By Dr. Jim Wood, University of Strathclyde, UK
This article provides a summary of the observations made at the Education and Dissemination session in Majorca, which was reasonably well attended and resulted in 3-4 hours of stimulating discussion.
The three procedural benchmarks are shown below.
Results obtained from all contributors are available for download for each benchmark, as well as results and the benchmarks themselves. The following observations are based on the results contained in these spreadsheets and also from the more comprehensive submissions made by participants.
1. Significant variation in the modelling, results, assessment and conclusions relating to fitness for purpose of such detail is apparent across analysts and industry sectors, for both static and fatigue situations.
2. Human error is apparent, including:
a. Mis-interpretation of boundary conditions;
b. Incorrect use of finite element functionality that altered physical response;
c. Reporting wrong results;
d. Using stress output directly at singularities;
e. Using averaged stresses at shell intersections.
3. Lack of “engineering common sense” is apparent. For example, not all contributors checked that the field stresses compared well with hand calculations, where appropriate.
4. From this limited linear elastic exercise:
a. The need for finite element knowledge is confirmed;
b. The need for general engineering education is confirmed;
c. The need for industry specific knowledge is confirmed;
d. The need for validation is confirmed;
e. The need for adequate QA procedures is also confirmed.
5. Established “common best practice” across the various industry sectors is not apparent.
6. Various guidelines exist for weld modelling and assessment in few industry sectors.
7. Use of experimentally derived results on real weld geometries is recognised as a necessary part of the assessment process for fatigue. It is how FEA results are obtained (often at locations where singularities exist) that provides variations in approach.
8. As with all analyses, the adequacy of any idealisation must be judged in terms of the purpose of the analysis being conducted. The idealisation of such fabrication detail will affect static and fatigue (and dynamic, buckling, limit and fracture assessments) to different degrees.
9. The influence of fabrication detail can be local or global in nature and this fact should be considered when judging adequacy. The details selected for consideration as “procedural benchmarks” have both local and global measures selected as targets and all showed variation.
10. It is possible to use shell models to obtain necessary stress data for fatigue assessment of such details, but care and understanding is necessary. It should also be recognised that shell models will produce finite converged results at intersections.
11. There would appear to be two distinct approaches to obtaining “hot-spot” stresses from finite element models:
a. A stress linearization procedure (not required with shell representations), designed to remove the peak stress component and leave the membrane and bending stress components. Such an approach will include gross geometric stress concentration effects. Some finite element systems provide post-processing tools for defining the “assessment section” in both 2D and 3D representations and for linearising the results. This approach is common in the Pressure Vessel industry.
b. A number of “extrapolation” approaches, with slight variations in the extrapolation procedures, are in use. These approaches invariably involve element sizes of the order of 0.4t and differ in whether linear or quadratic extrapolation is used to the hot-spot location (which is often a singularity in nonshell models). Some of these procedures also provide details of how the stress distributions from shell models should be displaced by up to half a shell thickness (depending on the angle of the intersection), before extrapolating to the hot-spot. However, it is recognised that specific Codes of Practice may not give the analyst any choice in which procedure to adopt.
12. Some fatigue assessment procedures require the use of the stress range on the weld throat area. Stresses plotted across the throat will show a highly non-linear variation. Although not always clear, it is likely that an average value of stress is required from the results, to provide consistency with hand calculations. Although not always clear, it is likely that a simple ‘membrane + bending’ value of stress, with peak component removed, is required from the results, to provide consistency with hand calculations.
13. Some analysts used thick shell elements. The fact that most did not, would perhaps indicate that participants from different disciplines do not have a common understanding of when plates and shells become thick.
14. Given the nature of the Displacement Finite Element Method and the details examined, it is perhaps not surprising that greatest agreement is apparent for global stiffness ( as measured by overall displacements), closely followed by field stresses (by definition away from local stress concentrations). Greatest variation is apparent for local stresses, which include finite values derived from distributions in the vicinity of singularities. In addition, as would be expected, greatest variation is apparent for very small target values, with best agreement generally for large values.
1. For this detail, the practice of displacing shell stress distributions by half a shell wall thickness before interpolating values at the “notional” position of weld toes (hot-spot), would seem unnecessary.
2. The various results provided by “Analyst Identifier 1” show remarkably little variation amongst 2D-Axi and shell models (with and without weld representation). Whilst inclusion of the weld stiffness (by whatever means) improves the comparison with the highly refined 2D-Axi results, it is not apparent that this additional complexity is merited over a simple shell representation and use of stresses at the location corresponding to the weld toe.
3. Although not considered in these benchmarks, it is noted that a simple shell intersection representation already has too much mass, without the addition of any measures designed to include the effect of the weld. This will have some bearing on dynamic analyses and weld models will result in a greater need to reduce the density of local elements for accurate representation.
1. The reason for the large variation in contact radius results for load case 2 is not apparent. This is clearly a function of global stiffness representation as well as the effectiveness of the contact methods used. Given the relatively good agreement on overall deflections in most cases, it must be assumed that the differences are largely due to the contact methods. This fact emphasises the need for adequate contact benchmarks.
2. The various results provided by “Analyst Identifier 1” show remarkably little variation amongst D-Axi and shell models for deflections, field stresses and weld-toe stresses, for load case 1. The poor comparisons for load case 2 are due to the lack of contact simulation in the shell model for load case 2.
3. Assuming the reinforcing plate to be integral did not provide good agreement for field stresses at the plate centre. The comparison of local stresses in the region of the weld are reasonable, particularly for those of larger magnitude. It is clear therefore, that if such an assumption is to be made, then care must be taken to ensure that both plates effectively act as one through use of a suitable number of spot or puddle welds. The results for the “central spot-weld” idealisation, would indicate that an “integral” behaviour may be possible with relatively few plate connections.
4. Neglecting the offset due to the reinforcing plate and assuming a double thickness integral representation over the reinforced area produced similar results to the “integral” idealisation with offset.
1. Only two participants showed that the problem was large displacement (subsequently confirmed by the coordinator), in spite of the tip deflection being less than the thickness of the plate.
Reductions in deflections and stresses are significant. The rules of thumb commonly used as a guide to when large displacement effects become significant for beams, plates and shells are clearly not applicable for this problem. The reason for this is apparent when the source of the non-linearity is given due consideration.
2. 3D models (shells and bricks) show variations in results across the width, which are obviously absent from 2D results. Not all contributors commented on this effect.
3. Neglecting the offset, even with correct plate thicknesses, fails to predict adequate values for overall stiffness, field stresses and local stresses. Analysts should therefore think carefully before neglecting offsets in plate/shell mid-surfaces, as their effects can have a global nature as well as local. For thinner plates/shells, large displacement effects may act to reduce the global effect of the offset, through local bending of the joint and effective realignment of the midsurfaces.
4. The modelling of contact between the lapped plates appears irrelevant for the relative joint sizes considered. The results for separate plates, with and without contact, and models where the plates were assumed integral appear similar. The latter model however, fails to pick up the stress singularity that exists at either end of the lap running between fillet weld roots. Almost all contributors failed to highlight this singularity, in any model.
The general consensus of those participating was that this was a worthwhile exercise, that should be of interest to the wider FE community. Given the level of participation, this fact was clearly not always recognised. It should be recognised that the relevance of the general observations clearly have broad interest to the entire finite element community, it should also be recognised that the relevance of the detail of the modelling strategies used is not confined to those involved in welding 15mm thick steel plate! It is now my task to try and pull together some sort of conclusions from this exercise. To this end, I have asked contributors to have a look at the final collated results and take the opportunity to comment on the results that they provided in relation to the rest. In addition, they have also been asked to have a look at the preliminary observations and to comment on these and add their own if necessary.
On receipt of everyone’s comments, I will then document the exercise. The final document is likely to consist of several parts…. An Introduction providing the background and aims of the project; the Procedural Benchmark Specifications; the “Round- Robin” results (with anonymity maintained); observations from the exercise and finally some conclusions regarding good and bad practice in the analysis and assessment of such details.
This final report is now available to download, as well as being available from NAFEMS in hard-copy format.