2004 ASME Pvp Conference

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STRESS INTENSITY FACTORS DUE TO RESIDUAL STRESSES IN T-PLATE WELDS

Noel P. ODowd, Kamran M. NikbinDepartment of Mechanical Engineering

Imperial College LondonSouth Kensington Campus, London SW7 2AZ

United KingdomEmail: [email protected]

Hyeong Y. LeeKorea Atomic Energy Research Institute

Dukjindong 150 Yuseong305-606, Korea

Robert C. WimporyJRC-European Commission Institute for Energy

Westerduinweg 31755 LE, PettenThe Netherlands

Farid R. BiglariDepartment of Mechanical Engineering

Amirkabir University of TechnologyHafez Avenue, Tehran

Iran

ABSTRACT Residual stress distributions in ferritic steel weldments have

been obtained using the neutron diffraction method. It is shownthat the transverse residual stress distribution for different platesizes and yield strength are of similar shape and magnitude whennormalised appropriately and peak stresses are on the order of the material yield strength. The resultant linear elastic stress in-tensity factors for these stress distributions have been obtained using the nite element method. It has been shown that the use of the recommended residual stress distributions in UK structuralintegrity procedures leads to a conservative assessment. Thestress intensity factors for the welded T-plate have been shownto be very similar to those obtained using a smooth edge cracked plate subjected to the same local stress eld

NOMENCLATURE

a crack lengthd distance between lattice planesd 0 distance between unstressed lattice planes E Youngs modulus J J integralK Linear elastic stress intensity factorK I Mode I stress intensity factorK II Mode II stress intensity factorQ weld heat input

r 0 estimate of size of weld plastic zoneW plate width strain neutron wavelength diffraction angle 0 diffraction angle for unstressed lattice planes stress y yield strength Poissons ratio

INTRODUCTIONIn this work, residual stress distributions in welded T-plates

are presented. The stress distributions have been measuring us-ing the neutron diffraction method, which determines the stresseld directly from the measured elastic strains. A high strengthsteel (designated SE 702, equivalent to the A517 Grade Q steel)

and a medium strength steel (BS EN 10025 Grade S355) havebeen examined. The former has a yield strength of 700 MPaand the latter has yield strength of 360 MPa. It has been foundthat the transverse residual stress distribution for different platesizes and yield strength are of similar shape and magnitude whennormalised appropriately and peak stresses are on the order of the material yield strength. The measured stresses are comparedwith the distributions provided in UK safety assessment proce-dures and the conservatism in the existing stress distributions is

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assessed. The linear elastic stress intensity factors arising fromthe residual stress distributions have also been determined usingthe nite element method and the results compared with thoseobtained from the stress distributions in the assessment proce-dures. It is found that the K values obtained using the recom-mended stress distributions are signicantly conservative. Theconservatism is reduced somewhat if a residual stress distribu-tion recently proposed for welded T-plates is used. The K valuesfor the T-plate have been compared with those obtained if theweld attachment is ignored and the T-plate treated as a smoothedge cracked plate. It is found that except for shallow cracks(a / W 0.1) the difference between the two K values is negligi-ble.

Weld GeometryThis paper focuses on the weld geometry shown in Fig. 1.

The weld was manufactured by Cresusot-Loire Industrie, France(CLI) from an SE 702 steel (SE 702 is the CLI equivalent to theA517 Grade Q steel.) The welding consumable used was Oer-likon Fluxol 42, which has a quoted yield stress and ultimatetensile strength of greater than 690 MPa and 760-900 MPa re-spectively. The weld is a full penetration MIG weld with a totalof 22 weld passes and a weld heat input of 3.6 kJ/mm was used.An alternating depositioning sequence was used and the plateswere preheated to 100 C to minimise distortion during the weld-ing process. No post weld heat treatment was carried out on theweld. The measured distributions in this weld will also be com-pared with recent measurements on a medium strength T-plateweld, [1] which has a similar geometry but different weld heat

input.Neutron diffraction measurements were carried out to mea-sure the stresses along a line at the weld toe through the plate(line AA in Fig. 1) on the centre line of the sample. Thethree normal stress components (designated normal, transverseand longitudinal, as indicated in Fig. 1) have been measured.The measurements have been carried out at the NFL facility of the University of Uppsala, Studsvik, Sweden. The total length of the welded plate is 910 mm (see Fig. 1) but in order to carry outthe measurements a 13.5 mm slice of the weld was cut from theplate.

The Neutron Diffraction MethodDiffraction methods for measuring residual stress can be

used to determine non-destructively the stress state inside asample, by measuring changes in lattice spacing from the un-stressed state. Neutrons have a penetration depth of several cmin most metals allowing the stress state deep inside a sample tobe determined [2].

When illuminated by radiation of wavelength, , similar tothe lattice spacing, crystalline materials diffract the radiation as

~35

910

500

50

248

W = 50

~10 ~8

A

A

Normal ( y)

Longitudinal ( z)Transverse ( x)

Figure 1. GEOMETRY OF SE702 T-PLATE WELD. ALL DIMENSIONSIN MM (NOT TO SCALE).

distinctive Bragg peaks. If the angle, , at which a peak occursis measured, Braggs law can be used to determine the latticespacing, d ,

2d sin = . (1

If the un-stressed lattice spacing and diffraction angle, are d 0 and

0 respectively, then the elastic strain, can be determined by thedifferentiated form of Eq. 1, i.e.

= d d 0

d = ( 0) cot . (2

The stress, , may then be obtained from the linear elastic prop-erties of the material and the measured elastic strain, , in therelevant directions.

For this work the neutron diffraction measurements were ob-tained on the instrument, REST, at the reactor source at Studsvik,Sweden. The instrument uses a monochromator which produces

a single wavelength neutron beam from the polychromatic beamemerging from the reactor. In order to obtain three mutually per-pendicular stress components (transverse, longitudinal and nor-mal stress) measurements were carried out with the specimenorientated as in Fig. 1 (for the longitudinal and transverse elasticstrain) and rotated through 90 in the plane of Fig. 1 (for the nor-mal elastic strain). Reference measurements were made in theparent material at an extremity of the sample to obtain the refer-ence diffraction angle, 0 for the unstressed material. The strain



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at a point is then measured relative to this strain-free angle us-ing Eq. 2. The three stress components are obtained from thethree normal strain components using Hookes law.

For a given neutron ux and diffractometer design the timetaken for a residual stress measurement is controlled by the dis-tance travelled by the neutrons to enter and exit the steel (theneutron path length) and the properties of thematerial being mea-sured. In order to reduce the neutron path length, relatively thinslices of the welds have been measured (13.5 mm). It has beenshown in [1] by comparison with hole drilling measurements ona full thickness T-plate that, although such slicing reduces the outof plane (longitudinal stress), it does not have a signicant effecton the in-plane (normal and transverse) stresses. A 2 22 mm 3sampling volume was used and measurements were made at 28locations across the specimen width. The 211 Bragg reectionwas chosen using a wavelength of 1.7 A. This yielded a reectionat approximately 2 = 93.5C. The total measurement time wasapproximately 72 hours (24 hours for each direction).

Results of Neutron Diffraction MeasurementsFigure 2(a) shows the residual stress distributions obtained

for the T-plate. The experimental error bars indicated in the g-ure are due to the uncertainty in locating the diffraction angleand is typically 0.01 degrees. This converts to an uncertaintyin stress of approx. 30 MPa. All other uncertainties are as-sumed to be negligible. It is seen in Fig. 2(a) that the longi-tudinal stresses remain high, even though a thin slice of weldhas been measured, indicating that the longitudinal stresses havenot completely relaxed. The magnitude of the peak transverse

stress is about 450 MPa (approximately 60% of the material yieldstrength) and occurs at a distance, y, about 5 mm from the weldtoe. Close to the weld toe, all three stresses fall considerablythe transverse stress at y = 1 mm is approx. 40 MPa (approx. 6%of the yield strength). It is expected that the normal stress willreduce to zero at the weld toe, due to the traction free conditionsthere, but the relatively low longitudinal and transverse stress atthe toe is somewhat surprising.

Figure 2(b) shows transverse residual stress measurementson a medium strength T-plate similar to the geometry examinedhere but with three plate widths, W . The material used in thiscase was a BS EN 10025 Grade S355 steel with average yieldstrength 358 MPa. These stresses have previously been reported

in [1]. The measurement for the smallest (25 mm) weld is anaverage of a number of neutron diffraction measurements at anumber of European facilities including Studsvik. In order tomake direct comparison between the distributions the distanceshave been normalised by plate width, W . As discussed in [1],it is seen that when distances are normalised by W , the stressdistributions are similar to one another. Note that in addition tobeing of different plate thickness, these welds also have differentdesign (the smallest is a llet weld,the largest a partially pene-

-200

-100

0

10 0

20 0

30 0

0 0 .2 0. 4 0 .6 0. 8 1

25 mm (Ave ra ge )50 mm100m

R e s

i d u a

l S t r e s s

( M P a

)

Norma lised Posi ti on (y /w)No rm alis ed po si ti on, y/W

-300

-200

-100

0

100

200

300

400

500

0 10. 0 20. 0 30. 0 40. 0 50. 0

Transverse

Longit udunal

No rm al

R e s

i d u a

l S t r e s s

( M P a

)

Norma lised Posi ti on (y w )po si ti on, y (mm)

(a)

(b)

Figure 2. RESIDUAL STRESS DISTRIBUTIONS FOR T-PLATE WELDS(a) HIGH STRENGTH STEEL PLATE, SE702 (b) MEDIUM STRENGTHSTEEL PLATE, Grade S355, OF VARIOUS SIZE, W .

trating weld).

In Fig. 3 a direct comparison between the measurementsfor the two 50 mm welds (from [1] and from the current work) isshown. It may be seen that when stresses are normalised by yieldstrength the peak stresses are similar, though for the high strengthplate, the normalised stresses are signicantly lower at the weldtoe. Further measurements will be carried out on this plate nearthe weld toe using neutron and x-ray (synchrotron) diffraction toinvestigate the stresses near the weld toe in more detail.



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-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0

Normalised Position /W

N o r m a

l i s e

d r e s

i d u a

l s t r e s s , /

y

BS7910R6Proposed upper boundGrade S355SE 702

Figure 3. MEASURED RESIDUAL STRESSES IN TWO 50 MM T-PLATES. ALSO INCLUDED ARE APPROXIMATE STRESS DISTRIBU-TIONS FOR WELDED T-PLATE

Approximation of transverse residual stress in T-plategeometries

In [1] an upper bound (conservative) estimate for the trans-verse stress in a T-plate weld was proposed as an alternative toexisting distributions in the failure assessment procedures, R6 [3]and BS 7910 [4]. This distribution was obtained by taking aBayesian average of all the T-plate data for the medium strengthplate and tting a bi-linear curve to the mean line. The curvewas then shifted upwards by 0 .25 y to provide the upper boundshown by the dash line in Fig. 3. This curve is a bi-linear rela-tionship starting from = y at the weld toe, y/ W = 0, decreas-ing to 0.05 y at y/ w = 0.275 and increasing to 0 .5 y at theedge of the plate y/ W = 1.0. Note that such a distribution willnot satisfy force and moment balance across the plate width.

In Fig. 3 a comparison of this distribution with the data forthe two 50 mm welded T-plates is provided. Also included in thegure are the R6 [3] and BS7910 [4] transverse residual stressdistributions for welded T-plates. For a ferritic steel, the R6 dis-tribution is given by a bi-linear distribution, with = y at y = 0

decreasing linearly to = 0 at y = r 0 = 122Q/ y, where Qis the weld heat input in kJ/mm. (The distance r 0 is an estimateof the weld plastic zone in a ferritic steel weld [5]). For the twowelds shown in Fig. 3 the value of r 0 is 25 mm for the SE702weld and 28 mm for the Grade 355 steel. Since these two val-ues are very close a single R6 curve is plotted with r 0 = 26 mm.Note that the validity range for the R6 distributions is for a yieldstrength range of 375 MPa < y < 420 MPa so the weld in thehigh strength steel falls outside this range. BS7910 provides two

transverse stress distributions for welded T-platesa distributionwhich has essentially the same form as the R6 distribution and apolynomial distribution, which can be used if the weld heat inputis unknown. This latter distribution is given as

= y 0.97 + 2.3267 ( y/ W ) 24.125( y/ W )2+42.485( y/ W )3 21.087( y/ W )4 , (3

and is plotted in Fig. 3 labelled BS7910.It may be seen that the R6 and BS7910 distributions provide

conservative estimates of the residual strss and the proposed dis-tribution provides a closer representation of the measured datafor the two weld geometries.

=

(ii)(i) (iii)

K (i) K (ii) = 0 K (iiii) =

Figure 4. SUPERPOSITION METHOD TO DETERMINE STRESS IN-TENSITY FACTORS

Calculation of stress intensity factors for welded T-plate

In service, cracks may form at the weld toe due to the stressconcentration there. Such cracks tend to be along the line A-Ain Fig. 1, i.e. normal to the transverse stress. A fracture as-sessment for such a crack will generally require the linear elasticstress intensity factor, K , due to the weld residual stress and anyadditional primary (mechanical) loading. Previous work [6] hasdetermined the stress intensity factors in the medium strength T-

plate using the weight function for a T-plate geometry proposedin [7]. However, the range of applicability of the weight func-tion in [7] is restricted to somewhat limited weld geometries andthe T-plate of Fig. 1 falls outside this range. Therefore, in thiswork the K value for cracks of different sizes at the weld toe dueto the weld residual stress have been determined using the niteelement method. Also determined for comparison are the stressintensity factors for the stress distributions provided in R6 andBS7910 and from the upper bound solution in [1].



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In this work, the stress intensity factors for the cracked T-plate have been calculated using superposition (see Fig. 4). Asillustrated in Fig. 4, to determine the value of K only the stressdistribution over the crack face is required, i.e. K (i) = K (iii) .For the current problem, the crack face loading is simply themeasured (or approximated) residual stress at the weld toe. Theapproach taken here is analogous to the weight function method,except for the fact that the K value from the crack face loadingis obtained directly using a nite element analysis, rather thanby using a weight function. Note that the use of superpositionassumes linear deformation and if the residual stress induces sig-nicant amounts of plastic deformation, the true crack tip drivingforce may be underestimated (or overestimated) by this method.In [8] a modied J integral was developed to allow the stressintensity factor due to a residual stress eld to be determined di-rectly. It was shown in [8] that, provided the plastic zone is small,the K -value obtained using linear superposition is almost identi-cal to that obtained from the J integral. This result provides con-dence in the application of the current approach. Note also thatin the R6 and BS7910 assessment procedures the linear elastic K value is required for the analysis and the effect of plasticity onthe stress intensity factor due to the residual stress is accountedfor through an additional parameter (apart from an option 3/level3 analysis where a full numerical analysis is required).

W

a

Figure 5. FINITE ELEMENT MESH USED IN STRESS INTENSITYFACTOR CALCULATION

Finite Element ProceduresA typical nite element mesh, which contains 13,000 plane

strain four noded elements is illustrated in Fig. 5. The smallestelement size is 0.03 mm (6 104W ). Because of the very densemesh near the weld toe the element boundaries are not visible inthis region of the gure. All calculations were carried out usingthe commercial nite element software package, ABAQUS [9].

The fracture mechanics parameters J and K are calculatedfrom path independent integrals using the built in facilities of ABAQUS. In [9], J is calculated using a standard domain integralimplementation and K is obtained using an interaction integralapproach (relevant only for a linear deformation). The advantageof the latter approach is that for mixed mode problems, both themode I and mode II intensity factors, K I and K II respectively, arecalculated. For a mode I linear elastic problem K = K I can beevaluated from J using the relationship (for plane strain),

K = JE 1 2 , (4where E and are the Youngs modulus and Poisson ratio re-spectively.

Although focused meshes are preferred when K and J valuesare required, [9], a very ne regular mesh is used in this work,

as it allows the variation of K with crack length to be examinedwithout changing the mesh design for each analysis. For one of the crack geometries ( a / W = 0.3) the value of K obtained usingthe regular mesh of Fig. 5 was found to differ by less than 3%from that obtained using a focused mesh.

Results of Finite Element AnalysisResults are rst presented for a uniform crack face stress dis-

tribution as this provides insight into the general problem. Fol-lowing this, the stress intensity factors for the measured and ap-proximate stress distributions are presented.

Uniform stress distributionFigure 6 shows the normalised K value obtained for a uni-

form stress along the crack plane ( i.e. = y across the platewidth) for 0 .1 < a / W < 0.7, where a is crack length (see Fig. 5).The values plotted are the mode I stress intensity factors deter-mined from the ABAQUS interaction integral. Typically, the Kvalues differ by no more than 2% over 25 domains and if the rstdomain (nearest the crack tip) is ignored, the difference is lessthan 1%. Similarly, if the rst J domain is ignored, the J valuesdiffer by no more than 1% over 24 domains.

Also included in Fig. 5 is the handbook solution for a singleedge notch specimen under tension loading (taken from [10]).

As well as providing condence in the analysis, the very closeagreements between the two solutions indicates that the effectof the weld and attachment on the stress intensity factor is neg-ligible. The difference between the handbook solution and thenite element solution for the T-plate ranges from approx. 7%at a / W = 0.1 to approx. 2% at a / W = 0.7 and in all cases thehandbook solution overestimates the K value (it is conservative).Note that this does not imply that for a general mechanical anal-ysis, the T-plate can be replaced by an edge cracked plate. For



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example, for remote tension loading, the weld toe will inducea local stress concentration (approx. equal to 3.0 for this weldgeometry) which must be included when calculating the stressintensity factor using the method of superposition. However, if the stress distribution at the weld toe is known, as is the case here,then (for a sufciently deep crack) the stress intensity factor canbe calculated ignoring the weld and attachment. This issue willbe discussed further in the next section.

The K values plotted in Fig. 6 are the mode I values obtainedfrom an interaction integral. As the cracked T-plate is not sym-metric (see Fig. 5), a small K II component is generated even fora uniform tensile stress on the crack faces. The magnitude of K II ranges from 8% of K I at a/ W = 0.1 to 0.1% at a / W = 0.7. (Note

that if the overall K value |K | = K 2 I + K 2 II for the T-plateis compared with the handbook solution for a single edge notchtension geometry, the agreement is even closer than that seen inFig. 6).

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7normalised crack length ( a/W )

n o r m a

l i s e

d S I F

, K / (

y

W )

T-plate

Smooth plate (from [10])

Figure 6. NORMALISED MODE I K -VALUES FOR T-PLATE WITH AUNIFORM STRESS DISTRIBUTION

Measured and representative residual stress distribu-tionsAs in the previous section, the stress intensity factor has

been obtained for seven values of crack size in the range, 0 .1

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2004 ASME Pvp Conference