German Delegation

Doc. XIII-2597-15

Fatigue Strength of Laser-Stake Welded T-Joints Subjected to

Combined Axial and Shear Loads

W. Fricke1, C. Robert

1, R. Peters

2, A. Sumpf

2

1) Institute for Ship Structural Design and Analysis

Hamburg University of Technology (TUHH), Hamburg, Germany 2) SLV Mecklenburg-Vorpommern GmbH, Rostock, Germany

Abstract

Laser-stake welding enables an economic production of all-steel sandwich panels that can be

used for steel bridges as well as for decks in ro/ro ships. Deck plates of 10 mm thickness can

be joined to interior web plates ensuring a weld throat thickness of 2 – 3 mm. In a research

project, fatigue tests were performed with laser-stake welds subjected to axial, shear and mul-

tiaxial in-phase loading and assessed by the nominal and the notch stress approach. In addi-

tion to possible effects of gaps between deck and web plates or of the steel strength, the ap-

plication of interaction formulae to laser-stake welds is checked as contained in Eurocode 3

and the IIW recommendations for the fatigue assessment of multiaxial loading. Furthermore,

the equivalent von Mises stress is applied using the notch stress approach. In this way, the

basis is provided for a safe design of laser-stake welded T-joints.

Key Words:

laser-stake weld, fatigue test, multiaxial loading, nominal stress approach, notch stress ap-

proach

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1 Introduction

In bridge as well as in ship construction, an interest exists to replace conventionally stiffened

deck plates by closed all-steel sandwich panels. An economic production of such panels and

similar hollow structures has become possible by laser-stake welding. Deck plates with

10 mm thickness can be laser-welded from outside in a stable process joining the interior web

plates with a weld throat thickness of 2 – 3 mm. Thus, larger dimensions and application are-

as than in the I-core sandwich panels previously developed by Meyer Werft [1] are now fea-

sible. However, experimentally verified design procedures of laser-stake welded T-joints are

presently missing. Neither the laser-stake welded joints are included in the actual standards

and classification rules, nor investigations exist about their strength under shear or combined

axial and shear loading.

Therefore, in a research project fatigue and ultimate load tests with axial, shear, bending and

multiaxial loading were performed at laser-stake as well as single-sided laser and fully-

penetrated laser-hybrid welds. In order to investigate the effect of unavoidable gaps in pro-

duction, specimens with a gap of about 0.5 mm between deck and web plate were produced.

An overview of the fatigue tests performed in the whole project, where also the Chair of Steel

Construction of the University of Dortmund was involved, is shown in the test matrix in Fig.

1. The tests with laser-stake welds subjected to axial, shear and multiaxial loading, indicated

in blue colour, are described in this document.

Fig. 1: Fatigue test matrix of the project with small-scale specimens;

tests described in this paper are indicated in blue colour

Particularly the fatigue assessment of multiaxially loaded laser-stake welds, as they occur in

the all-steel sandwich panels, is uncertain and probably too conservative in the design prac-

tice. The fatigue tests and local stress evaluation described in the following may serve as ba-

sis for a more reliable fatigue life assessment.

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2 Preparation of the Specimens

2.1 T- and Cruciform Joints for Axial Load Tests

The production of the specimens was performed at SLV Mecklenburg Vorpommern with a

CO2 laser of the type TRUMPF TLF12000 in a portal of tape TRUMPF TLC105. The weld-

ing speed for the 10 mm thick deck plates was 1 m/min with a maximum laser power of

9,7 kW. 700 mm long plates were used for welding, from which 50 mm wide specimens were

created by saw-cutting.

Two different specimen configurations were investigated in the axial load tests, the micro-

graphs of them are shown in Figs. 2 – 4. The 10 mm thick deck plates were welded to 5 or

8 mm thick web plates. The weld throat thickness was measured from the micrographs, vary-

ing between 2 and 3 mm. Steel of type S355 was used, in one series of specimens also S460

steel.

Fig. 2: Micrograph of a laser-stake

weld at 10 mm thick deck and 8 mm

thick web

Fig. 3: Micrograph of a cruciform joint with a

laser-stake weld at 10 mm thick deck and

5 mm thick web plate and with additional

10 mm web welded by hybrid process

For the cruciform joints, the weld reinforcement was removed from the deck plate after laser-

stake welding and the second, 10 mm thick web was attached (Fig. 3).

Part of the specimens were produced with a defined gap of 0.5 mm over 50% of the specimen

length (Fig. 4). This should simulate the real production tolerances and show their effect on

the fatigue strength. It was shown that the chosen gap width could be welded without non-

permissible irregularities without adapting the process parameters and that a slightly in-

creased weld throat thickness was achieved.

The hardness valued recorded during the production remained in all cases below 250 HV5.

2.2 Tubular Specimens for Shear and Multiaxial Load Tests

The specimens for the shear load tests consisted of 180 mm long tubulars with 8 mm wall

thickness and 114.3 mm outer diameter, to which two end plates were welded in the same

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way as described above.

The specimens for the multiaxial load tests consisted of two tubular sections with an interme-

diate plate (Fig. 5) so that the cruciform configuration could be arranged in the middle, allow-

ing a load introduction into the laser-stake weld without local bending.

Fig. 4: Micrograph of a laser-stake

weld with a gap between the 10 mm

thick deck and 8 mm thick web plate

Fig. 5: Arrangement for the production of the

tubular specimens

3. Fatigue Tests of Axially-Loaded Specimens

3.1 Performance and Results of the Fatigue Tests

The fatigue tests with axial loads were performed with the above described specimens on a

horizontal resonance testing machine at room temperature and about 30 Hz test frequency. As

mentioned above, two different geometrical configurations were investigated; their micro-

graphs are shown in Fig. 6. The T-joints were clamped directly at the machined faces of the

vertical plate, whereas the cruciform joints were produced at first by laser-stake welding and,

after grinding, a second, 10 mm thick plate was attached by laser welding. The cruciform

joint had the advantage that pure axial loading is acting in the weld under investigation,

whereas the clamping of the T-joint creates some compressive and bending stresses, the latter

during axial loading, see [6]. A comparison of the results should verify that the fatigue life is

not affected by the additional welding process and the different load application.

The evaluation based on nominal stresses in the weld area yields the S-N curves shown for

survival probability Ps = 97.7% (continuous lines) and Ps = 50% (dash-dotted lines). Charac-

teristic values at two million cycles are n = 52 N/mm2 for a prescribed slope exponent of k

= 3 and n = 76 N/mm2 for k = 5. The slope exponent k = 3 is used in relevant codes and

guidelines, e.g. Eurocode 3 [2] and IIW [7] for the fatigue assessment of welded joints. Ac-

cording to the proposal by Sonsino et al. [3] a slope exponent k = 5 is more suitable for rela-

tively thin plated joints with thickness t < 5 mm. Therefore, the S-N diagram shows both

curves. Additionally given are the scatter ratios T between the fatigue strengths for Ps = 10%

and 90%, being smaller for k = 5.

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Fig. 6: S-N diagram for axially-loaded laser-stake welds based on nominal stress range

The fatigue behaviour of laser-stake welds could be compared with the root failure of a fillet

weld. Therefore, the S-N diagram in Fig. 6 shows also the fatigue class FAT36 which has to

be assumed for the fatigue assessment of such a detail according to [2], being conservative.

The fatigue lives of the T-joints are within the scatter band of all results so that the effects of

clamping and additional welding are obviously negligible.

The fatigue test results of the different series do not reveal any effect of the steel strength or

the gap between deck and web plate. The application of local approaches such as the notch

stress approach might allow drawing additional conclusions.

3.2 Evaluation of the Fatigue Tests by the Notch Stress Approach

The notch stresses were computed for each specimen taking into account the angular and axi-

al misalignment or, in the case of T-joints, the web eccentricity. After the tests, the fracture

area was scanned with high resolution and measured using a CAD program so that the aver-

aged weld throat thickness and eccentricity could be computed for each specimen, see upper

left part of Fig. 7.

The computed geometry parameters were used in 2-dimensional finite element models (FE

models) which were created in ANSYS 14.0 with Plane183 elements for plane-strain state.

The ends of the slits were artificially rounded with the reference radius rref = 0.05 mm which

is recommended for thin-walled structures by IIW [4]. Previous investigations of axially

loaded laser-stake welds have shown [8] that this radius resulted in conservative fatigue as-

sessments, whereas the larger reference radius rref = 1 mm showed non-conservative fatigue

lives. The mesh fineness in the notch corresponded to the IIW recommendations [4].

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Fig. 7: Computation procedure for the weld geometry parameters and the stress range

of each specimen

The slits beside the laser-stake weld contained contact conditions, using the element types

Conta172 and Targe169 along the element boundaries. The other boundary conditions were

applied in two load steps (LS). LS 1 simulated the clamping of the specimen in the pulsator

by forcing the nodes along the clamped area into a horizontal plane (green boundary condi-

tions in Fig. 7). After clamping, the mid-planes of both specimen ends were located at the

same Y-coordinate. In LS 2, the axial load was applied to the model aligned in LS 1 (red

boundary conditions in Fig. 7). The notch stress range at the rounded slit ends was determined

by the difference between LS2 and LS 1. Geometrical nonlinearity was considered.

Fig. 8 shows the S-N results on the basis of notch stresses as well as the statistically evaluated

S-N curves for k = 3 and k = 5. Notch stresses at reference radii rref = 0.05 mm are assessed

with the fatigue class FAT630 using a slope exponent k = 3 according to the IIW recommen-

dations [4]. The laser-stake welds investigated here show a characteristic fatigue strength of

639 N/mm2. The statistical evaluation would yield a slope exponent k = 4.16. Again, the

evaluation with a fixed slope exponent of k = 5 results in a smaller scatter band.

Neither the results for the specimens with 0.5 mm gap between deck and web plate nor those

for the specimens made of steel S460 are outside the scatter band of the other specimens.

Therefore, an effect of these parameters on the fatigue strength of laser-stake welds can be

excluded. Also no difference could be found between the T- and cruciform joints so that no

influence of the clamping and the additional welding of the cruciform joints on the fatigue

strength of the laser-stake welds occurs.

It can be observed, however, that the slope of the S-N results of the specimens with 8 mm

thick webs is steeper than that of the specimens with 5 mm thick web, see black mean curve

of 8 mm thick cruciform joints in Fig. 8 and the computed slope exponent k = 2.92. k = 3

seems to fit the results better for this series. In the following comparison with the tests under

shear and multiaxial loads, only this axially-loaded series will be looked at.

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Fig. 8: S-N diagram for axially-loaded laser-stake welds based on notch stress ranges

4. Fatigue Tests of Shear and Multiaxially Loaded Specimens

4.1 Performance of the Fatigue Tests

The test arrangement for shear and multiaxial loading, the latter consisting of shear and axial

load, is shown in Fig. 9, where the tubular specimen with end plates can be seen, where tor-

sional moments have been introduced. The specimens for multiaxial loading contained the

additional intermediate plate (see right part of Fig. 9) to which the tubulars were welded on

both sides in the same way as in case of the cruciform joints described above for axial load-

ing, ensuring a homogeneous loading of the laser-stake weld without additional bending. The

specimens were loaded with constant in-phase acting axial and shear stress ranges. A load

ratio R = 0.07 was chosen to avoid slackening of the rods for load introduction.

The ratio between shear and axial stress range in the tubular was chosen as n/n = 1.0 in

the multiaxial tests. All multiaxially loaded and four out of 18 shear-loaded specimens were

subjected to air pressure of 1.5 bar in the tests so that the pressure loss could be taken as fail-

ure criterion corresponding to a through-weld crack.

By scanning the fracture surfaces and subsequent evaluation with a CAD system, see right

part of Fig. 12, the total weld area Aw as well as the area of stable crack propagation Acp after

through-weld cracking could be determined. Furthermore, the mean weld throat thickness tw

and the averaged weld eccentricity ew were evaluated for each specimen. Using the simplified

crack propagation law in eq. (1), the fatigue life until the theoretical pressure loss could be

estimated for the remaining 14 shear-loaded specimens:

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da/dN = C (n)m

(1)

where da is the length of crack propagation which results from the following:

da = Acp/tw (2)

dN is the number of load cycles between pressure loss and final fracture of specimen and n

the nominal shear stress range referring to the total weld throat area with mean thickness tw.

The constants C and m were determined by linear regression from the data of the four shear-

loaded specimens tested with air-pressure.

Fig. 9: Test arrangement for the shear and multiaxial load tests

4.2 Results of the Shear Load Tests

Fig. 10 shows the S-N diagram of all shear load tests, based on the individually computed

nominal shear stress range in the weld throat area and the life until through-weld cracking.

The individual results show that the gaps introduced by machining in the tubulars do not af-

fect the fatigue life. The statistical evaluation yields a very shallow S-N curve with k = 20.47.

This results in a large scatter ratio if the slope exponent k = 5 usual for shear loading is en-

forced. Nevertheless, the assessment with fatigue class FAT80 according to Eurocode 3 [2]

for shear-loaded welds would be conservative.

4.3 Results of the Multiaxial Load Tests

The test results are displayed in Fig. 11, based on the individually computed nominal stress

range in the weld throat area. As the nominal axial and shear stresses are equal, both can be

read from the vertical axis.

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Fig. 10: S-N results for the shear-loaded laser-stake welds based on nominal shear stress range

in the weld throat

Fig. 11: S-N results for the multiaxially loaded laser-stake welds based on nominal axial

and shear stress range in the weld throat

Also in these tests, the gaps do not affect the fatigue life. The statistical evaluation yields an

S-N curve with k = 5.59 so that a prescribed slope exponent of k = 5 results in a smaller scat-

ter ratio than k = 3. The fatigue assessment may be performed with an interaction curve which

is described below.

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4.4 Fatigue Assessment of Multiaxial Loading by Interaction Curves

Eurocode 3 [2] as well as the IIW recommendations [7] suggest an interaction formula in case

of combined axial and shear loading. The general expression is as follows:

(∆𝜎𝑐𝑜𝑚𝑏

∆𝜎(𝑁))𝑘𝜎+ (

∆𝜏𝑐𝑜𝑚𝑏

∆𝜏(𝑁))𝑘𝜏≤ 𝐷 (3)

The axial and shear stress ranges acting in combination are described by comb and comb.

(N) and (N) result from the S-N curves if pure axial and shear stress ranges are acting

with the given number of load cycles N. The total damage index D is set to unity if in-phase

loading with constant stress cycles is acting. Different parameters k and k are given in Eu-

rocode 3 (k = 3 and k = 5) and in the IIW recommendations (k = k = 2), the latter resulting

in an elliptical interaction curve. Fig. 12 compares both interaction curves together with the

characteristic fatigue strength obtained from the multiaxial load test, i.e. for N = 2106.

Fig. 12: Interaction curves and comparison with the characteristic values derived from the mul-

tiaxial fatigue test results

The evaluation according to IIW (lower continuous curve using the characteristic fatigue

strengths with k = 3 for axial load and k = 5 for shear load) results in a slightly conservative

assessment of multiaxial test results where k = 3 was used. However, the interaction curve by

Eurocode 3 (dashed curve) would yield non-conservative results if the slope exponents men-

tioned are used to obtain the characteristic fatigue strengths. Only if the characteristic values

are based on slope exponents gained from regression analysis, both interaction curves are

conservative (upper curves).

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5. Assessment of the Multiaxial Loading Using the Notch Stress Ap-

proach

The recorded geometrical parameters allowed the computation of the notch stress also in the

tubular specimens using the submodel technique in ANSYS 14.0, see left and centre part of

Fig. 13. Used were 20-noded solid elements of type Solid186 with quadratic displacement

function. The element sizes and properties at the reference radius rref = 0.05 mm in the sub-

model correspond to the IIW recommendation [4]. The element lengths in weld direction

were six times larger than in transverse direction of the notch as no stress gradient was ex-

pected here.

Fig. 13: Example of a recorded fracture surface and of a notch stress model for the

multiaxially loaded specimen

As already found for the results based on nominal stresses, the machined gap does not affect

the fatigue strength of the tubular specimens under axial, shear and multiaxial load, see the

results in Fig. 14. The results with and without gap are within the same scatter band which is

relatively narrow with T = 1.240 for the multiaxial and T = 1.203 for the shear load tests.

Also the results for the axial load tests are plotted in the S-N diagram. The crack front plotted

into the cracked area in Fig. 7 (blue hatched area in upper left part) shows that the failure cri-

terion for a crack through the weld throat is valid also for the axially-loaded specimens. After

total failure (end of test), the crack front has just reached the lower edge of the weld contour

which corresponds to the leak in the tubular specimen and the registration of the air pressure

loss if applied.

The slope exponents of the S-N curves in Fig. 14 obtained by regression analysis shows a

pronounced dependency from the type of loading. The axial load tests yield a slope exponent

k 3, the multiaxial load tests k 6 and the shear load tests a very shallow slope with k 22.

By evaluating the equivalent notch stress range according to von Mises, all load types can be

displayed in one diagram. Due to the different slope exponents in the three types of loading, a

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statistical evaluation of all results together would yield a rather wide scatter band with T =

1.639, which is larger than usually obtained from fatigue tests, where T = 1.44 would be

more typical [5]. Nevertheless, the fatigue assessment of the equivalent notch stress range

with the reference radius rref = 0.05 mm would be conservative if the fatigue class FAT560

associated to equivalent stressesis used according to the IIW recommendations [4], irrespec-

tive of the type of loading (see also FAT value shown in Fig. 14).

Fig. 14: S-N diagram of all specimens based on equivalent notch stress range

6 Summary and Conclusions

In a research project, basic investigations regarding the fatigue assessment of laser-stake

welds at T-joints have been performed. This type of welding can be used in all-steel sandwich

panels for bridge construction and ship structures. Fatigue tests were performed with laser-

stake welds connecting 10 mm thick deck plates with 5 or 8 mm thick web plates, applying

three types of loading, i.e. axial, shear and multiaxial loading, the latter combining axial and

shear loading. The characteristic fatigue strengths of the axial and shear load tests were used

to create interaction curves according to Eurocode 3 and IIW recommendations, allowing the

assessment of the multiaxial load tests. The following conclusions are drawn from the results

based on nominal stresses:

The assessment of pure axial and pure shear load in the laser-stake weld is conserva-

tive if the fatigue class for weld root failure in Eurocode 3 and IIW recommendations

is used.

The assessment of the multiaxial load tests using a slope exponent k = 3 of the S-N

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curve for the characteristic fatigue strength is only conservative for the interaction

curve proposed by IIW if also the the characteristic values of the individual load com-

ponents are based on fixed slope exponents (k = 3 for axial and k = 5 for shear load-

ing).

If the characteristic fatigue strengths are obtained with slope exponents from regres-

sion analysis, the fatigue assessment of the multiaxial load tests is conservative for

both Eurocode 3 and IIW recommendations.

The recorded geometric weld parameters allowed local finite element models to be created

where the slit ends are rounded by a reference radius rref = 0.05 mm and the equivalent notch

stress according to von Mises can be computed. The following conclusions are drawn from

the computations:

The assessment of the equivalent notch stress using the fatigue class FAT560 accord-

ing to IIW recommendations is conservative for all types of loading.

The fatigue tests with axial, shear and multiaxial loads show very different slope ex-

ponents of the S-N curves, varying between k 3 and k 22.

Specimens containing an intentional gap between deck and web plate showed that this did not

affect the fatigue strength under any type of loading. Also the steel strength (S460 in compar-

ison with S355) did not reveal any influence.

7 Acknowledgement

The investigations were performed within the project 16935 BG “Laser-welded T-Joints” of

the Research Association for Steel Application (FOSTA) which was funded with public

means within the programme "Industrial Cooperative Research" (IGF) by the German Federal

Ministry of Economics and Technology via the FOSTA and the Center of Maritime Technol-

ogies (CMT). The research partners are grateful for the financial support and thank also the

committee of industrial partners for their valuable comments and guidance.

8 References

[1] Roland, F.: Laserschweißen - Chancen, Probleme, Beispiele. Schiff & Hafen 2/1999, 78

– 84

[2] Eurocode 3: Bemessung und Konstruktion von Stahlbauten – Teil 1-9: Ermüdung; Deut-

sche Fassung EN 1993-1-9:2005 + AC:2009. DIN Deutsches Institut für Normung e.V.,

Beuth Verlag GmbH, Berlin, 2010

[3] Sonsino, C. M., Bruder, T., Baumgartner, J.: S-N Lines for Welded Thin Joints – Sug-

gested Slopes and FAT Values for Applying the Notch Stress Concept with Various Ref-

erence Radii. Welding in the World 54, R275-R392

[4] Fricke, W.: IIW Recommendations for the Fatigue Assessment of Welded Structures by

Notch Stress Analysis. Woodhead Publishing Limited, Cambridge 2012

[5] Haibach, E.: Betriebsfestigkeit: Verfahren und Daten zur Bauteilberechnung, VDI-Verlag

GmbH, Düsseldorf 1989

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[6] Frank, D., Remes, H., Romanoff, J.: J-integral-based approach to fatigue assessment of

laser stake-welded T-joints. Int. J. of Fatigue 47 (2013), 340-350

[7] Hobbacher, A.: Recommendations for Fatigue Design of Welded Joints and Components.

WRC Bulletin 520. New York, NY: Welding Research Council

[8] Fricke, W.: IIW Guideline for the assessment of weld root fatigue. Welding in the World

57 (2013), 753-791, DOI 10.1007/s40194-013-0066-y