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Fatigue of Structures and Materials by Schijve | Fatigue (Material) | Fracture

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Reprinted here with kind permission from the publishers. International Journal of Fatigue 25 (2003) 679–702 www.elsevier.com/locate/ijfatigue Review article Fatigue of structures and materials in the 20th century and the state of the art J. Schijve ∗ Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629HS Delft, The Netherlands Received 30 October 2002; received in revised form 22 January 2003; accepted 4 February 2003 Abstract The paper surveys the historical
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  International Journal of Fatigue 25 (2003) 679–702www.elsevier.com/locate/ijfatigue Review article Fatigue of structures and materials in the 20th century and thestate of the art  J. Schijve ∗  Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629HS Delft, The Netherlands Received 30 October 2002; received in revised form 22 January 2003; accepted 4 February 2003 Abstract The paper surveys the historical development of scientific and engineering knowledge about fatigue of materials and structuresin the 20th century. This includes fatigue as a material phenomenon, prediction models for fatigue properties of structures, andload spectra. The review leads to an inventory of the present state of the art. Some final remarks follow in an epilogue.  2003 Elsevier Science Ltd. All rights reserved. Keywords: Fatigue mechanism; Fatigue properties; Prediction; Load spectra; History Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6802. Fatigue of materials as a physical phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6822.1. Fatigue crack initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6822.2. Fractographic observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6832.3. More about fatigue crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6843. The S-N curve and the fatigue limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6873.1. Aspects of the S-N curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6873.2. The fatigue limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6884. Predictions and fatigue damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6894.1. The engineering need for prediction models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6894.2. Predictions based on the similarity of conditions (CA-loading) . . . . . . . . . . . . . . . . . 6904.3. Predictions based on fatigue damage accumulation (VA-loading) . . . . . . . . . . . . . . . . 6914.3.1. Fatigue damage description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6924.3.2. Fatigue crack growth under VA loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6935. Load spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6946. Evaluation of the present state of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6966.1. Prediction of the fatigue limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 ∗ Tel.: + 1-31-15-3695-194.  E-mail address: J.Schijve@lr.tudelft.nl (J. Schijve).  This paper was a keynote presentation at ECF14, Krakow, Poland,8–13 September 2002 and is reproduced by kind permission of EMAS Publishing. 0142-1123/03/$ - see front matter  2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0142-1123(03)00051-3 Reprinted here with kind permission from the publishers.  680 J. Schijve / International Journal of Fatigue 25 (2003) 679–702 6.2. Predictions of the fatigue life under CA loading . . . . . . . . . . . . . . . . . . . . . . . . . . 6976.3. Predictions on the fatigue strength of joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6986.4. Fatigue damage accumulation under VA loading . . . . . . . . . . . . . . . . . . . . . . . . . . 6986.5. Some ‘ smart ’ ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6997. Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 Nomenclature CA Constant amplitudeVA Variable amplitudeOL OverloadS f  Fatigue limit 1. Introduction An evaluation of fatigue of structures and materialsin the 20th century raises the question what happened inthe 19th century? The answer is that fatigue of structuresbecame evident as a by-product of the industrial revol-ution in the 19th century. In some more detail, it wasrecognized as a fracture phenomenon occurring after alarge numbers of load cycles where a single load of thesame magnitude would not do any harm. Fatigue failureswere frequently associated with steam engines, loco-motives and pumps. In the 19th century, it was con-sidered to be mysterious that a fatigue fracture did notshow visible plastic deformation. Systematic fatiguetests were done at a few laboratories, notably by AugustWo ¨ hler. It was recognized that small radii in thegeometry of the structure should be avoided. Fatigue wasconsidered to be an engineering problem, but the fatiguephenomenon occurring in the material was still largelyin the dark. Some people thought that fatigue implied achange from a fi brous to a crystalline, brittle structurein view of the absence of visible plastic deformation.A fundamental step regarding fatigue as a materialproblem was made in the beginningof the 20th centuryby Ewing and Humfrey in 1903[1].They carried out a microscopic investigation which showed that fatiguecrack nuclei start as microcracks in slip bands. Muchmore evidence about fatigue as a material phenomenonwas going to follow in the 20th century.Fatigue as a technical problem became evident aroundthe middle of the 19th century. About 100 years later,in the middle of the 20th century, the development of fatigue problems were reviewed in two historical papers by Peterson in 1950[2]and Timoshenko in 1954[3]. Both authors were already well-known for importantpublications. Peterson reviewed the discussion on fatigueproblems during meetings of the Institution of Mechan-ical Engineers at Birmingham held just before 1850. Healso mentioned historical ideas about fatigue as amaterial phenomenon and the microscopic studies car-ried out by Gough and co-workers and others around1930. Crack initiation occurred in slip bands and(quoting Peterson) “ one or more of these minute sourcesstarts to spread and this develops into a gross crack which, in general, meanders through the grains in zig- zag fashion in an average direction normal to the direc-tion of tensile stresses. It should be remembered, how-ever, that although the fractured surface generally fol-lows a normal stress field, the microscopic source of  failure is due to shear  ” . Peterson also refers to the con-cept of the ‘ endurance limit ’ , as already de fi ned byWo ¨ hler. In this paper the endurance limit is generallyreferred to as the fatigue limit which is an importantmaterial property for various engineering predictionson fatigue.Timoshenko in his review discussed the signi fi canceof stress distributions and emphasized stress concen-trations around notches. According to Timoshenko, theimportance was recognized by design engineers aroundthe end of the 19th century, and the knowledge wasfurther re fi ned in the beginning of the 20th century.Timoshenko referred to the signi fi cance of theoreticalstress analysis employing complex variables (Kolosov,Inglis, Mushkelisvili, Savin and others). But he con-sidered experimental studies on stress distributions andstress concentrations to be of prime importance. He men-tioned several developments on strain measurements,basically by using mechanical displacement meters,strain gauges and photo-elastic models. A famous book published in 1950 was Handbook of Experimental StressAnalysis by Hete ´ nyi[4].Timoshenko thought that great progress had been made. He also raised the question “ how does a high, localized stress weaken a machine part in service? This important question can be satisfac-  681  J. Schijve / International Journal of Fatigue 25 (2003) 679  – 702 torily answered only on the basis of an experimentalinvestigation ” .The above re ´ sume ´ of developments before 1950 nowseems to be ‘ old stuff  ’ , primarily because substantialimprovements of our present knowledge about fatigueoccurred in the second half of the 20th century. Theimprovements became possible due to the developmentof essentially new experimental facilities, computers andnumerical stress analysis. However, some basic conceptsremained, such as that fatigue in metallic materials isdue to cyclic slip, and stress concentrations contributeto a reduced fatigue endurance. One other characteristicissue of a more philosophical nature also remained, thequestion of whether fatigue is a material problem or anengineering problem, or both in some integrated way?The present paper primarily covers developments in thesecond half of the previous century. It is not the purposeto summarize all noteworthy happenings in a historicalsequence, also because informative reviews about thehistory of  ‘ fatigue ’ have been presentedin the lastdec- ades of the 20th century, e.g. by Mann[5],Schu ¨ tz[6],Smith[7]and others. Moreover, collections of signi fi -cant publications have been compiled[8,9].The empha- sis in this paper will be on how the present knowledgewas acquired. The development of fatigue problems of structures and materials in the 20th century was funda-mentally affected by milestone happenings, importantdiscoveries, and various concepts of understandingfatigue phenomena. Furthermore, the approach to solv-ing fatigue problems and the philosophy on the signi fi -cance of fatigue problems is of great interest.The efforts spent on fatigue investigations in the 20thcentury is tremendous, as illustrated by numerous publi-cations. John Mann[10]published books with referencesto fatigue. Later he continued this work to arrive at about100 000 references in the 20th century compared to lessthan 100 in the 19th century. The large number of publi-cations raises an obvious question. Is the problem so dif- fi cult and complex, or were we not clever enough toeliminate fatigue problems of our industrial products?Various conferences on fatigue of structures andmaterials are already planned for the forthcoming yearsof the 21st century implying that the fatigue problem isapparently not yet fully solved. If the problem still existsafter 100 years in the previous century, there is some-thing to be explained.In a recenttextbook [11]the author has used the pic- ture shown inFig. 1to survey prediction problems asso-ciated with fatigue properties of structures. The predic-tions are the output of a number of procedures andFig.1presents the scenario of the various aspects involved.The input problems occur in three categories: (i) designwork, (ii) basic information used for the predictions, and(iii) fatigue load spectra to which the structure is sub- jected. Each of the categories contains a number of sep-arate problems, which again can be subdivided into spe- Fig. 1. Survey of the various aspects of fatigue of structures[11]. ci fi c aspects, e.g. ‘  joints ’ cover welded joints,bolted joints, riveted joints, adhesively bonded joints.Fig. 1illustrates that the full problem can be very complexdepending on the structural design, type of material, pro-duction variables, load spectra and environment. Predic-tion models are presented in the literature and softwareis commercially available. The prediction of the fatigueperformance of a structure is the result of many stepsof the procedures adopted, and in general a number of plausible assumptions is involved. It implies that theaccuracy of the fi nal result can be limited, the more soif statistical variables also have to be considered. Thereliability of the prediction should be carefully evalu-ated, which requires a profound judgement, and also so-called engineering judgement, experience andintuition.It has persistently been emphasized in Ref.[11]thatphysical understanding of the fatigue phenomena isessential for the evaluation of fatigue predictions. Adesigner cannot simply rely on the validity of equations.Behind an equation is a physical model and the questionis whether the model is physically relevant for the prob-lem considered. This implies that each topic inFig. 1should also be a relevant subject for research, and thenumber of variables which can affect the fatiguebehavior of a structure is large. Without some satisfac-tory understanding of aspects involved, predictions onfatigue become inconceivable. In this paper, it will besummarized how the understanding in the previous cen-tury has been improved, sometimes as a qualitative con-cept, and in other cases also quantitatively. It shouldalready be said here that qualitative understanding canbe very important, even if a strictly quantitative analysisis not yet possible. The major topics discussed in thefollowing sections are associated with: (i) materialfatigue as a physical phenomenon (Section 2), (ii) theS-N curve and the fatigue limit (Section 3), (iii) predic-tion of fatigue properties (Section 4), and (iv) fatigue  682 J. Schijve / International Journal of Fatigue 25 (2003) 679  – 702 load spectra in service (Section 5). These topics are fi rstdiscussed to see the development of the knowledge aboutfatigue of structures and materials in the 20th century.Afterwards, the text covers an evaluation of the presentunderstanding also in relation to the engineering signi fi -cance (Section 6). The paper is concluded with somegeneral remarks about the present state of the art andexpectations for the 21st century (Section 7). 2. Fatigue of materials as a physical phenomenon 2.1. Fatigue crack initiation As said before, fatigue damage in steel in the 19thcentury was associated with a mysterious crystallizingof a fi brous structure. It was not yet de fi ned in physicalterms. In the fi rst half of the 20th century, cyclic slipwas considered to be essential for microcrack initiation.Cracks, even microcracks, imply decohesion in thematerial and should thus be considered to be damage.But is cyclic slip also damage, and what about cyclicstrain hardening in slip bands? In the thirties, Gough[12]postulated that fatigue crack initiation is a consequenceof exceeding the limit of local strain hardening. The ideawas adopted by Orowan in 1939[13]who argued thatthe local exhaustion of ductility leads to a localizedincrease of the stress and ultimately tocracking. Thisconcept was used in 1953 by Head[14]in a model forobtaining an equation for fatigue crack growth.An important question about the ductility exhaustiontheory is how cracking occurs on an atomic level. Stroh[15]analyzed the stress fi eld around a piled-up group of dislocations. According to him, the local stress canbecome suf  fi ciently high to cause local cleavage. How-ever, it was dif  fi cult to see why high local stresses cannot be relaxed near the material surface by plastic defor-mation in a basically ductile material. The ductilityexhausting theory did not become a credible crack initiation model, the moreso sincethe detection of stri-ations in the late 1950s[16,17]indicated that crack extension occurred in a cycle-by-cycle sequence, and notin jumps after intervals of cycles required for an increas-ing strain-hardening mechanism.In the 1950s, the knowledge of dislocations had beenwell developed. Cyclic slip was associated with cyclicdislocation movements. It is not surprising that peopletried to explain the initiation and crack growth in termsof creating crevices in the material or intrusions into thematerial surface as a result of some speci fi c dislocationmobilities. Interesting dislocation models were proposedin the 1950s, noteworthyby Cottrell and Hull, based onintersecting slip systems[18],and by Mott, based on generation of vacancies[19].Microscopic observations were made to see whether the proposed models for crack initiation and crack growth were in agreement with amodel. Severalpapers of historicalinterest were col- lected in 1957[20]and 1959[21]respectively. The microscopic work of Forsyth[22]on extrusions and intrusions in slip bands should be mentioned, seeFig. 2.Similar fi gures have been used by several authors to dis-cuss basic aspects of the fatigue crack initiation process.Three fundamental aspects are: the signi fi cance of thefree material surface, the irreversibility of cyclic slip,and environmental effects on microcrack initiation.Microcracks usually start at the free surface of thematerial, 1 also in unnotched specimens with a nominallyhomogeneous stress distribution tested under cyclic ten-sion. The restraint on cyclic slip is lower than inside thematerial because of the free surface at one side of thesurface material. Furthermore, microcracks start moreeasily in slip bandswith slip displacements normal tothe material surface[23]which seems to be logical when looking atFig. 2.It still remains to be questioned why cyclic slip is not reversible. Already in the 1950s, it wasunderstood that there are two reasons for non-reversi-bility. One argument is that (cyclic) strain hardeningoccurs which implies that not all dislocations return totheir srcinal position. Another important aspect is theinteraction with the environment. A slip step at the freesurface implies that fresh material is exposed to theenvironment. In a non-inert environment, most technicalmaterials are rapidly covered with a thin oxide layer, orsome chemisorption of foreign atoms of the environmentoccurs. An exact reversibility of slip is then prevented.  A valid and important conclusion is that fatigue crack initiation is a surface phenomenon .In the 1950s, microscopical investigations were stillmade with the optical microscope. It implies that crack nucleation is observed on the surface where it indeedoccurs. As soon as cracks are growing into the materialaway from the free surface, only the ends of the crack front can be observed at that free surface. It is question-able whether that information is representative for thegrowth process inside the material, a problem sometimesoverlooked. Microscopic observations on crack growthinside the material require that cross-sections of a speci- Fig.2. Geometry of slip at the material surface according to Forsyth[16]. 1 Microcrack initiation in certain alloys can also start at inclusionsclose to the surface, and even more subsurface due to residual stressdistributions.
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