Due to high stress concentrations, welded joints represent the most common locations of fatigue crack initiation in steel structures that are prone to fatigue. Welding affects material properties by the process of heating, cooling, and combining basic and additional material. Since welding is the primary process of joining elements in steel structures, it is obvious that fatigue assessment during the design and maintenance process becomes inevitable. There are many fatigue assessment methods of welded joints, but their precision remains questionable. This paper represents a review of the most common fatigue assessment methods used for welded steel joints. As a result of this review, areas that require additional research are highlighted.
During their lifetime, many steel structures such as road and railway bridges, oil and gas exploitation platforms (offshore platforms), windmills, and so on are subjected to a high number of repetitive cyclic stresses. Over time, those stresses can cause damage, such as cracks, at critical locations. This phenomenon is called “fatigue.” It can be defined as a progressive localised process in which damage continuously accumulates in a structure or structural element due to the effect of cyclic loading, which has much less intensity than the static resistance of an observed structure or structural detail. A study by Oehme [
Fatigue cracks are usually initiated at locations of a sudden change in the geometry or notch locations [
This paper presents a review of peculiarities of fatigue-critical welded joints and the most important methods for design and fatigue life assessment of welded steel structures that are prone to fatigue. Areas that require additional research are highlighted as a result of review.
The term “fatigue” was first mentioned in the 19th century to describe the failure of a structure or structural element subjected to cyclic loading. Research of fatigue was first carried out by August Wöhler who investigated the failure of train axles. He detected that structural loading that is well below its static resistance does not cause any damage. However, in the case of repeating the same loading over a prolonged period of time, it can cause failure of the structure or structural element. In the 19th century, fatigue was a mysterious phenomenon because fatigue damage could not be seen, and failure occurred without any warning. In the 20th century, it became known that cyclic (repeated) structural loading initiates the fatigue mechanism and, respectively, crack initiation and propagation. Since this fatigue phenomenon became recognised, much research has been conducted, and significant progress in developing fatigue assessment methods, understanding the mechanism of fatigue of structures and materials, and the designing of fatigue resistant details has been made. However, this phenomenon still requires further investigation [
A chronology of fatigue development from 1837 to 1994 is given by Schütz [
An understanding of the fatigue mechanism is a prerequisite when considering different factors that affect fatigue life and choosing appropriate assessment methods. The fatigue life of a structure or structural element is measured from the crack initiation and crack propagation phase. Cracks made by cyclic loading usually occur at the surface of a structural element where fatigue damage comes in the form of microscopic cracks in crystallographic slip planes. This phase is called the “Crack Initiation Phase.” Furthermore, cracks propagate from localised plastic strain to macroscopic size in a direction perpendicular to the loading direction, which presents the crack propagation phase [
Modern fatigue theories separately analysed every phase of the fatigue process. Crack initiation theories are based on the assumption that fatigue cracks appear with local stress or strain concentrations on the surface of a structural element because of different geometrical shapes like holes, notches, discontinuity, and so on. Crack propagation and final fracture (failure) is analysed by fracture mechanics which considers the crack propagation rate in relation to the stress state in crack tip.
Steel structures contain a large number of geometrically complex welded details. Welding affects the material properties during the process of heating, cooling, and by connecting base and additional material. This results with inhomogeneity within welds. Welds always contain certain imperfections such as notches, pores, voids, insufficient penetration, and incomplete connection of base and additional material. Impacts of imperfections on fatigue life of welded joints are reviewed by Hobbacher [
Stress concentration in weld location.
Welding is being conducted by melting base and additional material using a concentrated source of heat. The occurrence of residual stresses in a heat-affected zone and distortions of elements due to deformations caused by heating is a result of rapid cooling after welding. Local stress concentrations that are being added to cyclic stresses from external loading are caused by residual stresses on the weld root or toe and in certain cases fatigue life is reduced [
As previously mentioned, the two phases in the fatigue process are the crack initiation phase and the propagation phase. For nonwelded details that are prone to fatigue, most of the fatigue life is related to the crack initiation phase, while the crack propagation phase is negligible. Welded joints contain already mentioned imperfections in locations where cracks can begin to propagate with the first loading cycle. Therefore, the crack initiation phase is negligible in welded joints and the fatigue limit of welded details depends on the initial size of the imperfection inside the weld [
In order to improve welded steel details, it is possible to use postweld treatment methods. Most common are Burr grinding (BG), TIG dressing (TIG), hammer peening, needle peening, and HFMI (High Frequency Mechanical Impact) in order to remove imperfections caused by welding [
Fatigue damage already occurs with relatively small stresses, far from material yielding. That is why within different methods of fatigue assessment, stress assessment based on theory of elasticity is justified. A key role in fatigue resistance assessment of welded components is played by the precise assessment of the loading and geometry effect. That is almost impossible to achieve without use of advanced computer tools based on a finite element method. Examples of calculations of relevant loading within assessment of fatigue life can be found in [
An issue of fatigue of welded joints additionally complicates if cyclic stresses in welded details acts in more directions. This phenomenon is called multiaxial fatigue, which is considerably unfavourable for welded joints in relation to uniaxial fatigue [
Multiaxial fatigue loading can be proportional, when the direction of principal stresses is constant, and disproportional, when directions of stresses are variable through time. In case of proportional loading, EN 1993-1-9 [
Conservatism of interaction equations in EN 1993-1-9 [
Nowadays, advantages of multiaxial fatigue assessment by spectral analysis of stress are more recognized than classical stress time history. Time histories that are used for assessments often show large statistical variations, and every next stress recorded in time is different. Moreover, simulation of longer time history multiaxial stress amplitude can take time. These problems can be solved by the spectral approach and review of multiaxial fatigue assessment methods with the spectral approach given in [
Fatigue life assessment of welded joints is a very complex and challenging procedure. Welded joints in large steel structures can be subjected to various loading effects, depending on their geometric configuration and degree of complexity. Fatigue assessments explicitly or implicitly include comparison of loading, stresses or strains with their critical values which cause damages, strains, initial crack, or failure. Classical methods for stress state assessment, as well as databases with results of experimental research details, were very limited. Details of designing and modelling in practice were based on experience gained by a trial and error method [
Today there are many approaches for fatigue life assessment, depending on the way local stress concentration is taken into consideration. Global methods result directly from internal forces and moments in critical cross section under the assumption of linear stress distribution. Effects of local concentrations on the loading side are neglected. Local fatigue assessments result from local parameters (local stresses or deformations), taking into consideration effects of local geometry at the observed location. Most used variants of local and global approaches are shown with Figure
Global and local approaches for fatigue strength and fatigue life assessment [
Guidelines and standards for fatigue assessment are mostly based on a nominal stress approach, which is in fact a global concept. However, failure of structural elements due to fatigue is a localized process. Local parameters and geometry have the maximum effect on fatigue strength and fatigue life of structural elements. Comprehensive literature which contains local approaches for nonwelded and welded structures is collected by Radaj [
To conduct a precise fatigue assessment of welded steel structures, it is necessary to have equally accurate information about loading; even the smallest change in loading value could cause a big difference in the assessment results. Moreover, determination of loading by finite element method is idealization and does not include all the parameters that affect structural behaviour. The only way of getting the precise information about loading is trough field measurement, where real deformations can be measured and noted by different sensors attached to structural elements. In that way, the most precise foundation for fatigue assessment is being gained.
Long-term systems for monitoring structural conditions, the so-called Structural Health Monitoring Systems, are now more widely used and developed [
The first step in the fatigue reliability analysis of structures is the formulation of a mathematical model that would ideally include more variables that affect fatigue behaviour. After that, probability and statistical method analysis are conducted [
In fatigue assessment, the two main approaches that are mostly used during the designing phase and the assessment of reliability level are the S-N approaches in combination with the Miner rule and fracture mechanics which is used in phases of state assessments and assessment of residual fatigue life of structure. In the first instance, the purpose of fatigue analysis is to determine fatigue life of structure or structural element with target reliability or determination of inspection intervals, while in other cases, the aim is to determinate inspection intervals or remaining time to repair.
To successfully conduct an evaluation of the fatigue of steel structure, it is necessary to evaluate the fatigue life of every structural component. Detail resistance is represented by the corresponding S-N curve, which is obtained as a result of testing samples subjected to variable stresses of constant and variable amplitudes. It is determined as the relationship between variable stresses,
If curves are shown in logarithmic scale, lines are gained, Figure
Definitions of loadings and S-N curve welded details.
It can be seen from Figure
During fatigue assessment, characteristic details are classified into categories (FAT classes) in a way that one standardized curve represents more details. In standards, detail category represents details of stress range expressed as characteristic fatigue strength in MPa for number of stress cycles
As previously mentioned, S-N curves are based on experimental results obtained mostly under constant amplitudes, while in reality, details are subjected to stresses with variable amplitudes. Using a histogram, it is possible to show the variable stress spectrum where every block is defined by stress amplitude, Δ
Palmgren–Miner hypothesis of linear damage accumulation.
Figure
This procedure is called Palmgren–Miner Hypothesis of Linear damage accumulation, commonly known as the Miner rule [
Failure occurs when the sum of each partial damage equals one. The Miner rule can also be applied using the concept of equivalent stress range. It represents fictive constant amplitude stress range Δ
The fatigue life assessment of a stochastically loaded structure is related to the correlation of the stress spectrum and resistance of the considered detail. Stress spectrum is usually unknown and can be obtained by different measures and simulation. To obtain stress amplitudes from a stress history, it is necessary to use one of the stress range counting methods, such as the reservoir or rain flow method [
S-N approach does not differ from crack initiation and propagation, but considers the overall fatigue life of a structural element. In the case of geometrically complex structure details, where it is not possible to classify into a certain category, it is necessary to use more advanced methods for fatigue assessments (local approaches) which precisely determine stress values in the observed location. Application of local approaches is justified with the fact that even the fatigue process of local character cannot be well described by global approaches. Limit state function is formed by basic variables on a side of resistance and loading. Load model is defined by its own value and frequency of occurrence, while resistance model is obtained by fatigue tests. A review of the most used distribution functions for load and resistant model is given in [
As already mentioned, S-N curve represents the relationship between stress ranges with constant amplitudes and the number of stress ranges until failure. If it is about variable amplitudes, the Miner rule is used. For ergodic processes of stress ranges, stress history scatter can be neglected and damage
According to this model, failure occurs when
In that case, limit state function can be written as
Applying structural reliability methods, it is possible to calculate the probability of failure or reliability index for the fatigue life of structural detail which can be used as a foundation for decision-making for maintaining structure.
This is the most used approach for fatigue life assessment of steel structures that are prone to fatigue, and it is also adopted in standards. This approach is based on average stress in the corresponding cross section. The stress has been calculated by classical structural mechanics under the assumption of linear elastic theory. Local effect which causes stress magnification (concentration) is neglected, but it considers geometrical modification that has significant impact on stress variation (e.g., cut out holes). Local effects are implicitly taken into account by S-N curves. Figure
Nominal stress in a beam component.
Category of details and corresponding S-N curves based on nominal stresses are available in most design guidelines. Since the category of detail depends on element geometry, loading, and crack location, considered welded detail must be similar to detail that is given in guidelines.
Nominal stress-based approach is not suitable for geometrical complex details which cannot be assigned to corresponding S-N curve or in case that it is impossible to calculate nominal stress. In this case, it is necessary to use approaches that consider local effects (local approaches).
Initially, fatigue assessment of welded joints based on Hot Spot stress approach was used for welded joints of tube elements [
Examples of fatigue crack initiation locations in Hot Spot [
As previously mentioned, fatigue strength of every welded detail depends on imperfections inside the weld and local stress concentrations due to the effect of detail geometry or the notch effect inside weld. Total Hot Spot stress consists of components of membrane stresses, plate bending stresses, and the nonlinear stress component due to the notch effect on a weld toe, Figure
Total stress in Hot Spot.
The basic idea of the Hot Spot stress approach is to exclude the nonlinear component from a stress calculation since it is impossible to know in advance the actual geometry of the weld. In this approach, S-N curves should cover only those effects that are related to the local stress concentration inside a weld (notch effect) and local weld imperfections. Consequently, a smaller number of S-N curves are needed than that in cases of nominal stress approach. Hot Spot stress approach is mainly used when it is impossible to clearly define nominal stress due to complex geometry or in cases when considered detail cannot be categorized in one of the nominal stress categories given in standards.
In situations when nominal stress can be simply calculated, stress concentration factor
An example of application of stress concentration factors in calculations of Hot Spot stress in multiaxial fatigue assessment is given in [
In most cases, it is impossible to analytically determine Hot Spot stress. Then the Finite Element Method is used [
During the calculations by finite element method, obtained results often deviate from real state. The reason for that is geometrical idealization which neglects geometrical misalignments as a result of the fabrication process. They cause secondary bending moments which should be taken into account in a way to make a finite element model with idealized geometry, and then obtained nominal stress should be modified with factor
Hot Spot stresses can be also obtained by measurements on existing structures. Strain is measured in reference points from which extrapolation on the Hot Spot location is conducted, Figure
Definition of Hot Spot stress according to [
Hot Spot stress is derived by linearization of stresses outside the weld. According to IIW recommendations [
Fatigue assessment with this method follows the same procedure as the nominal stress approach. Hot Spot stress is compared with corresponding S-N curve of a certain structural detail. S-N curves for Hot Spot stresses can be found in [
However, the extrapolation procedures mentioned above lack consistency for general applications [
In order to remove or minimize finite element size effect on stress calculation, the mesh-insensitive structural stress method and master S-N curve approach [
Using the mesh-insensitive structural stress method, it is possible to extract structural stress parameter. Stress parameter has an ability to differentiate stress concentration effects with different joint types, which is not always possible with conventional Hot Spot Stress extrapolation. Due to its mesh insensitivity in finite element solutions, it is possible to use conventional finite element models with coarse mesh. The validation of such stress parameter is demonstrated in [
Structural stress is obtained by introducing equilibrium conditions, which indicate the mesh size insensitivity. Figure
(a) Local through thickness stress distribution obtained by finite element method and (b) corresponding simple structural stress distribution [
Within this paper, solid model with monotonic distribution will be presented. Definition of other models such as shell models or solid model with nonmonotonic distribution can be found in [
Structural stress calculation procedure [
Section B-B is a location where stresses can be obtained from a finite elements solution. By imposing equilibrium conditions between these two sections, structural stress components
Equation (
In paper [
Today, this approach is increasingly represented in the industry, and the guidelines for fatigue assessment with this approach can be found in the design codes [
Stress evaluation in notch with referent radii.
Local stress concentrations are caused by notches and other imperfections inside welded joints, which decreases fatigue life of the welded joint. Stresses inside the weld are a sum of local stresses which are caused by the geometry of details and stresses because of the weld itself. Notch stress (toe or root) of the weld can be very high depending on notch sharpness or radius [
In a fatigue assessment approach based on notch stress, there are two most used imaginative radii of 1 mm and 0.05 mm. Every notch in the weld root or toe is being modelled without discontinuity under assumption of linear elastic behaviour of material. Use of a fictive radius of 0.05 mm, which is based on the relation between the stress intensity factor and notch stress [
The reference radius of 1 mm is a fictive radius derived from microstructural support theory [
Fatigue assessment based on notch stress follows the same procedure as the nominal stress approach, with consideration of local effective notch stress instead of global stress. Assessment procedure is based on comparison of effective fatigue stress amplitude with certain S-N curve that represents resistance. Those kinds of curves are being suggested in IIW recommendations [
This approach was developed in the 1960s, relating to the estimated time for cracks to initiate inside the element subjected to fatigue. It is being used in cases when strain on the observed spot is not completely elastic, but contains a plastic component. To modulate the crack initiation period, an approach that considers repetitive local yielding is being used [
Due to all the above-mentioned peculiarities of welded joints, this approach should only be used in consideration of stress-strain cyclic properties of the base material in a welded joint [
Crack propagation in material that is prone to fatigue is described by fracture mechanics. This approach was first introduced by Paris et al. [
(a) S-N curve with given stress amplitudes in relation to number of stress variations. (b) Crack size in relation to number of variations for one test.
The relationship between geometrical imperfections, material properties, and stresses inside the detail [
Fracture mechanics studies the occurrence of initial crack and its propagation to the fracture. Crack growth follows a law known as the Paris–Erdogan law of crack growth [
Figure
Typical curve of crack growth inside metals.
Cracks inside the material can propagate in three modes. Mode I (Figure
Basic modes of crack propagation. (a) Mode I. (b) Mode II. (c) Mode III.
The total fatigue life of an element that is prone to fatigue can be obtained from the onset of the initiation period and stabile propagation period. In welded joints, the crack initiation period is quite short, so it can be neglected. Fatigue life of welded joints can be obtained with integration of the Paris–Erdogan law.
Equation (
J integral represents a mathematical description of the energy released during crack growth. It is introduced by Rice in 1968 [
CTOD represent the value of the crack separation surface due to plastification [
Today, fracture mechanics is one of the basic approaches for fatigue assessment of welded joints. Possible application of the fracture mechanics in fatigue assessments was shown by Hobbacher in his work [
There is a number of probabilistic research works on the fatigue of welded steel structures based on the fracture mechanics approach. Based on nondestructive evaluation (NDE) data, fracture mechanics probabilistic model, considering various uncertainties such as the initial crack size, material properties, and number of stress cycles, was proposed by Zhao and Haldar [
At
Based on the review of fatigue assessment methods of welded details in steel structures, the following conclusions can be drawn: Fatigue of welded details is still an insufficiently researched phenomenon which is under the influence of many parameters such as load, geometry, material quality, production process, and environmental effect. Because of their imperfections, welded joints additionally complicate the fatigue assessment process. Today, global approaches are adopted in the international standards for design and are best suited for engineering evaluations. With the nominal stresses approach, local effects are indirectly considered on the resistance side (S-N curve), and it is necessary just to determine nominal stress in observed location. Local approaches consider a bigger number of parameters on the load side, which decreases the necessary number of S-N curves. However, the possibility of a mistake increases, so the precision of an assessment depends on engineer’s experience. Local approaches, often unjustified, neglect the influence of residual stresses. In the future, it is necessary to further investigate the correlation between the numerical model and the actual behaviour of elements. The extrapolation procedures in Hot Spot approach lack consistency due to its sensitivity on finite element mesh size and element types at weld discontinuities. One of the solutions for this problem is the mesh-insensitive structural stress method and master S-N curve approach. An issue of welded joints is additionally complicated if the elements are subjected to multiaxial fatigue. Today, standards propose a number of interaction terms for the assessment of multiaxial fatigue, but expressions show a certain degree of conservatism. It is necessary to additionally investigate an effect of the components of nominal stress on the shear stress damage process, which could give better insight in interaction behaviour. Fracture mechanics describes the fatigue crack propagation, but it is still unexplored enough that it leaves space for further research, in particular, with multiaxial fatigue assessment and taking into account residual stresses. Regardless of the accuracy of the methods of fatigue assessment of welded details, the essential role remains to the load, whose intensity and frequency are very difficult to assume, particularly in the case of the large infrastructure welded steel structures prone to fatigue. Although crack initiation period for welded joints is negligible, it is possible to substantially extend it with variable postwelding treatments and thus increase the overall resistance of the welded joint prone to fatigue.
The authors declare that they have no conflicts of interest.