Chapter 6
Fatigue Strength of Welded Joints 1
6.1. Fatigue strength
6.1.1. Introduction
The observation of many failures in welded structures generally points the finger at fatigue as the main cause. Moreover, it has become apparent that for welded structures, admissible service stresses were very low in respect of the static stresses (yield strength, breaking strength) and that it was not enough to apply a safety coefficient based, for example, on a fraction of the yield strength to be certain of avoiding failure. Indeed, welds can introduce severe stress concentrations and which differ from one structural element to another.
For example, Figure 6.1 compares the fatigue performances of an E36 steel plate, and the same plate with a hole or two stiffeners welded longitudinally. Fatigue strength, which is conventionally given as 2x106 cycles, passes respectively from 260 (plain plate) and 180 (bored plate) to 70 MPa for the welded joint.
On the other hand, if we apply a sufficiently large safety coefficient to eliminate the possibility of rupture, the welded structure then becomes too large and is not competitive.
In fact, when designing a structure, every aspect of it must satisfy the three following conditions:
– fulfill its function as effectively as possible,
– be manufactured economically,
– ensure a defined in-service lifespan.
Figure 6.1. Comparison between the fatigue strengths of a holed or plain steel sheet and of a fillet weld
The consequences of the first two conditions lead, at the design stage, to a reduction in the safety coefficients, in order to decrease weight and costs. Unfortunately, this tendency conflicts with the need for an adequate lifespan and hence the safety of the structure where fatigue damage can occur. Moreover, the fatigue strength of actual structures cannot be defined uniquely in a theoretical way. This is why the only realistic approach to designing a structure that is subject to fatigue stresses is to relate the load levels applied to the fatigue strength data that correspond with each joint configuration used. To this end, each country has its own standards or recommendations. However, these codes are only applicable to certain types of metal structures.
The aim of this chapter is to present the principal parameters which influence the fatigue behavior of welded joints in both an analytical and diagrammatic way.
6.1.2. Fatigue failure of the principal welded joints
Welding operations result in the existence of stress concentrated areas where a fatigue crack may originate and expand from. These zones correspond, either with a geometric anomaly in the weld bead, an internal defect (lack of penetration, porosities) or external defects (undercuts, slag inclusions); their relative importance depends on the type of assembly and the type of loading applied in service.
6.1.2.1. Butt welded joints
Transverse butt welds
Figure 6.2 presents this type of assembly, which makes it possible to join two plates via a transverse welding perpendicular to the load axis.
For this type of joint, the fatigue crack starts at the weld toe and propagates through the thickness of sheet, perpendicular to the load direction. The crack is thus not the result of a defective welding or bad properties of the deposit metal, but the consequence of stress concentrations at the weld toe.
In this type of butt welded joint, the influence of the shape of the weld bead is important for determining the endurance characteristics of the joint. This depends greatly on the welding conditions.
Longitudinal butt welds
For longitudinal joints, the change of section due to a metal excess is now parallel with the direction of the applied load and it could be thought that the fatigue performance of these welds are better than those of transverse joints. However, this is not always the case.
The crack in this type of joint generally starts (see Figure 6.3) at the level of a welding stop and restart, for example, while changing an electrode, or starting from a deformation on the weld bead surface.
A good fatigue strength of longitudinal joints can only be obtained if they are continuous, and therefore if welding interruptions are avoided.
6.1.2.2. Fillet welded assemblies
a) Cruciform joints
There exist two types of cruciform joints, according to whether the weld beads transmit the load or not.
Non-load carrying fillet weld
In the first type (see Figures 6.4a and 6.4b), the fillet weld does not transmit the load in the solid metal sheet. In this case, the crack starts at the weld toe and propagates through the thickness of the plate in a plane perpendicular to that of the stress.
There is no advantage in making assemblies with fillet welds parallel to the stress direction (see Figure 6.4c). The crack then starts at the bead end and leads to a low fatigue strength. On the other hand, continuous longitudinal fillet welds present significant improvements in endurance over intermittent fillet welds.
Load-carrying fillet weld
In this type of joint, the entire load is transmitted by the weld (see Figure 6.5a).
In this case, in addition to the stress concentration zones located at the weld toe there are zones of acutely angled internal notches at the weld root. In general, the crack starts here then propagates in the deposited metal in an oblique direction compared to the load direction. This type of failure means that the assembly has relatively low endurance characteristics compared to the preceding welded joints. This is why the aim is to avoid starting a crack at the weld root; however the fact of increasing the throat thickness, by a thicker weld or a better penetration, is not always enough to ensure that the fatigue crack starts, this time, at the weld toe. In general, completely interpenetrating beads (see Figure 6.5b) notably improve the endurance properties.
In general, bead interpenetration is not always necessary to transfer crack initiation at the weld root to the weld toe. Figure 6.6 presents the geometric bead conditions necessary to pass from one type of failure to the other.
b) T-shaped joints
At first sight, this joint resembles half of a cruciform joint (see Figure 6.7) and should show a similar fatigue behavior. However, in this case, a third rupture mode is possible. If the bending stresses applied to the transverse element are in the same order of magnitude as the constraints applied directly to the T, the crack will be able to start on the other weld toes and propagate through the transverse element.
Figure 6.6. Cracking conditions of a cruciform joint. Influence of lack of penetration; from [LIE 73]
Figure 6.7. Fatigue cracking of a T-shaped weld when the transverse element undergoes a bending stress
6.1.3. Concept of nominal stress
An elementary weld joint can be regarded as an element with a notched structure, the weld bead constituting the notch. Just as for a notched part, the extent of the nominal stress range ΔσN is considered to have been extrapolated to the level of the crack initiation point.
Figure 6.8 represents ΔσN in the case of an assembly with a transverse stiffener submitted either to tension, or bending. The nominal stress is the distant stress, within the terms of material strength, i.e. without taking account of the local effect due to the weld or to the geometric effect, for example, in the presence of a stiffener for a T-shaped assembly. In tension, this stress is expressed by σn = F/S (F: force, S: section), and in bending, by σn = M.v/I (M: bending moment, I: inertia and v distance to neutral fiber).
Generally ΔσN is used on Wöhler diagrams (Δσ − NR), in order to plot the S-N curves (see Figure 6.9).
As will be seen later, the conventional endurance limit 2x106 cycles is often taken as a reference. For example, Figure 6.9 presents, for some types of assembly, the admissible stress levels suggested by the International Institute of Welding [CTI 00]. We should notice the relatively low values with respect to the yield strength of the base plate (Re ≥ 240 MPa). In fact, these admissible stress values simultaneously express the effect of the numerous parameters involved and the great disparity of test results on assemblies in their as-welded state.
6.1.4. Factors in welded joint endurance
The static resistance of a butt welded joint is in general equal to that of the base metal, the rupture occurring away from the weld bead (unless the weld itself is very poor). On the other hand, the fatigue strength is always lower for the welded joint. This varies according to many parameters, primarily relating to the assembly (base metal, added metal, HAZ) and the forces it undergoes (see Figure 6.10).
Figure 6.9. Typical S-N design curves of the IIS and corresponding construction details, showing the fatigue cracking site and the load direction under consideration
These various parameters which influence the fatigue behavior of welded joints can be put in three categories:
– geometric factors: bead shape, poor sheet alignment, welded element bending, assembly dimensions (sheet thickness, bead geometry);
– metallurgical factors: nature of the base metal, welding process (energy, metal filler product), welding defects, residual stress levels;
– factors related to the load: load pattern (constant or variable amplitude, stress ratio), stress gradient, stress biaxiality, environment.
Each of these many factors generally does not act on its own. Synergetic effects must often be taken into account, thus leading to various in-service stress levels.
6.1.4.1. Geometric factors
a) Weld bead shape
We can highlight the total influence of the weld bead by comparing the endurance limits obtained, for butt joints in their as-welded state, to the same welded joints when ground flush [LIE 73].
For flush joints, a slightly lower endurance limit is found (5 to 10%) than that of the base metal, while the endurance limit observed on as welded joints is definitely weaker (30 to 45%) than that of the base metal.
Actually, several authors have shown that it is necessary to consider, on the one hand, the macrogeometric effect due to the general bead profile and, on the other hand, the geometric effect induced by the welding defects located at the connection zone of the bead surface and the base metal skin.
Macrogeometric effect
As a consequence of the nature of welded joints, weld beads involve changes of section leading to stress concentration areas (see Figure 6.11).
If a welded joint is considered as a notched component, we can evaluate the corresponding stress concentration coefficient Kt = σmax/σnom (σmax: maximum stress at the notch tip, σnom: average stress in the section under a component load).
In the case of fillet welded joints, at the point between connection of the base metal and weld bead, values of the stress concentration coefficient ranging between 1.5 and 4.5 have been measured. This coefficient is about 3 for butt welds. These measurements do not take account for defects, which can exist at the point considered, and which can increase this stress concentration locally.
A better weld bead quality leads to an appreciable improvement in fatigue strength.
Figure 6.12. Correlations between the endurance limit of T-shaped assemblies subjected to bending (R = 1) and the weld toe radius or the flank angle [HUT 94]
For example, in the case of T assemblies submitted to bending loads, Figure 6.12 shows the correlations between the conventional endurance limit, Δσ2x106 cycles and the radius 
(at the weld toe radius) or the flank angle 
. and 
represent the average measurements recorded in each series of assemblies produced by all welding processes in a flat position [HUT 94].
Microgeometric effect
In addition to the stress concentrations caused by section changes, surface defects such as splits, undercuts, unevenness and edge faults, etc. are as just as likely engender failures.
For example, Figure 6.13 shows the role of undercuts on fatigue strength.
b) Plate thickness
For geometrically similar joints, the fatigue strength tends to decrease as the plate thickness increases [GUR 79]. Figure 6.14 presents the pattern of fatigue lives according to thickness for T assemblies, subjected to bending forces.
However, it is difficult to separate the effect of the flank angle θ, weld length, s, and plate thickness, t, through experiments; for a given configuration, when s/t decreases, ΔσN increases, as Figure 6.15 indicates [GUR 79].
Rather than s, it would undoubtedly be advisable to take into account the embedded plate length, conferred by the assembly [MAD 98] (2 s + thickness of the stiffener).
c) Misalignments
Figure 6.16 presents various axial or angular misalignments which can be found in welded joints. These defects lead to secondary bending moments which are added to the nominal stress.
Figure 6.15. Diagrammatic role of s/t (s: weld length; t: plate thickness) on fatigue strength; from [GUR 79]
Figure 6.16. Misalignments: a) axial, in a cruciform assembly; b) angular or c) in a butt welded joint; d) axial, due to a change of thickness in a butt welded joint; from [MAD 80]
The increase in nominal constraints due to a misalignment can be evaluated by various analytical expressions [MAD 80].
6.1.4.2. Metallurgical factors
a) Internal defects
Various internal defects can appear in the weld bead: slag inclusions, porosities or lack of penetration. A lack of penetration generally represents a high risk of fatigue crack initiation at the root.
Concerning slag inclusions and porosities, Figures 6.17 and 6.18 show, in the case of a butt welded assembly, that the reduction of fatigue strength must be taken into account.
Figure 6.17. Influence of the voluminal porosity percentage on the endurance of butt welded joints (testing in tension, R = 0); from [GUR 79]
Figure 6.18. Inclusion lengths influence on the endurance limit of butt welded joints (testing in tension); from [GUR 79]
b) Residual stresses
By definition, residual stresses form a system of internal stresses, in equilibrium, which exist in the absence of an external load. These stresses are generally the result of permanent plastic strains which are produced locally [LIE 97].
In a welded structure, these strains are the result of local heating and cooling cycles associated with welding. When the welded metal cools from the melting point, it tends to contract, but it is restrained by the adjacent base metal. The contraction must then be accommodated by the plastic strain of the filler metal.
This situation is further complicated by technological factors, such as joint type and size, the welding process used and the manner of depositing the filler metal. Nonetheless, the principle of considerable residual stresses existing in the filler metal remains the same.
In the case of multipass welding, these residual stresses can reach a yield strength close to a sheet’s crack initiation point.
Figure 6.19 gives an example of these stresses for a butt welded joint. When the weld is subjected to a load, this residual stress field is added to the cyclic stresses and, if it is under tension, the structure’s endurance decreases.
c) Welding processes
Generally, a welding process will lead to an optimized assembly endurance provided it gives rise to:
– small defects which are also low in number (TIG welding, welding under a solid flux),
– low residual stresses,
– a favorable weld bead with a low flank angle (automatic welding).
Figure 6.20 shows the test results achieved on specimens of E36 steel, welded manually, resulting in a convex bead, and specimens of the same steel, obtained by automatic welding under a solid flux, producing a concave bead. The fatigue strength of the samples produced by automatic welding is higher than that of the manually welded test pieces by approximately 40%.
Figure 6.20. Influence of the welding process on the fatigue strength of a welded joint in E36 steel; from [LIE 73]
In fact, more than the process, it is the setup of the welding operation which will exert a determining role on the fatigue behavior of assemblies. In particular, for an automatic welding process, the choice of the optimal welding parameters in respect to fatigue performance is a crucial factor.
d) Nature of the filler metal
It is obvious that the choice of filler metal depends on the nature of the base metal to be welded. For this choice, it is necessary to take the following points into account.
The filler metal (electrodes, wire) must assure mechanical characteristics of the molten metal compatible with those of the base metal, thus guaranteeing good continuity properties.
Ideally a filler containing little or no hydrogen will be chosen (for example, basic stoved electrodes).
For cruciform assemblies, achieving complete penetration of the filler in the base metal, perfect continuity in the center, and concave beads, leads to a fatigue strength close to that of butt welds. These conditions can be obtained by choosing electrodes with great penetration for the first passes and “shaped” electrodes, with good flow, for the final passes.
e) Nature of the base metal
Some joints, in their as-welded state, and formed from mild steel or high strength steels lead to similar Δσ values, for average low stresses. In this case, the relative insignificance of the yield strength is due mainly to the existence of high tensile residual stresses caused by welding (see Figure 6.21).
Figure 6.21. Fatigue strength of welded beams subjected to bending (R>0) (A36: YS = 240 MPa; A44: YS = 220 MPa; A 514: YS = 360 MPa)
The advantage of using steels with a higher yield strength is apparent, however, in various situations encountered in reality.
Case of high loads
We observe an improvement in the fatigue behavior of assemblies with an increase in yield strength, either in high stress ranges (medium cycles regime) as shown in Figure 6.22, or in the case of high mean stresses. Figure 6.23 schematizes this latter effect: on a Goodman-Smith diagram, the test results are placed on lines as a function of the mean stress, σm; when σm is low or zero, the results are comparable. Conversely, the effect of the plate yield strength is apparent when σm increases [COL 82]; in the two preceding cases of loading, it is the relation between σmax and YS that we should consider, (with σmax: maximum stress of the load cycle, YS: yield strength of the base metal).
Figure 6.22. Comparison of the fatigue behavior of E36 and E46 welded joints (tensile-compression test); from [LIE 73]
Case of variable amplitude loading
Such loading encountered on an in-service structure generally comprises a small number of high stress range cycles. In this very general case, it is often advantageous to use steels with a high yield strength.
Case of low Kt assemblies
Figure 6.24 illustrates the favorable effect achieved by an increase in the yield strength of the base plate steel on the conventional endurance limit Δσ2x106 for an as-welded butt assembly with low excess thickness [RAB 79].
Figure 6.23. Increase in the fatigue strength subjected to undulating stress by use of a higher performance steel; from [COL 82]
Figure 6.24. Effect of the yield strength of plate steel on the endurance limit of butt welded joints (R = 0); from [RAB 79]
f) Finishing treatments
The effect of finishing treatments (grinding, hammering or re-melting of the weld bead toe, shotpeening of pre-stressed welding, etc.) highlights substantial improvements (as much as doubling fatigue limits) in the fatigue behavior of welded joints, increasing with the yield strength of the base metal [LIE 91].
6.1.4.3. Nature of applied loads
Load pattern
In the case of interpenetrated beads, the comparison of results obtained, either in tension or in bending, reveals different stress gradients in the vicinity of the weld toe. The influence of these gradients leads to a reduction in the fatigue strength, for example by a thickness of a given plate, when the load passes from bending to tension.
For example, in the case of a butt welded steel assembly in E490 (thickness 8 mm), the fatigue strength Δσ2x106, determined by bending (R = 0.1), is 30% higher than that found in repeated tension.
In addition, an assembly subjected to bending is much less sensitive to a lack of penetration than the same assembly subjected to tension. This behavioral difference is explained by a different distribution of local stresses, either at the weld toe or at the weld root [LIE 92].
Stress ratio (R = σmin/σmax)
The stress ratio value (or the mean stress of the load cycle) has a certain influence on the endurance characteristics.
Figure 6.25. Effective stress level resulting from the superposition of the residual and external stresses
If Δσ is the fatigue strength for 2x106 cycles corresponding to a given level of R, the following expression can be written:
These relationships were obtained using tests carried out on small scale samples, taken from real structures. Consequently, the residual stress level in the samples was relatively low (even nil) with respect to that corresponding to a real structure.
In practice, when high residual stresses (close to YS) are expected to be present and that it is not possible to measure them, or to carry out a thermal relief treatment, it is accepted (see Figure 6.25) that, whatever the level of R, the maximum stress is equal to the elastic limit.
In a Goodman diagram (σmax or σmin as a function of σm), this practice amounts to considering the extent of admissible stress corresponding to a maximum stress equal to YS (see Figure 6.26).
Figure 6.26. Determination, on the Goodman diagram relative to the welded joint, of the maximum acceptable stress range in the presence of high residual stresses [COL 82]
Complex loading cases
Few results in the literature relate to examples of complex loading. Such cases are however envisaged in certain calculation methods. Generally, we consider the maximum principal stress applied perpendicular to the bead [CTI 00].
6.2. Dimensioning of joints in mechanized welding
Fatigue behavior is a major concern to designers of mechanized welded structures. Several design methods are proposed in the literature [LIE 00a]. The advantages and disadvantages of each method are presented here. Taking into account the current context, two methods are described in more detail: a method based on the extent of nominal stress and a method based on geometric stress [LIE 00b].
6.2.1. Position of the problem
The service lifespan of welded structures is indeed largely governed by the cyclic loading to which it is subjected. This must be evaluated for each assembly, starting from an understanding of the load applied. In fact, several design methods have been proposed (see Table 6.1) which offer many advantages and disadvantages.
The more general method based on the concept of nominal stress range, Δσn is that currently recommended in procedures. It is based on a network of S-N curves (or S = Δσn and N: the number of cycles to failure) corresponding to the principal construction details used.
The geometric structural stress method aims to reduce the number of S-N curves, by taking into account the effects of stiffness achieved by the geometry of a given assembly. It requires finite elements calculations or extensometric measurements, in order to define, on each assembly of a structure, the corresponding geometric structural stress. This method is mentioned in the recent regulations.
The use of stress or strain at the notch tip requires a precise definition, not only of the assembly’s geometry, but also of the local geometry right at the potential starting point of a fatigue crack, such as the weld toe. This local geometry varies along the weld toe depending on the welding process and renders such a definition problematic.
Fracture mechanics considers the structure once it is cracked and thus does not take into account the crack initiation phase, which is largely influenced by the quality of welding. The fatigue lives obtained are thus by default.
In light of their current importance, we will use this chapter to deal with the first two methods.
6.2.2. General method (current regulations)
In the contemporary fatigue regulations (for example, Eurocode 3, the procedure for civil engineering), S-N curves are used to dimension a welded joint [EURO 92]. The equation for these curves is N = C.S−m, where N is the number of cycles, S the nominal stress range and C, m the coefficients dependent on the welded joint. A detailed catalog of the curves is provided, making it possible to determine which class the assembly under consideration belongs and which S-N curve is applicable. The class generally corresponds with the characteristic value (acceptable) of the nominal stress range at 2x106 cycles (see Figure 6.27).
The S-N curves giving the number of acceptable cycles for constant amplitude loading have the following equation: N = C.Δσ−m, with m = 3 and a conventional stress limit defined at 5x106 cycles.
For variable amplitude loading (in service), the S-N curves to be selected, applying the cumulated damage method (Miner’s rule), are expressed by N = C.Δσ−m with m = 3 for N <5x106 cycles, m = 5 for N >5x106 cycles and a truncation limit for N >108 cycles.
The quality of the weld must conform to that required by the current welding regulations.
6.2.3. Verification methods
In the case of constant amplitude loading, checking or dimensioning a fatigue welded structure amounts to checking the following expression:
(for a given number of cycles, n) knowing that: 
or to check n ≤ N with n the number of cycles applied and N the number of cycles to failure for stress Δσs.
Figure 6.28. Checking welded structure under fatigue conditions in the case of constant amplitude loading
The general methodology of fatigue verification is described in Figure 6.29.
Advantages and disadvantages
This method is relatively simple to use if the nominal stress is clearly defined and the type of assembly indexed in the catalog. On the other hand, in the general case (complex structure/loading), the nominal stress cannot always be defined in terms of the resistance of materials and the reference frame is unknown.
Moreover, nominal stress does not take account of the assembly’s geometry. For example, it does not consider the presence of a welded fastener, or of that of the corresponding weld bead, and therefore of the stiffness imparted by them. This is why an S-N curve exists for each type of assembly and that, for the same assembly, there can be several curves, depending on the dimension of the assembly and the type of loading.
6.2.4. Geometric structural stress method
6.2.4.1. Principle of the method
It thus seems sensible to use another stress definition that takes account of the geometric effects of the welded connection, which includes not only the total geometry of the assembly but also the shape of the weld bead, the profile of connection between this bead and the base sheet metal, and, possibly of very local notch effects (see Figure 6.30).
Nevertheless, the definition of local stress is fraught with difficulty, both experimentally and in calculation; moreover, such a stress is random in value because of local geometric variations caused by welding operations. It is however obvious that the value of this local stress governs the fatigue life of the assembly to a certain extent. This stress particularly influences the duration of fatigue crack initiation.
Consequently, an intermediate step consists of adopting as a dimensioning stress the geometric stress, σG, which depends only on the assembly’s geometry and loading.
This method applies only for initiation at the weld toe, where the concept of geometric welding quality has some relevance.
The advantage of establishing S-N curves in geometric structural stress, as compared to existing curves which are established in nominal stress, is that we are then able to use only one S-N curve whatever the loading and whatever the geometry, for the same group of assemblies (for example fillet welds). Moreover, for real structures, where the nominal stress (distant stress) is often difficult to define, in particular because of the proximity of other connections, the geometric structural stress can be evaluated starting from finite element calculations on the whole of the structure and the assembly under consideration.
Moreover, starting from these S-N curves, certain assembly configurations not currently in the codes can be dimensioned. Thereafter, the use of the geometric structural stress makes it possible for S-N curves to be determined according to the welding quality, and thereby account for the local geometry of the weld bead.
However, there is not, at present, any general method to determine the geometric structural stress nor an associated S-N curve to cover every type assembly group for welded plates. On the other hand, such a method is clearly defined and used in the case of tubular assemblies in offshore oil rig construction, and in the case of assemblies of thin sheet steel in the automotive field [FAY 95].
Figure 6.30. Definition of local (σL), geometric (σG) and nominal (σn) stresses (example: assembly subjected to bending stress)
6.2.4.2. Definition of geometric stress
In Eurocode 3, the geometric stress is defined as: “the maximum principal stress in the parent metal, at the weld toe, taking into account the effects of stress concentration, due to the overall geometry of a particular detail of construction, but excluding the effects of local stress concentration, due to the geometry of the welding and discontinuities in the bead and the adjacent parent metal”.
Geometric structural stress is thus an aspect of design or dimensioning which takes account of the total geometry of the assemblies and the loadings; it thus does not have a physical meaning since it does not take account of the actual weld geometry of the bead. It is determined right from the weld toe, as representative of the stresses at the intersection (see Figure 6.31).
It can be obtained numerically by using the finite element method. The advantage of the finite elements method lies in it allowing the definition, not only of the maximum stress value, but also the point of greatest loading (hot spot) as well as the the stress field configuration throughout the structure.
Possible fields of application
In the case of structural analyzes, where the nominal stress is easy to determine and where the object to be calculated exists in procedural catalogs, the traditional method (S-N curve in nominal stress) can be used.
In the other cases, the geometric structural stress must be determined starting from a finite elements calculation, and this must be associated with S-N curves determined with the same definition of the geometric structural stress.
Determination of structural geometric stress
The finite elements method used must satisfy two criteria:
– evaluate a stress field, in the vicinity of the weld toe, as near to reality as possible,
– lead to a fast and inexpensive application.
For this, the type of element selected must be as simple as possible. All the elements located along the intersecting line of a surface must have the same dimension, or at least be in the direction perpendicular to the intersection; it is thus possible to the results being undesirably affected by the mesh size. In addition, it is important that the points where the stresses are calculated (Gaussion points) are correctly placed, i.e. outside the zone which has a 3D behavior, and if possible directly associated with the weld toe.
6.2.4.3. Practical use of the method
The method of geometric constraint applies to the points described hereafter.
Definition of the S-N design curve in structural geometric stress
The S-N design curve, in structural geometric stress, can be determined starting from tests carried out on assemblies for which the extent of calculated or measured stress is expressed in geometric stress and the number of cycles is that defined for this level of stress range according to the failure criterion [HUT 92].
Figure 6.32 presents the steps followed to determine the S-N curve, in structural geometric stress.
Calculation of the fatigue life of an assembly
Knowing the S-N curve in geometric (structural) stress for the type of assembly to be checked, the geometric stress method makes it possible to determine the fatigue life of the assembly, N (see Figure 6.33).
Determination of the S-N design curve in nominal stress, of a new construction detail
In the absence of experimental results, the geometric (structural) stress method can be applied to the determination of the S-N design curve, in nominal stress, of a construction object close to a case of the standard catalog or of the regulations [HUT 92].
In this case, we initially proceed with numerical modeling, both of the assembly considered and that of the catalog, before deducing the new S-N curve of the subject under consideration (see Figure 6.34).
6.3. Bibliography
[COL 82] COLLECTIF, La résistance à la fatigue des assemblages soudés à l’arc en acier de construction métallique, Collection ATS-OTUA, 1982.
[COL 85] COLLECTIF, Guides pratiques sur les ouvrages en mer, Assemblages tubulaires soudés, Editions Technip, 1985.
[CTI 00] CTICM, Recommandations pour la conception en fatigue des assemblages et des composants soudés, IIS — Document XIII — 1539-96, CTICM, 2000.
[EUR 92] EUROCODE, Design of Steel Structures — Chapter 9: Fatigue EUROCODE 3 (1992).
[FAY 95] FAYARD J.L., BIGNONNET A., DANG VAN K., “Fatigue design of welded thin sheet structures”, Fatigue Design 95, vol. II, September 1995.
[GUR 79] GURNEY T.R., Fatigue of Welded Structures, Cambridge University Press, 1979.
[HUT 92] HUTHER M., PARMENTIER G., HENRY J., Hot spot stress in cyclic fatigue for linear welded joints, IIS — Document XIII — 1466-92, 1992.
[HUT 94] HUTHER I., PRIMOT L., LIEURADE H.P., JANOSCH J.J., COLCHEN D., DEBIEZ S., “Influence de la qualité de la soudure sur la résistance à la fatigue d’un acier HLE du type E460”, Tôle en acier HLE, choix et mise en volume, Publications CETIM, 1994.
[HUT 99] HUTHER I., GORSKI S., LIEURADE H.P., LABORDE S., RECHO N., “Longitudinal non-loaded welded joints, geometric stress approach”, Welding in the World, vol. 43, no. 3, p. 20-26, 1999.
[LIE 73] LIEURADE H.P., “La résistance à la fatigue des assemblages soudés”, Journées “Métallurgie du soudage” (Société Française Métallurgie), Marseille, 8-9 November 1973.
[LIE 91] LIEURADE H.P., BIGNONNET A., “Les techniques d’amélioration de la tenue en fatigue des composants soudés”, Traitements de surface et composants mécaniques, Editions CETIM, p. 79-112, December 1991.
[LIE 92] LIEURADE H.P., WYSEUR M., TOURRADE J.C., “Effet de traitements de parachèvement sur le comportement en traction ondulée ou en flexion ondulée d’assemblages bout à bout en acier E 490”, La fatigue des composants et des structures soudés, Publication CETIM, 1992.
[LIE 97] LIEURADE H.P., “Rôle des contraintes résiduelles dans le comportement en fatigue des composants soudés”, Revue Française de Mécanique, no. 1997-3, p. 191-205, 1997.
[LIE 00a] LIEURADE H.P., HUTHER I., “Introduction aux méthodes de dimensionnement à la fatigue des composants soudés”, Mécanique et Industrie, vol. 1, no. 5, p. 465-477, 2000.
[LIE 00b] LIEURADE H.P., HUTHER I., “Dimensionnement des assemblages soudés en mécano-soudage, Calcul à la fatigue”, Soudage et Techniques convexes, p. 3-8, May-June 2000.
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1 Chapter written by Henri-Paul LIEURADE.