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Application of local approach to inhomogeneous welds.In¯uence of crack position and strength mismatch

T. Moltubakka,*, C. Thaulowa, Z.L. Zhangb

aDepartment of Machine Design and Materials Technology, Norwegian University of Science and Technology, N-7034,Trondheim, Norway

bSINTEF Materials Technology, N-7034, Trondheim, Norway

Received 16 December 1997; received in revised form 11 November 1998; accepted 16 November 1998

Abstract

In steel welds there is often a large variation in fracture toughness and mechanical properties betweenthe weld metal, base material and the various heat a�ected zone (HAZ) microstructures. The stress ®eldin front of a crack in a weldment can be noticeably a�ected by the strength mismatch between the weldmetal, HAZ and the base material. The crack position relative to the various microstructures will clearlyin¯uence the strength mismatch e�ect. In this paper the in¯uence of crack tip positioning on the fractureperformance of strength mismatched steel welds has been studied both experimentally and by FEManalysis. For a mismatched weld with local brittle zones small changes in crack tip location can giveconsiderable changes in the fracture performance of a CTOD specimen. A high degree of strengthmismatch increases the e�ect of crack positioning. Weld metal overmatch increases the stress level in theheat a�ected zone due to material constraint and thereby reduces the cleavage fracture resistance of theweldment when the coarse grained HAZ (CGHAZ) controls the fracture. The detrimental e�ect of highovermatch is most pronounced for specimens with notch position at fusion line and a short distance intothe brittle CGHAZ. The Weibull stress has been shown to be a suitable fracture parameter in the casewhere one microstructure clearly controls the cleavage fracture and the calculation of the Weibull stresstherefore can be limited to this zone. # 1998 Elsevier Science Ltd. All rights reserved.

Keywords: Fracture mechanics; Local approach; Local brittle zones; Weld metal mismatch; HAZ-toughness

Engineering Fracture Mechanics 62 (1999) 445±462

0013-7944/99/$ - see front matter # 1998 Elsevier Science Ltd. All rights reserved.PII: S0013-7944(98)00108-8

* Corresponding author. Tel.: +47-73-59-38-33; fax: +47-73-59-41-29

1. Introduction

Over the last few years a large number of studies have been carried out on the in¯uence ofthe strength mismatch on the fracture performance of welds [20,19,9,5]. Traditionally a higheryield strength in the weld metal than in the base material is preferred to direct eventualyielding to the base material where the toughness usually is better. Weld metal overmatch hasproved to be bene®cial in the case of cracks located in the middle of the weld metal. However,when the crack is located near the fusion line, weld metal overmatch causes a materialconstraint which increases the stresses locally in the heat a�ected zone (HAZ). This will give amore critical condition when the toughness in the coarse grained HAZ (CGHAZ) is mostcritical and the CGHAZ controls fracture initiation. Thus, whether weld metal overmatch isbene®cial or not depends, among other parameters, upon the position of the crack relative tothe microstructure that controls fracture [22].In fracture mechanics testing of steel weldments the results usually exhibit a large scatter.

The scatter is related to the heterogeneous properties of the weld and the statistical nature offracture [16,13,20]. Experimental evidence has shown that cleavage fracture is always associatedwith the formation of microcracks in regions which undergo inhomogeneous plasticdeformation [3]. The microcracks may have a large variation in size and orientation, and in astress ®eld with large gradients (like in front of a macro crack) the position of the microcrackswill be of major importance. The origins of the microcracks are often grain boundary carbidesor second phase particles [18,21]. In fracture mechanics testing of TMCP-steel welds,martensite±austenite (MA) particles have been found as nuclei for microcracks [8]. The secondstep in the fracture process, which is critical, is the propagation of these microcracks. A localapproach for characterizing cleavage fracture toughness has been proposed by the Frenchresearch group F.M. Beremin in terms of the so called Weibull stress [4]. The Weibull stress isa probabilistic fracture parameter that considers the statistical distribution of the extremevalues of microcrack size.In this study a large number of CTOD tests have been performed on weldments of high

strength steel. Two di�erent weld consumables were used for di�erent levels of strengthmismatch. Finite element calculations were carried out for various levels of strength mismatchand crack location relative to the fusion line. The di�erent cases were compared using theWeibull stress as a criterion for cleavage fracture.

Table 1Mechanical properties of base material and weld metals

Material Yield strength,sY [MPa]

Hardeningexponent, 1/n

Global mismatch,sWMY /s BM

Y

Local mismatch,sWMY /sHAZ

Y

Base material 450 15CGHAZ 530 9.5Weld metal 1 (evenmatch) 530 14 1.18 1.00

Weld metal 2 (overmatch) 643 14 1.43 1.21

T. Moltubakk et al. / Engineering Fracture Mechanics 62 (1999) 445±462446

2. Experimental results

2.1. Materials and specimens speci®cation

All the experimental work presented here was carried out in the European collaborativeproject ACCRIS [6]. A 50 mm thick TMCP steel plate of class 450 MPa steel was used for thisstudy. The tensile properties of the steel are shown in Table 1. The welded joints were preparedby multipass SAW using a heat input of about 3.5 kJ/mm and with a half K groove. Twodi�erent weld metals were used to obtain di�erent matching conditions. It was intended thatone weld should have overmatching weld metal and one weld should be evenmatched,however, as shown in Table 1, the result was two welds with di�erent levels of global weldmetal overmatch. Table 1 also show the tensile properties of a weld thermal simulatedspecimen given a thermal cycle corresponding to the CGHAZ of a weldment. The yieldstrength of the CGHAZ was higher than for the base material and equal to the yield strengthof the softer of the two weld metal (local evenmatch). The CGHAZ also exhibits higher strainhardening than both the base material and the weld metal.Forty-®ve BxB 3-point bend CTOD test specimens were prepared from both weldments. The

specimens were surface notched and the fatigue crack tip was aimed to hit at the fusion line.The tests were performed at ÿ108C.

2.2. Fracture toughness testing and results

Fig. 1 shows the cumulative distribution of the CTOD results1 for both weldments. For allspecimens cleavage fracture was observed. The cleavage fracture was, however, preceded by

Fig. 1. Cumulative distribution of the CTOD results.

1 The CTOD tests were carried out at Centro Svilupo Materiali, Italy.

T. Moltubakk et al. / Engineering Fracture Mechanics 62 (1999) 445±462 447

ductile tearing for about 50% of the specimens. For the majority of the specimens the cleavageinitiation point was located in the CGHAZ and initiation in the weld metal was very rare. Theinitiation point was often located in the CGHAZ less than 0.1 mm from the fusion line eventhough the fatigue crack tip sometimes was located in the weld metal. Metallographicexaminations revealed existence of TiN particles in the CGHAZ [6]. Fig. 1 indicates lowertoughness for the specimens with the highest overmatch. In the higher toughness region it is

Fig. 2. Cumulative distribution of the CTOD results for specimens with crack tip less than 0.5 mm from fusion line:

(a) specimens where ductile crack growth was not observed; (b) specimens where ductile crack growth was observed.


more di�cult to see a unique in¯uence of strength mismatch. It should be noted that the hightoughness observed for some specimens is often caused by crack tip positioning far away fromthe most brittle microstructures.In Fig. 2 the CTOD results are divided into two categories, one for specimens where ductile

crack growth was not observed (Fig. 2a) and one for specimens where ductile crack growthwas observed (Fig. 2b). The results for specimens with crack tip location further than 0.5 mm

Fig. 3. In¯uence of notch position on the fracture toughness: (a) local weld metal overmatch; (b) local weld metal

evenmatch.


from the fusion line were excluded from the plots. In the case where no ductile crack growthwas observed the overmatched specimens had signi®cant lower toughness than theevenmatched specimens. For the CTOD specimens where ductile crack growth was observed,the di�erence between the overmatched and the evenmatched specimens were negligible.Fig. 3 shows the in¯uence of crack tip location on the CTOD results for the overmatched

(Fig. 3a) and the evenmatched (Fig. 3b) specimens. The distance from the fatigue crack tip tothe fusion line is measured normal to the crack plane in the plane of the fracture initiationpoint. For the overmatched specimens the lowest toughness is observed for specimens withcrack tip location at the fusion line. Although the scatter is quite large, the results indicate thatthe toughness increases as the distance from the fatigue crack tip to the fusion line increases.The toughness increases most rapidly on the HAZ/BM side, but low toughness is recorded fora specimen with crack tip about 1.1 mm from the fusion line. This distance corresponds to thelocation of intercritical HAZ microstructure which has been found to be brittle also in severalother studies [1,11].Even though the toughness for the evenmatched specimens with crack tip at the fusion is

somewhat elevated, a similar tendency of notch positioning is shown for the evenmatchedspecimens and the overmatched specimens. The CTOD values increase for specimens withcrack tip further away from the fusion line both on the weld metal side and on the basematerial side. The e�ect of notch position seems, however, a bit larger for the overmatchedweld specimens than for the evenmatched weld specimens.

3. Numerical analysis

3.1. FE-model

The numerical simulations were carried out using a small scale yielding (SSY) model basedon a boundary layer formulation. Here, the remote displacements are given by the linear elasticsolution of the KI ®eld,

u�r,y� � KI1� nE

��r

2p

rcos

�y2

��3ÿ 4nÿ cos y�

v�r,y� � KI1� nE

��r

2p

rsin

�y2

��3ÿ 4nÿ cos y� �1�

where r and y are the polar co-ordinates in front of the crack tip, E is Young's modulus and nis the Poisson ratio. KI �

��EJ=�1ÿ n2�

punder plane strain conditions. A schematic illustration

of the model is shown in Fig. 4. The model was divided into three materials representing theweld metal, CGHAZ and the base material. In the present work, large strain incrementalplasticity analyses with a rate independent power law strain hardening materials were assumed:

si � si0

�1� �ep

i

ei0

�ni

�2�


where si is the ¯ow stress, �epi is the equivalent plastic strain, si0 is the yield stress, ei0 is the

yield strain ei0=si0/E, and ni is the strain hardening exponent for material i. The elasticproperties of the materials were de®ned by a Young's modulus E=210 GPa and a Poissonratio n=0.3. The base material had yield strength sY=500 MPa and the HAZ had yieldstrength sY=600 MPa in all calculations. The weld metal yield strength was varied from 500to 700 MPa. A strength hardening exponent of ni=0.07 was used for all materials de®nitions.In addition, a reference case with a yield strength 600 MPa for all material zones was analyzed.The combinations of material properties applied are summarized in Table 2. Of the materialsused in the simulation the combination 7±6±5 (overmatch) and 6±6±5 (evenmatch) should bequite comparable to the real welds (see Table 1).The CGHAZ was modeled with a width of D=0.6 mm and the position of the crack tip

position was varied from 0.2 mm into the weld metal to 0.5 mm into the HAZ/base materialside of the fusion line, see Fig. 4. The e�ect of crack position in a mismatched weld wasstudied earlier using the Weibull stress and with the crack placed at fusion line, 0.5 and 1.5 mminto the HAZ (2 mm wide HAZ) [10]. Crack positions in the weld metal were not consideredin that study and, due to the coarser variation of crack positions, the study was not able to

Fig. 4. Schematic illustration of SSY model based on boundary layer formulation.

Table 2Material combinations used in the FE calculationsa

Material combination sWMY

[MPa]sHAZY

[MPa]s BMY

[MPa]Global mismatch,

sWMY /s BM

Y

Local mismatch,sWMY /sHAZ

Y

6±6±6 600 600 600 1.0 1.07±6±5 700 600 500 1.4 1.166±6±5 600 600 500 1.2 1.05±6±5 500 600 500 1.0 0.83

a For all materials: E=210 GPa, n=0.3 and ni=0.07.


capture the e�ect of notch position obtained in the experiments, see Fig. 3. In this paper thee�ect of crack position is studied for various mismatch levels.The model was loaded until J=200 N/mm was reached. A value of J=200 N/mm

corresponds to a CTOD value of about 0.2 mm for the investigated materials (J12�sY�d underplane strain conditions).Fig. 5 shows the FE mesh of the whole model and magni®cations of the mesh at the crack

tip. The model had an initial crack tip opening of 0.02 mm and a total of 2642 eight-node

Fig. 5. FE mesh of whole model (a) and mesh at the crack tip (b).


plane strain elements. The smallest element at the crack tip was about 50 mm2, and acharacteristic element size 0.1� 0.1 mm was used in the near crack tip region. A reducedintegration scheme was used. All calculations were performed using the ABAQUS [7] program.In this paper a local approach was used to evaluate the results from the FE analysis. The

Weibull stress fracture parameter considers the distribution of maximum principal stress withinthe fracture process zone in front of a crack. Since plastic deformation is a precondition fornucleation of microcracks from an inclusion or a second-phase particle [3,16,21], the fractureprocess zone used for calculation of Weibull stress is normally de®ned as the region whereplastic ¯ow has occurred. For the examined steel weldments more than 80% of the specimenshad fracture initiation point in the CGHAZ. Alternatively the Weibull stress was therefore alsocalculated over just the plastic zone in the CGHAZ. The Weibull stress can for a two-dimensional model be given as

sW � Xk

i�1�s1k�mAk

A0

! 1m

�3�

where s1k is the maximum principal stress averaged over an element k, Ak is the area of theelement, A0 is a reference area (here a unit area) and m is the Weibull shape parameter. Theshape parameter m is material speci®c [23] and may vary for the di�erent microstructures in ainhomogeneous weldment. The Weibull shape parameter m=20 assumed in the present FEMcalculations, agrees well with values from the literature [4,16].

3.2. Results and discussion

The in¯uence of strength mismatch on the Weibull stress in case of a crack positioned at thefusion line is plotted in Fig. 6. Both in the case where the whole plastic area is taken as afracture process zone (Fig. 6a) and the case where only the plastic zone in the CGHAZ isregarded (Fig. 6b), the Weibull stress increases with increased weld metal yield strength. Thedi�erence in Weibull stress for the three cases with base material yield strength equal to 500MPa seems not to be in¯uenced by whether the Weibull stress is calculated over just the plasticdeformed region in the CGHAZ or the whole plastic region. The di�erence in Weibull stressbetween the extreme cases with material combination 7±6±5 and 5±6±5 is about 250 MPa for aJapplied=200 N/mm. From Japplied=30 N/mm only a minor increase in di�erence is observed.Fig. 7 shows the distribution of maximum principal stress in front of the crack tip for the

case with material combination 7±6±5. The crack tip is located at the fusion line. The ®gureshows unsymmetric stress contours. In the high strength material the stress contours extendsmostly in the y-direction normal to the crack plane while in the soft material the stresscontours extend most in the x-direction.Plotting the stress along straight axes normal to (Fig. 8a), and parallel to (Fig. 8b) the crack,

this can be seen more clearly. Close to the crack plane the stress is higher on the soft material(CGHAZ/BM) side than on the hard material (WM) side, see Fig. 8a. The stress level reduces,however, more rapidly for increasing distance away from the crack plane. As shown in Fig. 8b,at a distance 0.32 mm away from the crack plane close to the crack tip, the stress is higher on


the weld metal side than the CGHAZ/BM side. Further from the crack tip the stress in the soft

HAZ is higher than in the harder weld metal for constant distance from the crack plane.

Fig. 9 shows plot of Weibull stress as a function of load and crack tip position. The Weibull

stress is calculated over the plastic zone in both weld metal, base material and the CGHAZ.

For the models with a material combination 7±6±5, the Weibull stress is highest for crack tip

Fig. 6. In¯uence of strength mismatch on Weibull stress for crack tip located at the fusion line: (a) calculated fromWM, BM and HAZ; (b) calculated over the CGHAZ only.

Fig. 7. Distribution of maximum principal stress in front of the crack tip for the fusion line notched model.Material combination 7±6±5 and Japplied=200 N/mm.


location 0.2 mm in the weld metal and decreases monotonically for crack positions closer tothe base material. As long as the plastic zone is contained within one material, the maximumstress level is closely related to the yield strength and the stress level increases with increasingyield strength of the material at the tip. However, as the plastic zone extends into a softermaterial, the stress triaxiality in the hard material is gradually reduced. The maximum stresslevel will be lowered compared to a case where the plastic zone is contained within the highstrength material. At Japplied=200 N/mm the extreme di�erence in Weibull stress for thevarious crack positions is about 100 MPa.

Also for material combinations 6±6±5 (Fig. 9b) the highest Weibull stress is observed forcrack tip location 0.2 mm into the weld metal and the Weibull stress decreases monotonicallyas the crack tip is located closer to the soft base material. The e�ect of crack tip location issigni®cantly less pronounced for material combination 6±6±5 than for material combinations7±6±5. For the 6±6±5 combinations the maximum di�erence in Weibull stress for the variouscrack positions is only about 30 MPa at Japplied=200 N/mm.

The models with material combination 5±6±5 show almost no in¯uence of crack position(Fig. 9c). Only at low loads, JappliedR100 N/mm, is a slightly higher Weibull stress observedfor crack tip location 0.3 mm into the harder HAZ and a slightly lower stress for crack tiplocation 0.2 mm into the ``soft'' weld metal. The e�ect of crack positioning vanishes as theplastic zone extends beyond the borders of the harder CGHAZ and the base material and theweld metal dominate the yielded area.

The e�ect of crack position found by FE-modeling have a poor agreement with theexperimental results shown in Fig. 3. The FEM calculation where the models had weld metalovermatch indicated the largest probability for fracture for crack tip location in the weldmetal. In contrast, the experiments gave the lowest toughness for crack tip location at thefusion line. Since almost all cleavage initiation point was found in the CGHAZ, the probabilityfor initiation in the base material and the weld metal is very small. For the tested weldment thestresses in the weld metal and base material do not contribute to the fracture probability as

Fig. 8. Distribution of maximum principal stress along straight lines in front of the crack tip. Material combination7±6±5 and Jappl=200 N/mm: (a) normal of the crack plane; (b) parallel to the crack plane.


indicated by the FE modeling. There are however several other examples where the weld metalcan be as critical as the CGHAZ, and contribute to the fracture probability as the CGHAZ[15]. Fig. 9 shows that larger mismatch increases the in¯uence of notch position also when theweld metal and base material are as brittle as the CGHAZ.Fig. 10 shows a plot of Weibull stress calculated over the plastic zone in the CGHAZ only.

The results from the model with largest overmatch (7±6±5), Fig. 10a, reveal a distinctreduction in Weibull stress when the crack tip is moved from the fusion line into the weldmetal. Moving the crack tip into the CGHAZ has less e�ect, but one can see a slight increase

Fig. 9. In¯uence of crack tip position on Weibull stress: (a) material combination 7±6±5; (b) material combination

6±6±5; (c) material combination 5±6±5.


in Weibull stress for notch locations 0.1 and 0.2 mm compared to the fusion line crack tip.

Moving the crack tip further away from the fusion line into the CGHAZ reduces the Weibull

stress compared to fusion line crack tip location. The highest Weibull stress for material

combination 7±6±5 was observed for crack position 0.1 mm into the CGHAZ.

Also for the model with material combination 6±6±5 the Weibull stress is signi®cantly

reduced when the crack tip is moved from the fusion line into the weld metal. Moving the

crack tip into the CGHAZ slightly increases the Weibull stress compared to that for the crack

tip at the fusion line. The highest Weibull stress is calculated for crack tip position 0.2 mm

from the fusion line into the CGHAZ. The di�erence between crack positions between 0.1 and

Fig. 10. In¯uence of notch position on Weibull stress calculated over the CGHAZ only: (a) material combination 7±6±5; (b) material combination 6±6±5; (c) material combination 5±6±5.


0.3 mm into the CGHAZ is however minor, compared to small changes in crack position on

the weld metal side of the fusion line.

For material combination 5±6±5 (Fig. 10c), the highest Weibull stress is observed for crack

tip location in the middle of the ``hard'' CGHAZ. This position gives the largest area of the

fracture process zone and also a high stress level, since the reduction of constraint due to softer

surrounding material is less when the distance from the softer material increases.

When comparing the results from the FEM calculations with experimental results, a much

better correlation is found when the Weibull stress is calculated over just the plastic region in

the CGHAZ than over the whole plastic zone in the model. Fig. 11 shows the Weibull stress

for the di�erent crack positions in the case where the Weibull stress is calculated over the

whole plastic region (Fig. 11a), and when only the plastic region in the CGHAZ is considered

(Fig. 11b). The applied load is Japplied=200 N/mm. When the CGHAZ controls the fracture

alone, the in¯uence of crack position in the numerical analysis ®ts quite well the experimental

results. The calculations indicate that a crack position a small distance into the CGHAZ is

more critical than crack tip position at the fusion line which was observed as the most critical

position in the experiments, see Fig. 3. However, increasing strength mismatch moves the most

critical crack position closer to the fusion line. For the material combination 5±6±5 a crack

position 0.3 mm into the CGHAZ was most critical, for 6±6±5 a crack position 0.2 mm into

the CGHAZ and for 7±6±5 the most critical crack position was only 0.1 mm away from the

fusion line into the CGHAZ. In the FEM calculations, the width of the CGHAZ was set to

0.6 mm. This value was taken from metallographic observation of similar welds, where the

CGHAZ was de®ned as the region where the peak temperature during welding was higher than

12008C. Also, within this limited region the toughness and strength may vary considerably and

some di�erence between the FE results and the experiments should be expected.

Fig. 11. Weibull stress for di�erent crack positions. Japplied=200 N/mm. (a) Calculation over the whole plastic

region; (b) calculation over the plastic region in CGHAZ.


4. Discussion of the Weibull stress

All the FE calculations of the Weibull stress previously presented were carried out with aWeibull shape parameter m=20 taken from the literature [4,16]. Several procedures have beenproposed to estimate the shape parameter m and the Weibull scale parameter su in a two-parameter Weibull distribution [23]. The failure probability or, equivalently, the statisticaldistribution of the Weibull stress at cleavage failure should be unique for a given material andindependent of specimen geometry and size, and crack size and shape [12]. Constraint e�ects,asymmetric loading and thermal stresses are taken into account in the calculation of Weibullstress [23]. It is, however, still argued whether the shape parameter and scale parameter aretotally independent on geometry e�ects and loading conditions.A problem with estimating the scale and shape parameter for a weldment is that the weld

microstructures can rarely be treated as one single material. The scale and shape parametersmay be quite di�erent for the weld metal, the CGHAZ and the base material. If onemicrostructure is clearly the most brittle, calculating the Weibull stress over the plasticallydeformed zone of this microstructure may, however, give a reasonable shape and scaleparameter.Fig. 12 shows the relative contribution to the Weibull stress for a given stress level compared

to the same element having stress equal to the peak stress. For a Weibull shape parameterm=20 the contribution of an element with 80% of maximum stress is about 1% of an elementwith the peak stress. Fig. 7 show that for Japplied=200 N/mm, all stress contours higher than1700 MPa (10.7�s1max) are within a limited region with size about 2� 2 mm in front of thecrack tip. The contribution to the Weibull stress for stresses lower than 0.7 times the maximumstress vanishes.Fig. 12 shows that, for a Weibull shape factor m=10, stresses higher than 0.5 of the

maximum stress give a contribution to the Weibull stress, whereas for m=30 the stress levelhas to be higher than 0.8 of the maximum stress to give signi®cant contribution to the Weibullstress. Since only the highest stresses contribute to the Weibull stress, the notch positioning will

Fig. 12. Relative in¯uence of stress level on Weibull stress.


have larger in¯uence for a high shape parameter than for a low shape parameter. Themaximum stress level depends much upon the yield strength of the material in front of thecrack, and in an inhomogeneous weld the yield strength of the material in front of the cracktip can vary substantially for two di�erent crack tip locations.Fig. 13 shows how the Weibull stress increases with load for di�erent shape parameters. As

the load increases the maximum stress level will not increase signi®cantly, but a larger area willexhibit high stress level. As a result, the Weibull stress is initially highest for high shapefactors, but at higher load the Weibull stress is highest for low shape parameters. The Weibullstress becomes highest for small shape parameters when the size of the reference area A0

becomes small compared to the stresses area contributing to the Weibull stress (see Eq. (3)).The reference are (volume) scales the Weibull stress by (1/V0)

m, and estimation procedures forthe reference volume have also been established [12].In the fracture mechanics case with steep stress gradients in front of the crack tip, the mesh

size has a large in¯uence on the calculated Weibull stress [14]. In the present work the averagestress in an element was used in the calculation of the Weibull stress. Large elements causelarge stress variations within an element and the average stress will be signi®cantly lower thanthe peak stress. For small elements the average stress is much closer to the peak stress due toless stress variations. With the power expression ((s1�dV )m) used to calculate the contributionto the Weibull stress for a single element, the in¯uence of the highest stresses is enlarged. TheWeibull stress calculated for a model with ®ne mesh will be higher than for a model withcoarse mesh [14]. An alternative procedure for calculation of the Weibull stress, where eachintegration point gives a separate contribution to the calculated Weibull stress will give, due tothe large contribution of the peak stress in an element, a higher calculated Weibull stress thanwhen the stress is averaged over one element [14].In this study plastic deformation is taken as criterion for microcrack nucleation, and only

Fig. 13. E�ect of shape parameter on the Weibull stress. Homogeneous 6±6±6 material.


the yielded area contributes to the Weibull stress. Alternatively, the Weibull stress has beencalculated over the whole model or over a region where the maximum principal stress is abovea certain value (e.g. 2�sY) [2,17]. For low values of the shape factor m the selection ofcalculation area will in¯uence the Weibull stress.

5. Conclusions

Fracture mechanics testing of weldments with crack aimed to hit the fusion line revealed thelowest HAZ toughness for overmatched weld metal compared to evenmatching. The testsshowed a large in¯uence of crack positioning and the lowest toughness was observed forspecimens with the fatigue precrack located just at the fusion line.The in¯uence of notch position and material mismatch on brittle fracture was examined by

calculating the Weibull stress from two-dimensional FE models. In the numerical studies threedi�erent mismatch cases were analyzed and for each mismatch case. The crack tip position wasvaried systematically from 0.2 mm into the weld metal to 0.5 mm into the HAZ/base materialside of the fusion line. Two di�erent calculation procedures for the Weibull stress were used. Inone case the Weibull stress was calculated over the plastic zone in both the base material theCGHAZ and the weld metal. In the second case, only the stresses within the plastic zone in theCGHAZ contributed to the Weibull stress. When the calculation was limited to the CGHAZ, agood agreement with the experiments was obtained. The numerical studies verify theexperimental results, showing that the CGHAZ microstructure controls the fracture for theexamined welds. In the case of 100 MPa local weld metal to CGHAZ yield strengthovermatch, the highest Weibull stress was found for a notch position 0.1 mm away from thefusion line into the CGHAZ. For local evenmatch a notch location 0.2 mm away from thefusion line onto the CGHAZ gave the highest Weibull stress.The Weibull stress was calculated with a shape factor m=20. The shape factor has a large

in¯uence on the stress levels, which signi®cantly contributes to the Weibull stress. An increaseof the shape factor will increase the importance of the highest stresses and reduce the size ofthe area contributing to the Weibull stress. As a result, the in¯uence of notch positioning onthe calculated Weibull stress will also increase with increasing shape factor.

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