Finite Element to foreseen residual stress from the welding process
Most welding process involve local heating, therefore temperature distribution is not uniform and structural thermal stresses beyond the material yield [strongly dependent on the temperature] show up, which can create issues on the final design related to fatigue or even geometry distortions.
This local temperature field is enough to create metallurgical and phase changes. As the pool solidifies and shrinks, it begins to exert stresses on the surrounding weld metal and heat affected zones. When it first solidifies and the weld metal is hot, yield is very low and exerts little stresses. As it cools to ambient temperature, this stresses in the weld area increase and eventually reach the yield point leading to a tensile stress state prone to giving problems during the equipment operational life.
As it cools to ambient temperature, this stresses in the weld area increase and eventually reach the yield point leading to a tensile stress state prone to giving problems during the equipment operational life.
Often pressure vessel suppliers are asked by their clients on how the residual stresses would influence the expected structural performance. Those residual stresses, that in tension may lead to high local stress in weld regions of low notch toughness and, as a result, may initiate brittle cracks that can be propagated by low overall stresses that are normally present. Also, notice that residual stresses can be reduced using thermal or mechanical relief methods, but not always post weld treatments are performed for different reasons.
Residual Stress and Temperature contours
SDEA engineering team used a Finite Element Analysis [FEA] approach to foresee the residual stresses from a dissimilar weld between the tubular plate and the shell [see figure 1]. SA-516 Gr 70 against SA-965 F304 will be welded with ER 309L Mo.
The welding procedure includes the geometry detail of each pass and a two-staged coupled simulation involving a thermal stage and a posterior mechanical step that use the temperature field as an input from the previous model. This can be done because changes in the mechanical state do not cause a change in the thermal state, but the opposite doesn’t apply; so that in this study, computation of the temperature history during welding and subsequent cooling is completed first and then this temperature field is applied to the mechanical model as a body force to perform the residual stress analysis.
Heat input during welding is modelled by a distributed heat flux applying on individual element based data provided by the client for each pass. The amount of heat input is obtained from the next expression, that depends on electrode speed, energy applied and a welding efficiency factor.
Principal stress and contours after weld is finished
Is important to highlight the fact that the reduction in yield for temperatures above 700-800 °C will govern the melting transition. Image above shows the expansion coefficient used for the both materials to be welded, notice the different thermal properties are the ones responsible for different heat diffusion and different thermal strain response.
As expected, the high temperature in each pass relaxes the stresses as yield drops with temperature. Weld metal melts and gets to flow state where stresses are relieved; this effect is clear and can be seen in the images around.
As expected tensile stresses appear on the weld surface. Next plot represents the Von Mises stress on the weld surface for the top and bottom side:
The model was also assessed for protection against ratcheting. Ratcheting is a behavior in which plastic deformation accumulates due to, in this case, thermal stress. To evaluate the model against ratcheting, as well as in the previous point from this document, an elastic-plastic analysis was used, according to the guidelines provided by “ASME BPVC.VIII.2-2017” Part 5, point 5.5.7.
For this analysis, same model from plastic collapse was used. In addition to its boundary conditions, three thermal cycles were calculated, as required in the normative, by setting the following temperature profiles on the interior faces:
- Weld residual stresses were calculated using a non-linear FEA coupled thermo-mechanical analysis. As expected, tensile stresses appear at ambient temperature on the weld surface close to the material yield [in the range of 400 MPa].
- Stresses on the model were calculated using a non-linear FEA coupled thermo-mechanical analysis under operating loads, achieving convergence according to “ASME BPVC.VIII.2-2017 Part5” and thus satisfying the elastic plastic protection criteria
- Elastic-plastic ratcheting assessment was performed after three thermal cycles, according to “ASME BPVC.VIII.2-2017 Part5”. Two main dimensions on the shell were measured during the cycles, showing no permanent deformation due to the effect of the thermal loads. This condition satisfies the elastic plastic ratcheting assessment criteria as stipulated by the standard.
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