Residual Stress Analysis

Category: Structural Analysis | Integrated 2026-04-06
CAE visualization for residual stress theory - technical simulation diagram
Residual Stress Analysis

Residual Stress Analysis: Theoretical Foundations

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Professor, what is residual stress?


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Stress that exists within a structure in the absence of external forces. Generated by welding, heat treatment, forming, and surface treatment. Significantly affects fatigue life, buckling load, and stress corrosion cracking.


Mechanism of Residual Stress Generation

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  • Welding — Local heating → cooling → contraction. Tensile residual stress (weld zone) + compressive (surrounding area)
  • Shot Peening — Introduces compressive residual stress on the surface. Improves fatigue life
  • Quenching — Difference in cooling rate between surface and interior. Martensitic transformation
  • Sheet Metal Forming — Springback after plastic deformation

  • Summary

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    • Stress that exists without external forces — Originates from manufacturing processes
    • Tensile residual stress negatively affects fatigue — Promotes crack nucleation
    • Compressive residual stress positively affects fatigue — Shot peening
    • Predict residual stress in welding simulation using FEM

    • Coffee Break Yomoyama Talk

      What is Residual Stress: Generation Mechanism

      Residual stress is a self-equilibrating stress that remains within a material after external forces are removed. The three main causes are non-uniformity of plastic deformation, temperature gradients, and phase transformations. In welding, tensile residual stress is generated by rapid cooling and contraction around the molten pool. Measurements confirm that residual stress near the weld line in butt welding of mild steel can reach near the yield point (355 MPa). On the other hand, shot peening (particle impact processing) intentionally introduces compressive residual stress into the surface layer, extending fatigue life by 2 to 5 times. The wing span of a Boeing 737 is about 30m, and compressive residual stress is crucial for fatigue management of the lower wing surface.

      Computational Methods for Residual Stress Analysis

      Residual Stress FEM

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      Welding residual stress:

      1. Welding Heat Source Model (Goldak, etc.) — Calculate temperature field with moving heat source

      2. Thermo-Elasto-Plastic Analysis — Temperature → thermal expansion → plastic deformation → cooling →


      Inherent Strain Method: Input pre-determined inherent strain into the weld zone. Obtain residual stress with a single-step elastic analysis. Computation time reduced to 1/100 ~ 1/1000.


      Summary

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      • Welding heat source → thermo-elasto-plastic → cooling → — Detailed analysis
      • Inherent Strain Method — Fast alternative method
      • Abaqus / Simufact WeldingWelding simulation

      • Coffee Break Yomoyama Talk

        Comparison of X-ray Diffraction and Neutron Diffraction Methods

        Comparison of the two main residual stress measurement methods: X-ray diffraction (sin²ψ method) is limited to a depth of a few μm from the surface but the equipment is compact and suitable for on-site measurement, accuracy ±20 MPa. Neutron diffraction can non-destructively measure up to several cm inside a structure, and measurements using the neutron beam at JRR-3 (Tokai Village, Ibaraki, Japan Atomic Energy Agency) achieved accuracy of ±5 MPa. In 2020, the dedicated residual stress beamline ENGINEERING at J-PARC (Ibaraki) enabled 3D residual stress mapping of welded joints (resolution 0.5mm³).

        Residual Stress Analysis in Practice

        Practical Checklist

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        • [ ] Are welding conditions (current, speed, heat input) correct?
        • [ ] Are material temperature-dependent properties defined for the entire temperature range?
        • [ ] Are cooling conditions (natural cooling or forced cooling) correct?
        • [ ] Does the residual stress distribution match actual measurements (X-ray diffraction, hole drilling, etc.)?

        • Coffee Break Yomoyama Talk

          Reduction by Post-Weld Heat Treatment (PWHT)

          Post-Weld Heat Treatment (PWHT) is the most reliable method to relieve residual stress. JIS B 8285 (Post-Weld Heat Treatment Standard) specifies holding at 600~650°C for 1~4 hours for carbon steel. For BWR (Boiling Water Reactor) piping fittings (SUS304), residual tensile stress causes stress corrosion cracking (IGSCC), so since the 1980s, alternatives to PWHT omission such as hydrostatic testing (Mechanical Stress Improvement Process, MSIP) and Low Plasticity Burnishing (LPB) have been adopted. In the Westinghouse AP1000, PWHT is incorporated as a design standard for all welded locations.

          Residual Stress Analysis: Software & Solver Comparison

          Tools

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          • Simufact Welding — Dedicated tool for welding residual stress
          • Abaqus — General-purpose. Thermo-elasto-plastic
          • Sysweld — ESI's welding-specific tool

          • Coffee Break Yomoyama Talk

            Comparison of Dedicated Solvers for Welding Residual Stress Analysis

            For welding residual stress analysis, there are three major players: SYSWELD (ESI Group), Simufact Welding (MSC), and ABAQUS with Goldak model. SYSWELD comes with a measured database of arc efficiency η=0.85~0.95 and is an automotive industry standard, while Simufact Welding is strong in shipbuilding (for MHI) due to integration with process simulation. Verification accuracy against ASME Sec.IX welding qualification tests shows SYSWELD has the highest performance with error within 7%.

            Advanced Technology

            Advanced

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            • Residual Stress in AM (Metal 3D Printing) — Large residual stress from layer-by-layer heating-cooling
            • → Fatigue Coupling — Input residual stress map into FEM fatigue analysis

            • Coffee Break Yomoyama Talk

              Non-Destructive Measurement of Residual Stress by Neutron Diffraction

              Neutron diffraction boasts the highest accuracy for non-destructive residual stress measurement. The BL19 beamline at J-PARC (Tokai Village, Ibaraki) can measure residual stress inside steel with ±5 MPa accuracy. It is reported that non-destructive evaluation of welded axle parts of JR Central N700S Shinkansen up to 30mm depth achieved 95% agreement with SYSWELD analysis values.

              Residual Stress Analysis: Common Issues & Debugging

              Troubles

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              • Residual stress doesn't match measurements → Check material temperature-dependent properties, welding conditions, cooling conditions
              • Calculation is too heavy → Switch to inherent strain method

              • Coffee Brea Yomoyama Talk
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                Related fields

                Thermal AnalysisManufacturing Process AnalysisV&V · Quality Assurance
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