Fatigue Resistance

Abstract

Fatigue resistance is usually derived from constant or variable amplitude tests. The fatigue resistance data given here are based on published results from constant amplitude tests. Guidance on the direct use of fatigue test data is given in Sects. 3.7 and 4.5.

The original version of this chapter was revised. Belated correction has been updated. An erratum to this chapter is available at https://doi.org/10.1007/978-3-319-23757-2_8

The original version of this chapter was revised. An erratum to this chapter can be found at 10.1007/978-3-319-23757-2_7

3.1 Basic Principles

Fatigue resistance is usually derived from constant or variable amplitude tests. The fatigue resistance data given here are based on published results from constant amplitude tests. Guidance on the direct use of fatigue test data is given in Sects. 3.7 and 4.5.

As generally required, the fatigue resistance data presented here are expressed in terms of the same type of stress as that, used to determine the test data upon which they are based.

The present fatigue endurance resistance data for welded joints are expressed as S-N curves. However, there are different definitions of failure in conventional fatigue endurance testing. In general, small welded specimens are tested to complete rupture, which is usually very close to through-thickness cracking. In large components or vessels, the observation of a larger or through-wall crack is usually taken as a failure. The fatigue failure according to the present S-N curves effectively corresponds to through-section cracking. The S-N curves are of the form:

$$ N = \frac{C}{{\Delta \sigma^{m} }}\quad {\text{or}}\quad N = \frac{C}{{\Delta \tau^{m} }} $$

(3.1)

where the slope m may adopt different values over the range of possible fatigue lives, from the low endurance to the high cycle regime (see Sect. 3.2).

For fracture mechanics analyses, the fatigue resistance data are in the form of relationships between ΔK and the rate of fatigue crack propagation (da/dN). The fatigue crack growth rate data are derived by monitoring crack propagation in tests.

All fatigue resistance data are given as characteristic values, which are assumed to represent a survival probability of at least 95 %, calculated from the mean value on the basis of two-sided 75 % tolerance limits of the mean, unless otherwise stated (see Sect. 3.7). Other existing definitions as e.g. a survival probability of 95 % on the basis of 95 % one-sided limit of the mean or mean minus two standard deviations corresponding to a survival probability of 97.7 % are practically equal for engineering applications.

The (nominal) stress range should be within the limits of the elastic properties of the material. The range of the design values of the stress range shall not exceed 1.5 · f_y for nominal normal stresses or 1.5 · f_y/√3 for nominal shear stresses.

The fatigue resistance of a welded joint is also limited by the fatigue resistance of the parent material.

3.2 Fatigue Resistance of Classified Structural Details

The fatigue assessment of classified structural details and welded joints is based on the nominal stress range. In most cases, structural details are assessed on the basis of the maximum principal stress range in the section where potential fatigue cracking is considered. However, guidance is also given for the assessment of shear loaded details, based on the maximum shear stress range. Separate S-N curves are provided for consideration of normal or shear stress ranges, as illustrated in Figs. 3.1, 3.2 and 3.3 respectively.

Fig. 3.1

Fatigue resistance S-N curves for steel, normal stress, standard applications

Fig. 3.2

Fatigue resistance S-N curves for steel, normal stress, very high cycles applications

Fig. 3.3

Fatigue resistance S-N curves for aluminium, normal stress

Care must be taken to ensure that the stress used for the fatigue assessment is the same as that given in the tables of the classified structural details. Macro-structural hot spot stress concentrations not covered by the structural detail of the joint itself, e.g. large cut-outs in the vicinity of the joint, have to be accounted for by the use of a detailed stress analysis, e.g. finite element analysis, or appropriate stress concentration factors (see Sect. 2.2.2).

The fatigue curves are based on representative experimental investigations and thus include the effects of:

• structural hot spot stress concentrations due to the detail shown

• local stress concentrations due to the weld geometry

• weld imperfections consistent with normal fabrication standards

• direction of loading

• high residual stresses

• metallurgical conditions

• welding process (fusion welding, unless otherwise stated)

• inspection procedure (NDT), if specified

• post weld treatment, if specified

Furthermore, within the limits imposed by static strength considerations, the fatigue curves of welded joints are independent of the tensile strength of the material.

Each fatigue strength S-N curve is identified by the characteristic fatigue strength of the detail in MPa at 2 million cycles. This value is the fatigue class (FAT).

The slope of the fatigue strength S-N curves for details assessed on the basis of normal stresses (Fig. 3.1) is m = 3.00 if not stated expressly otherwise. The constant amplitude knee point is assumed to correspond to N = 10⁷ cycles.

The slope of the fatigue strength curves for details assessed on the basis of shear stresses (Figs. 3.2, 3.4, 3.5 and 3.6) is m = 5.00, but in this case the knee point is assumed to correspond to N = 10⁸ cycles.

Fig. 3.4

Fatigue resistance S-N curve for shear at steel, standard applications

Fig. 3.5

Fatigue resistance S-N curves for shear at steel, very high cycle applications

Fig. 3.6

Fatigue resistance S-N curve for shear at aluminium

The conventional assumption is that the S-N curves terminate at a fatigue limit, below which failure will not occur, or in which case the S-N curve becomes a horizontal line. Traditionally, this constant amplitude fatigue limit (CAFL), also referred as ‘knee point’, is defined in terms of the corresponding fatigue endurance on the S-N curve, N = 10⁷ being the most common assumption (see Fig. 3.1). However, new experimental data indicate that a CAFL does not exist and the S-N curve should continue on the basis of a further decline in stress range of about 10 % per decade in terms of cycles, which corresponds to a slope of m = 22.

This issue is only relevant if a design is expected to withstand very large numbers of stress cycles, such as for example at rotating welded machine parts. The matter is still under development and users should consult the latest relevant literature. Meanwhile, the nominal stress-based characteristic S-N curves are presented with the extrapolation beyond 10⁷ cycles at a slope of m = 22 in Figs. 3.2 and 3.3.

The descriptions of the structural details only partially include information about the weld size, shape and quality. The data refer to a standard quality as given in codes and standard welding procedures. For higher or lower qualities, conditions of welding may be specified and verified by test (Sect. 3.7).

As appropriate, the fatigue classes given in Table 3.1 shall be modified according to Sect. 3.5. The limitations on weld imperfections shall be considered (Sect. 3.8).

Table 3.1 Fatigue resistance values for structural details in steel and aluminium assessed on the basis of nominal stresses

All butt weld joints shall be fully fused and have full penetration welds, unless otherwise stated.

All the S-N curves for weld details are limited by the S-N curve for the parent metal, which may vary with material tensile strength. It is recommended that a higher fatigue class for the material than stated (i.e. FAT 160 for steel or FAT 71 for aluminium alloys) should only be assumed if verified by test.

The S-N curves for weld details refer to specific failure modes, generally fatigue crack growth from the weld toe through the base material, from the weld root trough the weld throat, or from the weld surface through the weld and then into the base material. In an assessment of a given weld detail it is important to consider all possible potential failure modes for the direction of loading. E.g. at cruciform joints with fillet welds, both potential failure modes, such as toe crack through plate and root crack through weld throat, have to be assessed.

3.3 Fatigue Resistance Assessed on the Basis of Structural Hot Spot Stress

3.3.1 Fatigue Resistance Using Reference S-N Curve

The S-N curves for assessing the fatigue resistance of a detail on the basis of structural hot spot stress (Sect. 2.2.3) are given in the Table 3.3 for steel and aluminium, where the definition of the FAT class is given in Sect. 3.2. The resistance values refer to the as-welded condition unless stated otherwise. The effects of high tensile residual stress are included. Only small effects of misalignment are included, see also Sect. 3.8.2. The weld shape should be similar to that shown below (Table 3.3).

Table 3.2 Fatigue resistance values for structural details on the basis of shear stress

Table 3.3 Fatigue resistance against structural hot spot stress

The design value of the structural hot spot stress range Δσ_hs shall not exceed 2 · f_y. The fatigue resistance of a welded joint is limited by the fatigue resistance of the base material.

For hollow section joints, special hot-spot stress design S-N curves have been recommended by the IIW [14]. These tubular joint design curves should not be applied to other types of structure.

3.3.2 Fatigue Resistance Using a Reference Detail

The tables of the fatigue resistance of structural details given in Sect. 3.2, or fatigue data from other sources which refer to a comparable detail, may be used. The reference detail should be chosen to be as similar as possible to the detail to be assessed.

Thus, the procedure will be:

• (a) Select a reference detail with known fatigue resistance, which is as similar as possible to the detail being assessed with respect to geometric and loading parameters.

• (b) Identify the type of stress in which the fatigue resistance is expressed. This is usually the nominal stress (as in the tables in Sect. 3.2).

• (c) Establish a FEA model of the reference detail and the detail to be assessed with the same type of meshing and elements following the recommendations given in Sect. 2.2.3.

• (d) Load the reference detail and the detail to be assessed with the stress identified in b).

• (e) Determine the structural hot spot stress σ_{hs, ref} of the reference detail and the structural hot spot stress σ_{hs, assess} of the detail to be assessed.

• (f) The fatigue resistance for 2 million cycles of the detail to be assessed FAT_assess is then calculated from fatigue class of the reference detail FAT_ref by:

$$ FAT_{assess} = \frac{{\sigma_{hs,\;ref} }}{{\sigma_{hs,\;assess} }}\,\cdot\,FAT_{ref} $$

(3.2)

3.4 Fatigue Resistance Assessed on the Basis of the Effective Notch Stress

3.4.1 Steel

The effective notch stress fatigue resistance against fatigue actions, as determined in Sect. 2.2.4 for steel [24], is given in Table 3.4. The definition of the FAT class is given in Sect. 3.2. The fatigue resistance value refers to the as-welded condition. The effect of high tensile residual stresses is included. The effect of possible misalignment is not included.

Table 3.4 Effective notch fatigue resistance for steel

The fatigue resistance of a weld toe is additionally limited by the fatigue resistance of the parent material, which is determined by the use of the structural hot-spot stress and the FAT class of the non-welded parent material. This additional check shall be performed according to Sect. 2.2.3.

3.4.2 Aluminium

The same regulations apply as for steel (Table 3.5).

Table 3.5 Effective notch fatigue resistance for aluminium

3.5 Fatigue Strength Modifications

3.5.1 Stress Ratio

3.5.1.1 Steel

For effective stress ratios, based on consideration of both applied and residual stresses, R < 0.5 a fatigue enhancement factor f(R) may be considered by multiplying the fatigue class of classified details by f(R). This factor depends on the level and direction of residual stresses. Here, all types of stress which are not considered in fatigue analysis and which are effective during service loading of the structure are regarded as residual stress. The ranking in categories I, II or III should be documented by the design office. If no reliable information on residual stress is available, an enhancement factor f(R) = 1 is recommended. Other factors should only be used if reliable information or estimations of the residual stress level are available [47].

The following cases are to be distinguished (Fig. 3.7):

Fig. 3.7

Enhancement factor f(R)

• I. Unwelded base material and wrought products with negligible residual stresses (<0.2 · f_y), stress relieved welded components, in which the effects of constraints or secondary stresses have been considered in analysis. No constraints in assembly

  $$ \begin{array}{*{20}l} {\text{f}}\left( {\text{R}} \right) = 1. 6 \hfill & \quad{\text{for}}\;{\text{R}} < - 1\,{\text{or}}\,{\text{completely}}\,{\text{in}}\,{\text{compression}} \hfill \\ {\text{f}}\left( {\text{R}} \right) = - 0. 4\cdot {\text{R}} + 1. 2\hfill & \quad{\text{for}} - 1\le {\text{R}} \le 0. 5 \hfill \\ {\text{f}}\left( {\text{R}} \right) = 1 \hfill & \quad{\text{for R }} > \, 0. 5 \hfill \\ \end{array} $$

  (3.3)

• II. Small-scale thin-walled simple structural elements containing short welds. Parts or components containing thermally cut edges. No constraints in assembly.

  $$\begin{array}{*{20}l} {\text{f}}\left( {\text{R}} \right) = 1.3 \hfill & \quad{\text{for}}\;{\text{R}} < - 1\,{\text{or}}\,{\text{completely}}\,{\text{in}}\,{\text{compression}} \hfill \\ {\text{f}}\left( {\text{R}} \right) = - 0.4\,\cdot\,{\text{R}} + 0.9 \hfill & \quad{\text{for}} - 1 \le {\text{R}} \le - 0.25 \hfill\\ {\text{f}}\left( {\text{R}} \right) = 1 \hfill &\quad {\text{for}}\,{\text{R}} > - 0.25 \hfill \\ \end{array}$$

  (3.4)

• III. Complex two- or three-dimensional welded components, components with global residual stresses, thick-walled components. The normal case for welded components and structures.

  $$ {\text{f}}\left( {\text{R}} \right) = 1\quad \quad \quad \quad {\text{no}}\,{\text{enhancement}} $$

  (3.5)

It should be noted that stress relief in welded joints is unlikely to be fully effective, and additional residual stresses may be introduced by lack of fit during assembly of prefabricated welded components, by displacements of abutments or for other reasons. Consequently, it is recommended that values of f(R) > 1 should only be adopted for welded components in very special circumstances. In several cases, stress relieving might reduce the fatigue properties as e.g. at TMCP steels by reduction of mechanical properties, or at weld roots in single sided butt welds or at fillet welds, by reduction of beneficial residual compressive stress.

Note::

For unwelded or stress relieved steel structures, a simplified approach may be used, which consists in considering only 60 % of the stresses in compression.

3.5.1.2 Aluminium

The same regulations as for steel are recommended.

3.5.2 Wall Thickness

Fatigue resistance modifications are required at the nominal stress method (see Sect. 3.2) and the hot spot structural stress method of type “a” at surface extrapolation as described in Sect. 3.3. It is not required at the effective notch stress method and at the fracture mechanics method (see Sects. 3.4 and 3.6).

3.5.2.1 Steel

The influence of plate thickness on fatigue strength should be taken into account in cases where the site for potential fatigue cracking is the weld toe. The fatigue resistance values given here for steel refer to a wall thickness up to 25 mm. The lower fatigue strength for thicker members is taken into consideration by multiplying the FAT class of the structural detail by the thickness reduction factor f(t):

$$ f(t) = \left( {\frac{{t_{ref} }}{{t_{eff} }}} \right)^{n} $$

(3.6)

where the reference thickness t_ref = 25 mm. The thickness correction exponent n is dependent on the effective thickness t_eff and the joint category (see Table 3.6) [45]. In the same way a benign thinness effect might be considered, but this should be verified by component test.

Table 3.6 Thickness correction exponents

The plate thickness correction factor is not required in the case of assessment based on effective notch stress procedure or fracture mechanics.

For the determination of t_eff, the following cases have to be distinguished (Fig. 3.8):

Fig. 3.8

Definition of toe distance L

$$ {\text{if}}\quad {{\mathbf{L}} \mathord{\left/ {\vphantom {{\mathbf{L}} {\mathbf{t}}}} \right. \kern-0pt} {\mathbf{t}}} > {\mathbf{2}}\quad {\text{then}}\quad {\mathbf{t}}_{{{\mathbf{eff}}}} = {\mathbf{t}} $$

(3.6a)

$$ {\text{if}}\quad {{\mathbf{L}} \mathord{\left/ {\vphantom {{\mathbf{L}} {\mathbf{t}}}} \right. \kern-0pt} {\mathbf{t}}} \le {\mathbf{2}}\quad {\text{then}}\quad {\mathbf{t}}_{{{\mathbf{eff}}}} = {\mathbf{0}}.{\mathbf{5}\,\cdot\,\mathbf{L}}\,{\text{or}}\,{\mathbf{t}}_{{{\mathbf{eff}}}} = {\mathbf{t}}\,\,{\text{which ever is the larger}} $$

3.5.2.2 Aluminium

The same rules as for steel are recommended.

3.5.3 Improvement Techniques

3.5.3.1 General

Post weld improvement techniques may increase the fatigue resistance, generally as a result of an improvement in the weld profile, the residual stress conditions or the environmental conditions of the welded joint. They may be used to increase the fatigue strength of new structures, notably if a weld detail is found to be critical, or as a part of repair or upgrading of an existing structure.

The main improvements techniques are:

• (a) Methods for improvement of weld profile:

  • Machining or grinding of but weld flush to the surface

  • Machining or grinding of the weld transition at the toe

  • Remelting of the weld toe by TIG-, plasma or laser dressing

• (b) Methods for improvement of residual stress conditions:

  • Peening (hammer-, needle-, shot-, brush-peening or ultrasonic treatment)

  • Overstressing (proof testing)

  • Stress relief

• (c) Methods for improvement of environmental conditions:

  • Painting

  • Resin coating

The effects of all improvement techniques are sensitive to the method of application and the applied loading, being most effective in the low stress high cycle regime. They may also depend on the material, the structural detail, the applied stress ratio and the dimensions of the welded joint. Consequently, fatigue tests for the verification of the procedure in the endurance range of interest are recommended (Sects. 3.7 and 2.2.2).

Recommendations are given below for the following post-welding weld toe improvement methods: grinding, TIG dressing, hammer and needle peening.

3.5.3.2 Applicability of Improvement Methods

The recommendations apply to all arc welded steel or aluminium components subjected to fluctuating or cyclic stress and designed to a fatigue limit state criterion. They are limited to structural steels with specified yield strengths up to 900 MPa and to weldable structural aluminium alloys commonly used in welded structures, primarily of the AA 5000 and AA 6000 series but including weldable Al-Zn-Mg alloys.

The recommendations apply to welded joints in plates, sections built up of plates or similar rolled or extruded shapes, and hollow sections. Unless otherwise specified, the plate thickness range for steel is 6 to 150 mm, while that for aluminium is 4 to 50 mm.

The recommended levels of improvement in fatigue strength only apply when used in conjunction with the nominal stress or structural hot spot stress method. They do not apply to the effective notch stress or fracture mechanics method.

The application is limited to joints operating at temperatures below the creep range. In general, the recommendations do not apply for low cycle fatigue conditions, so the nominal stress range is limited to $\Delta \sigma \le 1.5\,\cdot\,f_{y}$. Additional restrictions may apply for specific improvement procedures. It is important to note that the fatigue resistance of an improved weld is limited by the fatigue resistance S-N curve of the base material.

The improvement procedures described below, apply solely to the weld toe and hence to a potential fatigue crack growth starting from this point. Thus, weld details of the type illustrated in Fig. 3.9 are suitable for treatment. However, the benefit of an improvement technique could be reduced as a result of intervention of fatigue cracking from the weld root. Thus, details of the kind shown in Fig. 3.10 are less suitable. In general, all potential alternative sites for fatigue crack initiation (e.g. weld root or imperfections) in treated welded joints should be assessed in order to establish the fatigue life of the weld detail under consideration.

Fig. 3.9

Examples of joints suitable for improvement

Fig. 3.10

Examples of joints, in which an improvement might be limited by a possible root crack

The benefit factors due to the improvement techniques are presented as upgrades to the FAT class that applies to the as-welded joint. Alternative factors, including a possible change to a shallower, more favourable, slope of S-N curve for the improved weld, may be derived on the basis of special fatigue tests (see Sect. 4.5).

A profile improvement can sometimes assist in the application of a residual stress technique and vice versa (e.g. grinding before peening in the case of a poor weld profile or shot peening a dirty surface before TIG dressing). However, a higher benefit factor than that applicable for the second technique alone can only be justified on the basis of special fatigue tests.

3.5.3.3 Grinding

Weld toe fatigue cracks initiate at undercut, cold laps or the sharp crack-like imperfections, just a few tenths of a millimetre deep, which are an inherent feature of most arc welds. The aim of grinding is firstly to remove these imperfections and secondly to create a smooth transition between weld and plate, thus, reducing the stress concentration. All embedded imperfections revealed by grinding must be repaired. For the details of the grinding procedure see Ref. [46].

The benefit of grinding is given as a factor on the stress range of the fatigue class of the non-improved joint, see Tables 3.7 and 3.8.

Table 3.7 FAT classes for use with nominal stress at joints improved by grinding

Table 3.8 FAT classes for use with structural hot-spot stress at joints improved by grinding

The thickness correction exponent according to Sect. 3.5.2 Table 3.6 is n = 0.2.

3.5.3.4 TIG Dressing

By TIG (tungsten inert gas) dressing, the weld toe is remolten in order to remove the weld toe imperfections and to produce a smooth transition from the weld to plate surface, thus reducing the stress concentration. The recommendations (Tables 3.9 and 3.10) apply to partial or full penetration arc welded in steels with a specified yield strength up to 900 MPa and to wall thicknesses ≥ 10 mm operating in a non-corrosive environment or under conditions of corrosion protection. The details of the procedure are described in Ref. [46].

Table 3.9 FAT classes for use with nominal stress at joints improved by TIG dressing

Table 3.10 FAT classes for use with structural hot-spot stress at joints improved by TIG dressing

The thickness correction exponent according to chapter 3.5.2 Table 3.6 is n = 0.2.

A possible interaction between heat treatment and TIG dressing at aluminium alloys should be considered.

3.5.3.5 Hammer Peening

By hammer peening, the material is plastically deformed at the weld toe in order to introduce beneficial compressive residual stresses. The recommendations are restricted to steels with specified yield strengths up to 900 MPa and structural aluminium alloys, both operating in non-corrosive environments or under conditions of corrosion protection. The recommendations apply for plate thicknesses from 10 to 50 mm in steel and 5 to 25 mm in aluminium and to arc welded fillet welds with a minimum weld leg length of 0.1 × t, where t is the thickness of the stressed plate (Tables 3.11 and 3.12). The details of the procedure are described in Ref. [46].

Table 3.11 FAT classes for use with nominal stress at joints improved by hammer peening

Table 3.12 FAT classes for use with structural hot-spot stress at joints improved by hammer peening

Special requirements apply when establishing the benefit of hammer peening:

• (a) Maximum amount of nominal compressive stress in load spectrum including proof loading <0.25 f_y (for aluminium, use f_y of heat affected zone)

• (b) The S-N curve for the hammer peened weld is is used in conjunction with an effective stress range that depends on applied stress ratio R = minσ/maxσ as follows:

  if R < 0:

  The S-N resistance curve is used with full stress range Δσ

  if 0 < R ≤ 0.4:

  The S-N resistance curve is used with the maximum stress σ_max

  if R > 0.4:

  Then there is no benefit

For wall thicknesses bigger than 25 mm, the thickness correction for as-welded joints still applies (see 3.5).

3.5.3.6 Needle Peening

By needle peening, the material is plastically deformed at the weld toe in order to introduce beneficial compressive residual stresses. The details of the procedure are described in [46].

Special requirements apply when establishing the benefit of needle peening:

• (a) Maximum amount of nominal compressive stress in load spectrum including proof loading ≤ 0.25 f_y (for aluminium, use f_y of heat affected zone), see Tables 3.13 and 3.14.

  Table 3.13 FAT classes for use with nominal stress at joints improved by needle peening

  Table 3.14 FAT classes for structural hot-spot stress at joints improved by needle peening

• (b) The S-N curve for needle peened weld is expressed in terms of an effective stress range that depends on applied R ratio as follows:

  if R < 0:

  The S-N resistance curve is used with full stress range Δσ

  if 0 < R ≤ 0.4:

  The S-N resistance curve is used with the maximum stress σ_max

  If R > 0.4:

  Then there is no benefit

For wall thicknesses bigger than 25 mm, the thickness correction for as-welded joints still applies (see 3.5).

3.5.4 Effect of Elevated Temperatures

One of the main material parameters governing the fatigue resistance is the modulus of elasticity E which decreases with increase in temperature. So the fatigue resistance at elevated temperatures (HT) may be calculated as

$$ FAT_{HT} = FAT_{20^\circ C}\,\cdot\,\frac{{E_{HT} }}{{E_{20^\circ C} }} $$

(3.7)

3.5.4.1 Steel

For higher temperatures, the fatigue resistance data may be modified by the reduction factor given in Fig. 3.11. This fatigue reduction factor is a conservative approach and might be relaxed according to test evidence or applicable codes. Creep effects are not covered here.

Fig. 3.11

Fatigue strength reduction factor for steel at elevated temperatures

3.5.4.2 Aluminium

The fatigue data given here refer to operation temperatures lower than 70 °C. This value is a conservative approach. It may be raised according to test evidence or an applicable code.

3.5.5 Effect of Corrosion

The fatigue resistance data given here refer to non-corrosive environments. Normal protection against atmospheric corrosion is assumed. A corrosive environment or unprotected exposure to atmospheric conditions may reduce the fatigue class. The position of the corresponding constant amplitude fatigue limit (CAFL or knee point) of the SN curve (traditionally the fatigue limit) may also be reduced considerably. The effect depends on the spectrum of fatigue actions and on the time of exposure.

For steel, except stainless steel, in marine environment not more than 70 % of the fatigue resistance values in terms of stress range shall be applied and no fatigue limit or knee point of the S-N curve shall be considered. In fracture mechanics crack propagation calculations the constant C₀ in the Paris power law shall be multiplied by a factor of 3.0. A threshold ΔΚ value shall not be considered.

No further specific recommendations are given for corrosion fatigue assessment. If no service experience is available, monitoring of the structure in service is recommended.

3.6 Fatigue Resistance Assessed on the Basis of Crack Propagation Analysis

The resistance of a material against cyclic crack propagation is characterized by the material parameters of the “Paris” power law of crack propagation

$$ \frac{da}{dN} = C_{0} \cdot\Delta K^{m} \quad if\quad\Delta K < K_{th} \quad else\quad \frac{da}{dN} = 0 $$

(3.8)

where the material parameters are

C₀:

Constant of the power law

m:

Exponent of the power law

ΔK:

Range of cyclic stress intensity factor

ΔK_th:

Threshold value of stress intensity, under which no crack propagation is assumed

R:

K_min/K_max, taking all stresses including residual stresses into account (see Sect. 3.5.1)

In the absence of specified or measured material parameters, the values given below are recommended. They are characteristic values.

For elevated temperatures other than room temperature or for metallic materials other than steel, the crack propagation parameters vary with the modulus of elasticity E and may be determined accordingly.

$$ C = C_{0,\,steel}\,\cdot\,\left( {\frac{{E_{steel} }}{E}} \right)^{m} $$

(3.9)

$$ \Delta K_{th} =\Delta K_{th,\,steel}\,\cdot\,\left( {\frac{E}{{E_{steel} }}} \right) $$

(3.10)

3.6.1 Steel

See Table 3.15

Table 3.15 Parameters of the Paris power law and threshold data for steel

3.6.2 Aluminium

See Table 3.16

Table 3.16 Parameters of the Paris power law and threshold data for aluminium

3.6.3 Correlation of Fracture Mechanics to Other Verification Methods

The biggest portion of service life of welded joints is spent in crack propagation. So, estimates of fatigue life or the fatigue class FAT can be made by fracture mechanics calculations using appropriate parameters. The calculations should be verified at known structural details. A possible example of a set of parameters could be:

a_i = 0.1 mm:

Initial crack size parameter (fitted value)

a_i:c_i = 1:

Initial aspect ratio (at butt welds ground flush a_i:c_i = 0.1)

a_f = min(t/2; 12.5 mm):

Final crack size parameter (t is wall thickness)

r = t/25:

Toe radius for most cases

θ = 45°:

Weld angle for most cases, 30° for butt welds

m = 3.0:

Exponent of the Paris-Erdogan power law

At cruciform joints or butt welds with partial penetration, the one half of the root gap shall be taken as the initial crack size parameter. Since the existence of a high stress concentration at the root gaps and a rapid growth in “c”-direction, a through-going crack or at least an initial aspect ratio a_i:c_i = 0.1 may be assumed and a two-dimensional analysis may be adequate.

At butt welds ground flush, the point of a possible crack initiation may be located in the weld metal. Thus the constant for weld metal shall be taken, and a_i:c_i = 0.1 is recommended. For material parameters see Table 3.17.

Table 3.17 Constants Co of the power law for correlation (units in N and mm)

Misalignment shall be considered either in determination of the stress distribution by finite element analysis or by modification of the results of fracture mechanics calculations. See chapter 3.8.2.

3.7 Fatigue Resistance Determination by Testing

3.7.1 General Considerations

Fatigue tests may be used to establish a fatigue resistance curve for a component or a structural detail, or the resistance of a material against (non critical) cyclic crack propagation.

It is recommended that test results are obtained at constant stress ratios R. The S-N data should be presented in a graph showing log(endurance in cycles) as the abscissa and log(range of fatigue actions) as the ordinate. For crack propagation data, the log(stress intensity factor range) should be the abscissa and the log(crack propagation rate) the ordinate.

Experimental fatigue data are scattered, with the extent of scatter tending to be greatest in the low stress/low crack propagation regime (e.g. see Fig. 3.12). For statistical evaluation, a Gaussian log-normal distribution should be assumed. If possible, at least 10 specimens should be tested.

Fig. 3.12

Scatter band in S-N curve

Many methods of statistical evaluation are available. However, the most common approach for analysing fatigue data is to fit S-N or crack propagation curves by regression analysis, taking log(N) or log(da/dN) as the dependent variable.

Test results should be analysed to produce characteristic values (subscript k). These are values that represent 95 % survival probability (i.e. 5 % failure probability) calculated from the mean on the basis of a two-sided confidence of 75 %. More details on the use of the confidence level and formulae are given below.

At higher test cycles than about two or ten million cycles, the staircase method is recommended for testing and evaluation [70]. For a combined evaluation of failed and run-out specimens, maximum likelihood method is recommmended [71].

3.7.2 Evaluation of Test Data

Different methods for fatigue testing exist. For the derivation of S-N curves, testing at two stress range levels (Δσ) to give fatigue lives within the range of 5 × 10⁴ to 10⁶ cycles is preferred. For obtaining fracture mechanics crack propagation parameters, the range of stress intensity factor (ΔK) should be varied between the threshold and the critical level for fracture.

For the evaluation of test data originating from a test series, the characteristic values are calculated by the following procedure:

• (a) Calculate log₁₀ of all data: Stress range Δσ and number of cycles N, or stress intensity factor range ΔK and crack propagation rate da/dN.

• (b) Calculate exponents m and constant logC (or logC₀ respectively) of the formulae:

  $$ {\text{for}}\,{\text{S - N}}\,{\text{curve}}\quad { \log }N = { \log }C - m\,\cdot\,{ \log }\Delta \sigma $$

  (3.11)
  $$ {\text{for}}\,{\text{crack}}\,{\text{propagation}}\quad { \log }\left( {\frac{da}{dN}} \right) = { \log }C_{\text{0}} + m\,\cdot\,{ \log }\Delta K $$

  (3.12)

  by linear regression taking stress or stress intensity factor range as the independent variable, i.e. logN = f(log Δσ) or log(da/dN) = f(log ΔK).

  The number and the spread of the data pairs should be critically assessed. If the number of pairs of test data n < 10, or if the data are not sufficiently evenly distributed to determine m accurately, a fixed value of m should be taken, as derived from other tests under comparable conditions, e.g. m = 3 for steel and aluminium welded joints at stiff and thick-walled components. In all cases, the standard deviation of the exponent m shall be determined for a subsequent check if the pre-fixed exponent, e.g. m = 3, is still reasonable. For other conditions other slopes might be also adequate.

  Values x_i equal to logC or logC₀ are calculated from the (N, Δσ)_i or (da/dN, ΔK)_i test results using the above equations.

• (c) Calculate mean x_m and the standard deviation Stdv of logC (or logC₀ respectively) using m obtained in b).

  $$ x_{m} = \frac{{\sum {x_{i} } }}{n}\quad \quad Stdv = \sqrt {\frac{{\sum {(x_{m} - x_{i} )^{2} } }}{n - 1}} $$

  (3.13)

• d) Calculate the characteristic values x_k by the formulae

  The values of k are given in Table 3.18.

  Table 3.18 Values of k for the calculation of characteristic values

  $$ {\text{S}} - {\text{N data}}:\,\,\,\,\,x_{k} = x_{m} - k\,\cdot\,Stdv $$

  (3.14)
  $$ {\text{Crack propagation rate}}:\,\,\,\,\,x_{k} = x_{m} + k\,\cdot\,Stdv $$

  (3.15)
  $$ {\text{Values of }}{\mathbf{k}}:\,\,\,\,\,k = 1.645\,\cdot\,\left( {1 + \frac{1}{\sqrt n }} \right) $$

  (3.16)

For more details and information, see Appendix 6.4 and Refs. [68–72, 75].

In the case of S-N data, proper account should be taken of the fact that residual stresses are usually low in small-scale specimens. The results should be corrected to allow for the greater effects of residual stresses in real components and structures. Examples of ways to achieve this are by testing at high R values, e.g. R = 0.5, or by testing at R = 0 and lowering the fatigue strength at 2 million cycles (FAT) by 20 %.

3.7.3 Evaluation of Data Collections

Usually data collections do not originate from a single statistical population. These heterogeneous populations of data require a special consideration in order to avoid problems arising from the wide scatter.

The evaluation procedure should consist of the following steps:

• 1. Calculate the constant log C of the S-N Wöhler curve for each data point (see Sect. 3.7.2.) using anticipated knowledge of the slope exponent from comparable test series, e.g. slope m = 3.00 for steel or aluminium.

• 2. Plot all values log C in a Gaussian probability chart, showing the values of log C on the abscissa and the cumulative survival probability on the ordinate.

• 3. Check the probability plot for heterogeneity of the population. If it is heterogeneous, separate the portion of the population which is of interest (see illustration on Figs. 3.13 and 3.14).

  Fig. 3.13

  

  Example of scatter in data collections

  Fig. 3.14

  

  Example of a heterogeneous population

• 4. Evaluate the interesting portion of population according to Sect. 3.7.2., which is the portion of the lowest values of log C.

3.8 Fatigue Resistance of Joints with Weld Imperfections

3.8.1 General

3.8.1.1 Types of Imperfections

The types of imperfections covered in this document are listed below. Other imperfections, not yet covered, may be assessed by assuming similar imperfections with comparable notch effect. Definitions are given in Ref. [48–50].

Imperfect shape

All types of misalignment including centre-line mismatch (linear misalignment) and angular misalignment (angular distortion, roofing, peaking).

Undercut

Volumetric discontinuities

Gas pores and cavities of any shape.

Solid inclusions, such as isolated slag, slag lines, flux, oxides and metallic inclusions.

Planar discontinuities

All types of cracks or crack-like imperfections, such as lack of fusion or lack of penetration (Note that for certain structural details intentional lack of penetration is already covered, e.g. partial penetration butt welds or fillet welded cruciform joints.

If a volumetric discontinuity is surface breaking or near the surface, or if there is any doubt about the type of an embedded discontinuity, it shall be assessed like a planar discontinuity.

3.8.1.2 Effects and Assessment of Imperfections

Three effects of geometrical imperfections can be distinguished, as summarized in Table 3.19.

Table 3.19 Categorization and assessment procedure for weld imperfections

Increase of general stress level

This is the effect of all types of misalignment due to secondary bending. The additional stress magnification factor can be calculated by appropriate formulae. The fatigue resistance of the structural detail under consideration is to be lowered by division by this factor.

Local notch effect

Here, interaction with other notches present in the welded joint is decisive. Two cases are to be distinguished:

Additive notch effect

If the location of the notch due to the weld imperfection coincides with a structural discontinuity associated with the geometry of the weld shape (e.g. weld toe), then the fatigue resistance of the welded joint is decreased by the additive notch effect. This may be the case at weld shape imperfections.

Competitive notch effect

If the location of the notch due to the weld imperfection does not coincide with a structural geometry associated with the shape geometry of the weld, the notches are in competition. Both notches are assessed separately. The notch giving the lowest fatigue resistance is governing.

Crack-like imperfections

Planar discontinuities, such as cracks or crack-like imperfections, which require only a short period for crack initiation, are assessed using fracture mechanics on the basis that their fatigue lives consist entirely of crack propagation.

After inspection and detection of a weld imperfection, the first step of the assessment procedure is to determine the type and the effect of the imperfection as given here.

If a weld imperfection cannot be clearly identified as a type or an effect of the types listed here, it is recommended that it is assumed to be crack-like [54, 57].

3.8.2 Misalignment

Misalignment in axially loaded joints leads to an increase of stress in the welded joint due to the occurrence of secondary shell bending stresses [55, 56]. The resulting stress is calculated by stress analysis or by using the formulae for the stress magnification factor k_m given in Table (3.20) and in Appendix 6.3.

Table 3.20 Consideration of stress magnification factors due to misalignment

Secondary shell bending stresses do not occur in continuous welds longitudinally loaded or in joints loaded in pure bending, and so misalignment will not reduce the fatigue resistance. However, misalignment in components, e.g. beams, subject to overall bending may cause secondary bending stresses in parts of the component, where the through-thickness stress gradient is small, e.g. in the flange of a beam, where the stress is effectively axial. Such cases should be assessed.

Some allowance for misalignment is already included in the tables of classified structural details (3.2). In particular, the data for transverse butt welds are directly applicable for misalignment which results in an increase of stress up to 30 %, while for the cruciform joints the increase can be up to 45 %. In the case of the structural hot spot stress and the effective notch stress assessment methods, a small but inevitable amount of misalignment corresponding to a stress magnification factor of k_m = 1.05 is already included in the fatigue resistance S-N curves (Table 3.20).

Additional requirements apply for the joints listed in Table 3.20. The effect of a larger misalignment has to be additionally considered in the local stress (structural hot spot stress or effective notch stress). The misalignment effect may be present even in the vicinity of supporting structures. A corresponding stress increase must be taken into account also in crack propagation analyses. In all those cases where the stress magnification factor is calculated directly, use is made of an effective stress magnification factor k_m,eff.

$$ k_{m,\;eff} = \frac{{k_{m,\;calculated}}}{{k_{{m},\;\text{already covered}}}} $$

(3.17)

For joints containing both linear and angular misalignment, both stress magnification factors should be applied using the formula:

$$ k_{m} = 1 + (k_{m,\;axial} - 1) + (k_{m,\;angular} - 1) $$

(3.18)

Since misalignment reduces the fatigue resistance, either the calculated applied stress is multiplied by k_m,eff or the allowable stress range obtained from the relevant resistance S-N curve is divided by k_m,eff.

Table 3.20 tabulates the factors k_m which are already covered in the different verification methods. Actual or specified fabrication tolerances may be assessed by the formulae given in Sect. 6.3.

3.8.3 Undercut

The basis for the assessment of undercut is the ratio u/t, i.e. depth of undercut to plate thickness. Though undercut is an additive notch, it is already considered to a limited extent in the tables of fatigue resistance of classified structural details (Sect. 3.2).

Undercut does not reduce the fatigue resistance of welds which are only loaded in the longitudinal direction, i.e. parallel to the undercut.

3.8.3.1 Steel

See Table 3.21

Table 3.21 Acceptance levels for weld toe undercut in steel

3.8.3.2 Aluminium

See Table 3.22

Table 3.22 Acceptance levels for weld toe undercut in aluminium

3.8.4 Porosity and Inclusions

Embedded volumetric discontinuities, such as porosity and inclusions, are considered as competitive weld imperfections which can provide alternative sites for fatigue crack initiation to those covered by the fatigue resistance tables of classified structural details (Sect. 3.2).

Before assessing the imperfections with respect to fatigue, it should be verified that the conditions apply for competitive notches, i.e. that the anticipated sites of crack initiation in the fatigue resistance tables do not coincide with the porosity or inclusions to be assessed and that there is no interaction between them.

It is important to ensure that there is no interaction between multiple weld imperfections, be they of the same or different type. Combined porosity or inclusions shall be treated as a single large imperfection. The defect interaction criteria given in Sect. 3.8.5 for the assessment of cracks also apply for adjacent inclusions. Worm holes shall be assessed as slag inclusions.

If there is any doubt about the coalescence of porosity or inclusions in the wall thickness direction or about the distance from the surface, the imperfections shall be assessed as cracks. It must be verified by NDT that the porosity or inclusions are embedded and volumetric. If there is any doubt, they are to be treated as cracks.

The parameter for assessing porosity is the maximum percentage of projected area of porosity in the radiograph; for inclusions, it is the maximum length. Directly adjacent inclusions are regarded as a single one.

3.8.4.1 Steel

See Table 3.23

Table 3.23 Acceptance levels for porosity and inclusions in welds in steel

3.8.4.2 Aluminium

Table 3.24 Acceptance levels for porosity and inclusions in welds in aluminium

Tungsten inclusions have no effect on fatigue behaviour and therefore do not need to be assessed (Table 3.24).

3.8.5 Crack-like Imperfections

3.8.5.1 General Procedure

Planar discontinuities, cracks or crack-like defects are identified by non-destructive testing and inspection. NDT indications are idealized as elliptical cracks (Fig. 3.15) for which the stress intensity factor is calculated according to Sect. 2.2.5.

Fig. 3.15

Transformation of NDT indications into elliptic or semi-elliptic cracks

For embedded cracks, the shape is idealized by a circumscribing ellipse, which is measured by its two half-axes a and c. The crack parameter a (crack depth) is the half-axis of the ellipse in the direction of the crack growth to be assessed. The remaining perpendicular half-axis is the half length of the crack c. The wall thickness parameter t is the distance from the centre of the ellipse to the nearest surface (Fig. 3.16). If a/t > 0.75, the defect should be re-categorized as a surface crack.

Fig. 3.16

Crack dimensions for assessment

Surface cracks are described in terms of a circumscribing half-ellipse. The thickness parameter is wall thickness t. If a/t > 0.75, the defect is regarded as being fully penetrating and is to be re-categorized as a centre crack or an edge crack, whichever is applicable.

For details of dimensions of cracks and re-categorization see Appendix 6.2.

3.8.5.2 Simplified Procedure

The simplified procedure makes use of the fatigue resistance at 2 · 10⁶ cycles (analogous to FAT classes for the classified structural details) for ranges of crack types, sizes and shapes, of which the data are presented in Tables 3.25. These were obtained by integration of the crack propagation law for steel, given in Sect. 3.6.1, between the limits of an initial crack size a_i and a final crack size of 50 % of the wall thickness. In addition, use was made of the correction functions and the local weld geometry correction given in Sect. 6.2.4. (See Tables 6.1 and 6.3, also 6.14).

Table 3.25 Stress ranges at 2 · 10⁶ cycles (FAT classes in N/mm²) of welds containing cracks for the simplified procedure (following 3 pages)

In assessing a defect by the simplified procedure, the stress range Δσ_i corresponding to the initial crack size parameter a_i and the stress range Δσ_c for the critical crack size parameter a_c are identified. The stress range Δσ or the FAT class corresponding to a crack propagation from a_i to a_c in 2 · 10⁶ cycles is then calculated by:

$$ \Delta \sigma = \sqrt[3]{{\Delta \sigma_{i}^{3} -\Delta \sigma_{c}^{3} }} $$

(3.19)

The tables may be used for aluminium by dividing the resistance stress ranges at 2 · 10⁶ cycles (FAT classes) for steel by 3.

The tables have been calculated using Ref. [40, 42] with a constant of Co = 5.21e-13 [N; mm] and an exponent of m = 3.0 in order to cover the worst case under normal operation and environmental conditions. Corrosion is not considered. A possible misalignment has to be considered explicitly according to Table 3.20.

Note::

The different definition of t for surface and embedded cracks in Table 3.25 shall be considered according to Fig. 3.16.