Elastic follow-up (EFU) is a complex and influencing phenomenon in pressure vessels and piping systems. It affects the performance of structural components at elevated temperatures. Quantification of elastic follow-up is challenging since it’s still not clearly defined in the ASME Boiler & Pressure Vessel Code. Pressure vessels and piping under operating load over time can exhibit mixed elastic follow-up trajectories due to inelasticity. Typically, secondary, and primary load are present at the onset which can redistribute over time due to strain accumulation and stress relaxation during elastic-follow-up. ASME Boiler & Pressure Vessel Code Div. 5, limits strain accumulation via criteria in regions outside of the elastic core. However, a method that directly addresses Elastic follow-up, would be advantageous in establishing actual margins against elastic follow-up during the design phase. The phenomenon has been well studied with various assemblages of uniaxial models, showing load and displacement controlled and mixed responses.

This study will present a method of assessing elastic follow up in finite element models. The method is based on the R5 elastic follow-up factor (EFF) expression that has been readily derived in the uniaxial case and employed by authors. Essentially the Von Mises equivalent strains are obtained from both a linear elastic and inelastic 3D finite element models subject to thermal (secondary) and pressure (primary) loading. The linear elastic model establishes the hypothetical initial elastic stress and the inelastic model will map the inelastic response through time. The Von Mises equivalent strains are then substituted into R5 expression, which are obtained from the onset linear-elastic model and the time varying inelastic model to map the elastic follow up and through time. The results are benchmarked against uniaxial results having combined primary and secondary loading.

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