The Significance of Fatigue Crack Initiation for Predictions of the Fatigue Limit of Specimens and...

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The significance of fatigue crack initiation for predictions of the fatigue limit of specimens and structures Jaap Schijve Delft University of Technology, Faculty of Aerospace Engineering, P.O. Box 5058, 2600 GB Delft, The Netherlands article info Article history: Received 30 August 2013 Received in revised form 28 October 2013 Accepted 31 October 2013 Available online 15 November 2013 Keywords: Crack initiation phenomenon Fatigue limit Fatigue notch effect Welded joints abstract The fatigue life of specimens and structures covers two periods: a crack initiation period and a crack growth period. Micro-crack nucleation and initial micro-crack growth are a surface phenomenon con- trolled by the local stress cycles at the material surface. The subsequent macro-crack growth is depending on the fatigue crack growth resistance of the material as a bulk property. The fatigue behaviour in both periods is qualitatively reasonably well understood. However, the quantitative analysis is problematic. Moreover the number of variables which can effect the fatigue behaviour of specimens and structures is large. The paper is focussed on realistic understanding of the prediction problem, especially on the pre- diction of the fatigue limit of notched specimens and structures. The effect of a salt water environment on the fatigue limit is discussed. As a special topic comments are presented on the notch effect of welded joints. Short comings of the so-called effective notch concept are indicated. Comments on the design rec- ommendations of the International Institute of Welding are presented. The significance of realistic exper- iments and a profound FE-analysis are emphasized. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction It is noteworthy that fatigue of various structures still remains a practical problem, for instance for aircraft, cars, cranes, bridges, off- shore structures, etc. This situation is a consequence of several developments associated with new types of structures, desirable weight reductions of the structure, new production techniques and materials. Safety and economic arguments are also important, especially in view of a more intensive and longer utilization of structures in service. As a consequence one thing did not change. There is still a risk of crack initiation and subsequent propagation to failure of structures in service. In the present paper the main emphasis is on the prediction of the fatigue limit and the phenomenon of fatigue crack initiation. First the concept of the fatigue limit is discussed. How should it be defined? The fatigue limit is of great interest for the design of- fice of the industry in view of the question whether fatigue cracks may occur in the required life time of a structure in service. By fi- nite-analysis (FE) the stress distribution will be obtained which will reveal stress concentrations around critical notches. Stress concentration factors (K t ) can then be used to start predictions on a fatigue limit. Predictions are associated with the similarity be- tween the geometry and production of the structure and the con- ditions of laboratory specimens for which fatigue data are available. There is some rational understanding of the similarity, and also of the limitations of the similarity. This is a major theme of the present paper with the purpose to emphasize fundamental understanding. First the crack initiation and initial crack growth are discussed, including the effect of corrosion. It is followed by comments on methods for the prediction of the fatigue limit of notched struc- tural elements. Fatigue of welded joints are discussed in a separate section. The discussion is summarized in a number of conclusions. 2. Crack initiation and the fatigue limit The fatigue life encompasses two periods, the crack initiation period and the crack growth period until failure, see Fig. 1, which also presents the parameters, K t and K relevant to the two periods. Micro-crack initiation preferably occurs at the material surface be- cause of the low constraint on cyclic plasticity, see Fig. 2. As long as a micro-crack is still present in a single grain the growth depends on the material structure in that grain, including the crystallo- graphic orientation of the grains and possible inclusions. The first micro-crack growth is a surface phenomenon. At a later stage the micro-crack will penetrate into surrounding grains, both along the material surface and in the depth direction away from the material surface see Fig. 3. It implies that crack growth occurs along a crack front through a number of adjacent grains. Crack growth then is no longer depending upon the surface condition, but pri- marily on the crack growth resistance as a bulk property of the material. If this occurs the crack growth rate can be correlated with 0142-1123/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2013.10.022 E-mail addresses: [email protected], [email protected] International Journal of Fatigue 61 (2014) 39–45 Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue

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Jaap Schijve

Transcript of The Significance of Fatigue Crack Initiation for Predictions of the Fatigue Limit of Specimens and...

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    Fatigue notch effectWelded joints

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    the fatigue limit is discussed. As a special topic comments are presented on the notch effect of welded

    rious scraft, cis a ctypes, new

    may occur in the required life time of a structure in service. By -nite-analysis (FE) the stress distribution will be obtained whichwill reveal stress concentrations around critical notches. Stressconcentration factors (Kt) can then be used to start predictionson a fatigue limit. Predictions are associated with the similarity be-tween the geometry and production of the structure and the con-ditions of laboratory specimens for which fatigue data areavailable. There is some rational understanding of the similarity,

    see Fig. 1, whichthe two periods.terial surfe Fig. 2. As

    a micro-crack is still present in a single grain the growth don the material structure in that grain, including the crygraphic orientation of the grains and possible inclusions. Tmicro-crack growth is a surface phenomenon. At a later stage themicro-crack will penetrate into surrounding grains, both alongthe material surface and in the depth direction away from thematerial surface see Fig. 3. It implies that crack growth occurs alonga crack front through a number of adjacent grains. Crack growththen is no longer depending upon the surface condition, but pri-marily on the crack growth resistance as a bulk property of thematerial. If this occurs the crack growth rate can be correlated with

    International Journal of Fatigue 61 (2014) 3945

    Contents lists availab

    u

    lsE-mail addresses: [email protected], [email protected] fatigue limit and the phenomenon of fatigue crack initiation.First the concept of the fatigue limit is discussed. How should itbe dened? The fatigue limit is of great interest for the design of-ce of the industry in view of the question whether fatigue cracks

    period and the crack growth period until failure,also presents the parameters, Kt and K relevant toMicro-crack initiation preferably occurs at the macause of the low constraint on cyclic plasticity, se0142-1123/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijfatigue.2013.10.022ace be-long asependsstallo-he rstThere is still a risk of crack initiation and subsequent propagationto failure of structures in service.

    In the present paper the main emphasis is on the prediction of

    2. Crack initiation and the fatigue limit

    The fatigue life encompasses two periods, the crack initiationstructures in service. As a consequence one thing did not change.and materials. Safety and economic arguments are also important,especially in view of a more intensive and longer utilization of

    section. The discussion is summarized in a number of conclusions.1. Introduction

    It is noteworthy that fatigue of vapractical problem, for instance for airshore structures, etc. This situationdevelopments associated with newweight reductions of the structurejoints. Short comings of the so-called effective notch concept are indicated. Comments on the design rec-ommendations of the International Institute of Welding are presented. The signicance of realistic exper-iments and a profound FE-analysis are emphasized.

    2013 Elsevier Ltd. All rights reserved.

    tructures still remains aars, cranes, bridges, off-onsequence of severalof structures, desirableproduction techniques

    and also of the limitations of the similarity. This is a major themeof the present paper with the purpose to emphasize fundamentalunderstanding.

    First the crack initiation and initial crack growth are discussed,including the effect of corrosion. It is followed by comments onmethods for the prediction of the fatigue limit of notched struc-tural elements. Fatigue of welded joints are discussed in a separateCrack initiation phenomenonFatigue limit

    is large. The paper is focussed on realistic understanding of the prediction problem, especially on the pre-diction of the fatigue limit of notched specimens and structures. The effect of a salt water environment onThe signicance of fatigue crack initiatiolimit of specimens and structures

    Jaap SchijveDelft University of Technology, Faculty of Aerospace Engineering, P.O. Box 5058, 2600 G

    a r t i c l e i n f o

    Article history:Received 30 August 2013Received in revised form 28 October 2013Accepted 31 October 2013Available online 15 November 2013

    Keywords:

    a b s t r a c t

    The fatigue life of specimgrowth period. Micro-cractrolled by the local stress con the fatigue crack growtperiods is qualitatively reaMoreover the number of v

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    journal homepage: www.eand structures covers two periods: a crack initiation period and a crackucleation and initial micro-crack growth are a surface phenomenon con-s at the material surface. The subsequent macro-crack growth is dependingsistance of the material as a bulk property. The fatigue behaviour in bothably well understood. However, the quantitative analysis is problematic.bles which can effect the fatigue behaviour of specimens and structuresfor predictions of the fatigue

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    40 J. Schijve / International Jourstress intensity factors. In each load cycle a still microscopicallysmall crack extension occurs. It can lead to striations which canbe observed in the electron microscope.

    In the initial crack initiation period a micro-crack is presented,while in the subsequent crack growth period the fatigue crack maybe labelled as a macro-crack, although it may still be invisible. Son-sino [2] considered the crack propagation period in full-scale testson a large welded structure to start as a size of 1 mm which wasdetected by a DC potential drop technique. Other small sizes maybe considered. The transition from micro-crack growth to macro-crack growth is a gradual process. It is pointed out in [1] that thetransition cannot precisely be dened. Nevertheless the transitiondoes occur. The important conclusion to be drawn here is that pre-dictions on the fatigue limit should be associated with consideringthe conditions for micro-crack initiation. As soon as the crack isgrowing as a macro-crack a nal failure will occur.

    The fact that rather small cracks can still grow has been shownin various investigations. As an example Fig. 4 with data of Wanhill[3] for small cracks at DK-values below DKthr. It may be stated herethat the threshold DK is irrelevant for crack growth under con-stant-amplitude loading. A threshold to crack growth can be

    Fig. 2. Cross section of the initial fatigue crack starting at the material surface [1].

    Crack front

    Free surface

    Fig. 3. Top view of a fatigue crack with the crack front passing through many grains[1].phases and factors.

    of Fatigue 61 (2014) 3945observed only under variable-amplitude loading as a result of crackclosure [1].

    The question now is how to dene a fatigue limit. Historicallythe fatigue limit was considered to represent a knee-point in theSN curve at a fatigue life of 2.106 cycles, see Fig. 5. But other N-values for an apparent kneepoint can be found in the literature.A tendency towards a horizontal SN curves for large enduranceshas also been observed in many fatigue test programs. Fatigue fail-ures for N > 2.107 then were rarely observed and tests were gener-ally not continued for fatigue lives exceeding 108 cycles.

    An entirely different behaviour occurs in fatigue tests in saltwater The detrimental effect of salt water on fatigue propertiesis a well known phenomenon for engineering materials. In theliterature it has frequently been illustrated by SN curves, includ-ing a systematic effect of the load frequency. Those curves alsosuggests that a fatigue limit does not exist by fatigue in saltwater. It is usually associated with an electro-chemical process.If salt water can enter a fatigue crack it will move to the tip of

    Fig. 4. Micro-cracks grow at DK < Kth [3].

  • the crack due to cyclic crack opening and closure. It then canactivate the decohesion mechanism. Chloride ions are supposedto contribute to decohesion at the crack tip. Crack extension oc-curs during the load rising part of the load cycle. Illustrative re-sults are shown in Fig. 6. Six different wave shapes were used inthis investigation. Two different loading rates were applied, and alarger crack rate was observed for the slower loading rate, com-pare ABC with DEF. During a slower loading rate there is more

    3. The prediction of the fatigue limit of notched specimens

    The prediction of the fatigue limit of a notched structural ele-ment is a realistic problem for engineering design purposes. In gen-eral terms the fatigue limit is then supposed to be the maximumcyclic stress level for which fatigue crack initiation does not occur.It is tacitly assumed that there are no cracks at all. In view of theprevious discussion it is possible that a micro-crack has been initi-ated which however did not succeed in growing to a macro-crack.A physical argument for that behaviour is that the early crack ini-tiation at the material surface occurs under plane stress conditionsat the free surface. After growing into the material there is a con-version to a plane strain situation which will reduce cyclic plastic-ity, also on a microscopic level. Further more, the tip of a growingcrack can meet with barriers in the structure of the material, suchas grain boundaries or pearlite bands in steel. It implies that a moreaccurate denition of the fatigue limit should include the conditionthat cyclic loading must lead to micro-crack initiation followed bymacro-crack growth. This question was investigated by Frost et al.[6,7]. They noted that an initially microscopically small fatiguecrack stopped growing any further. If this occurs in a fatigue testto obtain data for SN curves such an arrested micro-crack is invis-ible and the result of the test will be recorded as a runout. In phys-ical terms it cannot be said that fatigue damage did not occur, butit did not produce a visible fatigue crack and thus not a nal failure.

    micro-crack growth

    (log) S

    (log) N N = 2 106

    macro-crack growth

    Fig. 5. Schematic SN curve with knee-point and different crack growth areas.

    J. Schijve / International Journal of Fatigue 61 (2014) 3945 41time for a corrosive contribution to crack extension. However,the three highly different holding times at the maximum loaddid not have a systematic effect. Apparently the loading ratehas a signicant effect on the fatigue crack growth in salt water.A similar effect of the rise time of the load cycle has been ob-served for an aluminium alloy [5]. The observations were ob-tained for macro-crack growth. It may be expected that asimilar effect will occur for micro-crack growth because smallcracks are also opening and closing. Quantitative data can onlybe obtained by experiments, but it may well be expected thatthis corrosion phenomenon can occur at rather low amplitudesbelow the engineering fatigue limit. It then can lead to macro-crack growth and a fatigue failure after very high numbers of cy-cles. It appears that a fatigue limit is absent.Fig. 6. Effect of the loading rate and hold times at maximum load on fatigue craIn view of the above arguments it will be clear that a realisticprediction of the fatigue limit cannot be a simple procedure. Inthe previous century the need for engineering predictions of fati-gue properties was still supposed to be required for design pur-poses. The effect of notches, such as holes, should be accountedfor. It was generally thought that the prediction of fatigue proper-ties of notched elements must be derived from the fatigue proper-ties of unnotched specimens. The latter properties were assumedto be characteristic for the fatigue behaviour of a material. Nowconsider the comparison made in Fig. 7. The unnotched specimenis loaded to the stress level of the fatigue limit of the unnotchedmaterial. The notched specimen is loaded with the correspondingpeak stress equal to the fatigue limit of the unnotched material.ck growth in 0.22 C-steel in lake water. Results of Atkinson and Lindley [4].

  • nalIt might imply that the same crack initiation and initial micro-crack growth will occur in both specimen. The fatigue limit ofthe notched specimen (symbol Sfk) would then simply be obtainedby dividing the fatigue limit of the unnotched material by Kt.

    Sfk Sf1=Kt 1However, is has been shown in numerous fatigue test programs

    that the reduction factor is smaller than Kt. The fatigue reductionfactor (symbol Kf) is dened as:

    Kf Sf1=Sfk 2Kf is also labelled as the fatigue notch factor. Experimental evi-

    dence thus indicated:

    Kf < Kt 3From an engineering point of view this is favourable because

    (b) Fatigue limit Sf1(a) Fatigue limit SfkQuestion: Sfk = Sf1/Kt (?)

    Fig. 7. Similarity concept by comparing stress ranges in notched and unnotchedspecimens [1].

    42 J. Schijve / International Jourthe reduction of the fatigue strength by a notch is smaller than pre-dicted by a reduction factor equal to Kt. The reduction is smaller forhigh-strength/low ductility materials, and larger and thus morefavourable for low strength/high ductility materials.

    In retrospect, the assumption that Kf = Kt is not logical. It is truethat the fatigue mechanism is similar in unnotched and notchedspecimens, but there are fundamental differences between thetwo specimens. In an unnotched specimen a homogeneous stressdistribution is present in a large volume of the specimen. The crosssection is circular and the surface nish is excellent. In the notchedspecimen a local stress concentration occurs in a small volume ofthe specimen. Various cross sections and a variety of surface nishqualities are adopted. They can be accounted for by experience ob-tained in comparative fatigue tests [1].

    In the previous century several ideas have been proposed to ac-count for the stress gradient at the root of a notch. Proposals to ac-count for the steep gradient were presented by Neuber [8] and byPeterson [9]. They are briey summarized below.

    3.1. Prediction method of Neuber

    Neuber is the author of a famous book on elastic stress distribu-tions in notched elements (rst edition in 1937, translated in 1946[8]). Later Neuber noticed that the Kt-values obtained by an elasticstress analysis considerably overestimated the notch severity ob-served in fatigue experiments. He then suggested in the secondedition of his book that an average stress level in a thin surfacelayer at the root of the notch should be considered instead of Speakat the material surface. Although not strictly related to this thinlayer concept he proposed a reduced stress concentration factorKN with the following equation:

    KN 1 Kt 11 A=qp 4

    In this equation q is the radius at the root of the notch. The va-lue of A is a material constant which should follow from experi-mental results. Later it was proposed by Kuhn and Hardrath [10]that A should be a function of the static strength of the material.For a stronger material the value of A should be smaller. ForA = 0 in Eq. (4) the result is KN = Kt. It agrees with the experiencethat high-strength materials are rather notch fatigue sensitive.For low strength materials which usually are more ductile the va-lue of A is relatively large and KN in Eq. (3) will become smallerwhich also agrees with experience. Eq. (4) with the constants pro-posed by Kuhn and Hardrath was substantiated by experimentalresults, and the equation thus is no longer based on physicalassumptions. Actually it is data tting of results of fatigue tests.

    3.2. Prediction method of Peterson

    Peterson has published a book Stress Concentration Factors[9] which is a most valuable collection of Kt-values as a functionof dimensional ratios of notch congurations. Peterson also con-sidered the experimental evidence of Kf-values being lower thanthe theoretical Kt-values. He suggested that instead of Speak thesomewhat lower stress level at a specic small distance belowthe surface should be considered to be the effective peak stress.Peterson then proposed a KfKt relation, which is:

    Kf 1 Kt 11 aq 5

    In this equation a is depending on the material for which Pet-erson proposed certain values which led to a good correlation withexperimental results. Again the intrinsic nature of the equation innon-physical. As shown in [1] predictions obtained with Eqs. (4)and (5) differ by no more that 10%.

    Starting from a stress level somewhat below the material sur-face in order to explain why Kf < Kt is a strange approach. However,if the above equations can still produce a reasonable estimate ofthe fatigue limit, they still can be useful for reasonable estimates.But physically the derivation of the equations is in contradictionwith the actual phenomenon. In general crack initiation starts atthe material surface, and not at a certain distance below the mate-rial surface. Even more important, the stress along the surface ofthe notch does not rapidly decrease in contrast to the sharp de-crease of the peak stress in the depth direction away from thematerial surface, see Fig. 8.

    It may be recalled here that the KfKt correlation discussed inthis section applies to the fatigue limit only, and not to SN curves.Furthermore, it should be realized that the application of a Kf-factor to estimate fatigue properties of notched elements is a largeextrapolation step. It starts with data of unnotched specimen forwhich Kt is about 1.0 which then must lead to fatigue limit datafor notched specimens with Kt in a range from 2 to 4. If a new alloyis developed the unnotched fatigue limit is frequently presented asa basic material property. However, it does not show anythingabout the fatigue-notch sensitivity of the material. Fatigue test re-sults of notched specimens are more instructive for design pur-

    of Fatigue 61 (2014) 3945poses. For more complex joints it is well recognized thatinstructive fatigue tests should be carried out on joints specimens.This applies to riveted joints, lugs and welded joints. In riveted

  • nal ojoints and lugs fretting corrosion occurs which cannot be incorpo-rated in a mathematical evaluation. However, for welded joints thesituation is different although also complex. Comments arepresented in the following section.

    4. Fatigue of welded joints

    Fatigue of welded joints is generally considered to be a specicproblem. It is different from general structural fatigue problemsbecause of the various welding techniques and the large varietyof applications. An excellent survey of analysing fatigue propertiesof welded joints was published by Radaj in 1996 [11]. It includesthe historical development of knowledge and considerations tobe taken into account for fatigue problems. Radaj emphasized thesignicance of local design aspects of welded joints in order to ar-rive at improved fatigue properties. The problem of fatigue of

    Stress distribution near the edge of the hole

    Plate with circular hole loaded in tension

    Fig. 8. Steep reduction of the peak stress perpendicular to the edge of hole.However, slow reduction of the stress level along the edge of the hole [1].

    J. Schijve / International Jourwelded joints was also extensively discussed by several authorsin papers collected in a book by Radaj et al. [12]. Also in these pa-pers the local design approach of welded joints is emphasized inorder to explore the fatigue performance. The question to be ad-dressed here is associated with prediction issues, and primarilywith the predictions of the fatigue limit. The fatigue limit is rele-vant for considering the risk of fatigue crack initiation in weldedstructures in service, especially for large structures such as pres-sure vessels, ships and offshore structures. But there are morewelded structures for which fatigue failures are not acceptable. As-pects to be considered in the present paper are associated with thequestion whether a fatigue limit of a welded joint does exist andwhether predictions of the fatigue limit for design purposes arepossible.

    4.1. The fatigue limit of welded joints

    Prediction problems of welded structures are addressed inRecommendations for fatigue design of welded joints and compo-nents, an extensive document of the International Institute ofWelding (IIW) [13]. In this document the denition of the fatiguelimit is the fatigue strength at a fatigue life N = 107. For high cycleapplications it is assumed that the SN curve is still sloping downbetween N = 107 and 109, see Fig. 9. In this graph the SN curvesillustrate a series of different fatigue qualities of welded joints. Itvaries from a high quality (the upper curve) to a poor quality(the bottom curve). In each quality group different congurationsof welded structures can be present. The correlation between thequality and the SN curves as shown in Fig. 9 was established byconsidering test results of comprehensive fatigue test programs.

    The curves imply that a specic fatigue limit is always associ-ated with the same nite life part of the corresponding SN curve.That is strange. The fatigue limit is a matter of crack initiation only.But the fatigue life N of an SN curve includes both a crack initia-tion period and a crack growth period. The crack growth period isdepending on the crack growth resistance of the material. How-ever, crack initiation is a surface phenomenon depending on sur-face conditions, and not on the crack growth resistance of thematerial. It appears that there is a generalization in the IIW-docu-ment which is difcult to understand.

    In the IIW document the fatigue limit is also associated with aknee-point of the SN curve at N = 107. Some fatigue failures be-tween N = 107 and N = 108 are observed in various fatigue test pro-grams together with a few runouts. It is still somewhatcumbersome to consider the linearly sloping down of the SN

    Fig. 9. Fatigue resistance SN curves for steel and very high cycles applicationaccording to the IIW Recommendations [13].Fatigue strength at N = 107

    f Fatigue 61 (2014) 3945 43curves in Fig. 9 up to N = 109. Fatigue failures in the range of thefatigue life between 108 and 109 cycles suggest a very slow crackgrowth. Imagine a crack growth rate of 1 atomic distance(0.3 nm) in a cycle. It require about 30,000,000 cycles to grow1 cm. It is difcult to speculate about a fatigue crack growth mech-anism in terms of metal physics to cope with this result. It is well-known that the material in a welded joint is not homogeneous.There are heat affected zones with various material structuresand residual stresses. But even then it is hard to understand howan extremely high fatigue life can be obtained. Only a time depen-dent mechanism can explain such a result. It can occur during cor-rosion fatigue in a salt water environment as discussed before.Diffusion processes may also be assumed for some time dependentphenomenon, which then offers some difcult speculation on de-tails of such a phenomenon.

    4.2. The concept of the effective notch stress

    In view of problems associated with predictions of SN curvesof welded joints a new concept has been proposed for this purpose.It is based on the introduction of a so-called effective notch occur-ring at the toe of a weld [14]. The prole of the weld is by denitionreplaced by a circular rounding with a specic radius q, see Fig. 10.The stress distribution around the notch can then be calculated

  • instead of a single q-value. As mentioned in [15] the most obviousratio is q/t with t being the local plate thickness. A value q/t = 0.1may be useful but this should still be explored. Anyway it is ex-pected that a constant q/t-value in a FE analysis can be instructivefor design purposes because it indicate the severity of the stressdistribution around the toe of a weld. However, the effective Kt-va-lue cannot be adopted for considering the fatigue crack growthresistance. It implies that using the effective Kt for evaluating SN curves is questionable. It could be useful for prediction of a fati-gue limit. But it then will meet with the same problems as dis-cussed in Section 3 for simple geometric notches.

    4.3. Full-scale fatigue tests on a large welded structure reported bySonsino

    Recently an interesting investigation has been reported by Son-sino [2]. It is summarized here because it covers the overall topic of

    (a) Cruciform joint and butt joint loaded in tension.

    44 J. Schijve / International Journal of Fatigue 61 (2014) 3945with FE techniques. A local peak stress (Smax) and a correspondingKt-value are obtained. This information is supposed to be charac-teristic for the severity of the stress distribution around a weldand thus for the fatigue severity. The value of Smax or Kt is proposedto be a new parameter which can be adopted for evaluating the fa-tigue performance of welded joints. The size of q is a ctitiousparameter and thus will lead to ctitious Kt-values. But neverthe-less, it can produce useful information about the severity of thestress level of different welded joints. It also can give useful infor-mation if structural modications are considered to improve thefatigue performance of a structure. It then is used for the evalua-tion of the improved design. Actually it implies that a FE analysisis used as a design tool.

    However, it was also proposed to use the effective stress levelfor fatigue life predictions. Some agreement between predictionsand experimental results were reported, but it was also noted thatthe agreement can depend on the size of the ctitious radius q. Dif-

    (b) The same joints with fictitious rounding of weld toes and roots.

    Fig. 10. Different types of welds with rounded corners at the edges of the welds[11].ferent values for q are mentioned in the literature to improve thecorrelation between predicted trends and experimental results[15]. Because Kt-values are depending on non-dimensional ratiosof two dimensions the present author concluded in [16] that someeffective ratio of two relevant dimensions should be adopted

    Fig. 11. Tubular welded K-node ifatigue of welded structures. Fatigue tests were carried out on largewelded K-node elements of an offshore structures, see Fig. 11. Thetests were carried out under both constant-amplitude loading andservice-simulation variable-amplitude loading employing an off-shore load spectrum. A sea-water environment was applied whichfurther increased the realistic nature of the experiments. Observa-tions were made on crack initiation and subsequent crack growth.The crack initiation period was supposed to be nished after acrack with a depth of 1.0 mm under the material surface was ob-tained. The crack depth was measured with a DC potential droptechnique. The end of the crack growth period was dened as thebreak through of the fatigue failure until the full wall thicknessof the local structure. A stress analysis of the structure with FE cal-culations was made to reveal the most critical location for crackinitiation in the welds. Strain gage measurements were also madefor the same purpose.

    The investigation of Sonsino is most instructive. A major con-clusion for each new welded structures is that a FE-analysis is apowerful tool to indicate the most fatigue critical locations, to allo-cate possible fatigue problems and to consider arguments forsafety factors and a risk analysis. However, resonably accurate pre-dictions on a fatigue limit and the crack initiation life will remain adifcult problem, the more so because these properties depend ondetails of the weld prole. The best solution is to perform a realisticfatigue test, but that can be expensive. Tests on details of the struc-ture can be useful, but the local thickness and welding conditionsshould be representative. If predictions on the crack growth periodare made, fracture mechanics procedures must be used. It appearsn an off-shore structure [2].

  • that research efforts on this topic are worthwhile, also in view ofthe complexity of welded joints. Crack growth tests and the corre-sponding analysis of the stress intensity factors are then necessary.

    7. In the IIW document it is suggested that SN curves can indicatethe fatigue performance of a structure. This is misleadingbecause it neglects that the fatigue life comprises a crack initi-ation period and a crack growth period. The fatigue limit and

    J. Schijve / International Journal of Fatigue 61 (2014) 3945 455. Summarizing conclusions

    5.1. Elementary comments

    1. The fatigue life of specimens and structures covers two periods:a crack initiation period and a crack growth period. Micro-cracknucleation and initial micro-crack growth are a surface phe-nomenon controlled by local stress cycles at the material sur-face. In the second period the initially small crack growth isdriven by the cyclic stress intensity around the crack front.The crack growth rate then depends on the crack growth resis-tance of the material. It is no longer a surface phenomenon. Thecrack initiation mechanism and the crack growth mechanismare essentially different.

    2. The denition of the fatigue limit should be associated with theoccurrence of micro-crack nucleation followed by macro-crackgrowth. If this does not occur, the fatigue load is below the fati-gue limit.

    3. Fatigue crack growth in salt water will be activated by an elec-tro-chemical process during the rising part of a load cycle. Theeffect depends on the loading rate, but not on hold times at themaximum load. Due to the corrosion effect fatigue crack growthis possible at very small load amplitudes which then can lead tofailure. A fatigue limit appears to be absent.

    5.2. About the fatigue limit and notch effects

    4. Predictions on the fatigue limit of notched specimens are usu-ally based on employing an assumed similarity with the fatiguelimit of unnotched specimen. However, the stress distributionin notched and unnotched specimens are entirely different.The similarity is absent. It implies that the notch sensitivity ofa material should be investigated with notched specimens only.

    5. The fatigue reduction factor Kf is smaller than the stress concen-tration factor Kt. The difference is smaller for high-strengthmaterials. Two KfKt equations published in the literature arein reasonable agreement with experimental results. However,the arguments adopted in the literature to explain why Kf < Ktare questionable. Stresses along the surface of notch root radiusare more relevant than a stress level at some distance below thesurface.

    5.3. Some comments on fatigue of welded joints

    6. The number of variables of welded joints which are signicantfor the fatigue properties of a welded structure is very large.As a result it is difcult for a designer to arrive at well docu-mented rules to obtain trustworthy estimates of the fatiguelimit and the fatigue life of a welded structure. Much experienceis presented in the Recommendations for Fatigue Design ofWelded Joints and Components published by the InternationalInstitute of Welding. Experience and engineering judgement areessential to deal with fatigue prediction problems of weldedstructures.the SN curve are not necessarily interrelated.8. The new concept of the effective notch stress has been pro-

    posed to arrive at a prediction model for obtaining SN curvesfor welded joints. Kt-values derived with this model can beinstructive for revealing the severity of the stress level at theroot of a weld. However, for this purpose the model should beimproved by replacing the ctitious root radius by a ratio ofthe radius and the local plate thickness of the structure. Thesuggestion that the effective notch stress concept can be usedfor predictions on SN curves of a welded structure ismisleading.

    9. A profound FE analysis of the entire welded structure is a pow-erful tool for design purposes to indicate the most fatigue crit-ical locations in a structure. Results of the maximum stresslevels thus obtained can be evaluated for achieving a satisfac-tory design including safety considerations.

    Acknowledgment

    Correspondence with professor C.M. Sonsino was informativeand stimulated the author to write the present paper.

    References

    [1] Schijve J. Fatigue of structures and materials. 2nd ed. Springer; 2009.[2] Sonsino CM. Comparison of different local design concepts for the structural

    durability assessment of welded offshore K-nodes. Int J Fatigue2012;34:2734.

    [3] Wanhill RJH. Durability analysis using short and long fatigue crack growthdata. Aircraft Damage Assessment and Repair. The Institution of Engineering,Australia. Barton: Australia; 1991.

    [4] Atkinson JD, Lindley TC. Effect of stress waveform and hold-time onenvironmentally assisted fatigue crack propagation in a C-Mn structuralsteel. Met Sci 1979;13:4448.

    [5] Schijve J. The signicance of fracture mechanisms for the application offracture mechanics to fatigue crack growth in Al-alloy structures andmaterials. In: Proc USAF aircraft structural integrity program conference, SanAntonio, 1999.

    [6] Frost NE, Phillips CE. Studies in the formation and propagation of cracks infatigue specimens. In: Proc int conference on fatigue of metals, London,September 1956. The Institution of Mechanical Engineers, 1956. p. 52026.

    [7] Frost NE, Marsh KJ, Pook LP. Metal fatigue. Oxford: Clarendon; 1974.[8] Neuber H. Kerbspannungslehre. Springer, Berlin, 1937 [2nd ed. 1958].

    Translation: theory of notch stresses [Edwards JW, Trans.], Ann Arbor:Michigan; 1946.

    [9] Peterson RE. Stress concentration factors. New York: John Wiley & Sons; 1974.[10] Kuhn P, Hardrath HF. An engineering method for estimating notch-size effect

    in fatigue tests of steel. Report NACA TN 2805, 1952.[11] Radaj D. Review of fatigue strength assessment of nonwelded and welded

    structures based on local parameters. Int J Fatigue 1996;18:15370.[12] Radaj D, Sonsino CM, Fricke W. Fatigue assessment of welded joints by local

    approaches. 2nd ed. Woodhead Publishing Limited; 2006.[13] Hobbacher A. Recommendations for fatigue design of welded joints and

    components. IIW document IIW-1823-07, December 2008.[14] Morgenstern C, Sonsino CM, Hobbacher A, Sorbe F. Fatigue design of

    aluminium welded joints by the local stress concept with the ctitiousnotch radius of rf = 1 mm. Int J Fatigue 2006;28:88190.

    [15] Sonsino CM, Bruder Th, Baumgartner J. SN lined for welded thin joints suggested slopes and FAT values for applying the notch stress concept withvarious reference radii. Weld World 2010;54:R375.

    [16] Schijve J. Fatigue predictions of welded joints and the effective notch stressconcept. Int J Fatigue 2012;45:318.

    The significance of fatigue crack initiation for predictions of the fatigue limit of specimens and structures1 Introduction2 Crack initiation and the fatigue limit3 The prediction of the fatigue limit of notched specimens3.1 Prediction method of Neuber3.2 Prediction method of Peterson

    4 Fatigue of welded joints4.1 The fatigue limit of welded joints4.2 The concept of the effective notch stress4.3 Full-scale fatigue tests on a large welded structure reported by Sonsino

    5 Summarizing conclusions5.1 Elementary comments5.2 About the fatigue limit and notch effects5.3 Some comments on fatigue of welded joints

    AcknowledgmentReferences