Q & A Session

We had an interesting and lively Q&A session during the "Some Failures & Studies With Lessons Learned - Fatigue" webinar and we wanted to share with you the questions that we didn't have the time to address during the event.

Q: Where on the Wind Turbine was the Fillet?

A: The shaft shoulder fillet radius is annotated on the slide graphic (immediately adjacent to the position of cracking, at the top of the curved end top surface of the keyway). This keyway held a gear in place and so would be highly stressed during power transmission).

Q: It would be helpful to know what materials are involved, e.g. steel or aluminium?

A: The materials of the wind turbine shaft was a steel, as was the lighting columns and mitred bend.

Q: Do you know of any place where there is good guidance on how to use the results from a Finite Element Analysis to perform a fatigue assessment?

A: I believe the NAFEMS Computational Structural Mechanics Working Group have commissioned a book in this area and the NAFEMS publication “Finite Element Based Fatigue Calculations” by Bishop & Sherratt (2000) is a useful start. Generally your software vendor would have manuals that would also be useful.

Q: Which type of elements have you used to mesh the weld junction which creates the singularity? Is there a specific type of element?

A: Not sure which slide you are referring to, but in general any structural element … 3D 2-D axi as appropriate will converge towards to infinity with mesh refinement, at a singularity. Each mesh will give a finite value at the singularity but will never give a converged value. I used a p-element formulation in my singularity studies as each element adapted up to an 8^th order polynomial, but ordinary h-elements (with or without midside nodes) could be used.

Q: I have seen Baud curve idea applied to a weld - smoothing the shape at worst place - but someone biased it the wrong way.

A: Do you have a ref? Sounds interesting.

Q: Does the galvanizing induce residual stress?

A: We never measured galvanized residual stress levels, but no doubt they would exist … but not to the extent of the compressive residual stresses evident in the Martensitic steel weld cladding. The galvanizing is only there as a corrosion protection.

Q: Could you please explain more about how ratcheting works?

A: Ratchetting is when with each load/unload cycle the resulting total strain increase more than the latter’s value of the previous loading cycle. Ratchetting is associated with material plasticity and normally occurs when there is at least a constant primary stress and alternating secondary stress e.g. beam under constant tension and cyclic bending moment. If the stress response in the structure or vessel is wholly elastic the phenomena of ratchetting does not occur since each stressed point in the structure would go back (theoretically) to its zero stressed state upon removal of the load, elastic strains would also go down to zero upon unloading. If the case is that during the loading cycle some parts of the structure go into the plastic state then upon unloading the remaining elastic material wants to go back to its original condition while the plastic part just wants to retain its new dimensions. This is easily demonstrated in a tensile test of a uniaxial specimen. Because of this phenomena there is what I like to call a tug of war between the elastic and plastic material so that upon unloading, the elastic and plastic material remain a little stressed so that equilibrium of the stress field within the material is obtained, these are what we call residual stress fields which can result in slight distortion of the component and that is why if we drill or cut a component having residual stresses this will cause further distortion until the stress field achieves equilibrium again for the new geometrical state – Have you ever tried to cut through a hot extruded angle iron in the longitudinal direction?

Ratchetting occurs with each load and unload cycle and the total strain at a particular point in the structure where the phenomena is occurring will increase with number of cycles. When this happens, different material/structural responses can take place:

1. If the load level is high, ratchetting continues to take place, the strains increase with every cycle, stress strain loops grow and grow with each load cycle until plasticity spreads so much that plastic collapse of the component occurs, other words for ratchetting are progressive deformation & incremental collapse.
2. If the load level is not so high, ratchetting may occur during the first few load/unload cycles and then stops. This occurs because a state is reached in which the resulting residual stress field and associated deformation cause the stress response to be wholly elastic with each load/unload cycle. This situation is called elastic shakedown i.e. the component response shakes down or settles to an elastic behaviour.
3. A situation called plastic shakedown can occur for a situation where the stress response is deformation controlled rather than load controlled. In this case the strains do not grow with each load/unload cycle and the stress strain hysterises loop is contained. In this case failure does not take place due to incremental collapse or ratchetting but due to low cycle fatigue. The latter, in contrast with high cycle fatigue is associated with a lot of plasticity. Having said that, the microscopic failure mechanism for low and high cycle is the same i.e. regions subjected to positive and negative stresses form an intergranular crack that grows with number of cycles. For high cycle fatigue, the plastic region is very much smaller than in low cycle fatigue failures and mainly caused by the stress concentration factor at the crack tip. A very simple example for a low cycle fatigue failure is that of subjecting a paperclip wire to positive and negative plastic bending stresses (displacement controlled), Material of the clip fails after about 10 to 15 cycles.

A nice example of ratcheting occurring is a simple experiment in which a length of soft solder wire goes over a pulley and is used to lift a weight upwards and downwards. The tension in the wire, provided by the weight provides a Primary Stress and the cyclic bending of the solder wire as it rolls over the curved pulley wheel, provides a necessary cyclic Secondary Stress. The ratchetting manifests itself as accumulating axial plastic strain that results in the solder wire getting longer with each cycle of lifting up and down … until it breaks.

The above situations are catered for in EN13445 Part 3 Annex B and in ASME B&PVC Part 5. EN13445 in particular points towards achieving shakedown after a small number of cycles either by using full cyclic analysis or using other methods of checking based on classical shakedown bound theorems. This avoids ratchetting or incremental collapse. This philosophy of design may produce a conservative design.

Classical shakedown bound theorems presented by Melan and Koiter and others provide an alternative to full elastic-plastic simulation of the behaviour. Methods using Melan's theorem are particularly appropriate in design since they give a conservative lower bound to the actual shakedown load. Melan’s theorem uses equilibrium considerations to determine a lower bound to the shakedown load. Koiter’s theorem uses compatibility considerations to determine an upper bound to the shakedown load.

Melan's shakedown theorem states;

"A first order theory linear-elastic ideal-plastic model with associated flow law will shake down under a cyclic action if a time-independent self-stress field can be found such that the sum of this self-stress field and the cyclically varying elastic stress field for the given cyclic action is compatible with the yield condition."

A computational method based on the above shakedown theorem is described in the NAFEMS Introduction to Design by Analysis of Pressure Systems and Components web-based-learning module.

The ASME and API codes have two approaches to check for ratcheting - the elastic approach and the elastic plastic approach. Elastic analysis provides an approximate value for the shakedown load and a better way (both in the amount of conservatism and accuracy and also in methodology) is to use elastic plastic analysis. Both codes currently specify an elastic perfectly plastic material model. The elastic analysis approach is based in obtaining linearised stresses and stress classification to be able to calculate the membrane + bending stress at particular points in the component model. Linearisation of stresses can normally be done automatically by most commercially available FE application software but the analyst must select the classification lines and further classify stresses. If shell elements rather than solid elements are used there is no need for stress linearization but stress classification is required. Nowadays pressure vessel code of standard committees encourage analysts to use the elastic plastic approach which is a direct approach and results in better predictions for ratcheting/shakedown loads notwithstanding the fact that the method circumvents the problems associated with elastic analysis.

The NAFEMS Introduction to Design by Analysis of Pressure Systems and Components web-based-learning module does not cover API 579 but the ratcheting check is very similar to the ASME code Section VIII Div. 2 if not the same.