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Fatigue Assessment of Steel and Aluminium Welds From FEA

A Guide to the Fatigue Assessment of Steel and Aluminium Welds From FEA

We have experience of weld design and fatigue calculations for rail, process industry and automotive clients. Contact us to discuss good practice in welded structure design and analysis. These brief notes outline some of the techniques that can be used to asses the fatigue lifes of bolted and welded joints. It references some of the important standards that are available for guiding these calculations.

For smooth machined parts, not exposed to hostile environment and free of residual stress, a different procedure is appropriate (eg see [1], [2]). It is assumed that the basis for the calculations are stress results from a finite element analysis of the structure in question.

The older design standards used for fatigue assessment, [3], [5], were written in the '70s, a time before finite element analysis was widely used and apply mainly to beam type structures. To assess a structure, nominal stresses were calculated using strength of materials methods. So the fatigue (or "S-N") curves given in the standards are based on nominal stresses in a fatigue test specimen, at a distance away from the welded feature being tested.

However, with the widespread deployment of FE packages, it has become possible to make a more detailed assessment of the stress field close to a weld. Here, the stresses are usually increased because of stress concentrations from geometry and from the weld toe (if modelled). If these peak stresses are used together with S-N curves based on nominal stresses, an excessively conservative - and expensive - design will be the result. Also, in a complex structure, the stress field varies greatly from point to point, so that it is often difficult to determine which stress to use as a "nominal" stress for assessment.
Another method more suited to the application of finite element results to fatigue lifing of welds is the "hot-spot" stress method, proposed by Niemi and others, overcomes this difficulty. These notes give recommendations for its application, with some reference to the older nominal stress approach.

Standards

Steel: use BS 7608 [3] for plane and bolted features, for welded joints where a nominal stress is clearly apparent and for assessing weld throat failure. Use Niemi's Hot Spot method [4] for welded features where the stress field varies.

Aluminium: use BS 8118 [5] or preferably Eurocode 9 [6] for plane and bolted features, for welded joints where a nominal stress is clearly apparent and for assessing weld throat failure. Use Eurocode 9, Table 5.2.7 for welded features where the stress field varies.

Tips for Using FE Models with Fatigue Lifing Standards

Apply the range of load in the fatigue cycle to the model, as the fatigue strength is governed only by the magnitude of the cycle stress range (fig 1). So, if the load case is eg a vertical acceleration of 1 ± 0.15g, the range of acceleration that should be applied to the finite element model is 0.3g. Of course there are exceptions to this, often where the cycle is predominately compressive. These exceptions will probably be discussed in the appendices of the standard you are using. When comparing stresses with a fatigue lifing standard, do not model the weld unless: a) it is large compared to the size of the surrounding structure, so contributing significantly to its stiffness, or b) the stress within the weld is required to assess weld throat failure.

Make sure that the fatigue curve data you are using is from the mean minus 2 standard deviations curve (the dotted green line in fig 2, see also equation 1, section 4 in [3]).
Check to see if a size effect applies to the feature, eg section 4.3.2 of [3]. This can sometimes be beneficial. Examine the finite element results on the model with property and material averaging turned off. This avoids averaging stresses, not only across material boundaries, but also across boundaries where the plate thicknesses are different (applicable to shell elements models only). It may also be considered meaningless to compare the stress averaged across two plates meeting at a welded joint, when the standard to which the stress is being compared is intended to refer to a single plate.
At a particular detail, look at the magnitude of both the maximum and minimum principal stresses from the finite element results. Perform the assessment on the one with the largest magnitude. Although only cyclic tensile stresses can drive fatigue crack growth, as-welded structures are regarded as having high tensile residual stresses. A compressive cycle imposed on this therefore results in a cyclic tensile stress. In methods of classification based on nominal stress eg [3], [5] and appropriate parts of [6], the direction of the largest principal stress in relation to the line of the weld is important. Eg, in [3], if the principal stress is predominantly parallel to the line of a full penetration weld in a T-joint, class C is appropriate, if perpendicular then class F, which has much lower fatigue strengths than C. The definition of "predominantly" can usually be found in the standard or authority being used and should be carefully checked. Usually it goes something like:

(eg see section 4.3.4 (2) of [6]) In a quick, initial assessment, assume the class with the lowest fatigue strength applies. In [4], a slightly different approach is used (see sketch below), where the stress for assessment is either: a) the largest principal stress in the direction between 45 and 135 degrees to weld line or b) the stress component normal to the weld line, whichever of a) or b) is the greatest.

The view of the whole finite element model shows up the places where the stress is highest. To get a value for assessment, zoom in on the detail and select a few elements in the vicinity of the peak stress. Re-plot the selection, with maximum value labels turned on. This should show up the value of the peak stress, or plot with fringe values.

The Hot Spot mehod demands that nodes are located at precise distances from the weld toe or plate centre line. If another method is used, create a mesh with nodes at or close to features where stresses are likely to peak or at weld toes.

Many loadcase specifications or practical loading situations demand that there be more than one fatigue load range imposed on the model. Usually, the damage from all these must be summed to see if the total is less than 1 (Miner's law). The damage at a particular feature is given by n_i/N_i, where, in load case i, n_i cycles (typically 2 x 10⁶ or 10⁷) are applied to the structure at a stress range of i. The mean minus 2 standard deviations S-N curve can be represented typically by equation (3) of [3]:


Ds_i^m.N_i = C      


where C and m are constants, so that the required life at Ds_i, N_i = C/ Ds_i^m.  Also from the S-N curve, the stress range corresponding to n_i is Ds_o so that n_i = C/ Ds_o^m.  The damage is then given by:    

                                    n_i/N_i = (C/ Ds_o^m)/( C/ Ds_i^m) = [Ds_i/Ds_o]^m           

so damage can be calculated directly from the stress range obtained from the FE results.

Typically, the S-N curve is broken into up to 3 sections, eg for aluminium [6], gradient m changes to m+2 beyond 5 x 10⁶ cycles for loading histories with more than one range magnitude and flattens out beyond 10⁸ cycles.  For this type of S-N curve damage, determination is easier in an Excel spreadsheet using the IF function to see which section of the S-N curve applies for a particular value of Ds_i. 

If the damage is zero, then the life of the detail is infinite and vice versa.   

* Does not include classes applicable only to 7020

Welded Joints
In a shell element FE model, a bolt will usually be represented by a beam element linking nodes in adjacent planes of shell elements. This simple approach gives the forces in the bolt, but spuriously high stresses are developed in the shell elements connected to the nodes to which the beam elements are also connected. These stresses should not be used for fatigue assessment. Instead, find the largest (in magnitude) principal stress around the circumference of a circle in the bolted plate, centred on the bolt. The circle should be 3 times the washer diameter associated with the bolt size. Use this stress with the appropriate S-N curve from the above table.

For a quick, initial assessment, at a particular detail, pick out the principal stress (major or minor) with the largest magnitude as described previously Use this stress with the appropriate S-N curve from the above table. This is a better assessment if used with [4] or table 5.2.7 of [6]. For all other classes quoted above it is too conservative. If it flags a failure, look at stresses at the weld toe position with [4] or table 5.2.7 of [6]. Don't use [3] or [5] unless an area of nominal stress is clearly apparent near the weld. If a failure is still flagged, then sub-model the critical area using 3D elements.

If a detail fails with total damage > 1, a closer examination of it should be performed before considering re-design. A sub-model of the detail using 20 noded brick elements, with at least two elements through the plate thickness, should be constructed, loaded by displacements from the main model. The model should not include the weld (but see section 2). Stresses at the weld toe should then be obtained using the extrapolation methods described in [4].

For the classes concerned with cracking in the weld itself (eg class W welds in [3], class 14 in [5] and see section 4.4.2 in [6]), the stress normal to the weld throat width is calculated in a very simplified way (eg, see sections 6.7.8 and 6.7.9 in [5]). If this has to be done in an FE model, try modelling the fillet(s) as a single, 15 noded, wedge element, as shown below:



For a quick, initial assessment, at a particular detail, pick out the principal stress (major or minor) with the largest magnitude as described previously. Use this stress with the appropriate S-N curve from the above table. This is a better assessment if used with [4] or table 5.2.7 of [6]. For all other classes quoted above it is too conservative. If it flags a failure, look at stresses at the weld toe position with [4] or table 5.2.7 of [6]. Don't use [3] or [5] unless an area of nominal stress is clearly apparent near the weld. If a failure is still flagged, then sub-model the critical area using 3D elements.

In the finite element stress results, get the centroidal stress of the wedge element in the direction normal to the throat width, ie the orange arrow, and use this for assessment to the appropriate class.
In desperation, weld improvement by toe grinding, shot peening, TIG dressing or plasma dressing may be considered. Some standards quantify the increase in fatigue strength which can be obtained (eg, see section 4.3.4 of [3]). However, it should be remembered that toe grinding must be done sufficiently deeply to remove the toe crack (eg, see fig 11 of [3] and fig E.2.2 of [6]). On thin plates, this may cause the thickness of metal to be reduced too much, especially if the extrusion thickness is at the lower bound of the tolerance band. Grinding should always be done so that the grinding marks are perpendicular to the line of the weld toe, NOT parallel to it.

Shot or hammer peening is only effective if the material is thick enough to support the compressive stresses induced at a sufficient level to keep the toe cracks from propagating. Peening will probably not do any good for aluminium < 4 or 5 mm thick.

References

1. BREL "Design Rules & Aids", Volume 2, "Structures".
2. "Metal Fatigue in Engineering", Fuchs, H O, Stephens, R I, Wiley, 1980.
3. "Fatigue design and assessment of steel structures", BS 7608:1993.
4. "Structural hot-spot stress approach to fatigue analysis of welded components", by E Niemi, Intenational Institute of Welding, 2002.
5. "Structural use of aluminium. Part 1. Code of practice for design", BS 8118: Part 1: 1991.
6. "Eurocode 9: Design of aluminium structures", parts 1-1 and 2, DD ENV 1999-1-1:2000 and DD ENV 1999-2:2000.

Selected Bibliography

1. "Fatigue Design Rules for Welded Steel Joints", Gurney, T R, TWI Research Bulletin, Vol 17, 1976.
2. "Fatigue Design Rules for Welded Structures", Maddox, S J, in :"Progress in Structural Engineering and Materials", Vol 2, No 1, 2000.
3. "Interim Fatigue Design Recommendations for Filllet Welded Joints under Complex Loading", Maddox, S J, Razmjoo, in "Fatigue and Fracture of Engeering Materials and Structures", Vol 24, No 5, 2001.
4. "Hot-spot fatigue data for welded steel and aluminium as a basis for design", Maddox, S J, IIW Document No XIII-1900a-01, 2001.
5. "Comparison of different calculation methods for structural stresses at welded joints", Doerk, O, Fricke, W, Weissenborn, C, Spock, IIW Document No XIII-1919-02, 2002.
6. "Improving the fatigue strength of welded joints by grinding - techniques and benefits", Booth, G S, in "Metal Construction", July, 1986.

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