Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 1/8

FATIGUE ASSESSMENT OF TUBULAR WELDED CONNECTIONS WITH THE STRUCTURAL STRESS APPROACH

Fabien Contia, Laurent Verneya, André Bignonnetb

aBureau Veritas, 92046 Paris La Défense, France

bAndré Bignonnet Consulting, 49750 Beaulieu, France

Abstract The fatigue behaviour of tubular joints for offshore structures was analyzed within the framework of a European programme in the 70s and 80s. The objective of this paper is to summarize the application of Dang Van Fatigue criterion with the structural stress approach for several tests of this database. Then, some issues are briefly discussed like meshing strategy, stress concentration factor, fatigue curve, the weld toe influence, and a comparison with the hot spot stress methodology currently used for the design of offshore structure.

1 INTRODUCTION Since the building of the first offshore steel jackets several decades ago, tubular welded joints fatigue design experienced great advances and has become more reliable today. This progress was sorely driven by European research programs: United Kingdom Offshore Steels Research Project (UKOSRP – 1975 to 1986) and European Coal and Steel Community project (ECSC – 1981) which led to the Hot Spot Stress approach widely adopted by offshore standards and common practices. However, the recent problematic of ageing structures reassessment prompts us to give it a second thought in order to enhance fatigue life prediction’s accuracy and identify existing conservatisms. Based on ECSC tubular joints tests database, the following paper will develop another standpoint by improving structural stress assessment’s accuracy and appraising the influence of multiaxial stress fields using Dang Van fatigue criterion.

2 HOT SPOT STRESS DESIGN METHODOLOGY FOR OFFSHORE APPLICATIONS

2.1 Definition of hot spot stress Fatigue design of offshore tubular welded joints is based upon the hot spot stress methodology derived from Radenkovic [4] early proposals. Conceptually, this S-N approach considers the design stress to be the geometric or “hot spot” stress that characterizes the connection overall geometry via non-dimensioned ratios and excludes stresses due to notch discontinuity at weld toe as well as residual stresses. This is illustrated in Fig 1.

Chord

Brace

Stress

Geometric Stress

Notch stress

Notch region

Nominal stress

Chord

Brace

Stress

Geometric Stress

Notch stress

Notch region

Nominal stress

Figure 1. Notch region and geometric hot spot stress definition

Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 2/8

In practice, hot spot stress is obtained by strain gauges measurements on tubular joints testing or by finite elements analyses where maximal principal stress is extrapolated to the weld toe from sample points chosen outside the notch region. At this stage, a relevant design stress is accessible to the engineer using structural calculations.

2.2 Stress concentration factors Conventional design of offshore jackets is carried out using beam models, thus allowing only nominal stresses computation. Hot spot stress is then determined using parametric formulas providing the stress concentration factor for the considered loading mode (axial, in plane bending, out of plane bending) and simple joint type (T/Y, K, KT, X). This straightforward procedure however suffers from some restrictions that are only partially addressed in the design codes: First, the calculated stress concentration factors are invariant with weld toe length whereas ECSC database screening shows fatigue life improvement with longer weld toes due to hot spot stress reduction. Second, they include chord bending stress that is more linked to chord boundary conditions rather than joint geometry. Lastly, they only provide maximum values around the brace/chord intersection whereas the various loading modes lead to different hot spot positions. Even if they are a great help at the design stage allowing time effective fatigue design of jackets tubular welded joints, the use of stress concentration factors can provide inaccuracies in hot spot stress assessment. Consequently, precise fatigue life assessment of ageing structures’ tubular joints may be improved using direct determination of hot spot stress via finite elements modelling. Moreover, under certain modelling considerations, this approach is more flexible and opens the door to multiaxial fatigue assessment that will be presented in the following.

3 DANG VAN FATIGUE CRITERION This fatigue model is presented in detail in [3], where different structural applications are besides given. In this model, the material is considered as a heterogeneous microstructure submitted to cyclic loading and fatigue corresponds to limit of possibility of local elastic shakedown. Thanks to this assumption, local stabilised cyclic stress field σ(t) can be calculated (see [3]). It must be noticed that the local stress in the stabilized state is chosen in preference to plastic strain or dissipative energy, which is also contained in the elastic shakedown hypothesis. The main reasons are that these latter quantities are not easy to evaluate since, in high cycle fatigue, plastic deformations are heterogeneous and occur only in some misoriented grains. Moreover, the increases per cycle of theses quantities are so tiny that such ways of estimating them lead to big errors and great uncertainties in predicting the fatigue resistance. In order to assess potential fatigue failure, local shear amplitude for a given material plane τha(t) and hydrostatic tension p(t) derived from σ(t) were chosen as pertinent parameters. The fatigue criterion retained is a linear relation between these quantities. The fatigue limit state can be written in the following form:

( )( )( )( ) ( ) ( )

+==−

tpattF

btF

hah

h

.

0

τσσ

where a and b are material constants that can be determined by two simple types of fatigue experiments; b for instance corresponds to the fatigue limit in simple shear. General application of this criterion requires the determination of the plane on which the set (τha(t), p(t)) is a «maximum» relative to the criterion during the time. Therefore, the general procedure determining F(σ) requires the double maximization of the aforementioned expression over time and material planes:

( ) ( ) ( )[ ][ ]tpatMaxMaxF hatPlanes h

.+= τσπ

where τha(t) is the local shear amplitude on plane πh at time t. The set of parameters satisfying the maximization procedure occurring on the critical plane πh

* is then noted (τha*, p*).

At last, it is also frequent in some applications to use the concept of local equivalent stress for a life duration Ni defined by:

**,0 .paihai +=ττ

Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 3/8

4 FATIGUE ASSESSMENT OF TUBULAR JOINTS USING A MULTIA XIAL CRITERION

4.1 A structural approach Current practice in offshore tubular welded joints, based on hot spot structural stress, considers the design stress to an extrapolated principal stress outside the notch region. This uniaxial approach is useful to many applications but is unable to handle multiaxial loadings which influence the fatigue strength of welded joints. To overcome this difficulty and clarify the description of the design stress, we extend the structural approach proposed for tubular joints using the concepts which are at the origin of the Fracture Mechanics. Actually, it is known that the mechanical state in the highly damaged crack tip zone, called the process zone, is inaccessible by the usual mechanics of solids. In this zone, the material is neither really continuous nor homogeneous and the local strains are not small. Nevertheless, the stress solution obtained from linear homogeneous and isotropic elasticity in small strains allows the correct description of the mechanical state outside the process zone. Although it is erroneous at the vicinity of the crack tip, it makes sense in terms of an asymptotic solution which allows the correct control and the interpretation of the phenomena produced in the process zone. Likewise, we will look for a way to build the asymptotic solution which allows the correct control and interpretation of the phenomena produced in the critical zone of the weld. For that purpose we adopt an approach which combines testing and calculations with meshing rules taking into account the local rigidity due to the weld instead of the local geometry of the weld itself (as it is the case in Fracture Mechanics, where the actual geometry of the crack tip is not taken into account) which is a very hazardous data. Therefore, the fatigue design can be based on a structural stress calculation from a finite element analysis. On this basis we can establish design rules for welded structures [1] [2] with a structural approach and a unique S-N curve where S is a local equivalent stress defined from τ and p at the Hot Spot as described in the next paragraph.

4.2 Computing procedure Some computational methods applicable to the prediction of fatigue strength have been proposed by different researchers. In the automotive industry, J.L. Fayard et al. [2] developed with PSA Peugeot Citroen an efficient numerical tool to evaluate the asymptotic mechanical field which defines precisely the design stress state and allows the prediction of the fatigue strength of continuous arc-welded structures. The thin shell theory was considered to be the most appropriate calculation method to solve the fatigue life prediction problem of automotive thin welded plates. Given the high diameter to thickness ratios of tubular joints, this hypothesis will be reused for tubular applications. However, in a thin shell finite element model, sheets are described by their mean surfaces. The outstanding difficulty in using such meshes lies in the modelling of the mean surface intersection. In fact, this zone exhibits 3D behaviour, whereas a thin shell model only produces biaxial stresses. Moreover, at the intersection of thin shells, where hot spots commonly appear, the stress gradient can be rather steep, so that stress calculations are very sensitive to the mesh size. It is therefore necessary to define a meshing methodology which can be systematically applied to any welded connection. On this basis, a design rule was established [2] as shown in Fig. 2.

Figure 2. Meshing rule for design stress state assessment [1] [2]

Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 4/8

The first idea was to reproduce as precisely as possible the local rigidity induced by the weld to the joint, which modifies the local stress distribution. The other principal idea that supports the meshing strategy was to simulate the stress flow from one sheet to another throughout the weld. For that purpose, rigid body elements were used to link the two shells. The «good rule», associated with a design stress representing faithfully the fatigue phenomenon and an appropriated failure criterion, is the one that allows the interpretation of all the experimental results with the minimum scatter. Thus, the size of the elements at the intersection area has been particularly defined such that the geometrical stress is calculated at the weld, precisely where cracks commonly appear, without extrapolation at nodes. The application to tubular joints requires specific modelling considerations in order to take into account the chord geometry at crown and saddle points when fatigue cracks are the most likely to initiate (see Fig. 3 and 4).

Saddle

Crown

Saddle

Crown

Figure 3. Tubular joints saddle and crown points

Figure 4. Tubular joints specific meshing rule

Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 5/8

The applicability of this meshing procedure for hot spot stress field assessment on tubular joints was checked comparing stress concentration factor values obtained with different methods for a T joint under axial loading. The results summarised in the Tab. 1 show the consistency of the approach.

Assessment method SCF value Discrepancy with test (%)Real scale test 6.55 -Extrapolation on volumetric elements model 6.91 5.5Extrapolation on shell elements model 6.97 6.41Fayard et al. meshing methodology 6.92 5.65Efthymiou parametric 7.51 14.66

Table 1. Stress concentration factors comparison for T joint

4.3 Fatigue assessment The failure criterion N has been defined differently from initial proposals [1] wherein the critical crack size was defined as the size from which the crack left the influence of the local effects, which are at the origin of crack nucleation. In the ECSC tubular joints database, the number of cycles corresponding to the definition above, characterized by a significant increase in the crack growth rate and a strong decrease of the signal of strain gauges situated in the vicinity of the hot spot, was seldom documented. Thus, the number of cycles corresponding to the more classical through thickness cracking failure criterion was used instead. Design stress calculation is carried out considering the computed stress state σ at the hot spot. Using Bignonnet and Dang Van results [1], a local equivalent stress τ0 can be defined regardless of the number of cycles. Thus, ai being independent of N for high cycle fatigue applications (see page 2), the equivalent stress formulation given in [1] for steel welded joints will be considered:

**0 .33.0 pha += ττ

The expression above allows convenient use for practical engineering applications since fatigue life assessment is driven by a unique parameter τ0. Thus, the widespread tubular welded joints design procedure using an S-N curve plus Miner’s law can be adapted with a τ0 -N line in lieu of a usual S-N curve. Such a specific τ0 –N curve based on ECSC tubular joints fatigue testing [9] has been determined following the design stress assessment procedure detailed above. The database screening criteria retained only T joints where the weld profile was closely documented since this information is crucial regarding stress assessment accuracy. In addition, a meshing tool was developed to handle tubular joints specific meshing rules (see Fig. 5).

Figure 5: T tubular joint mesh

Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 6/8

Then, since the tests were performed under simple axial or bending loading modes, the hot spot stress field follows a proportional evolution, thus allowing the analytical calculation of the design stress with a unique static computation and without following the complete procedure of double maximization through time and material planes. Raw scatter plot of design stress versus number of cycles to failure (Fig. 6) exhibits a significant scale effect due to the failure criterion considered. Therefore, the design stress was multiplied by a thickness correction factor of ( ) 3.016T classically used in tubular joints fatigue design. Assuming a Basquin formulation for

the τ0 –N curve, a 50% probability of survival mean curve was defined. The characteristic values were also assessed in accordance with [12] in order to define a 95% probability of survival design curve (Fig. 7). Lastly, it must be noted that a slope change at 107 cycles according to Haibach formulation was retained for both curves in order to take account of variable amplitude loadings due to the design seastates in the application of Miner’s law.

Figure 6. τ0 –N scatter plot

1.00

10.00

100.00

1000.00

1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+09

N

τ0

Design curve Test data Figure 7. Design τ0 –N line for tubular joints application

Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 7/8

4.4 Applications The approach presented above was implemented on a real offshore platform (Fig. 8) where only a tubular joint was modelled with the meshing methodology aforementioned. It must be noted that the design stress is assessed using the same procedure that the one employed for fatigue curve building, which makes the whole approach consistent.

Figure 8. Hydrodynamic loading on offshore platform structure For the sake of simplicity, a unique wave was considered for the fatigue life assessment. Given that a wave loading is not a strictly proportional loading since various members can be impacted at different wave stages, the calculation of the design stress cannot be done immediately. Instead, the general maximization procedure is executed using a specific tool developed for offshore applications. The present loading was applied with and without the jacket dead weight in order to compare fatigue predictions relative to Dang Van criterion. For both cases, the load path in a (τha

*, p*) diagram in the critical plane is plotted in Fig. 9. Associated lifetimes compared with the traditional hot spot approach (Tab 2) show that the methodology is consistent with the existing approach and enables the consideration of the beneficial effect of compression in legs that was already observed in tubular joints testing under compression [10].

Figure 9. Load path

Assessment method / Loadcase Wave Wave + Jacket dead weightHot spot stress (uniaxial) 358000 cycles 358000 cyclesStructural stress (multiaxial) 339000 cycles 441000 cycles

Table 2. Allowable number of cycles comparison

Fatigue Design 2009 – 25-26 November 2009 – Senlis, France

Page 8/8

5 CONCLUSION The structural stress approach proved to be applicable to tubular welded structures multiaxial fatigue assessment and showed the relevance of the consideration of the structure’s dead weight. Moreover, implementing the meshing methodology presented in this paper allowed direct weld toe positioning and structural stress field assessment without stress extrapolation thus providing accurate estimations. Further investigations would be needed in order to obtain a database including various levels of multiaxiality for fatigue curve building. In particular, fatigue testing of chord members under compression load which represent jacket legs would be helpful to consolidate this application of the methodology presented for offshore platforms.

6 REFERENCES [1] Bignonnet A., Dang Van, K.: Structural Stress Approach for Fatigue Design of Welded Structures –

Symposium Fatigue Design ‘2007- Cetim 21-22 Nov 2007. [2] Dang Van, K., Bignonnet, A., Fayard, J-L., Assessment of Welded Structures by a Structural Multiaxial

Fatigue Approach, In Biaxial/Multiaxial Fatigue and Fracture, Ed. A. Carpinteri, M. De Freitas, A. Spagnoli, ESIS/STP31, pp3-22, Elsevier 2003.

[3] Dang Van, K., Fatigue Analysis by the Multi-scale Approach, High Cycle Metal Fatigue, From Theory to Applications, C.I.S.M. Courses and Lectures N° 392, Ed. Ky Dang Van & Ioannis V. Papadopoulos, Springer 1999 pp.57,88.

[4] Radenkovic, D. (1981), Stress Analysis in tubular joints. Proceedings of the international conference, «Steel in Marine Structures», pp. 71-118, Paris. DOC EUR 7347 Pub IRSID – France.

[5] Huther, M., Henry, J.: Recommendation for the hot spot stress definition in welded joints/Recommandation pour la définition de la contrainte au point chaud dans les assemblages soudés. Doc IIW/IIS – XV-772-91, 1991

[6] European Steel Research Seminar, Cambridge UK, 27-29 Nov. 1978 [7] Steel in Marine Structures, Int. conference Paris 5-8 Oct 1981, ECSC [8] Steel In Marine Structures, Delft The Netherlands June 15-18, 1987, Ed. C. Noordhoek & C. de Back.

Elsevier [9] Offshore tubular joint test data sheet, ECSC 1981. [10] Bomel tubular joints design guide, Dec. 1999 [11] API Recommended Practice 2A - WSD 21st Edition, Oct. 2005 [12] IIW Document XIII-2151-07 / XV-1254-07. «Recommendations for fatigue design of welded joints and

components», May 2007