Stress Relaxation and Creep Relaxation

Category: Structural Analysis | Integrated 2026-04-06
CAE visualization for creep relaxation theory - technical simulation diagram
Stress Relaxation and Creep Relaxation

Stress Relaxation and Creep Relaxation: Theoretical Foundations

What is Stress Relaxation?

🧑‍🎓

Professor, how is stress relaxation different from creep?


🎓

Creep is an increase in strain over time under constant stress. Stress relaxation is a decrease in stress over time under constant strain. They are different aspects of the same viscoelastic phenomenon. Typical examples include the decrease in bolt preload and the loss of sealing force in rubber.


$$ \sigma(t) = \sigma_0 \exp(-t/\tau) \quad \text{(Maxwell Model)} $$

Summary

🎓
  • Stress decreases under constant strain — The other side of creep
  • Maxwell Model — Exponential decay
  • Generalized with Prony series — Multiple Maxwell elements

  • Coffee Break Yomoyama Talk

    The Deep Relationship Between Relaxation and Displacement Control

    Creep and relaxation are merely the "stress-controlled version" and "displacement-controlled version" of the same material phenomenon. "Stress relaxation" under constant displacement, where stress decreases, becomes a problem in applications like bolted joints. For example, the JIS B 1083 fastening design guidelines recommend evaluating the residual axial force ratio after 10 years using relaxation calculations based on Norton's law when using steel bolts at 200°C or higher. There are cases where retightening is mandated when the force falls below 80% of the initial axial force.

    Computational Methods for Stress Relaxation and Creep Relaxation

    FEM Settings

    🎓

    Abaqus: VISCOELASTIC, TIME=PRONY + VISCO step. Define relaxation using Prony series.


    Summary

    🎓
    • Prony series + *VISCO — Standard setting
    • Fit Prony series from DMA test data

    • Coffee Break Yomoyama Talk

      Collaboration with Prony Series

      In creep relaxation analysis, long-term behavior is often represented by Prony series (parallel combination of Maxwell elements). Time step selection greatly influences accuracy. For example, the concrete creep coefficient φ in DIN EN 1992-1-1 (Eurocode 2) covers 1 to 50 years on a logarithmic time axis with about 5 to 7 steps. In Abaqus, data can be input directly into "*VISCOELASTIC, TIME=PRONY" or automatic fitting is possible using the Time-Temperature Superposition tool.

      Stress Relaxation and Creep Relaxation in Practice

      Practical Checklist

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      • [ ] Is the relaxation time based on test data?
      • [ ] Does it include temperature dependence?
      • [ ] Is long-term extrapolation reasonable?

      • Coffee Break Yomoyama Talk

        Relaxation in Bolted Joints: Practice in Nuclear Power Piping

        Creep relaxation is a serious issue in bolt fastening design for nuclear power plants. For example, in GE BWR piping flange sections, it was confirmed that 316L stainless steel bolts lost 35% of their initial tightening force after 10 years of operation at 300°C. The ASME Section III standard specifies a fatigue evaluation procedure that explicitly considers creep relaxation. This mechanism can be reproduced with ANSYS's CREEP module.

        Stress Relaxation and Creep Relaxation: Software & Solver Comparison

        Tools

        🎓

        All solvers support Prony series. Abaqus's *VISCOELASTIC is the most flexible.


        Coffee Break Yomoyama Talk

        Implementation of Creep Laws by Vendors: From Norton's Law to Dorn's Law

        Implementation of creep laws varies significantly between solvers. MSC Nastran standardly implements the Norton-Bailey law in time-hardening form, while ABAQUS also allows strain-hardening selection. ANSYS supports six types of creep laws via Implicit Creep Equations. In a comparative case for high-pressure steam turbine blade design, the creep strain after 1,000 hours differed by 20% between solvers even with the same material constants.

        Advanced Technologies

        Advanced

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        • Fractional Derivative Viscoelasticity — Covers wide time scales with few parameters
        • Long-term Relaxation Extrapolation — Predicts long-term behavior from accelerated tests using WLF law

        • Coffee Break Yomoyama Talk

          Pioneers in Creep Research: High-Temperature Deformation of Gas Turbine Blades

          Engineering research on metal creep became full-scale in the 1950s during the development of the Rolls-Royce Avon turbojet engine. To explain the phenomenon where IN-100 nickel alloy blades elongated by 0.3mm after 1,000 hours of operation at a turbine inlet temperature of 1,050°C, the Norton-Bailey creep law was optimized against measured data. This is now inherited in ABAQUS as the CREEP material option.

          Stress Relaxation and Creep Relaxation: Common Issues & Debugging

          Troubles

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          • No relaxation occurs → Check for *VISCO step
          • Discrepancy in relaxation rate → Check Prony's $\tau$

          • Coffee Break Yomoyama Talk

            Convergence Difficulties in Creep Analysis: Practical Time Increment Control

            The main cause of convergence failure in creep/stress relaxation analysis is improper time increment settings. In ABAQUS/Standard, the default `CETOL` (creep strain error tolerance) of 0.005 is coarse, causing frequent Increment Cutback in rapid creep regions at high temperatures. In practice, a two-stage setting is recommended: using a fine `CETOL=0.0001` only in the primary creep region and larger increments in the secondary creep region.

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