish constitutive implementation, data conversion, boundary conditions and structural interaction. Automated regression tests are valuable when material cards or solver versions are updated; a small suite of element and benchmark cases can show immediately whether a change has altered the predicted creep response.

Verification evidence and independent challenge

The verification record should be reproducible by another analyst. Preserve the equations implemented, parameter values with units, solver options, element formulation, time-integration controls and numerical tolerances used in each benchmark. Plot FEA and analytical or calibration-data results on the same axes and quantify differences in the response measures relevant to the later component assessment. Where practical, compare an additional benchmark with an independent implementation, published solution or second solver to reduce the risk of reproducing the same setup error twice. Verification should also cover interpolation outside the exact calibration points, because the production model will normally traverse a continuum of stress and temperature. None of this validates the constitutive law for service; it establishes that the selected law and data have been implemented consistently enough for validation and engineering use to begin.

Model verification is a necessary step before using creep FEA results for engineering decisions. A single-element test, an analytical comparison and a material-data reproduction should be performed and documented. Without verification, the FEA results may contain numerical errors that are indistinguishable from real physical effects.