Lecture 12.1: Basic Introduction to FatigueOBJECTIVE/SCOPE:To summarize the main factors affecting fatigue strength, as opposed to static strength, of welded joints and to illustrate the method of carrying out a fatigue check.PREREQUISITESLecture 11.1.2: Introduction to Connection DesignLecture 11.2.1: Generalities on Welded ConnectionsRELATED LECTURESLecture 12.12: Determination of Stress Intensity FactorsLecture 12.13: Fracture Mechanics Applied to FatigueSUMMARYThis lecture gives an explanation of the mechanism of fatigue and the influence of welding on that mechanism. It summaries the primary factors affecting fatigue strength and introduces S-N Curves. The classification of fatigue details is presented and important details reviewed. The calculation of stress range is summarised. The principal types of fatigue loading and the bases for their calculation are presented with an introduction to cycle counting and damage calculations for mixed amplitude loading.NOTATIONa design weld strength parameterDsRstress rangeDsDnon-propagating stress, i.e. the constant amplitude stress range below which cracks will not growN endurance number of cycles.1. INTRODUCTION1.1 Nature of FatigueFatigue is the mechanism whereby cracks grow in a structure. Growth only occurs under fluctuating stress. Final failure generally occurs in regions of tensile stress when the reduced cross-section becomes insufficient to carry the peak load without rupture. Whilst the loading on the structure is stationary the crack does not grow under normal service temperatures. Many structures, such as building frames, do not experience sufficient fluctuating stress to give rise to fatigue problems. Others do, such as bridges, cranes, and offshore structures, where the live loading is a higher proportion of the total load.1.2 How Welds FatigueIn welded steel structures, fatigue cracks will almost certainly start to grow from welds, rather than other details, because: Most welding processes leave minute metallurgical discontinuities from which cracks may grow. As a result, the initiation period, which is normally needed to start a crack in plain wrought material, is either very short or no-existent. Cracks therefore spend most of their life propagating, i.e. getting longer. Most structural welds have a rough profile. Sharp changes of direction generally occur at the toes of butt welds and at the toes and roots of fillet welds, see Figure 1. These points cause local stress concentrations of the type shown in Figure 2. Small discontinuities close to these points will therefore react as though they are in a more highly stressed member and grow faster.

1.3 Crack Growth HistoryThe study of fracture mechanisms shows that the growth rate of a crack is proportional to the square root of its length, given the same stress fluctuation and degree of stress concentration. For this reason fatigue cracks spend most of their life as very small cracks which are hard to detect. Only in the last stages of life does the crack start to cause a significant loss of cross-section area, as shown in Figure 3. This behaviour poses problems for in-service inspection of structures.

2. FATIGUE STRENGTH2.1 Definition of Fatigue Strength and Fatigue LifeThe fatigue strength of a welded component is defined as the stress range (R) which fluctuating at constant amplitude, causes failure of the component after a specified number of cycles (N). The stress range is the difference between the maximum and minimum points in the cycle, see Figure 4. The number of cycles to failure is known as the endurance or fatigue life.

2.2 Primary Factors Affecting Fatigue LifeFor practical design purposes there are two main factors which affect the fatigue life of a detail, namely: The stress range (R) at the location of crack initiation. There are special rules for calculating this range. The fatigue strength of the detail. This strength is primarily a function of the geometry and is defined by the parameter 'a', which varies from joint to joint.The fatigue life (N), or endurance, in number of cycles to failure can be calculated from the expression:

where m is a constant, which for most welded details is equal to 3. Predictions of life are therefore particularly sensitive to accuracy of stress prediction.2.3 S-N CurveThe expression linking N andRmcan be plotted on a logarithmic scale as a straight line, Equation (2), and is referred to as an S-N curve. An example is shown in Figure 5. The relationship holds for a wide range of endurance. It is limited at the low endurance end by static failure when the ultimate material strength is exceeded. At endurances exceeding about 5-10 million cycles the stress ranges are generally too small to permit propagation under constant amplitude loading. This limit is called the non-propagating stress (D). Below this stress range cracks will not grow.

For design purposes it is usual to use design S-N curves which give fatigue strengths about 25% below the mean failure values, as shown in Figure 5. 'a' is used to define these lines.2.4 Effect of Mean StressIn non-welded details the endurance is reduced as the mean stress becomes more tensile. In welded details the endurance is not usually reduced in those circumstances. This behaviour occurs because the weld shrinkage stresses (or residual stresses), which are locked into the weld regions at fabrication, often attain tensile yield. The crack cannot distinguish between applied and residual stress. Thus, for the purposes of design, the S-N curve always assumes the worst, i.e. that the maximum stress in the cycle is at yield point in tension. It is particularly important to appreciate this point as it means that fatigue cracks can grow in parts of members which are nominally 'in compression'.2.5 Effect of Mechanical StrengthThe rate of crack growth is not significantly affected by variations in proof stress or ultimate tensile strength within the range of low alloy steels used for general structural purposes. These properties only affect the initiation period, which, being negligible in welds, results in little influence on fatigue life. This behaviour contrasts with the fatigue of non-welded details where increased mechanical strength generally results in improved fatigue strength, as shown in Figure 6.

3. CLASSIFICATION OF DETAILS3.1 Detail ClassesThe fatigue strength parameter (K2) of different welded details varies according to the severity of the stress concentration effect. As there are a wide variety of detail in common use, details with similar K2values are grouped together into a single detail class and given a single K2value.This data has been obtained from constant amplitude fatigue tests on simple specimens containing different welded detail types. For the most commonly used details, it has been found convenient to divide the results into fourteen main classes. The classes are:

As shown in Figure 7, these classes can be plotted as a family of S-N curves. The difference in stress range between neighbouring curves is usually between 15 and 20%.

The above table has been taken from Eurocode 3 [1]. It does not include S-N data for unstiffened hollow tubular joints.3.2 Detail TypesThere are usually a number of detail types within each class. Each type has a very specific description which defines the geometry both microscopically and macroscopically. The main features that affect the detail type, and hence its classification, are: Form of the member:e.g. plate, rolled section, reinforcing bar. Location of anticipated crack initiation:The location must be defined with respect to the direction of stress fluctuation. A given structural joint may contain more than one potential initiation site, in which case the joint may fall into two or more detail types. Leading dimensions:e.g. weld shape, size of component, proximity of edges, abruptness of change of cross-section. Fabrication requirements:e.g. type of weld process, any grinding smooth of particular parts of the joint. Inspection requirements:Special inspection procedures may be required on higher class details to ensure that detrimental welding defects are not present.It should be noted that if fatigue is critical in the design, the extra controls on fabrication incurred by the last two requirements may increase the total cost significantly above that for purely static strength.Examples of different types of welded detail and their classes are shown in Eurocode 3: Part 1.1 [1].3.3 Commonly Used Detail TypesFigure 8 shows some of the most important details to look out for in welded steelwork.

They are: Load carrying fillet welds and partial penetration butt welds. These details are category 36 for failure starting at the root and propagating through the throat. Welded attachments on edges. They are category 45. Note that the attachment weld may not be transferring any stress. Failure is from the weld toe into the member. Ends of long flat plates, e.g. cover plates are category 50. Most short attachments in the stress direction are category 80 or 71 as long as they are not at an edge. Transverse full penetration butt welds can range from category 12,5 to 36 depending on how they are made. Long continuous welds on site welded structures are found to be category 100.It should be borne in mind that most potential fatigue sites on welded structures are found to be category 80 or below.4. STRESS PARAMETERS FOR FATIGUE4.1 Stress AreaThe stress areas are essentially similar to those used for static design. For a crack starting at a weld toe, the cross-section of the member through which propagation occurs is used. For a crack starting at the root, and propagating through the weld throat, the minimum throat area is used, as shown in Figure 8a.4.2 Calculation of Stress RangeThe force fluctuation in the structure must be calculated elastically. No plastic redistribution is permitted.The stress on the critical cross-section is the principal stress at the position of the weld toe (in the case of weld toes cracks). Simple elastic theory is used assuming plane sections remain plane, see Figure 9. The effect of the local stress concentration caused by the weld profile is ignored as this is already catered for by the parameter 'd' which determines the weld class.

In the case of throat failures, the vector sum of the stresses on the weld throat at the position of highest vector stress along the weld is used, as in static design.Exceptions to these rules occur in the case of unstiffened joints between slender members such as tubes. In this case the stress parameter is the Hot Spot Stress. This stress is calculated at the point of expected crack initiation, taking into account the true elastic deformation in the joint, i.e. not assuming plane sections to remain plane.4.3 Effects of Geometrical Stress Concentrations and Other EffectsWhere a member has large changes in cross-section, e.g. at access holes, there will be regions of stress concentration due to the change of geometry. In static design the stresses are based on the net area as plastic redistribution will normally reduce these peaks at ultimate load. With fatigue this is not so, and if there is a welded detail in the area of the geometrical stress raiser the true stress must be used, as shown in Figure 10.

4.4 Secondary EffectsSimilarly any secondary effects, such as those due to joint fixity in latticed structures, and shear lag and other distortional effects in slender beams, are allowed for in calculating the stresses.5. LOADINGS FOR FATIGUE5.1 Types of LoadingExamples of structures and the loads which can cause fatigue are:Bridges: Commercial vehicles, goods trainsCranes: Lifting, rolling and inertial loadsOffshore structures: WavesSlender chimneys: Wind gustingThe designer's objective is to anticipate the sequence of service loading throughout the structure's life. The magnitude of the peak load, which is vital for static design purposes, is generally of little concern as it only represents one cycle in millions. For example, highway bridge girders may experience 100 million significant cycles in their lifetime. The sequence is important because it affects the stress range, particularly if the structure is loaded by more than one independent load system.For convenience, loadings are usually simplified into a load spectrum, which defines a series of bands of constant load levels, and the number of times that each band is experienced, as shown in Figure 11.

Slender structures, with natural frequencies low enough to respond to the loading frequency, may suffer dynamic magnification of stress. This magnification can shorten the life considerably.A useful source of information on fatigue loading is Eurocode 1 [2].5.2 Cycle CountingIn practice most stress histories in real structures are of the variable amplitude type, shown in Figure 12, as opposed to the constant amplitude shown in Figure 4. Such histories pose a problem in defining the number and amplitude of the cycles.

The first step is to break the sequence into a stress spectrum as shown in Figure 12 using a cycle counting method. There are various methods in use. The two most used are the Rainflow Method and the Reservoir Method. The latter, which is easy to use by hand for short stress histories, is described inLecture 12.2. The former is more convenient for analysing long stress histories using a computer.6. CALCULATION OF DAMAGEUnder variable amplitude loading the life is estimated by calculation of the total damage done by each cycle in the stress spectrum. In practice the spectrum is simplified into a manageable number of bands, as shown in Figure 13.

The damage done by each band in the spectrum is defined aswhere n is the required number of cycles in the band during the design life and N is the endurance under that stress range, see Figure 14.

If failure is to be prevented before the end of the specified design life, the Palmgren-Miner's Rule must be compiled with. This rule states that the damage done by all bands together must not exceed unity, i.e.:

It should be noted that, when variable amplitude loading occurs, the bands in the spectrum withvalues less thanDmay still cause damage. Damage occurs because the larger amplitude cycles may start to propagate the crack. Once it starts to grow lower cycles become effective. In this case, the horizontal constant amplitude fatigue limitDshown in Figure 5, is replaced by a sloping line with a log gradient of.7. CONCLUDING SUMMARY Fatigue and static failure (whether by rupture or buckling) are dependent on very different factors, namely:- Fatigue depends on the whole service loading sequence (not one extreme load event).- Fatigue of welds is not improved by better mechanical properties.- Fatigue is very sensitive to the geometry of details.- Fatigue requires more accurate prediction of elastic stress.- Fatigue makes more demands on workmanship and inspection. It is therefore important to check early in the design whether fatigue is likely to be critical. Acceptable margins of safety against static collapse cannot be relied upon to give adequate safety against fatigue. Areas with a high live/dead stress ratio and low category 36 details should be checked first. The check must cover any welded attachment to a member, however insignificant, and not just the main structural connections. Note that this check should include welded additions to the structure in service. If fatigue is critical, then the choice of details will be limited. Simplicity of detail and smoothness of stress path should be sought. Be prepared for fatigue critical structures to cost more.8. REFERENCES[1] Eurocode 3: "Design of Steel Structures": ENV1993-1-1: Part 1.1: General Rules and Rules for Buildings, CEN 1992.[2] Eurocode 1: "Basis of Design and Actions on Structures", CEN (in preparation).9. ADDITIONAL READING1. Maddox, S.J. "Fatigue Strength of Welded Structures", Cambridge, Abington Publishing, 1991.2. Gurney, T. R., "Fatigue of Welded Structures", 2nd ed., Cambridge University Press, 1991.3. Narayanan, R. (ed), "Structures Subjected to Repeated Loading", London, Elsevier Applied Science, 1991.

Lecture 12.2: Advanced Introduction toFatigueOBJECTIVE/SCOPE:To introduce the main concepts and definitions regarding the fatigue process and to identify the main factors that influence the fatigue performance of materials, components and structures.PREREQUISITESLecture 12.1: Basic Introduction to FatigueRELATED LECTURESSUMMARYThe physical process of the initiation of fatigue cracks in smooth and notched test specimens under the influence of repeated loads is described and the relevance of this process for the fatigue of real structures is discussed.The basis of different stress cycle counting procedures is explained for variable amplitude loading. Exceedance diagram and frequency spectrum effects are described.1. INTRODUCTIONFatigue is commonly referred to as a process in which damage is accumulated in a material undergoing fluctuating loading, eventually resulting in failure even if the maximum load is well below the elastic limit of the material. Fatigue is a process of local strength reduction that occurs in engineering materials such as metallic alloys, polymers and composites, eg. concrete and fibre reinforced plastics. Although the phenomenological details of the process may differ from one material to another the following definition given by ASTM [1] encompasses fatigue failures in all materials:Fatigue - the process ofprogressive localisedpermanent structural change occurring in a material subjected to conditions that produce fluctuating stresses and strains at some point or points and that may culminate in cracks or complete fracture after a sufficient number of fluctuations.The important features of the process relevant to fatigue in metallic materials are indicated by the underlined words in the definition above. Fatigue is a progressive process in which the damage develops slowly in the early stages and accelerates very quickly towards the end. Thus the first stage consists of a crack initiation phase, which for smooth and mildly notched parts that are subjected to small loads cycles may occupy more than 90 percent of the life. In most case cases the initiation process is confined to a small area, usually of high local stress, where the damage accumulates during stressing. In adjacent parts of the components, with only slightly lower stresses, no fatigue damage may occur and these parts thus have an infinite fatigue life. The initiation process usually results in a number of micro-cracks that may grow more or less independently until one crack becomes dominant through a coalescence process at the microcracks start to interact. Under steady fatigue loading this crack grows slowly, but starts to accelerate when the reduction of the cross-section increases the local stress field near the crack front. Final failure occur as an unstable fracture when the remaining area is too small to support the load. These stages in the fatigue process can in many cases be related to distinctive features of the fracture surface of components that have failed under fluctuating loads, the presence of these features can therefore be used to identify fatigue as the probable cause of failure.2. CHARACTERISTICS OF FATIGUE FRACTURE SURFACESTypical fracture surfaces in mechanical components that were subjected to fatigue loads are shown in Slide 1. One characteristic feature of the surface morphology which is evident in both macrographs is the flat, smooth region of the surface exhibiting beach marks (also called clamshell marks). This part represents the portion of the fracture surface over which the crack grew in a stable, slow mode. The rougher regions, showing evidence of large plastic deformation, is the final fracture area through which the crack progressed in an unstable mode. The beach marks may form concentric rings that point toward the areas of initiation. The origin of the fatigue crack may be more or less distinct. In some cases a defect may be identified as the origin of the crack, in other cases there is no apparent reason why the crack should start at a particular point in a fracture surface. If the critical section is at a high stress concentration fatigue initiation may occur at many points, in contrast to the case of unnotched parts where the crack usually grows from one point only see Figure 1. While the presence of any defects at the origin may indicate the cause of the fatigue failure, the crack propagation area may yield some information regarding the magnitude of the fatigue loads and also about the variation in the loading pattern. Firstly, the relative magnitude of the areas of slow-growth and final fracture regions give an indication of the maximum stresses and the fracture toughness of the material. Thus, a large final fracture area for a given material indicates a high maximum load, whereas a small area indicates that the load was lower at fracture. Similarly, for a fixed maximum stress, the relative area corresponding to slow crack growth increases with the fracture toughness of the material (or with the tensile strength if the final fracture is a fully ductile overload fracture).

Slide 1 : Typical fatigue failures in steel components.Beach marks are formed when the crack grows intermittently and at different rates during random variations in the loading pattern under the influence of a changing corrosive environment. Beach marks are therefore not observed in the surfaces of fatigue specimens tested under constant amplitude loading conditions without any start-stop periods. The average crack growth is of the order of a few millimetres per million cycles in high cycle fatigue, and it is clear that the distance between bands in the beach marks are not a measure of the rate of crack advance per load cycle. However, examination by electron microscope at magnifications between 1,000x and 30,000x may reveal characteristic surface ripples called fatigue striations, see Slide 2. Although somewhat similar in appearance, these lines are not the beach marks described above as one beach mark may contain thousands of striations. During constant amplitude fatigue loading at relatively high growth rates in ductile material such as stainless steels and aluminium alloys the striation spacing represents the crack advancement per load cycle. However, in low stress, high cycle fatigue where the striation spacing is less than one atomic spacing (- 2.5 x 10-8m) per cycle. Under these conditions the crack does not advance simultaneously along the crack front, growth occurring instead only along some portions during a few cycles, then arrests while growth occurs along other segments. Striations as shown in Figure 3 are not seen if the crack grows by other mechanisms such as microvoid coalescence or, in brittle materials, microclevage. In structural steels the crack can propagate by all three mechanism, and striations may be difficult to observe. Slide 3 shows an example of beach marks and striations in the fracture originating at a large defect in a welded C-Mn steel with a yield strength of about 360Mpa.

Slide 2 : Striations in an aluminium alloy.

Slide 3 : Fatigue failures in the Alexander L Kielland platform.

3. NATURE OF THE FATIGUE PROCESSFrom the description of the characteristics of fatigue fracture surfaces, three stages in the fatigue process may be identified:Stage I: Crack initiationStage II: Propagation of one dominant crackStage III: Final fractureFatigue cracking in metals is always associated with the accumulation of irreversible plastic strain. The crack process which is discussed in the following applies to smooth specimens made of ductile materials.In high cycle fatigue the maximum stress in cyclic loads that eventually cause fatigue failure may be well below the elastic limit of the material, and large scale plastic deformation does not occur. However, at a free surface plastic strains may accumulate as a result of dislocation movements. Dislocations are line defects in the lattice structure which can move and multiply under the action of shear stresses, leaving a permanent deformation. Dislocation mobility and hence the amount of deformation (or slip) is greater at a free surface than in the interior of crystalline materials due to lack of constraint from grain boundaries. Grains in polycrystalline structural metals are individually oriented in a random manner. Each grain, however, has an ordered atomic structure giving rise to directional properties. Deformation for example, takes place on crystallographic planes of easy slip along which dislocations can move more easily than other planes. Since slip is controlled primarily by shear stress, slip deformation takes place along crystallographic planes that are orientated close to 45to the tensile stress direction. The results of such deformation is atomic planes sliding relative to each other, resulting in a roughening of the surface in slip bands. During further cycling slip band deformation is intensified at the surface and extending into the interior of the grain, resulting in so-called persistent slip bands, (PSB's). The name originated from the observation in early studies of fatigue that slip band would reappear - "persist" - at the same location after a thin surface layer was removed by elastopolishing. The accumulation of local plastic flow result in surface ridges and troughs called extrusions and intrusions, respectively, Figure 2. The cohesion between the layers in slip band is weakened by oxidation of fresh surfaces and hardening of the strained material. At some point in this process small cracks develop in the intrusions. These microcracks grow along slip planes, ie. a shear stress driven process. Growth in the shear mode, called stage I crack growth extends over a few grains. During continued cycling the microcracks in different grains coalesce resulting in one or a few dominating cracks. The stress field associated with the dominating crack cause further growth under the primary action of maximum principal stress; this is called stage II growth. The crack path is now essentially perpendicular to the tensile stress axis. Crack advancement is, however, still influenced by the crystallographic orientation of the grains and the crack grows in a zigzag path along slip planes and cleavage planes from grain to grain, see Figure 3. Most fatigue cracks advance across grain boundaries as indicated in Figure 3, ie. in a transcrystalline mode. However, at high temperatures or in a corrosive environment, grain boundaries may become weaker than the grain matrix, resulting in intercrystalline crack growth. The fracture surface created by stage II crack growth are in ductile metals characterised by striations whose density and width can be related to the applied stress level.

Since crack nucleation is related to the magnitude of stress, any stress concentration in the form of external or internal surface flaws can marked reduce fatigue life, in particular when the initiation phase occupies a significant portion of the total life. Thus a part with a smooth, polished surface generally has a higher fatigue strength than one with a rough surface. Crack initiation can also be facilitated by inclusions, which act as internal stress raisers. In ductile materials slip band deformations at inclusions are higher than elsewhere and fatigue cracks may initiate here unless other stress raisers dominate.In high strength materials, notably steels and aluminium alloys, a different initiation mechanism is often observed. In such materials, which are highly resistant to slip deformation, the interface between the matrix and inclusion may be relatively weak, and cracks will start here if decohesion occurs at the inclusion surface, aided by the increased stress/strain field around the inclusion. Slide 4 shows small fatigue cracks originating at inclusions in a high strength steel. Alternatively, a hard brittle inclusion may break and a fatigue crack may initiate at the edges of the cleavage fracture.

Slide 4 : Fatigue crack initiation at an inclusion in a high strength steel alloy.From the discussion above it is evidently not possible to make a clear distinction between crack nucleation and stage I growth. "Crack initiation" is thus a rather imprecise term used to describe a series of events leading to stage II crack. Although the initiation stage includes some crack growth, the small scale of the crack compared with microstructural dimensions such as grain size invalidates a fracture mechanics based analysis of this growth phase. Instead, local stresses and strains are commonly related to material constants in prediction models used to estimate the length of stage I. The material constants are normally obtained from tests on smooth specimens subjected to stress or strain controlled cycling.4. FATIGUE LOADINGThe simplest form of stress spectrum to which a structural element may be subjected is a sinusoidal or constant amplitude stress-time history with a constant mean load, as illustrated in Figure 4. Since this is a loading pattern which is easily defined and simple to reproduce in the laboratory it forms the basis for most fatigue tests. The following six parameters are used to define a constant amplitude stress cycle:

Smax = maximum stress in the cycleSmin = minimum stress in the cycleSm= mean stress in the cycle = (Smax+ Smin)/2Sa= stress amplitude = (SmaxSmin)/2AS = stress range = Smax- Smin= 2SaR = stress ratio = Smin/SmaxThe stress cycle is uniquely defined by any two of these quantities, except combinations of stress range and stress amplitude. Various stress patterns are shown in Figure 5, with definitions in accordance with ISO [2] terminology.

The stress range is the primary parameter influencing fatigue life, with mean stress as a secondary parameter. The stress ratio is often used as an indication of the influence of mean loads, but the effect of a constant mean load is not the same as for a constant mean stress. The difference between S-N curves with constant mean stress or constant R-ratio is discussed in the section on fatigue testing.The test frequency is needed to define a stress history, but in the fatigue of metallic materials the frequency is not an important parameter, except at high temperatures when creep interacts with fatigue, or when corrosion influences fatigue life. In both cases a lower test frequency results in a shorter life.Typical stress-time histories obtained from real structures are one shown in Figure 6. The sequence in Figure 6a has a constant mean stress, individual stress cycles are easily identifiable, and it necessary to evaluate this stress history in terms of stress range only. The more "random" stress variations in Figure 10b is called a broad band process because the power density function (a plot of energy vs. frequency) spans a wide frequency range, in contrast to the one in Figure 6a which contains essentially one frequency. The difference is illustrated in Figure 7. The load history in Figure 6 can be interpreted as a variation of the main load with superimposed smaller excursions that could be caused by eg. second order vibrations or by electronic noise in the load acquisition system. In case of true mean load variations not only the range but also the mean of each cycle needs to be recorded in order to estimate the influence of mean load on the damage accumulation. In both cases it is necessary to eliminate the smaller cycles since they may be below the fatigue limit and therefore cause no fatigue damage, or because they do not represent real load cycles. Thus a more complicated evaluation procedure is required for identifying and counting individual major stress cycles and their associated mean stresses. Counting methods such as the range pair, rainflow and the reservoir methods are designed to achieve this. These procedures are described in paragraph 7.

5. FATIGUE LIFE DATAThe total fatigue life in terms of cycles to failure can be expressed as:Nt = Ni+ Np (1)where Niand Npare number of cycles spent in the initiation and propagation stages, respectively. As noted, the two stages are distinctly different in nature and different material parameters control their length. The life of unnotched components, for example, is dominated by crack initiation. In sharply notched parts, however, or in parts containing crack-life defects, eg. welded joints, the crack growth stage dominates and crack propagation data may be used in an assessment of fatigue life using fracture mechanics analysis. Therefore different test methods are necessary to assess the fatigue properties of these types of components.5.1 Fatigue Strength CurvesFatigue data for components whose lives consist of an initiation phase followed by crack propagation are usually presented in the form of S-N curves, where applied stress S is plotted against total cycles to failure, N (= Nt). As the stress decreases, the life in cycles to failure increases, as illustrated in Figure 8. The S-N curves for ferrous and titanium alloys exhibit a limiting stress below which failure does not occur; this is called the fatigue or the endurance limit. The branch point or "knee" of the curve lies normally in the 105to 107cycle range. In aluminium and other nonferrous alloys there is no stress asymptote and a finite fatigue life exists at any stress level. All materials, however, exhibit a relatively flat curve in the high-cycle region, ie. at lives longer than about 105cycles.

A characteristic feature of fatigue tests is the large scatter in fatigue strength data, this is particularly evident when a number of specimens are tested at the same stress level, as illustrated in Figure 9. Plotting the data for a given stress level along a logarithmic endurance axis gives a distribution which can be approximated by the Gaussian (or normal) distribution, hence endurance data are said to have a log normal distribution. Alternatively the Weibull distribution may be used, but the choice is not important since about 200 specimens, tested at the same stress level, are required to make a statistically significant distinction between the two distributions. This number is about one order of magnitude larger than the quantity of specimens that typically are available for fatigue testing at one stress level.

Assuming the life distribution to be log normal, the associated mean life curve and the standard deviation can be used to define a design S-N curve for any desired probability of failure.When the crack propagation stage dominates fatigue life, design data may be obtained from crack growth curves, an example of which is shown schematically in Figure 10. The stress intensity factor K uniquely describes the stress field near the crack tip, and is therefore used in the design against unstable fracture. Likewise, the range of the stress intensity factor,K, may be expected to govern fatigue crack growth. The validity of this assumption was first proved by Paris [3], and later verified by many other researchers. The crack growth curve, which has a sigmoidal shape, spans three regions as indicated schematically in Figure 10. In Region I the crack growth rate drops off asymptotically asK is reduced towards a limit or threshold,Kth, below which no crack growth takes place. Life fatigue endurance data, crack growth data show considerable scatter and test results must be evaluated by statistical methods in order to derive useful design data.5.2 Fatigue TestingThe basis for any design methodology aimed at preventing fatigue failures is data characterising the fatigue strength of components and structures. Fatigue testing is therefore essential for the fatigue design process. The ideal fatigue test may be defined as a test in which an actual structure is subjected to the service load spectrum of that structure. However, life estimates are required before the design is finalised or details of the loading history are known. Additionally, each structure will experience a particular load history that is unique for that structure, so many simplifications and assumptions need to be made regarding the test stress sequence which is going to represent the many types of service histories that can occur in practice.Fatigue testing is therefore performed in several ways, depending on the stage the design or production of the structure has reached or the intended use of the data. The following four main types of tests can be identified:1. Stress-life testing of small specimens.2. Strain-life testing of small specimens.3. Crack growth testing.4. S-N tests of components.5. Prototype testing for design validation.The first three tests are idealised tests that produce information on the material response. The use of the results from these tests in life prediction of components and structures requires additional knowledge of influencing factors related to the geometry, size, surface condition and corrosive environment. S-N tests of components are also normally standardised tests that make life predictions more accurate compared with the three other tests because the uncertainties regarding the influence of notches and surface conditions are reduced. Service loading or variable amplitude testing normally requires a knowledge of the response of the actual structure to the loading environment, and is therefore normally used only for prototype or component testing at a late stage in the production process.Rotating bending machines were used in the past to generate large amounts of test data in a relatively inexpensive way. Two types are shown schematically in Figure 11. The computer-controlled closed loop testing machines are widely used in all modern fatigue testing laboratories. Most are equipped with hydraulic grips that facilitate the insertion and removal of specimens. A schematic diagram of such a testing machine is shown in Figure 12. These machines are capable of a precise control of almost any type of stress-time, strain-time or load pattern and are therefore replacing other types of testing machines.

5.3 Presentation of Fatigue Test DataAmong the first systematic fatigue investigations reported in the literature are those set up and conducted by the German railway engineer, August Whler, between 1852 and 1870. He performed tests on full scale railway axles and also small scale bending, axial and torsion tests on several types of materials. Typical examples of Whler's original data are shown in Figure 13. These data are presented in what is now well known as Whler or S-N diagrams. Such diagrams are still commonly used in the presentation of fatigue data, although the stress axis is often on a logarithmic scale in contrast to Whler's linear stress axis. Basquin's equation is often fitted to test data, it has the form:SaNb = constant (2)where Sais the stress amplitude, and b is the slope. When both axes have logarithmic scales, Basquin's equation becomes a straight line.

Other types of diagrams are used, for instance to demonstrate the influence of mean stress; examples are the Smith or Haigh diagrams which are shown in Figure 14. Low cycle fatigue data are almost universally plotted in strain vs. life diagrams since strain is a more meaningful and more easily measurable parameter than stress when the stress exceeds the elastic limit.

6. PRIMARY FACTORS AFFECTING FATIGUE LIFEThe difference in fatigue behaviour of full scale machine or structural components as compared with small laboratory specimens of the same material is sometimes striking. In the majority of cases the real life component exhibits a considerably poorer fatigue performance than the laboratory specimen although the computed stresses are the same. This difference in fatigue response can be examined in a systematic manner by evaluating the various factors that influence fatigue strength. Qualitative and quantitative assessments of these effects are presented in the following paragraphs.6.1 Material EffectsEffect of static strength on basic S-N dataFor small unnotched, polished specimens tested in rotating bending or fully reversed axial loading there is a strong correlation between the high-cycle fatigue strengths at 106to 107cycles (or fatigue limit) So, and the ultimate tensile strength Su. For many steel materials the fatigue limit (amplitude) is approximately 50% of the tensile strength, ie. So= 0.5 Su. The ratio of the alternating fatigue strength Soto the ultimate tensile strength Suis called the fatigue ratio. The relationship between the fatigue limit and the ultimate tensile strength is shown in Figure 15 for carbon and alloy steels. The majority of data are grouped between the lines corresponding to fatigue ratios of 0.6 and 0.35. Another feature is that the fatigue strength does not increase significantly for Su>1400 Mpa. Other relationships between fatigue strength and static strength properties based on statistical analysis of test data may be found in the literature.

For real life components, the effects of notches, surface roughness and corrosion reduce the fatigue strength, the effects being strongest for the higher strength materials. The variation in fatigue strength with the tensile strength is illustrated in Figure 16. The data in Figure 16 are consistent with the fact that cracks are quickly initiated in components that are sharply notched or subjected to severe corrosion. The fatigue life then consists almost entirely of crack growth. Crack growth is very little influenced by the static strength of the material, as illustrated in Figure 16, and the fatigue lives of sharply notched parts are therefore almost independent of the tensile strength. An important example is welded joints which always contain small crack-like defects from which crack start growing after a very short initiation period. Consequently the fatigue design stresses in current design rules for welded joints are independent of the ultimate tensile strength.

Crack Growth DataFatigue crack growth rates seem to be much less dependent on static strength properties than crack initiation, at least within a given alloy system. In a comparison of crack growth data for many different types of steel, with yield strengths from 250 to about 2000 Mpa levels of steel, Barsom [4] found that grouping the steels according to microstructure would minimise scatter. His data for ferritic-pearlitic, matensitic and austenitic are shown in Figure 17. Also shown in the same diagram is a common scatter band which indicates a relatively small difference in crack growth behaviour between the three classes of steel. While data for aluminium alloys show a larger scatter than for steels, it is still possible to define a common scatter band. Recognising that different alloy systems seem to have their characteristic crack growth curves, attempts have been made to correlate crack growth data on the basis of the following expression= C (3)An implication of Equation 3 is that at equal crack growth rates, a crack in a steel plate can sustain three times higher stress than the same crack in an aluminium plate. Thus, a rough assessment of the fatigue strength of an aluminium component whose life is dominated by crack growth can be obtained by dividing the fatigue strength of a similarly shaped steel component by three.

6.2 Mean Stress EffectsIn 1870 Whler identified the stress amplitude as the primary loading variable in fatigue testing; however, the static or mean stress also affects fatigue life as shown schematically in Figure 10. In general, a tensile mean stress reduces fatigue life while a compressive mean stress increases life. Mean stress effects are presented either by the mean stress itself as a parameter or the stress ratio, R. Although the two are interrelated through:Sm = Sa (4)the effects on life are not the same, ie. testing with a constant value of R does not have the same effect on life as a constant value of Sm, the difference is shown schematically in Figure 18.

As indicated in Figure 19a, testing at a constant R value means that the mean stress decreases when the stress range is reduced, therefore testing at R = constant gives a better S-N curve than the Sm= constant curve, as indicated in Figure 19b. It should also be noted that when the same data set is plotted in an S-N diagram with R = constant or with Sm= constant the two S-N curves appear to be different, as shown in Figure 20.

The effect of mean stress on the fatigue strength is commonly presented in Haigh diagrams as shown in Figure 21, where Sa/ Sois plotted against Sm/ Su. Sois the fatigue strength at a given life under fully reversed (Sm= 0,R = -1) conditions. Suis the ultimate tensile strength. The data points thus represent combinations of Saand Smgiving that life. The results were obtained for small unnotched specimens, tested at various tensile mean stresses. The straight lines are the modified Goodman and the Soderberg lines, and the curved line is the Gerber parabola. These are empirical relationships that are represented by the following equations:Modified Goodman Sa/So+ Sm/Su= 1 (5)Gerber Sa/ So+ (Sm/ Su)2= 1 (6)Soderberg Sa/ So+ Sm/ Sy= 1 (7)

The Gerber curves gives a reasonably good fit to the data, but some points fall below the line, ie. on the unsafe side. The Goodman line represents a lower of the data, while the Soderberg line is a relatively conservative lower bound that is sometimes used in design. These expressions should be used with care in design of actual components since the effects of notches, surface condition, size and environment are not accounted for. Also stress interaction effect due to mean load variation during spectrum loading might modify the mean stress effects given in the three equations.6.3 Notch EffectsFatigue is a weakest link process which depends on the local stress in a small area. While the higher strain at a notch makes no significant contribution to the overall deformation, cracks may start growing here and eventually result in fracture of the part. It is therefore necessary to calculate the local stress and relate this to the fatigue behaviour of the notched component. A first approximation is to use the S-N curve for unnotched specimens and reduce the stress by the Ktfactor. An example of this approach is shown in Figure 22 for a sharply notched steel specimen. The predicted curve fits reasonably well in the high cycle region, but at shorter lives the calculated curve is far too conservative. The tendency shown in Figure 22 is in fact a general one, namely that the actual strength reduction in fatigues is less than that predicted by the stress concentration factor. Instead the fatigue notch factor Kfis used to evaluate the effect of notches in fatigue. Kfis defined as the unnotched to notched fatigue strength, obtained in fatigue tests:

Kf = (8)From Figure 22 it is evident that Kfvaries with fatigue life, however, Kfis commonly defined as the ratio between the fatigue limits. With this definition Kfis less than Kt, the stress increase due to the notch is therefore not fully effective in fatigue. The difference between Kfand Ktarise from several sources. Firstly, the material in the notch may be subject to cyclic softening during fatigue loading and the local stress is reduced. Secondly, the material in the small region at the bottom of the notch experiences a support effect caused by the constraint from the surrounding material so that the average strain in the critical region is less than that indicated by the elastic stress concentration factor. Finally, there is a statistical variability effect arising from the fact that the highly stressed region at the notch root is small, so there is a smaller probability of finding a weak spot.The notch sensitivity q is a measure of how the material in the notch responds to fatigue cycling, ie. how Kfis related to Kt. q is defined as the ratio of effective stress increase in fatigue due to the notch, to the theoretical stress increase given by the elastic stress concentration factor. Thus, with reference to Figure 21

wheremax,effis the effective maximum stress, see Figure 23. This definition of Kfprovides a scale for q that ranges from zero to unity. When q = 0, Kf= Kt= 1 and the material is fully insensitive to notches, ie. a notch does not lower the fatigue strength. For extremely ductile, low strength materials such as annealed copper, q approaches 0. Also materials with large defects, eg. grey cast iron with graphite flakes have values of q close to 0. Hard brittle materials have values of q close to unity. In general q is found to be a function of both material and the notch root radius. The concept of notch sensitivity therefore also incorporates a notch size effect.

The fatigue notch factor applies to the high cycle range, at shorter lives Kfapproaches unity as the S-N curves for notched and unnotched specimens converge and coincide at N = 1/4 (tensile test). In experimental investigations involving ductile materials it was found that the fatigue notch factor need to be applied only to the alternating part of the stress cycle and not to the mean stress. For brittle materials, however, Kfshould be applied to the mean stress as well.6.4 Size EffectsAlthough a size effect is implicit in the fatigue notch factor approach, a size reduction factor is normally employed in when designing against fatigue. The need for this additional size correlation arises from the fact that the notch size effect saturates at notch root radii larger than about 3-4mm, ie. KfKt, while it is well known from tests on full scale components, also unnotched ones, that the fatigue strength continues to drop off with increasing size, without any apparent limit.The size effect in fatigue is generally ascribed to the following sources: A statistical size effect, which is an inherent feature of the fatigue process the nature of fatigue crack initiation which is a weakest link process where a crack initiates when variables such as internal and external stresses, geometry, defect size and number, and material properties combine to give optimum conditions for crack nucleation and growth. Increasing size therefore produces a higher probability of a weak location. A technological size effect, which is due to the different material processing route and different fabrication processes experienced by large and small parts. Different surface conditions and residual stresses are important aspects of this type of size effect. A geometrical size also called the stress gradient effect. This effect is due to the lower stress gradient present in a thick section compared with a thin one, see Figure 24. If a defect, in the form of a surface scratch or a weld defect, has the same depth in the thin and thick parts, the defect in the thick part will experience a higher stress than the one in the thin part, due to the difference in stress gradient, as indicated in Figure 24. A stress increase effect, due to incomplete geometric scaling of the micro-geometry of the notch. This takes place if the notch radius is not scaled up with other dimensions.

Examples of components for which the latter effect is important are welded joints and threaded fasteners. The critical locations for crack initiation are the weld toe and the thread root, respectively. In both cases the local stress is a function of the ratio of thickness (diameter) to the notch radius. In welds the toe radius is determined by the welding process and is therefore essentially constant for different size joints. The t/r ratio therefore increases and also the local stress when the plate is made thicker, with r remaining constant. A similar situation exists for bolts, due to the fact that the thread root radius is scaled to the thread pitch, rather than the diameter for standard (eg. ISO) threads. Since the pitch increases much slower than the diameter the result is an increase in the notch stress with bolt size. For bolts as well as welded joints the increased notch acuity effect comes in addition to the notch size effect discussed earlier, the result is that the experimentally determined size effects for these components are among the strongest recorded. An example of size effects for welded joints is shown in Figure 25. The solid line represents current design practice, according to eg. Eurocode 3 and the UK Department of Energy Guidance Notes. The equation for this line is given by:= (10)

The exponent n, the slope of the lines in Figure 25a, is the size correction exponent.The experimental data points indicate that the thickness correction with n = 1/4 is on the unsafe side in some cases. As indicated in Figure 25a thickness correction exponent of n = 1/3 instead of the current value of 1/4 gives a better fit to the data in Figure 25a. For unwelded plates and low stress concentration joints in Figure 25b a value of n = 1/5 seems appropriate [7].There is experimental evidence that indicate a relationship between the stress gradient and the size effect. Based on an analysis of experimental data similar the following size reduction factor has been proposed to account for the larger stress gradient found in notched specimens [8].n = 0.10 + 0.15 log Kt (11)6.5 Effects of Surface FinishAlmost all fatigue cracks nucleate at the surface since slip occurs easier here than in the interior. Additionally, simple fracture mechanics considerations show that surface defects and notches are much more damaging than internal defects of similar size. The physical condition and stress situation at the surface is therefore of prime importance for the fatigue performance. One of the important variables influencing the fatigue strength, the surface finish, commonly characterised by Ru, the average surface roughness which is the mean distance between peaks and troughs over a specified measuring distance. The effect of surface finish is determined by comparing the fatigue limit of specimens with a given surface finish with the fatigue limit of highly polished standard specimens. The surface reduction factor Cris the defined as the ratio between the two fatigue limits. Since steels become increasingly more notch sensitive with higher strength, the surface factor Crdecreases with increasing tensile strength, Su.

6.6 Residual Stress EffectsResidual stresses or internal stresses are produced when a region of a part is strained beyond the elastic limit while other regions are elastically deformed. When the force or deformation causing the deformation are removed, the elastically deformed material springs back and impose residual stresses in the plastically deformed material. Yielding can be caused by thermal expansion as well as by external force. The residual stresses are of the opposite sign to the initially applied stress. Therefore, if a notched member is loaded in tension until yielding occurs, the notch root will experience a compressive stress after unloading. Welding stresses which are locked in when the weld metal contracts during cooling are an example of highly damaging stresses that cannot be avoided during fabrication. These stresses are of yield stress magnitude and tensile and compressive stresses must always balance each other, as indicated in Figure 26. The high tensile welding stresses contribute to a large extent to the poor fatigue performance of welded joints.

Stresses can be introduced by mechanical methods, for example by simply loading the part the same way service loading acts until local plastic deformation occurs. Local surface deformation a such as shot peening or rolling are other mechanical methods frequently used in industrial applications. Cold rolling is the preferred method to improve the fatigue strength by axi-symmetric parts such as axles and crankshafts. Bolt threads formed by rolling are much more resistant to fatigue loading than cut threads. Shot peening and hammer peening have been shown to be highly effective methods for increasing the fatigue strength of welded joints.Thermal processes produce a hardened surface layer with a high compressive stress, often of yield stress magnitude. The high hardness also produces a wear resistant surface; in many cases this may be the primary reason for performing the hardness treatment. Surface hardening can be accomplished by carburising, nitriding or induction hardening.Since the magnitude of internal stresses is related to the yield stress their effect on fatigue performance is stronger the higher strength of the material. Improving the fatigue life of components or structures by introducing residual stresses is therefore normally only cost effective for higher strength materials.Residual stresses have a similar influence on fatigue life as externally imposed mean stresses, ie. a tensile stress reduces fatigue life while a compressive stress increases life. There is, however, an important difference which relates to the stability of residual stresses. While an externally imposed mean stress, eg. stress caused by dead weight always acts (as long as the load is present), residual stress may relax with time, especially if there are high peaks in the load spectrum that cause local yielding at stress concentrations.6.8 Effects of CorrosionCorrosion in fresh or salt water can have a very detrimental effect on the fatigue strength of engineering materials. Even distilled water may reduce the high-cycle fatigue strength to less than two thirds of its value in dry air.Figure 27 schematically shows typical S-N curves for the effect of corrosion on unnotched steel specimens. Precorrosion, prior to fatigue testing introduces notch-like pits that act as stress raisers. The synergistic nature of corrosion fatigue is illustrated in the figure by the drastic lower fatigue strength which is obtained when corrosion and fatigue cycling act simultaneously. The strongest effect of corrosion is observed for unnotched specimens, the fatigue strength reduction is much less for notched specimens, as shown in Figure 28.

Protection against corrosion can successfully be achieved by surface coatings, either by paint systems or through the use of metal coatings. Metal coating are deposited either by galvanic or electrolytic deposition or by spraying. The preferred method for marine structures, however, is cathodic protection which is obtained by the use of sacrificial anodes or, more infrequently, by impressed current. The use of cathodic protection normally restores the high cycle fatigue strength of welded structural steels to its in-air value, while at higher stresses hydrogen embrittlement effects may reduce the fatigue life by a factor of 3 to 4 on life.7. CYCLE COUNTING PROCEDURE FOR VARIABLE AMPLITUDE LOADINGIn practice the pattern of the stress history with time at any particular detail is likely to be irregular and may indeed be random. A more realistic pattern of loading would involve a sequence of loads of different magnitude producing a stress history perhaps as shown in Figure 29. The problem now arises as to what is meant by a cycle and what is the corresponding stress range. A number of alternative methods of stress cycle counting have been proposed to overcome this difficulty. The methods most commonly adopted for use in connection with Codes and Standards are the 'reservoir' or the 'rainflow' method.

7.1 The Reservoir MethodThe basis of the reservoir method is shown in Figure 30 using the stress time history as Figure 29. it should be assumed that a stress time history of this kind has been obtained from strain gauges attached to the structure at the detail under consideration or has been estimated by computer simulation. It is important that the results analysed should be representative of long term behaviour. To analyse these results, a representative period is chosen so that the peak stress level repeats itself and a line is drawn to join the two peaks as shown in Figure 30a. The region between these two peaks is then regarded as being filled with water to form a reservoir. The procedure is then to take the lowest trough position and imaging that one opens a tap to drain the reservoir. Water drains out from this trough T1but remains tapped in adjacent troughs separated by intermediate peaks as shown in Figure 30b. The draining of the first trough T1corresponds to one cycle of stress range Stas shown, and the remaining level of water is now lowered to the level of the next highest peak. A tap is now opened at the next lowest trough T2as shown in Figure 30c and the water allowed to drain out. The height of the water released by this operation corresponds to one cycle of stress range S2. This procedure is continued sequentially through each next lowest trough, gradually building up a series of numbers of cycles of different stress ranges. It is also essential to allow for the one cycle from zero to peak stress. For the particular stress time history shown in Figure 29 the results obtained from the sample time period taken would be:

1 cycle at 120N/mm2, 1 at 100N/mm2, 4 at 80N/mm2, 6 at 60N/mm2, 10 at 30N/mm2.The important principle of the above procedure is the recognition that by taking the difference between the lowest and highest stress levels (trough and peak) it is ensured that the greatest possible stress range is counted first, and this procedure is repeated sequentially so that the highest ranges are identified as the random fluctuations take place. In the assessment of the effects of the different cycles the greatest damage is caused by the higher stress ranges since the design curves follow a relationship of the kind SmN=constant. The reservoir method procedure does ensure that practical combinations of minima and maxima are considered together whereas this is not always the case in other stress cycle coating procedures.An alternative way of carrying out the reservoir cycle counting method is to turn the diagram upside down and use the complementary part of the diagram as shown in Figure 31. This version of the reservoir method gives identical results to the normal method but has the advantage of including the major cycle of stress from zero to maximum and back.

7.2 The 'Rainflow' Counting MethodThe alternative 'rainflow' cycle counting procedure is illustrated in Figure 32a for the same stress time history of Figure 29. This is essentially the same picture turned onto its side as shown in Figure 32a. Water (rain) is allowed to fall from the top onto the pattern considered as a roof structure and the paths followed by the rain are followed. However it is important that a number of standard rules are followed and the procedure is rather more complex and subject to error than the reservoir method. For each leg of the roof an imaginary flow of water is introduced at its highest point as shown by the dots in Figure 32b. The flow of water is followed for the outermost starting point first, allowing the water to drop onto any parts of the roof below and continue to drain until it falls off the roof completely. The width from the stress level at which the water started until it left the roof represents the magnitude of one cycle of stress. It is necessary to follow the flow paths from each starting point sequentially, moving progressively in from the points which are furthest out. If however the flow reaches a position where water has drained from a previous flow, it is terminated at that point as shown in Figure 32c for the flow starting from position 3 terminated by the previous flow position 1. The stress range for a cycle terminated in this way is limited to the width between the starting point and the termination point. The complete rainflow diagram for the stress pattern of Figure 29 is shown in Figure 32d. This procedure when correctly applied also counts the highest stress range cycles first and ensures that only practical combinations of minima and maxima within a sequence are considered. The rainflow method is somewhat more difficult to apply correctly than the reservoir method and it is recommended that both for teaching and for design purposes the reservoir method should be used. The results for the stress ranges from the rainflow method applied to the stress history from Figure 29 are identical to those from the reservoir method ie.1 cycle at 120N/mm2, 1 at 100N/mm2, 4 at 80N/mm2, 6 at 60N/mm2, 10 at 30N/mm2.

There are two other cycle counting methods, the 'range pair counting' method and the 'mean crossing level' which are sometimes used although they tend not to be specified in Codes.Example 1This design example is based on the stress cycle history of Figure 29 as analysed above for stress cycle counting purposes. Firstly the stress history represents a relatively short time period, and has to be extrapolated to represent the total required life. Obviously the first requirement is to ascertain the required design life, and to multiply the numbers of cycles of each stress range determined as above by the ratio of the design life to the period represented by the sample time record taken. For example, if the design life was 20 years, and the sample time period was 6 hours, the numbers of cycles should be multiplied by 20 x 365 x 4 = 29200. Caution should be exercised with such an extrapolation however, as to whether such a short length time sample is representative of long term behaviour. For example in the case of a bridge structure the traffic flows are likely to vary at different times of day, peaking at rush hour times and falling to low values in the middle of the night. Furthermore there is possibility that the heaviest loads may not have occurred during the sampling time considered. Problems of extrapolation from samples to full data are common in the statistical world and statistical procedures may be necessary to ensure that potential differences in scaling up the data are allowed for. To a large extent this depends on the absolute size of the sample taken.To check whether the design is satisfactory for any particular detail, it is necessary to decide on the appropriate design S-N design curve for the detail. The basis of doing this for Eurocode 3 will be explained inLecture 12.9. For present purposes it will be assumed that the stress history of Figure 29 analysed above applies to a detail for which the design S-N curve is S90, for which the design life is 2 x 106cycles at stress range 90N/mm2with slope - 1/3 continued down to a stress level of 66N/mm2at design life 5 x 106cycles, with a change in slope to -1/5 on down to a stress range of 36N/mm2which is the fatigue limit at 10 million cycles. For a twenty year design life assuming the stress history of Figure 29 is representative of 6 hours typical loading the following table can be constructed:

For these assumptions the loading is acceptable for the detail and life required. Indeed the 'Damage Sum' value of 0.1174 based on a 20 year design life indicates the available design life is 20/0.1174 = 170 years. For this particular case the stress range of 60N/mm2fell in the intermediate range between 36 and 66N/mm2and the available life N was calculated using the changed slope of the S-N curve for this region. The stress range of 30N/mm2is below the cut off for the S90 classification and does not contribute to the fatigue damage.7.3 Exceedance Diagram MethodsA convenient way of summarising the fatigue loading applied to structures is by the use of exceedance diagrams. These diagrams present a summary of the magnitude of a particular event against the number of times this magnitude is exceeded. Whilst in principle this presentation can be applied to a wide variety of phenomena for the purposes of fatigue analyses the appropriate form is a graph of log (number of times exceeded) against the occurrence of different stress levels. An example is shown in Figure 33. This might represent the stresses caused at a particular location in a bridge by traffic passing over r by wave loading of an offshore structure. A typical feature of natural phenomena of this kind is that the number of exceedances increases as the stress level decreases. The form of the exceedance diagram for natural phenomena of this kind is often close to linear as shown. It is important to note that the diagram represents exceedances so that any particular point on the graph includes all of the numbers of cycles of stress range above that value. For use in fatigue analysis using Miner's law the requirement is a summary of the numbers of cycles of each stress level occurring. Thus the loading represented by the exceedance diagram of Figure 33 can be treated as an equivalent histogram with cycles as follows:

Some of the stress ranges will be found to be below the fatigue limit and hence will not contribute to the Miners law damage sum. For example for the detail considered in Example 1 above, the cut off limit was 36N/mm2and the stress ranges of 20N/mm2would not contribute to the fatigue damage. The stress ranges above this level will contribute however and their effects must be included. This is done by finding the value ofSmN separately for the remaining stress levels above and below the change in slope of the S-N curve, and for the figures given above this will be found to be 5.692 x 1010for stress ranges of 80N/mm2and above, and 1.621 x 1015for the 40 and 60N/mm2stress ranges. For an S90 detail with the spectrum of loading shown above, the fatigue damage from each part of the S-N curve has to be calculated based on the appropriate value of SmN=constant as follows:+ = 0.298From these figures the damage sum factor calculated as 0.298 is acceptable. Detailed examination of the figures leading up to this result would indicate that the majority of the damage calculated occurs at the lowest stress ranges of 40 and 60N/mm2contributing to the S5N part of the design curve.7.4 Block LoadingBlock loading is a particular case of an exceedance diagram.Consider the particular case of a one lane bridge structure on which the loading is idealised as falling into three categories. Suppose that there are n1heavy lorries travelling across the bridge during its lifetime, and that at a particular welded detail each lorry causes a stress range S1. In addition there are n2medium lorries which cause a stress range S2, and n3cars which cause a stress range S3at the same welded detail as they cross the bridge. To assess the combined effect of the different stress ranges all being applied in some form of sequence the procedure adopted is to assume that the damage caused by each individual group of cycles of a given stress range is the same as would be caused under constant amplitude loading at that stress range. It is necessary first to decide on the appropriate classification for the geometric detail being considered and to identify the appropriate S-N design curve. For present purposes, let us assume that the design curve is as shown in Figure 34. If the only fatigue loading applied to the bridge was the crossing of the heavy lorries with stress range S1at the detail concerned, the available design life would be N1cycles as shown in Figure 34. In fact the number of cycles applied at this stress range is n1. It is assumed that the fatigue damage caused at stress range Stis n1/N1. Similarly if the only fatigue loading applied to the bridge was the crossing of the medium lorries with stress range S2the available design life would be N2and the fatigue damage caused would be n2/N2. For the passage of the cars at stress range S3the available design life if this was the only loading would be N3and the fatigue damage caused would be n3/N3. When all three loadings occur together the assumption for design purposes is that the total fatigue damage is the sum of that occurring at each individual stress range independently. This is known as the Palmgren-Miner law of linear damage, or more simply as Miner's law and is summarised as follows:

+ + + .... + = 1 (11)7.5 Frequency and Spectrum AspectsIt is not uncommon for loading to occur at more than one frequency. It is generally considered that for non aggressive environmental conditions, eg. steel in air, there is little or no effect of frequency on constant amplitude fatigue behaviour. In aggressive conditions however, eg. steel in seawater, there may be significant effects of frequency on the crack growth mechanism leading to increased crack growth rates, shorter lives and reduction or elimination of the fatigue limit. In particular it is necessary in fatigue testing of materials where environmental conditions may be important to carry out the testing at the same frequency as that of the service loading. An example of this is the effect of wave loading on offshore structures where a typical frequency of waves is about 0.16Hz. Clearly this has major implications on the time required for testing since to accumulate one million cycles at 0.16Hz would take about 70 days whereas a conventional test in air at say 16Hz would reach the same life in less than 1 day. With any structure the response of the structure to dynamic loading depends on the frequency or rate of the applied loading and on the vibration characteristics of the structure itself. It is most important for the designer to ensure that the natural resonance frequencies of the structure are well separated from the frequencies of applied loading which may occur. Even so the structure may respond with frequencies of stress fluctuation which are a combination of the applied loading frequency and its own natural vibration frequencies. Furthermore since the magnitude of the loading may also vary with time it is necessary to consider both time domain and frequency domain aspects. Figure 35 shows a typical frequency domain response for stress fluctuations at a particular location in an offshore structure. This diagram gives information on number of times different stress levels are exceeded as well as the frequency data. The peaks at about 0.16Hz correspond to the applied loading whereas the higher frequency peaks are those due to the vibration response of the structure.

With variable amplitude fatigue loading of this kind there are additional complexities with regard to frequency effects to be considered. Where the stressing occurs close to or at a single frequency the condition is known as 'narrow band' and when there are a range of different frequencies involved it is known as 'broad band'. If the frequency domain response of Figure 35 is converted back into the time domain response in which the data was originally recorded the result would look like Figure 36. Clearly some assumptions must have been in the conversion of one diagram into the other and in this case it is that stress cycle counting has been carried out by the reservoir method. In Figure 36 however, it is clear that because the higher frequency stress cycles are superimposed on top of the lower frequency cycles, some of the higher frequency cycles occur at higher mean stress or stress ratio.

8. CONCLUDING SUMMARY In this lecture it has been shown that fatigue is a weakest link process of a statistical nature in which a crack will initiate at a location where stress, local and global geometry, defects and material properties combine to give a worst case situation. The crack thus nucleates at a local peak spot, and may cause failure of the structure, even if the rest of the structure has a high fatigue resistance. Good fatigue design practice is therefore based on close attention to details that increases the stress locally and therefore are potentially initiation sites for fatigue cracks. A positive aspect of the local nature of the fatigue process is that only a relatively small area of highly stressed material need to be improved in order to increase the load carrying capacity of the structure when fatigue is the limiting design criterion. Another general conclusion is that increasing the size of a structure generally leads to a lower strength with respect to brittle fracture as well as fatigue. Size effects must therefore be properly accounted for. The larger number of factors influencing fatigue strength makes the combined effects of these factors very difficult to predict. The safest way to obtain design data is therefore still to perform fatigue tests on prototype components with realistic environmental conditions. A normal structural design analysis must be carried out for the maximum design loads and for a series of intermediate loads with known number of occurrences in the design life to give stress results at typical details. Alternatively if the application Code gives an equivalent constant amplitude loading condition and associated number of cycles this loading should be applied and stresses determined. The stresses should be analysed for range of variation in principal stress or of direct stress aligned perpendicular or parallel to the geometric detail as defined in Eurocode 3. Treatments for shear stresses are given in Eurocode 3. The stress ranges should be multiplied by appropriate partial factors, and for variable amplitude loading either combined together to give an equivalent constant amplitude stress range and number of cycles or used to sum up fatigue damage. The correct detail classification must be identified for typical critical details and the applied fatigue damage for the design life checked against the design S-N curve for the detail concerned. If the design is not satisfactory either the stress ranges must be reduced or the detail changed until satisfactory results are obtained.9. REFERENCES1. Metals Handbook, ASM 1985.2. ISO Standard, 373 - 1964.3. P.C. Paris and F. Erdogan, "A Critical Analysis of Crack Propagation Laws", Trans, ASME, Vol. 85, No. 4, 1963.4. J.M. Barsom, "Fatigue Crack Propagation", Trans, ASME, SEr. B, No.4, 1971.5. H. Neuber, "Kerbspannungslehre", Springer, 1958.6. R.E. Peterson, "Stress Concentration Factors", John Wiley & Sons, 1974.7. O. rjaster et al, "Effect of Plate Thickness on the Fatigue Properties of a Low Carbon Micro-Alloyed Steel", Proc. 3rd Int. ECSC Conf. on Steel in Marine Structures (SIMS'87), Delft, 15-18 June 1987.8. P. J. Haagensen, "Size Effects in Fatigue of Non-Welded Components", Proc. 9th Int, Conf. on Offshore Mechanics and Arctic Engineering, (OMAE), Houston, Texas, 18-23 February 1990.

Lecture 12.3: Effect of Workmanship onFatigue Strength of Longitudinal andTransverse WeldsOBJECTIVE/SCOPEIdentification of factors influencing the fatigue strength of welded joints and of the consequences for design, fabrication and inspection.PREREQUISITESLecture 12.1: Basic Introduction to FatigueLecture 12.6: Fatigue Behaviour of Bolted ConnectionsRELATED LECTURESLecture 3.4: Welding ProcessesLecture 3.6: Inspection/QA AssuranceSUMMARYThe data on fatigue strength given in Eurocode 3 [1] are briefly reviewed. The strengths of longitudinal and transverse welds are related to the quality of workmanship. The need for inspection and the limitations of non-destructive testing are examined. The implications for economic design, detailing and specification are set out.1. INTRODUCTIONAny joint in a structure or in any part of it is a potential point of weakness, both in static strength and in fatigue.For fatigue the potential weakness is evident from the fatigue strength data given in Eurocode 3 [1] (Figure 1). There the perfect plate is in detail category 160, which is the fatigue strength at 2.106cycles, whilst the joint detail with the worst geometry and hence stress concentration, is in category 36.

In a welded joint potential sites for initiation of a fatigue crack are:1. In the parent metal of either part joined, adjacent to:(i) the end of the weld(ii) a weld toe(iii) a change of direction of the weld.2. In the weld metal itself, starting from:(i) the weld root(ii) the weld surface(iii) an internal flaw.Even one type of joint, the longitudinal fillet or butt weld, can fall into any one of four categories, from 140 to 100, depending on workmanship, see Figure 2.

Transverse butt welds can have an even wider range of strengths (Figure 2) - from category 125 to category 36, 7 categories in all. If one excludes butt welds made from one side only, with and without backing strips, i.e. detail categories 71, 50 and 36, four categories are left for "good" butt welds. Here the category depends on both weld geometry and workmanship.Other welds (transverse fillets, welds to attachments, etc.) also show wide variations in strength depending on geometry and workmanship.It is important to note that a number of other (usually accidental) results of poor workmanship can reduce the performance of a detail to below what its category would indicate:(a) weld spatter(b) accidental arc strikes(c) unauthorised attachments(d) corrosion pitting(e) weld flaws, particularly in transverse butt welds(f) poor fit-up(g) eccentricity and misalignment.Most of these are largely unquantifiable and must be controlled by adequate inspection and repair.It is the purpose of this lecture to describe in greater detail welded joints and the matters to be considered by the designer before deciding the fatigue strength that will be used in calculations.2. LONGITUDINAL WELDSThe highest category for longitudinal welds, 140, applies only where there are "no significant flaws". This implies automatic welding, no stop/start positions, no slag inclusions or blow holes - near perfection "demonstrated by specialist inspection".The next category down, 125, requires automatic welding and expert repair, followed by inspection, of any accidental stop/start positions. Leaving stop/start positions brings the category of longitudinal fillet welds down to 112 and that of longitudinal butt welds down to 100.Manual fillet or butt welds and one-sided butt welds are all in category 100, as are "repaired" welds.There is experimental evidence that small slag inclusions can bring the strength of a longitudinal fillet weld down to category 90.A lower limit to the strength of defective longitudinal fillet welds is probably that of an intermittent weld, category 80, or even the end of such a weld at a cope hole, category 71.3. TRANSVERSE BUTT WELDSTransverse butt welds can reach category 125 when "high quality welding" is obtained and proved to have been achieved by later inspection. Amongst other requirements, the proposed welding standard limits solid inclusions in such welds to a width of 2mm and a length of 6mm, thus acknowledging the importance of internal defects.Lower quality welds fall into category 112 provided the welds are ground flush. Otherwise they are in category 90, or 80 for splices in rolled sections or girders. Here the category depends on the weld profile and the likely quality of workmanship; internal defects are not mentioned.In fact, internal defects have at least as great an influence on the fatigue strength of transverse butt welds as does the weld profile.Another factor which affects the strength of splices in girders, and which is not mentioned explicitly in the description of the detail categories, is the order in which the welds are made. This can affect the level of residual stress.The test results shown in Figure 3 illustrate these points. They are all results of tests on transverse butt welds shown against the grid of lines representing the fatigue strengths given in Eurocode 3 [1] for the various detail categories. The short thick lines represent test results on small plate specimens, 40mm wide and 10mm thick. All other points represent results from tests of complete beams.

The results range from category 112 for the plate specimens down to category 63 or so for a butt joint in a rolled I beam.The reasons for this spread of results are partly weld quality and partly residual stresses caused by different welding procedures.3.1 Effect of Internal Defects.It is likely that the plate specimens were reasonably free from internal defects. The butt welds in the plate girder flanges, shown as large circles, contained various small defects, in the range of 3mm2to 30mm2from which the cracks leading to failure originated. Allowing for the fact that the plate girder flanges were 35mm thick, all results would fit into category 112. So would the results from tests on small girders with 25mm thick flanges, shown as triangles.The results shown as small dots were obtained for a butt weld between a rolled and a built-up I section. The failure was due to a large "lack of fusion" defect in the 30mm thick flange directly above the web to which it was joined by 24mm radii. The defect had an area of about 80mm2and is sketched in Figure 4 and was attributed to faulty weld preparation. It must be pointed out, however, that it was the work of experienced fabricators, who clearly had not appreciated the difficulty of achieving full penetration at this point.

Even allowing for size effect, one would put this result into category 63. There is no information on the strength of such welds in Eurocode 3 - they should not be used. A British Standard, BS5400: Part 10 puts such welds in a class which corresponds, as regards strength, to category 63 [2]. This classification fits the test results.These few test results suffice to indicate that internal weld defects occur and that they have a decisive influence on the fatigue strength of a welded joint.To determine this effect quantitatively, a fracture mechanics study has been undertaken, based on fatigue test results from butt welds containing known defects. The results were used to obtain basic fracture mechanics data. These results showed the scatter typical of all fatigue test results. A lower bound of the values was then used to calculate the fatigue strength of butt welds of various thicknesses containing defects of various sizes. The defect size was expressed as an area; a reasonable approximation which avoided the need to give two dimensions for every defect and to investigate various shapes.The figures shown in Figure 5 are approximate and were obtained by interpolation, and some extrapolation, from the results produced by the investigation.

The agreement between these figures and the few large beam results is quite good.It will be noted that near surface defects cause a greater loss of fatigue strength than deep ones and that a 12mm2defect, such as suggested in the draft welding standard [1], would bring a butt weld strength down to category 100, or even 90 if near the surface.It is clear, therefore, that high fatigue strength in a butt weld requires nearly perfect welds.3.2 Effect of Welding ProcedureThe results in Figure 3 showing the effect of different welding procedures and, hence, residual stress are the two groups of squares.They were obtained from tests on butt joints through rolled I sections. The higher set, full squares, were from specimens in which the flange butt welds were made before the web butt welds. The lower set, open squares, were obtained from specimens in which the reverse procedure had been used - web butt weld first, then flange butt welds so that their contraction was resisted by the web.One set fits category 100, the other category 80 - a considerable loss of strength through using the wrong weld sequence.These results do not stand alone; similar ones have been obtained in the United States and they are confirmed by the results shown by the circles on the figure.These results were obtained from plate girder specimens with 35mm thick flanges. The full circles show results from specimens in which only the flange plates were butt welded, and that before they were welded to the webs. Allowing for size effect, they fit category 112 or, possibly, 125. The open circles are results from butt welds right through similar plate girders. They are little, if any, worse than those shown by full circles.However, the welding procedure, shown in Figure 6, was designed to minimise residual stresses in the flange welds. Initially, the webs were not welded to the flange for some 110mm either side of the joint, the flange butt welds were made first, then the web butt weld and, finally, the web was welded to the flanges. This weld also served to close the small slot which had been left under the flange butt weld to allow radiography of these welds. Cope holes were neither needed nor provided.

It is clear from these results that butt joints right through a girder can have the same fatigue strength as a butt weld through a plate provided that the right welding procedure is specified by the designer and followed in the fabrication shops. Otherwise there is a loss of fatigue strength of the order of 25%.The results were obtained from tests on plate girders, but the conclusions have a wider application. They apply, for example, to joints in portal frames at or near the corners and any situation where there is a risk of high restraint of butt welds.There is some evidence that similar considerations apply to welding attachments to girders. In one test, plates welded to the compression flange of a plate girder caused early cracks, as was expected. When similar attachments were welded to the flange plate before it was welded to the girder, no cracks were observed at about double the endurance; again an improvement of about 25% in the fatigue strength.Given the effect welding procedure can have on the fatigue strength of a joint, it must be considered at the design stage and be specified; it cannot be left to the fabricator.4. OTHER WELDS4.1 GeneralSo far discussion has been limited to those types of weld (