Time Stepping in Creep FEA

The role of time stepping

In creep FEA, the analysis proceeds in time steps. At each step, the creep strain increment is computed from the creep law, the stress is updated, and the equilibrium is solved. The time step size determines the accuracy and the computational cost. The creep strain increment per step must be small enough that the stress change within the step is captured — if the step is too large, the creep strain is computed at the old stress (which may be significantly different from the current stress), introducing error. The time stepping is the backbone of the creep FEA, and the choice of step size is one of the most important user-controlled parameters.

Time increment selection

The time increment must be small enough to capture the creep rate changes. The fastest changes occur in the primary creep stage, where the creep rate decreases rapidly. In the secondary stage, the creep rate is approximately constant, and larger steps may be used. In the tertiary stage, the creep rate accelerates, and smaller steps may again be needed. A common guideline is that the creep strain increment per step should not exceed a small fraction of the total expected creep strain (e.g. 1% or less). Another guideline is that the stress change per step should not exceed a small fraction of the current stress (e.g. a few percent). The step size should be smaller in the early stages (primary creep, rapid stress redistribution) and may be larger in the later stages (secondary creep, steady state).

Time increment guidelines (illustrative):

  1. Strain-based criterion:
     Delta_eps_creep per step < 0.01 * eps_creep_total
     Delta_t < 0.01 * eps_creep_total / eps_dot_creep

  2. Stress-based criterion:
     Delta_sigma per step < 0.05 * sigma_current
     Delta_t < 0.05 * sigma / (E * eps_dot_creep)

  3. Stress redistribution criterion:
     Use smaller steps during primary creep
     (rapid redistribution), larger during secondary

where:
  Delta_t = time increment [s]
  Delta_eps_creep = creep strain increment per step
  eps_dot_creep = current creep rate [1/s]
  sigma = current stress [Pa]
  E = elastic modulus [Pa]

These are starting guidelines only — verify
convergence by comparing results with
progressively smaller time steps.

Accuracy and solution stability

The accuracy of the creep FEA depends on the time step size. Too large a step introduces error in the creep strain (computed at an outdated stress) and in the stress redistribution (the redistribution within the step is not captured). The error may accumulate over many steps, giving a significantly incorrect final result. The stability of the solution also depends on the time step. For explicit time integration (where the creep strain is computed from the stress at the start of the step), the solution may be unstable if the step is too large — the stress may oscillate or diverge. For implicit integration (where the creep strain is computed from the stress at the end of the step, iteratively), the solution is generally more stable but may still have accuracy issues with large steps. The stability and accuracy should be verified by a time-step convergence study.

Long-duration simulation

For long service lives (e.g. 100,000 hours or more), the creep FEA may involve a very large number of time steps if a small, uniform step size is used. This may be computationally prohibitive. Several strategies address this. First, variable time stepping: small steps in the early stages (primary creep, rapid redistribution) and larger steps in the later stages (secondary creep, steady state). Second, adaptive time stepping: the FEA code automatically adjusts the step size based on the creep rate or the stress change. Third, the use of the steady-state creep stress distribution as an approximation for long-term assessment (skipping the transient redistribution). Fourth, the use of a parametric rupture correlation (e.g. Larson-Miller) instead of a full FEA for the long-term rupture life, using the FEA only for the deformation and stress redistribution. The strategy should be selected based on the required accuracy and the available computational resources.

Adaptive time stepping

Many FEA codes offer adaptive (automatic) time stepping for creep analysis. The code monitors the creep rate, the stress change or the convergence residual and adjusts the step size accordingly. If the creep rate is high or the stress is changing rapidly, the step size is reduced. If the creep rate is low and the stress is stable, the step size is increased. The adaptive strategy can significantly reduce the total number of steps while maintaining accuracy. The user typically specifies a tolerance (the maximum creep strain increment or stress change per step) and the code determines the step size. The adaptive stepping should be verified — the user should check that the code is using reasonable step sizes and that the results are not sensitive to the tolerance setting.

Verification of time-step independence

The time-step independence of the results should be verified. This is done by running the analysis with progressively smaller time steps (or tighter adaptive tolerances) and comparing the key results (creep strain, stress, displacement at the critical location). If the results converge (do not change significantly with smaller steps), the time stepping is adequate. If the results change, the step size is too large and must be reduced. The time-step convergence study should be documented as part of the analysis verification. The study should use at least three step sizes (e.g. the baseline, half and quarter) and should show that the baseline result is within an acceptable tolerance of the converged result.

• Creep FEA Convergence & Numerical Stability
• Creep Model Verification

Aligning increments with the real service history

Time-step size should be driven not only by constitutive rate but also by changes in the applied history. Start-up ramps, pressure changes, bolt-up sequences, thermal transients, dwells, shutdowns and repeated cycles introduce points at which the loading derivative changes. Step boundaries should be placed at these events so that a large increment does not average across physically different states. Within a long dwell the step size may grow once the response becomes smooth, while the beginning of a dwell often needs finer resolution because stress redistribution is fastest there. For repeated missions, it can be efficient to resolve early cycles in detail, demonstrate whether the state approaches a repeatable pattern, and then use an appropriately justified cycle-jump or block strategy if supported by the constitutive model. Any acceleration technique must preserve the accumulated internal variables that govern subsequent creep response.

Demonstrating time-discretisation adequacy

Solver convergence at every increment does not prove that the time discretisation is accurate. A time-step study should compare engineering quantities that matter to the assessment, such as peak and end-of-dwell creep strain, relaxed stress, accumulated damage, joint load transfer and critical displacement. Refine the increments in the periods where those quantities change most rapidly and confirm that the conclusions are stable. The comparison should use the same physical times in each run rather than simply comparing the last available output frame. When automatic stepping is used, record the accepted increments and any repeated cutbacks: frequent cutbacks can indicate a constitutive, contact or loading discontinuity that deserves investigation. The final report should state the time-stepping controls and show why further refinement would not change the engineering decision.

The time step size is one of the most important parameters in creep FEA. Too large a step gives inaccurate results; too small a step is computationally expensive. Always perform a time-step convergence study to verify that the results are independent of the step size, and use adaptive stepping for long-duration analyses.