Fatigue strength of notched specimens made of 40CrMoV13.9 under multiaxial loading

The work deals with multiaxial fatigue strength of notched round bars made of 40CrMoV13.9 steel and tested under combined tension and torsion loading, both in-phase and out-of-phase. The axis-symmetric V-notches present a constant notch root radius, 1 mm, and a notch opening angle of 90°; the notch root radius is equal to 4 mm in the semi-circular notches where the strength in the high cycle fatigue regime is usually controlled by the theoretical stress concentration factor, being the notch root radius large enough to result in a notch sensitivity index equals to unity. In both geometries the diameter of the net transverse area is 12 mm.The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. Altogether more than 120 new fatigue data are summarised in the present work, corresponding to a one-year of testing programme.All fatigue data are presented first in terms of nominal stress amplitudes referred to the net area and then re-analysed in terms of the mean value of the strain energy density evaluated over a given, crescent shape volume embracing the stress concentration region. For the specific steel, the radius of the control volume is found to be independent of the loading mode.     

Fatigue life behaviour of TiAlN and TiAlN/CrN coated notched P20 steel specimens

The performance of single layer TiAlN and multilayered TiAlN/CrN physical vapour deposition coatings deposited on AISI P20 steel substrate in affecting overall fatigue resistance of notched specimens was assessed and compared with the performance of the uncoated counterparts. V‐shaped circumferential notches on cylindrical specimens were adopted for fatigue tests. Surface coating characteristics such as hardness, elastic modulus and microstrains were measured and found to be different and often larger than those of the steel substrate. Unlike the un‐notched (smooth) coated specimens, which are known to exhibit large improvements in fatigue life in the high cycle fatigue regime, considerable reductions in fatigue life of the coated notched samples were observed. This was understood to be because of the coating's brittleness, which induces at the notch tip early and frequent fatigue crack initiations, especially in the case of multiple layered coatings. Scanning electron microscope images showed more crack initiation sites in both the coated specimens compared with the uncoated specimen. Also, presence of dimples on the surface confirmed dimple rupture mechanism in the ductile steel substrate in the coated and uncoated specimens.     

Fatigue performance of butt welds between cast steel joint and steel tubular members

Cast steel joints have gained increasing popularity for use in engineering. The fatigue performance of butt welds between cast steel joint and steel tubular members, however, is not yet well characterized. A series of fatigue tests were conducted on a new type of welding detail, cast steel joint with sloped end and integrated backing ring (Type C), for butt welds between cast steel joint and steel tubular members. Fatigue failure mechanism and S–N curves obtained from the tests were compared with those of Type A connection with backing ring and Type B cast steel joint with integrated nose obtained in literature. Fatigue behaviours of all three welding details were successfully predicted by local strain approach, the results of which are consistent with test results, especially for Types A and B welding details. According to the results of tests and analysis, fatigue cracking of butt welds between cast steel joint and steel tubular members always initiates from the bottom of the weld root, and the fatigue performance of Type C welding detail is better than those of Types A and B because of its lower stress concentration level. A simplified fatigue design equation was then proposed based on the results of local strain approach, in which the fatigue notch factor was adopted in fatigue behaviour evaluation. The accuracy of this simplified fatigue design equation was verified for Type C welding details with various geometry configurations.     

Fatigue life of welded joints according to energy criteria in the critical plane

We have determined theoretical notch coefficients with use of the fictitious radius in tube-tube and flange-tube welds. The parameter of normal and shear strain energy density in critical planes is applied for estimation of fatigue life under cyclic conditions of pure bending, pure torsion and combined proportional bending with torsion. The critical planes were determined with use of two methods based on the maximum parameters of, respectively, normal and shear strain energy density. __________ Translated from Problemy Prochnosti, No. 4, pp. 118–124, July–August, 2006.     

Fatigue crack initiation in notched specimens of 17Mn4 steel

Fatigue crack initiation life is predicted for notched bend specimens with two different notch acuities and two stress ratios using the equivalent strain energy density method. The material used was 17Mn4 steel, widely applied in pressure vessel construction. The monotonic and cyclic mechanical properties and the strain-life constants were experimental determined in this work. A comparison was made between predicted and experimental lives obtained for two different optically measured crack lengths. Good agreement was obtained for stress ratios, R, of 0 and −1, and for two notch stress concentration factor values. The observed mean stress effect on crack initiation lives is well modelled in the prediction by the method used with calculation of both strain range and mean stress at the root of the notch.     

Fatigue notch sensitivity of steel blunt-notched specimens

The notch sensitivity of three steels with similar plain fatigue limits was analysed and modelled. The analysis was made by using a model previously derived which estimated the fatigue limit of blunt notched components by means of the parameter k_td defined as the stress concentration introduced by the notch at a distance d from the notch root surface equal to the distance between microstructural barriers. The analyses show how the first two or three microstructural barriers define the fatigue limit and the fatigue notch sensitivity of blunt notched specimens.     

Multiaxial fatigue of V‐notched steel specimens: a non‐conventional application of the local energy method

The paper deals with the multi‐axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V‐notched specimens were subjected to combined tension and torsion loading, both in‐phase and out‐of‐phase, under two nominal load ratios, R=?1 and R= 0, also taking into account the influence of the biaxiality ratio, λ=τ_a/σ_a. The notch geometry of all axi‐symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V‐notch angle of 90° and a net section diameter of 12 mm. The results from multi‐axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of non‐propagating cracks measured from some run‐out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V‐notch tip. The control volume is found to be dependent on the loading mode.     

Fatigue-relevant stress field parameters of welded lap joints: pointed slit tip compared with keyhole notch

The notch stress intensity factor (NSIF) based analytical frame is applied to the slit tips (or weld roots) of welded joints with inclusion of the T-stress component. This T-stress can be determined from FE models evaluating the ligament stresses close to the pointed slit tip. An alternative analytical frame is presented for the corresponding keyhole notches based on analytical solutions from the literature, which are applied to the ligament stresses.
In the slit tip models, the mean local strain energy density (SED) with inclusion of the T-stress effect is determined analytically and numerically in comparison, using two different fatigue-relevant control radii,  R ₀= 0.28 mm and  R ₀= 0.15 mm, the former value well proven for thick-sheet welded joints made of structural steel. The latter smaller value is tentatively proposed for thin-sheet welded joints, in the direction suggested in the recent literature where a reduction of the microstructural support length for laser beam welds and resistance spot welds is recommended. The FEM-based and analytical stress concentration factors (SCF) for the lap joint keyhole model and also the SED values for the corresponding pointed slit tips are found to be in good agreement. The  J -integral consisting of the first and second component (the latter containing the T-stress) is compared with the corresponding SED values.     

Fatigue strength analysis of notched aluminium specimens using the highly stressed volume method

This paper describes a methodology to analyse the fatigue strength of notched aluminium 7075 T7531 specimens using the highly stressed volume method. A straightforward test setup was developed to load test samples with different stress concentrations in repeated bending at high frequency. The highly stressed volumes are precisely determined using static finite element analysis in combination with Matlab for post‐processing. Mean values of the local endurable stress amplitudes are calculated by means of the staircase method. The results indicate that the highly stressed volume can be used as an accurate and efficient design parameter to take the notch‐effect in aluminium components into account.     

Fatigue properties of notched specimens made of FeP04 steel

Fatigue properties of specimens with different notches made of FeP04 steel are presented. The specimens are characterized by double symmetric lateral notches with radius of the notch root ranging from ρ = 0.2 to 10 mm. An MTS 809 servohydraulic device was used for the tests. All fatigue tests were performed under force control by imposing a constant value of the nominal load ratio (R = 0) and a load amplitude P _a  = 6 kN for the notch root ρ = 0.2 mm and 7 kN for the notch roots ρ = 1.25, 2.5 and 10 mm. The test frequency varied from 13 to 15 Hz. During the tests performed under constant loading, we observe the fatigue weakening of the material and an increase in strain.     

High temperature fatigue tests of un-notched and notched specimens made of 40CrMoV13.9 steel

The present paper summarizes data from uniaxial-tension stress-controlled fatigue tests on specimens made of 40CrMoV13.9 steel. Tests are performed varying temperature, from room temperature up to 650 °C. This steel is commonly employed for hot-rolling of metals and it is subjected, in service, to a combination of mechanical and thermal loadings. Two geometries are considered: plain specimens and plates weakened by symmetric V-notches, with opening angle and tip radius being equal to 90 degrees and 1 mm, respectively. The present work is motivated by the fact that, at the best of authors’ knowledge, only a limited number of works dealing with high-temperature fatigue are reported in the literature for the medium/high cycle fatigue regime; in particular, no results seem to be available for 40CrMoV13.9 steel when tested at elevated temperature in the presence of notch effects.After a brief review of the recent literature, the experimental procedure is described in detail and the new data from un-notched and notched specimens are summarized in terms of stress range, at the considered temperatures, for a total of 60 new experimental data. Finally, fatigue data from un-notched and notched specimens are re-analyzed by means of the mean value of the strain energy density (SED), employed here as the critical fatigue parameter, able to summarize in the same scatter band data from different temperatures.     

Fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values

Weld bead geometry cannot, by its nature, be precisely defined. Parameters such as bead shape and toe radius vary from joint to joint even in well-controlled manufacturing operations. In the present paper the weld toe region is modelled as a sharp, zero radius, V-shaped notch and the intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). When the constancy of the angle included between weld flanks and main plates is assured and the angle is large enough to make mode II contribution non-singular, mode I NSIF can be directly used to summarise the fatigue strength of welded joints having very different geometry. By using a large amount of experimental data taken from the literature and related to a V-notch angle of 135°, two NSIF-based bands are reported for steel and aluminium welded joints under a nominal load ratio about equal to zero. A third band is reported for steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch and units for NSIFs are the same as conventional SIF used in LEFM. Afterwards, in order to overcome the problem related to the variability of the V-notch opening angle, the synthesis is made by simply using a scalar quantity, i.e. the mean value of the strain energy averaged in the structural volume surrounding the notch tips. This energy is given in closed form on the basis of the relevant NSIFs for modes I and II and the radius R_C of the averaging zone is carefully identified with reference to conventional arc welding processes. R_C for welded joints made of steel and aluminium considered here is 0.28 mm and 0.12 mm, respectively. Different values of R_C might characterise welded joints obtained from high-power processes, in particular from automated laser beam welding. The local-energy based criterion is applied to steel welded joints under prevailing mode I (with failures both at the weld root and toe) and to aluminium welded joints under mode I and mixed load modes (with mode II contribution prevailing on that ascribable to mode I). Surprising, the mean value of ΔW related to the two groups of welded materials was found practically coincident at 2 million cycles. More than 750 fatigue data have been considered in the analyses reported herein.     

Fatigue strength analysis of welded joints in closed steel sections in rail vehicles

A great need exists for practicability and reliability analyses of the various dimensioning concepts in railway vehicle production, as currently parts are commonly sized according to the nominal stress concept. Although Finite Element Analysis is used for the dimensioning of parts according to the nominal stress concept, no use is made of the locally resolved information from these calculation methods. Concepts based on local stress are highly applicable, as the Finite Element Analysis allows detailed modelling of critical areas of parts.     

A synthesis of the push‐pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss

The energy dissipated to the surroundings as heat in a unit volume of material per cycle, Q, was recently proposed as fatigue damage index, and it was successfully applied to rationalise fatigue data obtained by carrying out stress‐controlled and strain‐controlled fatigue tests on AISI 304 L stainless steel plain and hole specimens. In this paper, it is shown that the Q parameter is independent on thermal and mechanical boundary conditions occurring during experiments. After that, additional stress‐controlled fatigue tests on plain and notched specimens characterised by smaller notch tip radii than those tested previously have been performed. Present data have been compared with previous ones, and it was found that all available results can be synthesised in terms of the energy parameter Q into a unique scatter band, independently on the testing conditions (stress‐controlled or strain‐controlled) and on the specimens' geometry (plain or notched). About 100 data were included in the statistical analysis to characterise the energy‐based scatter band of the material. Finally, some limitations of applicability of the experimental technique adopted in the present paper are discussed.     

Comparative analysis of fatigue life predictions in central notched specimens of Al–Mg–Si alloys

The fatigue behaviour of an Al–Mg–Si alloy was studied using notched specimens. Fatigue tests were conducted at two stress ratios R= 0 and R= 0.4 on thin plates with a central hole. Constant and block variable loading amplitudes were applied to the specimens using a servo‐hydraulic machine. The applicability of the local strain approach method to the prediction of the fatigue life was investigated for this type of discontinuity. Two methods, the equivalent strain energy density approach and a modified stress–strain intensity field approach, were used to predict the fatigue strength. For the second one an elastic–plastic finite element analysis was carried out in order to obtain the local strain and stress distributions near the notch root. Based on Miner's rule an equivalent stress was used to correlate the fatigue lives for the variable amplitude histories. The experimental results were compared with the predicted results obtained by the two methods investigated and better agreement was found with the stress–strain field intensity approach, while the strain energy approach gave more conservative results. Miner's rule gives a good correlation between the variable amplitude and constant amplitude results.     

A notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry

In the Notch Stress Intensity Factor (N‐SIF) approach the weld toe region is modelled as a sharp V‐shaped corner and local stress distributions in planar problems can be expressed in closed form on the basis of the relevant mode I and mode II N‐SIFs. Initially thought of as parameters suitable for quantifying only the crack initiation life, N‐SIFs were shown able to predict also the total fatigue life, at least when a large part of the life is spent as in the propagation of small cracks in the highly stressed region close to the notch tip. While the assumption of a welded toe radius equal to zero seems to be reasonable in many cases of practical interest, it is well known that some welding procedures are able to assure the presence of a mean value of the weld toe radius substantially different from zero. Under such conditions any N‐SIF‐based prediction is expected to underestimate the fatigue life. In order to investigate the degree of conservatism, a total of 128 fillet welded specimens are re‐analysed in the present work by using an energy‐based N‐SIF approach. The local weld toe geometry, characterised by its angle and radius, has been measured with accuracy for the actual test series. The aim of the work is to determine if the N‐SIF‐based model is capable of taking into account the large variability of the toe angle, and to quantify the inaccuracy in the predictions due to the simplification of setting the toe radius equal to zero.     

Fatigue strength assessment of partial and full‐penetration steel and aluminium butt‐welded joints according to the peak stress method

In fatigue design of welded joints, the local approach based on the notch stress intensity factors (NSIFs) assumes that the weld toe profile is a sharp V‐notch having a tip radius equal to zero, while the root side is a pre‐crack in the structure. The peak stress method (PSM) is an engineering, FE‐oriented application of the NSIF approach to fatigue design of welded joints, which takes advantage of the elastic peak stresses from FE analyses carried out by using a given mesh pattern, where the element type is kept constant and the average element size can be chosen arbitrarily within a given range. The meshes required for the PSM application are rather coarse if compared with those necessary to evaluate the NSIFs from the local stress distributions. In this paper, the PSM is extended for the first time to butt‐welded joints in steel as well as in aluminium alloys, by comparing a number of experimental data taken from the literature with the design scatter bands previously calibrated on results relevant only to fillet‐welded joints. A major problem in the case of butt‐welded joints is to define the weld bead geometry with reasonable accuracy. Only in few cases such geometrical data were available, and this fact made the application of the local approaches more difficult. Provided the local geometry is defined, the PSM can be easily applied: a properly defined design stress, that is, the equivalent peak stress, is shown (i) to single out the crack initiation point in cases where competition between root and toe failure exists and (ii) to correlate with good approximation all analysed experimental data.     

A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings

Full penetration T butt weld joints between a tube and its flange are considered, subjected to pure bending, pure torsion and a combination of these loading modes. The model treats the weld toe like a sharp V‐notch, in which mode I and mode III stress distributions are combined to give an equivalent notch stress intensity factor (N‐SIF) and assess the high cycle fatigue strength of the welded joints. The N‐SIF‐based approach is then extended to low/medium cycle fatigue, considering fatigue curves for pure bending and pure torsion having the same slope or, alternatively, different slopes. The expression for the equivalent N‐SIF is justified on the basis of the variation of the deviatoric strain energy in a small volume of material surrounding the weld toe. The energy is averaged in a critical volume of radius R_C and given in closed form as a function of the mode I and mode III N‐SIFs. The value of R_C is explicitly referred to high cycle fatigue conditions, the material being modelled as isotropic and linear elastic. R_C is thought of as a material property, independent in principle of the nominal load ratio. To validate the proposal, several experimental data taken from the literature are re‐analysed. Such data were obtained by testing under pure bending, pure torsion and combined bending and torsion, welded joints made of fine‐grained Fe E 460 steel and of age‐hardened AlSi1MgMn aluminium alloy. Under high cycle fatigue conditions the critical radius R_C was found to be close to 0.40 mm for welded joints made of Fe E 460 steel and close to 0.10 mm for those made of AlSi1MgMn alloy. Under low/medium cycle fatigue, the expression for energy has been modified by using directly the experimental slopes of the pure bending and pure torsion fatigue curves.     

Fatigue crack initiation and growth in AlMg4.5Mn butt weldments

The fatigue life of full-penetration and partial-penetration 5 and 25  mm thickness AlMg4.5Mn (AA5083) aluminium alloy butt weldments was investigated under ( R = 0 and R = − 1) constant amplitude loading. The fatigue lives of the tested specimens were predicted using an analytical model which estimated both the crack initiation and crack growth portions of the total fatigue life. The fatigue life of partial-penetration weldments was found to be substantially less than that of full-penetration weldments because of the greater stress concentrations of the incomplete joint penetration and the consequent absence of a substantial crack-initiation life period. Tensile mean stresses ( R = 0 versus R = − 1-test conditions) markedly reduced the fatigue life of the weldments studied and greatly diminished the duration of the fatigue crack growth period. The extra material provided by the weld reinforcement noticeably increased the fatigue life of the partial-penetration weldments. Weld angular distortion-induced bending stresses greatly affected the smaller thickness (5  mm) full-penetration weldments offsetting the fatigue strength bonus anticipated for small-size weldments. Except for the predictions for R = − 1 full-penetration weldments at long life, which the analytical model underestimated, the agreement between experiment and analytical prediction was within a factor of 2, that is, as good as can be generally expected.