Notch stress intensity factors and fatigue strength of aluminium

International Journal of Fatigue23(2001)

225–232

https://www.360docs.net/doc/7011882718.html,/locate/ijfatigue

Notch stress intensity factors and fatigue strength of aluminium

and steel welded joints

https://www.360docs.net/doc/7011882718.html,zzarin a,*,P.Livieri b

a Department of Management and Engineering,University of Padova,Stradella S.Nicola3,36100Vicenza,Italy

b Department of Engineering,University of Ferrara,Via Saragat1,44100Ferrara,Italy

Received12June2000;received in revised form21September2000;accepted21September2000

Abstract

According to a recent and appropriate de?nition,stress?eld parameters,namely notch stress intensity factors(N-SIFs),can be used to predict the fatigue behaviour of mechanical components weakened by V-shaped re-entrant corners,where the singularity in the stress distribution makes any failure criterion based on elastic peak stress no longer https://www.360docs.net/doc/7011882718.html,monly thought of as parameters able to control the fatigue crack initiation life,N-SIFs are,under certain circumstances,also useful for predicting the component total fatigue life.The fatigue strength of aluminium welded joints with different geometries and thicknesses are summar-ised in a single scatter band by using an N-SIF-based approach.The statistical analysis is carried out taking into account experimental data already reported in the literature,referring to welded joints with a thickness ranging from3to24mm.Results of steel and aluminium welded joints are then compared:at high number fatigue life,the relative fatigue strength is slightly greater than2,in agreement with the value previously reported in the literature for butt spliced bolted joints.The value of the theoretical exponent quantifying the scale effect(0.326against0.25suggested by Eurocodes)is discussed.?2001Published by Elsevier Science Ltd. Keywords:Fatigue;Welded joints;Notch stress intensity factors

1.Introduction

Williams[1]was able to demonstrate that in the con-text of the elasticity theory,the asymptotic stress state near a re-entrant corner is singular and its degree of singularity is a function of the only notch opening angle. The stress?eld intensity depends on the overall geometry of the component and the far-?eld loading.In the context of a stress?eld theory,a?eld parameter called the“notch stress intensity factor”(hereafter N-SIF)was explicitly de?ned by Nui et al.[2]and applied

to the fracture toughness of brittle materials.Afterwards, the N-SIF concept was used by Boukharouba et al.and

by Verreman and Nie for fatigue crack initiation esti-mates at notches[3]and weld toes[3,4].Recently,an analytical background able to quantify different stress components,such as the in?uence of symmetric and

*Corresponding author.Tel.:+39-0444-998-711;fax:+39-0444-

998-888.

E-mail address:plazzarin@gest.unipd.it(https://www.360docs.net/doc/7011882718.html,zzarin).

0142-1123/01/$-see front matter?2001Published by Elsevier Science Ltd. PII:S0142-1123(00)00086-4anti-symmetric stress?elds,supported the N-SIF de?-nition[5].Due to weld geometry,both components are always present at the weld toe,also under a remote uni-axial load,and vary from case to case according to the global geometry of the joint.Thus,two notch stress intensity factors K N1and K N2(for opening and sliding modes)were determined by means of a?nite element analysis and then plotted as a function of the main geo-metrical parameters of the joints[5].So,in the highly stressed region in the neighbourhood of the weld toe, stress components can be predicted on the basis of a linear combination of K N1and K N2;this could be useful, particularly along the virtual direction of fatigue crack propagation(when a well-established linear elastic frac-ture mechanics approach is used to predict the fatigue life of the joints[6–9])and on the surface free edge (where strain gauges are generally placed in experi-mental approaches).

It has already been shown in[5,10]that the total fatigue life of transverse non-load-carrying?llet welded joints could be ef?ciently predicted by using only the K N1factor,the contribution due to the sliding mode being

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non singular for that type of joint.Note that most of the weld details classi?ed by Eurocode3and other national standards in force exhibit mean values of the V-shaped notch opening angles close to135°.Thus,neglecting the in?uence of K N2in the fatigue failure criterion should be reasonable in all these cases,while comparing the K N1 of different units(due to variations of the opening angles)is not[5,10,11].It was already highlighted[12] that a precise theoretical link exists(due to Bueckner’s superposition principle)between the conventional MFLE stress intensity factor K I and the N-SIFs K N1and K N2. The aims of this paper are as follows:

?to extend the N-SIF-based approach,previously applied only to steel weldments,to aluminium welded joints;

?to compare the fatigue strength of steel and alu-minium welded joints of different geometry on the basis of the relevant N-SIFs;

?to brie?y discuss the exponent quantifying the size effect by comparing theoretical predictions(based only on Williams’Mode I singularity)and results of

a statistical re-analysis involving all the experimental

data considered herein.The theoretical penalty exponent is more penalising than that suggested by Eurocodes.

2.Singular stress?elds due to sharp corners

Williams[1]stated that,even in a re-entrant V-shaped corner,as happens in a crack,the Mode I(and often Mode II)stress?eld is singular close to the tip.Then, in a polar frame of reference(r,J)(see Fig.1),the stress ?eld is de?ned within two constants(a1and a2)and can always be written as the sum of the symmetric?eld,with stress singularity of the1/r1?l1type,and the anti-sym-metric?eld,with stress singularity of the1/r1?l2type:

?s J s r t r J??l1r l1?1a1?f1,J(J)f1,r(J)f1,r J(J)??l2r l2?1a2?f2,J(J)f2,r(J)f2,r J(J)?(1)

where l1and l2are,as is well known,the?rst eigen-values for Mode I and Mode II,respectively,in Willi-ams’equations[1].Obviously,when l2is greater than 1.0,only Mode I is singular.This happens when2a is greater than102°.

It is possible to present Williams’formulae for stress components as explicit functions of the N-SIFs[5].For Mode I stress distributions

are:Fig.1.Coordinate system and geometrical parameters for the analy-ses of the welded joints.

?s J s r t r J?r=0?1?2p r l1?1K N1(1+l1)+c1(1?l1)??(1+l1)cos(1?l1)J

(3?l1)cos(1?l1)J

(1?l1)sin(1?l1)J???c1(1?l1)?cos(1+l1)J?cos(1+l1)J sin(1+l1)J??(2) For Mode II:

?s J s r t r J?r=0?1?2p r l2?1K N2(1?l2)+c2(1+l2)???(1+l2)sin(1?l2)J

?(3?l2)sin(1?l2)J

(1?l2)cos(1?l2)J??

227

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?

?sin(1+l 2)J sin(1+l 2)J cos(1+l 2)J

??

(3)

General expressions of the coef?cients in Eqs.(2)and (3)are reported in [5,10].Since all the series of welded joints considered in the present analyses will be charac-terised by an opening angle 2a =135°,it is suf?cient to give here only the parameter values associated with this particular angle:l 1=0.674,l 2=1.302,c 1=4.153,c 2=?0.569.

Two convenient expressions of N-SIFs for welded joints are the following [5]:K N 1

?k 1s n t

1?l 1

(4a)K N 2?k 2s n t

1?l 2

(4b)

where k i are non-dimensional coef?cients analogous to the theoretical stress concentration factors K t ,s n is the remotely applied nominal stress and t is the main plate thickness.Looking at Eqs.(2)and (3),it is worth noting that when q =0,s r and s q depend only on Mode I distri-bution while,on the contrary,the t r q component is asso-ciated with Mode II.So,by plotting stress distributions along the bisector of a particular geometry,there is a zone in the neighbourhood of the weld toe where the s ij /r l i ?1ratios have a constant value (Fig.2).As a conse-quence,K N 1and K N

2can be univocally determined since,on the basis of Eqs.(2)and (3),the intensities of the stress distributions are ruled just on such parameters.It is worth noting that only Mode I stress distribution is singular in Fig.2while,in contrast,Mode II stress components are null when r =0.

As soon as K N 1and K N

2are known,the relevant non-dimensional coef?cients k 1and k 2can easily be com-puted by means of Eq.

(4a,b).

Fig.2.Plots of stresses along the bisector.

Expressions for k 1and k 2have already been reported for transverse non-load carrying ?llet welded joints sub-jected to tensile stresses [5]or bending stresses [10].It is useful to report here such expressions,since most welded details considered herein refer to just such types of joints.Traction:

k 1?1.212?0.495e ?0.985(2h /t )

(5a)?1.259e ?1.120(2h /t )?0.485(L /t )k 2?0.508?0.797e ?1.959(2h /t )

(5b)

?2.723e ?1.126(2h /t )?0.769(L /t )Bending:

k 1?0.900?0.326e ?5.289(2h /t )

(6a)

?0.474e ?3.064(2h /t )?1.420(L /t )k 2?0.818?1.760e ?5.356(2h /t )

(6b)?1.851e ?2.982(2h /t )?1.026(L /t )

According to symbols shown in Fig.1,h is the height of the weld bead and L the transverse plate thickness.Estimates based on Eqs.(5a,b)are accurate when 0?L /t ?3.0and 0.25?2h /t ?2.5[5]while limits for Eqs.(6a,b)are 0.2?L /t ?5.0and 0.25?2h /t ?2.5[10].Out of these geometrical conditions,a ?nite element analysis should be carried out,according to the procedures detailed in [5].

3.Fatigue strength data in terms of N-SIFs Tables 1and 2summarise geometrical and fatigue

strength data related both to steel and aluminium welded joints,respectively.Those pertinent to steel joints have already been partly analysed in [5,10].

Table 3reports materials,welding processes and post-welding conditions for all the series considered.Original data are reported in the well-known books by Maddox [6]and Gurney [7,9]as well as in two papers by Kihl and Sarkani [13,14].Most data refer to transverse non-load-carrying ?llet joints;some series,however,con-sider welded joints of a different type.In all cases,the nominal value of the notch tip radius is to be considered null (as the weld toes are always represented by sharp V-shaped notches in the original papers),while the opening angle 2a is 135°.The relevant k 1coef?cients are sum-marised in Tables 1and 2.It is worth noting that the main plate thickness ranges between 6and 100mm in steel welded joints,and between 3and 24mm in alu-minium welded joints.The variability of the transverse plates is even more pronounced (3–200mm).

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Table1

Geometrical and fatigue strength properties of steel welded joints(nominal load ratio R?0)a

Welded joint geometry?K N1,50%[MPa Series Load type t[mm]L/t2h/t k1?s n,50%[MPa] [Ref.No.]mm0.326]

N=5·106N=5·106

St-1cruciform-nlc[6]T130.769 1.231 1.1479.5209.4

St-2cruciform-nlc[6]T50 1.0000.640 1.1059.6234.2

St-3cruciform-nlc[6]T1000.5000.3200.8855.5219.8

St-4cruciform-nlc[7]T130.2310.7690.9791.7204.8

St-5cruciform-nlc[7]T130.769 1.231 1.1476.7202.0

St-6cruciform-nlc[7]T250.1200.4000.7993.9211.1

St-7cruciform-nlc[7]T25 1.2800.720 1.1566.0217.4

St-8cruciform-nlc[7]T258.800 1.200 1.3659.7231.8

St-9cruciform-nlc[7]T380.3420.4210.8768.7196.3

St-10cruciform-nlc[7]T38 5.7890.789 1.4145.5209.5

St-11cruciform-nlc[7]T1000.0300.1000.5595.7236.6

St-12cruciform-nlc[7]T100 2.2000.300 1.2740.1228.7

St-13cruciform-nlc[7]B250.1200.4000.7987.9198.6

St-14cruciform-nlc[7]B500.0600.2000.6698.1232.4

St-15cruciform-nlc[7]B1000.0300.1000.59b94.5248.1

St-16cruciform-nlc[7]B1000.1300.1600.6875.1230.6

St-17cruciform-nlc[13]T6 1.0000.750 1.11103.1205.7

St-18cruciform-nlc[13]T19 1.0000.750 1.1177.8226.0

St-19cruciform-nlc[13]T25 1.0000.750 1.1157.4182.2

St-20cruciform-nlc[13]T11 1.0000.750 1.11107.4261.0

St-21cruciform-nlc[14]T11 1.0000.750 1.1193.6227.3

St-22cruciform-nlc[9]T6 1.000 2.000 1.2093.6201.4

St-23T-nlc[9]B6 1.000 2.000 1.07b111.3213.5

St-24cruciform-lc[9]T6 1.000 2.000 1.45b98.6255.8

a Type of test:T=traction;B=bending.Type of?llet:nlc=non-load carrying?llet weld;lc=load-carrying?llet weld.

b For the series1–14,16–22,k1has been determined by means of Eqs.(5a)–(6a).In the remaining cases,k1has been determined by means of an“ad hoc”?nite element analysis.

Table2

Geometrical and fatigue strength properties of aluminium welded joints(nominal load ratio R?0.1)a

Welded joint?K N1,50%

?s n,50%

Series geometry[Ref.Load type t[mm]L/t2h/t K m k1[MPa

[MPa] No.]mm0.326]

N=5·106N=5·106

AL1cruciform-nlc[8]T3 1.000 3.000 1.14 1.2259.3103.2

AL2cruciform-nlc[8]T6 1.000 2.333 1.09 1.2145.397.8

AL3cruciform-nlc[8]T12 1.000 1.667 1.08 1.1940.5108.6

AL4cruciform-nlc[8]T24 1.000 1.708 1.01 1.1929.197.7

AL5cruciform-nlc[8]T240.2500.583 1.050.9140.9105.0

AL6cruciform-nlc[8]T120.500 1.167 1.25 1.1038.094.1

AL7T-nlc[17]T120.833 1.333 1.000.93b43.189.7

AL8T-nlc[16]T12 1.000 1.333 1.000.93b53.0110.3

AL9cruciform-lc[16]T12 1.000 1.333 1.00 1.73b28.0108.8

AL10cruciform-lc[15]T12 1.000 1.060 1.00 2.07b26.3122.5

a Type of test:T=traction;B=bending.Type of?llet:nlc=non-load carrying?llet weld;lc=load-carrying?llet weld.

b For the series AL1–AL6,k1has been determined by means of Eqs.(5a)–(6a).In the remaining cases,k1has been determined by?nite element analyses.

Fig.3summarises steel welded joint data,all referring to a nominal load ratio R?0,in a single scatter band (mean values±two standard deviations),of which the top and bottom lines refer to a probability of survival equal to 2.3and97.7%,respectively.At N ref=5·106cycles to failure,the mean value of?K N1is211 MPa·mm0.326while the T K scatter index(T K= K N1,Ps=2.3%/K N1,Ps=97.7%)is1.85.

As far as the aluminium welded joints are concerned, six series were reported in a well-documented contri-

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Table3

Steel and aluminium welding material type and welding conditions

Series Material Yield stress[MPa]Welding process Conditions

St-1÷St-3BS4360:50360÷398Manual metal arc welding As-welded

St-4÷St-16BS4360:50290÷405Manual metal arc welding As-welded with spot-heated

St-17÷St-20HSLA-80598÷671Gas metal arc welding(pulse)As-welded

St-21HSLA-80?671Gas metal arc welding As-welded

St-22÷St-24Steel UTS515MPa412Metal inert gas As-welded

AL1÷AL66061-T6277÷298Gas metal arc welding As-welded

AL75083-H3255Metal inert gas As-welded

AL8,AL96061-T651?250Metal inert gas As-welded

AL10Al Zn Mg1304Metal inert gas

As-welded

Fig.3.Fatigue strength of aluminium and steel welded joints as a function of Mode I N-SIFactor.Scatter band related to mean values±2standard deviations.

bution due,once again,to Maddox[8].In this paper,all ?gures of the joint geometry are interested by sharp V-shaped notches,the total fatigue life being thought of as fatigue crack propagation life.The remaining four series are due to Jacoby[15],Ribeiro et al.[16]and Meneghetti [17].Also,for such series it is not possible to give an upper bound for the real weld toes,since this information is not explicitly given in the original papers.All fatigue tests were carried out with a nominal load ratio R about equal to0.1.

Under the hypothesis of log-normal distributions of the number of cycles to failure,the mean values of ?s n,50%have been determined by a least-square method.

One might note that?s n,50%values pertinent to the series tested by Maddox are slightly different from the values tabled in[8].This is because Maddox performed a best-?tting analysis of fatigue data by imposing a Wo¨hler curve slope equal to4.0for all the series tested by him. Maddox’data also take into account secondary bending effects,quanti?ed by the experimental coef?cient K m, determined in[8]by means of strain gauge measure-ments.For the remaining series in Table2,K m is equal to unity.Aluminium welded joints show a mean value of?K N1=99MPa·mm0.326at5·106cycles to failure,while the T K index practically coincides with the steel joint value(1.80against1.85).

Due to the limited number of experimental data con-sistent with those shown in Fig.3,for the time being it is not possible to extend the approach to different nomi-

nal load ratios,with the aim of quantifying the differ-ences with respect to the R?0case.However,two series of experimental data reported in[14]and not considered

in Table1show that:(a)the mean?K N1curve goes down slightly when R=0.33(with a decrease in strength of

about5%at5million cycles);(b)conversely,the mean ?K N1curve goes up in the presence of negative mean stresses(R=?2),the difference in strength being more

pronounced with respect to the former case.It is natural to think that these trends will be con?rmed,being in agreement with the results obtained with the conven-tional nominal stress approach.

Finally,it might be useful to note that the mean ?K N1values for steel and aluminium joints are in a ratio of2.1.The same ratio had been shown for butt splice bolted joints[19](nominal stress amplitude equal to88 MPa for steel;41MPa for aluminium),where such a geometry made a comparison still possible in terms of nominal stresses.

3.1.Size effect

The size effect is predicted by Eq.(2),where the pen-alty exponent g=1?l1is different from that reported in the Eurocodes(0.326against0.25,where,as far as the authors are aware,the latter value is empirical in nature). Due to the availability of experimental data and the accuracy of the sources considered,we have looked for the value of the exponent g which minimises q,q being de?ned as follows:

q??

??s n j

?s nref?

k1ref

k1j?t ref t j

?g?2(7)

As reference values,we have chosen t=25mm for steel welded joints(and,in particular,the series St-6has been taken as the reference series)and t=12mm for alu-

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minium welded joints (series AL-3).Fig.4plots the ratio q /q min against g .It is interesting to note that,at least for the joints considered herein,characterised by a nomi-nal value of the notch tip radius equal to zero,the scatter is minimised corresponding to the theoretical value based on Williams’eigenvalue for steel,at g =0.30for aluminium.

Support for the present analysis is given in a recent contribution by Macdonald and Haagensen [18]who emphasise the fact that assessment of recent research data has indicated the in?uence of a thickness stronger than g =0.25,so that in the latest HSE and API/ISO revision for offshore structures,a higher penalty factor of g =0.30is imposed.

4.Further developments of the N-SIF-based approach and some answers to reviewers

Due to lucky circumstances,the paper was reviewed by two anonymous referees whose suggestions and care-ful judgements (both those favourable and those quite critical)have been greatly appreciated by the authors.Some problems raised by the referees are intriguing,needing further investigation to be fully clari?ed and so they are surely of interest for many researchers engaged in fatigue design of components weakened by sharp stress raisers.For this reason,we have decided to report faithfully the referees’opinions here.

Reviewer A wrote that “the conservative assumption that the weld toe radius is equal to zero is helpful,because weld toe radius is not easy to measure,needs time and is affected by a large scatter”.Nevertheless,“this presentation of the fatigue resistance of the welded joints is of limited interest”for two reasons:

(a)“it not easy to use the fatigue resistance curve for a weld toe geometry with an included angle different from 135°”(in that units for K N 1are no longer

MPa·mm 0.326

);

(b)“it is not possible to appreciate directly the fatigue reduction factor in presence of smooth welded

joints”.

Fig.4.Minimum values of q for aluminium and steel welded joints.

Reviewer A also wrote that the discussion “about the thickness effect is a more interesting contribution.It is based on the assumption that thickness effect is due to the stress gradient precisely described by the exponent of singularity”.In his opinion,the N-SIF-based analysis implies that:

(c)“the thickness effect depends on the weld toe angle (so a universal value cannot be accepted)”;(d)“loading modes have no direct effect (which is not a true assumption)”.

Only point (d)can be easily confuted.Different expressions are used in the paper for welded joints sub-jected to tensile loading and bending loading.This sim-ply means that loading modes (and not only the global geometry)in?uence the intensity of the stress distri-butions in the neighbourhood of the sharp notch (but not the degree of singularity [20],which depends only on 2a ).When given in terms of nominal stress ranges,the fatigue strength of welded joints subjected to bending loads is generally recognised as greater than that exhib-ited by the same joint under tensile loads.A reduction of 13%in averaged terms is reported by Hobbacher [21],a reduction ranging from 0%to 25%is shown in [20].This scatter is no longer statistically signi?cant if N-SIFs are used instead of nominal stresses for the simple reason that N-SIFs include the loading mode effect.Note that series St-11,12,15,16in Table 1(t =100mm)show a ?K N 1value that ranges,for bending and tensile loads,from 229to 248MPa·mm 0.326.

Point (c)re?ects exactly the authors’opinion when the geometry is weakened by sharp V-shaped notches.However,as soon as a notch with a tip radius r constant and different from zero is present,the situation becomes more complex.Obviously,stress distribution due to a rounded notch does not coincide with that of the sharp V-notch.A small zone exists in the close neighbourhood of the notch tip where the stress distribution substantially depends only on r ,so that its features can be considered to a certain degree “universal”.Moreover,the stress gradient is not constant but varies as a function of the distance from the notch tip.Outside this limited zone,of which the dimensions are about 0.3r ,the in?uence of the opening angle becomes important and the stress gradient coincides with that related to the corresponding sharp V-shaped notch.The properties of the material determine whether the fatigue strength is controlled by the former or the latter zone.

With regard to point (a),the authors agree with the reviewer.However,it is evident that an opening angle of about 135°represents the most common geometry and that small variations of the angle could be tolerated by engineers engaged in fatigue problems.One should also note that in a very accurate multi-parameter design optimisation of load-carrying ?llet cruciform joints car-

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ried out by Radaj and Zang[22](see also Radaj and

Sonsino[23]),the only geometrical parameter con-

sidered constant is the opening angle.Conversely,there

is no doubt that,from a theoretical point of view,the

complex units of K N1do not allow a direct comparison

between joints with different opening angle.The prob-

lem,already highlighted by Hasebe et al.[24],can be

overcome either by introducing a virtual crack at the

notch toe[24,12]or by using,perhaps by taking a small

step forward,Eqs.(2)and(3)to determine the energy

in a small sector of radius R surrounding the sharp notch

[25].Such energy is strictly correlated to K N1and K N2but

it obviously has the merit to be expressed in Nmm/mm3.

As regards point(b),Hasebe et al.[24]were able to

demonstrate that a precise analytical link exists between

the N-SIF(determined for sharp-V-shaped notches under

Mode I conditions)and the elastic peak stress value of

a rounded V-shaped notch,the notch tip radius being

small but different from zero.More precisely,Hasebe et

al.wrote[24]:

K N1?lim r→0C?r1?l1s q,max(8)

where symbols of the original paper have been upgraded

to current symbols.The parameter C?was summarised

for several notch opening angles in[24].Eq.(8)makes

it evident that using K N1or s q,max(after having intro-

duced a small notch tip radius r)results in exactly the

same fatigue predictions.Obviously,in real cases,one

would use Eq.(8)in the presence of a well-de?ned value

of r(for example r f=1,according to Radaj’s?ctitious

weld toe/root radius[26]).By using a complex potential

function and Neuber’s conformal mapping,an equation

analogous to Eq.(8)was reported also in[27]:

K N1??2p[1+l1+c1(1?l1)]

4?q?1q

?1?l1r1?l1s q,max(9)

?1.22·r1?l1·s q,max

where,on the right side of Eq.(9),a coef?cient valid for the2a=135°case is introduced.In Eq.(9),due to the absence of the limit condition r→0,K N1was not thought of as numerically coincident with the value per-tinent to the r=0case.Eq.(9),without upgrading K N1, results in a strong simpli?cation in the peak stress evalu-ation,but also some degree of inaccuracy.The problem is that of de?ning this degree of inaccuracy.Table4 gives a precise idea of the errors for two geometries with L/t=0.5and1.0.The differences between analytical and?nite element results vary from case to case,their mean value being about10%.Note that some formulae summarised in[28],and suitable for estimating peak stress in cruciform welded joints,are acknowledged as being able to provide a substantially equivalent degree of accuracy[23].

It is evident that Eqs.(8)and(9)provide a bridging Table4

Stress concentration factor K t of transverse non-load-carrying?llet welded joints under tensile loads(in all FE analyses t=20mm, 2h/t=1,see Fig.1).Values of k1determined according to Eq.(5a))

r/t L/t k1Eq.(5a)K t Eq.(9)K t FEM

0.020.5 1.075 3.43 3.83

0.050.5 1.075 2.54 2.85

0.10.5 1.075 2.03 2.30

0.20.5 1.075 1.62 1.88

0.021 1.144 3.65 4.02

0.051 1.144 2.71 3.00

0.11 1.144 2.16 2.41

0.21 1.144 1.72 1.95 between the N-SIF approach and Radaj’s notch stress approach for welded joints[26,23],where fatigue predic-tions can be performed on the basis of s q,max(that is on the basis of the theoretical stress concentration factor K t),but only after having introduced a precise value of the?ctitious notch tip radius(r f=1mm in most welded details of practical interest,but also r f=0.25mm for spot-welded overlap joints made in rolled steels, r f=0.2mm for cruciform joints in the presence of longi-tudinal shear loading[23]).

Reviewer B“fully agrees with the N-SIF approach”since it“is based on a principle of similitude and over-comes problems encountered with predictions using a local strain approach and/or an integration of Paris’relationship”.He has been“convinced for years that this is the best way for predicting the life of welded joint (as-welded)and that it should be included in codes”. Asking the authors to discuss the fatigue fracture of welded joints and to explain why the approach works, he helps them by providing the following convincing explanation:“A severe notch with a very small toe radius results in a short microstructural initiation life—even without toe‘defects’—and in an immediate crack propagation;this explains why the in?uence of a micro-structure is weak.Furthermore,most of the life is con-sumed at short crack depth,within the singularity;that explains why good correlation is obtained with total fatigue life.”

In addition,it might be useful to remember that LEFM stress intensity factor K I is analytically correlated to N-SIFs[12].A conventional evaluation of residual life from an initial crack value of0.3mm(the crack being thought of as through the thickness)turned out to be in a ratio of1:3to experimental total life,having assumed the exponent in the Paris law as being equal to3.0[12]. In conclusion,N-SIF is easy to calculate,and plays an essential role in short microstructural initiation life,short crack life and crack propagation life.

https://www.360docs.net/doc/7011882718.html,zzarin,P.Livieri/International Journal of Fatigue23(2001)225–232

5.Conclusions

Notch stress intensity factors(N-SIFs)have been used,in a single scatter band,to summarise fatigue properties of aluminium welded joints(cruciform and T non-load-carrying or load-carrying?llet weld joints). More precisely,fatigue total life(and not only fatigue crack initiation life)has been correlated to the relevant Mode I N-SIFs,i.e.?K N1.Welded joints were character-ised by a thickness ranging between3and24mm,able to put in evidence any scale effect.Fatigue properties of aluminium welded joints have been compared with those related to steel welded joints(of which the main plate thickness varied from6to100mm).The mean?K N1 values turn out to be in a ratio slightly greater than2.0, while the scatter band size(mean value±2standard deviations)practically coincides.

Taking into account the only singular stress distri-bution(associated to Mode I fracture),the exponent quantifying the scale effect penalty is0.326,which is quite different from the0.25value suggested by the Eur-ocodes.In the presence of a weld toe radius approaching zero,a statistical re-analysis of all fatigue data showed that a value equal to0.3was more realistic both for alu-minium and steel welded joints.It is worth noting that in some recent standards on off-shore structures,the exponent0.3has already substituted the0.25value present in Eurocodes.

Finally,the link between Mode I N-SIF and the peak value of the maximum linear elastic stress(determined in the presence of a small weld toe radius)was discussed. References

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