![]() ![]() Applying a Stress Linearization in COMSOL Multiphysics®Ī stress linearization does not affect the analysis as such it is a type of result presentation. Licensed under CC BY-SA 3.0, via Wikimedia Commons. Image by Björn Appel, Benutername Warden. ![]() Thus, the actual local stress is not even meaningful to compute, so we must resort to methods based on nominal stresses.Ī weld in a pipe used for district heating. Typically, the local geometry at the weld is not even well defined (unless it is a very high-quality weld that has been ground smooth). In this case, stress linearization can provide a useful tool for converting the 3D stress state back into a set of nominal stresses.įor instance, this situation can occur when analyzing welds. Because of this, we might end up in a situation where using the accurate results of a full 3D analysis leads to a highly conservative design. The effects of local stress concentrations are already taken into account by providing low allowable nominal stresses. When we do a full 3D analysis, the effect can be that we get results that are “too good”. Some rules for qualifying structural elements are based on the stresses being “hand calculated” or the result of a shell or plate analysis. Other Applications of Stress Linearization The purpose is to avoid plastic strains accumulating in each load cycle, which can lead to a fast failure due to low-cycle fatigue. The requirement on the secondary stresses is set to avoid cyclic plastic deformation upon repeated loading–unloading cycles. It should be noted that because pressure vessels often operate at elevated temperatures, room temperature values of allowed stresses might not be sufficient. The stresses are normalized by the yield stress. The fundamental ASME criteria for primary stresses. In the figure below, the collapse interaction curve is compared with the stress limits imposed by the code. ![]() The discussion above tells us why: The bending stress reduces the stress over part of the section.Īs noted above, the detailed stress state is not important when it comes to static failure, as the stress distribution in the collapse state is fully determined by the force and moment equilibrium. Interestingly enough, this means that if the membrane stress is at the limit allowed by the first criterion, it is still allowed to add a certain amount of bending stress. There are similar requirements, but with higher safety factors against reaching the ultimate stress.Secondary stresses are allowed to reach twice the yield limit.This is because incipient yield is not equal to the full collapse of the section in this case. If there are only bending stresses, the safety factor against collapse is again 1.5. The stress intensity from the sum of membrane and bending stress should not exceed the yield stress.This gives a safety factor of 1.5 against plastic collapse when only membrane stresses are present. The stress intensity (Tresca equivalent stress) from the primary membrane stresses should not exceed two-thirds of the yield stress.Without going into detail, the basic requirements of the code are: The choice of SCL is not unique, so here we must use our engineering judgment to find the critical locations.Īlthough not fully correct (but conservative), the linearized stresses are sometimes viewed as equivalent to the primary stresses. Secondary stresses do not lead to a collapse when they exceed elastic limits, since they are just redistributed.ĭuring the analysis, the stress is studied along a number of lines through the section, referred to as stress classification lines (SCLs). Typically, secondary stresses are local effects caused by either geometric discontinuities or displacement-controlled loading. Secondary stresses are caused by other effects. Here, we are required to classify stresses as either primary or secondary.Ī primary stress is a stress that is required for maintaining force and moment equilibrium. The concept of stress linearization is an important part of the qualification of pressure vessels, as described in ASME Boiler & Pressure Vessel Code, Section III, Division 1, Subsection NB. If the structure is subjected to cyclic loading, the peak stresses are of utmost importance, as they determine the risk of fatigue crack initiation at the surface. The safety factor, which is implicit in the bending collapse, must also be taken into account. Using the true peak stress gives an overly conservative design. The conclusion is that for determining safety conditions within plastic collapse, the linearized stress is the relevant parameter, since it is proportional to the axial force and bending moment. The difference can be explained by the fact that a small plastic hardening is used in the model to stabilize the analysis. This value matches the final parameter value of 0.76 rather well.
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