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Residual stress: Elastic shakedown in fillet welded plate

Welding residual stresses exist in various welded structures such as ships and offshore structures.  According to load levels during operation of the structure, the as-welded residual stresses can be relaxed or redistributed.  The elastic shakedown phenomenon; defined as a plastic deformation during the first few load cycles followed by an elastic response which is associated with a limit called the shakedown limit, can be considered as one of the reasons for the stress relaxation or redistribution.

There have been various research studies into the shakedown of residual stresses in welded structures, however, the focus has been on the influence of shakedown on fatigue behaviour of the plate, and hence on the relaxation of residual stresses at the surface of the plate. Fillet welds are more common in offshore applications and are considered more critical in fatigue due to the stress concentration at the weld toe.  Despite this, experimental research on the shakedown of residual stresses in fillet welds is very rare.

Therefore, this research was undertaken to address the above and the objectives were to:

  • Build on a recent study conducted on butt welded steel plates which found that the residual stresses, both transverse and longitudinal components, redistributed through the thickness depending on the relaxation at the top surface
  • Use experimental testing to study the effect of elastic shakedown in the redistribution of pre-existing residual stress fields in a fillet weld plate, manufactured in line with ship design and welding procedures using DH36, a ship building steel.
Figure 1. a) Initial weld model, b) test specimen model following cutting
Figure 1. a) Initial weld model, b) test specimen model following cutting

The fillet welds were subjected to different levels of shakedown under tensile cyclic load.  Neutron diffraction was used to measure residual stresses in these plates in the as-welded state and after elastic shakedown.  A mixed hardening model was determined for both weld and base material:

  • An elastic-plastic model with a combination of one isotropic hardening and three kinematic hardenings. The isotropic hardening R and the kinematic hardening are defined as follows:

𝑅̇ = 𝑏(𝑄 − 𝑅)𝑝) Μ‡

𝛼̇𝑖 = 2/3 πΆπ‘–πœ€Μ‡π‘ − 𝛾𝑖𝛼̇𝑖𝑝̇

where 𝑏, 𝑄, 𝐢1, 𝐢2, 𝐢3, 𝛾1, 𝛾2 and 𝛾3 are material parameters, 𝑝̇ is the rate of accumulated plasticity and πœ€Μ‡π‘ is plastic strain

  • A shakedown limit analysis based on plastic work dissipation (W^P) was developed as the shakedown criterion to estimate the shakedown limit on the component:

π‘Šπ‘ = Σ ∫ πœŽπ‘–π‘–Δπœ€π‘–π‘–

where 𝑉𝑒 is the volume of an element and N is the number of elements.

  • A sequentially coupled thermo-mechanical analysis of the fillet welding was performed on the weld plate shown in fig. 1a. The numerical fillet weld model was then cut to the dimension of a mechanical load model as shown in fig.1b.

Furthermore, the redistribution of residual stresses due to elastic shakedown was quantified through experimental measurements:

  • Three tensile load cycles were applied on the plate across the weld along the transverse direction
  • Neutron diffraction ENGIN-X instrument at the UK’s ISIS pulsed neutron source was used to determine residual stresses in the initial state and after different load cycles at 30 locations in the plane shown in fig.2.

Elastic shakedown limit: results imply that in the absence of residual stress field, any cyclic load within 1.2 times the yield strength applied in this setup will achieve elastic-shakedown state.

Transverse residual stress distribution on the base plate: results found that after three loading cycles, the maximum value of tensile transverse residual stress at 2.5mm below the top surface is 237 greater than that in the as-welded condition.  However, the maximum tensile stress at 2.5mm above the bottom surface is similar to the as-welded condition and after one and three loading cycles.  See Figure 3.

Effect of elastic shakedown: for simple plates and weld joints like butt welds, it can be said that the structure is stable and will achieve an elastic-shakedown state, if the combination of residual stresses along the load direction after a few cycles and the applied load is within the elastic shakedown limit.  In the case of fillet welds, since the residual stress component perpendicular to the loading direction is undergoing relaxation, both stress components parallel and perpendicular to the load direction should be considered to confirm elastic shakedown or steady state.  If the applied load does not relax the residual stress components in the first few cycles, the structure is expected to follow cyclic plasticity or ratcheting over each load cycle.

Summary

In summary, the following two conclusions can be drawn from this study: firstly, that the shakedown limit of fillet welded geometry can be estimated based on a simplified method using plastic work done as a shakedown criterion.  Secondly, that experimental measurement of residual stress redistribution after three load cycles is able to show that there is only minimal redistribution / relaxation in the transverse residual stress component even though the load applied was along this component.

Finally, based on the experimental evidence, the conservative level of the residual stress relaxation rule in BS 7910 may require re-investigation.

Figure 2. Neutron diffraction measurement plane
Figure 2. Neutron diffraction measurement plane
Figure 3. RS redistribution across the weld at 2.5mm above and below the bottom and top surfaces respectively
Figure 3. RS redistribution across the weld at 2.5mm above and below the bottom and top surfaces respectively
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