Fatigue Design Curves Research Articles

Effect of strain ratio and pre-strain on the low-cycle fatigue behavior of 4130X steel at different strain amplitudes

This study investigates the impacts of strain ratio and pre-strain on the low-cycle fatigue properties and microscopic damage mechanisms of 4130X steel across varying strain amplitudes. Under symmetric loading, initial cycles at low strain amplitudes demonstrate clear peak/valley stress hardening followed by cyclic softening in later stages of fatigue. In contrast, the hardening behavior vanishes at higher strain amplitudes. Increasing strain ratio and pre-strain cause the initial hardening behavior at low strain amplitudes to gradually disappear. Additionally, at lower strain amplitudes, fatigue life decreases as strain ratio and pre-strain rise, attributed to substantial tensile mean stress. Microscopic examination reveals that symmetric cyclic loading at low strain amplitudes releases stress concentrations caused by quenched and tempered processing and reduces both dislocation density and localized plastic strain. Conversely, at higher strain ratios and pre-strains, increased tensile mean stresses not only intensify dislocation multiplication, resulting in high dislocation density, but also activate multi-slip system, leading to dislocation cross-slip. Moreover, at a high strain amplitude of 0.45 %, pre-strain aids in martensite recovery and promotes dislocation annihilation during recovery, thus inducing cyclic softening. Finally, the fatigue lives under varied loading conditions are compared with the fatigue design curve prescribed by ASME VIII-II code.

Study on low cycle fatigue properties of Cr-Mo steel in 50 MPa gaseous hydrogen

At present, a lack of fatigue design curves for Cr-Mo steel in high-pressure gaseous hydrogen worldwide impedes the use of the design fatigue curve (S-N curve) evaluation for vessel fatigue design, necessitating reliance on fracture mechanics methods related to the initial crack size. In this study, strain-controlled fatigue tests with a strain ratio of −1 were carried out in 50 MPa gaseous hydrogen to study the low cycle fatigue properties of Cr-Mo steel. Results indicate that hydrogen reduces the fatigue life of 4130X under high strain amplitudes. Under 0.5 % strain amplitude, different from characteristics of ductile fracture in air, the fracture in 50 MPa gaseous hydrogen showed quasi-cleavage and intergranular fracture characteristics. Based on the test results, the S-N curve in 50 MPa gaseous hydrogen was obtained with fatigue life safety factor 20 and stress amplitude safety factor 2. The S-N curve in 50 MPa gaseous hydrogen is under the curve in KD-320.2 M of the 2023 ASME Boiler & Pressure Vessel Code VIII-3, which does not consider the effect of hydrogen, when the number of cycles to failure is less than 1×106. This indicates that the fatigue life calculated by the S-N curve in KD-320.2 M cannot ensure that 50 MPa high-pressure hydrogen storage vessels avoid fatigue failure under high stress amplitudes.

Critical distance-based fatigue evaluation of welded joints in steel bridge under bending loading

Welded joints are prone to fatigue cracking under bending loading in steel bridges. However, certain design curves for these joints primarily focus on tensile or bending-tension loads, potentially leading to inaccurate assessments. This study conducted bending fatigue tests on fillet welded joints (FWJs), evaluating the suitability of specification methods for assessing their fatigue performance and attempting to determine the strength curves required for fatigue assessment. Furthermore, it validated the feasibility of the traditional theory of critical distance (TCD) in predicting the fatigue life of FWJs under bending loading. On this basis, a TCD assessment method incorporating the welding residual stress (WRS) was proposed. The results indicate that the fatigue design curve of the specifications provides conservative predictions for the fatigue performance of FWJs under bending loading, and FAT112 from Eurocode3 may be suitable for fatigue assessment using hot-spot stress and nominal stress methods. Furthermore, predicting fatigue life for FWJs under bending loading with traditional TCD is feasible. Compared to traditional TCD, the proposed method significantly improves prediction accuracy, with a minimum scatter factor of just 1.5. The proposed TCD not only considers the WRS effect but also reduce the need for numerous fatigue tests to establish the design curve for a specific welded joint.

Re-evaluation of fatigue design curves for offshore wind monopile foundations using thick as-welded test specimens

The dominant majority of existing offshore wind turbines are supported using monopile foundations which are fabricated by welding thick steel plates. In the current fatigue design recommendations for welded steel structures, which are commonly used in the design of monopile structures, the initial inverse slope of the S-N curve is fixed to −3. The historic rationales for this assumption are the ease of fatigue life calculations, the effect of long-range residual stresses that were not originally captured in the test data on thin welded specimens, and analogy with fatigue crack growth. While this introduces an unquantified level of conservatism to deterministic fatigue calculations, it was an acceptable (and wise) assumption when the S-N design curves were generated a few decades ago; however, current designs and assessments require more accurate calculations and the need to more confidently quantify the likelihoods attached to these evaluations. In the present study, it is argued that unlike large braced structures (e.g. jackets) in which long-range residual stresses may remain in place as fatigue cracks propagate, in circumferential welds of monopile structures the natural relaxation of residual stresses, in the absence of long-range residual stresses, must be accounted for by performing fatigue tests on thick welded samples. This paper presents a thorough analysis of the fatigue test results obtained from 50 mm thick as-welded samples with representative profiles of residual stresses that exist in monopiles. Basic and advanced statistical approaches were employed in the analysis and higher values of inverse slope were found using the large thickness test data. The results from this study are compared with the recommended fatigue design curves available in international standards. The outcomes from this research draw important observations concerning the need to employ an appropriate value of inverse slope in the design of monopile structures by excluding the conservative approach imposed by a fixed value of −3 which was originally implemented for braced structures with the assumption of large and long-range residual stresses.

Fatigue assessment of steel tube-to-flange welded joints with reinforcement ribs subjected to multiaxial loads according to the Peak Stress Method

In fatigue design of welded structures, the Peak Stress Method (PSM) is a FE-oriented tool to estimate the Notch Stress Intensity Factors (NSIFs). In compliance with proper fatigue design curves validated against more than 1300 experimental data, the PSM allows to estimate the fatigue lifetime of welded structures made of either aluminium alloys or structural steels and subjected to uniaxial and multiaxial loadings. Moreover, an interactive analysis tool has also been developed in Ansys® Mechanical to automate PSM application on welded structures and support the FE analyst. In this work, the fatigue strength of complex steel tube-to-flange welded joints with reinforcement ribs has been experimentally investigated under pure bending, pure torsion and in-phase as well as out-of-phase combined bending-torsion loadings. The tested joint consists of a steel SHS tube having 6.3 mm thickness, which is joined at both ends to a 15-mm-thick flange. In addition, tube and flanges are joined by fillet welding to 6-mm-thick steel reinforcement ribs. A test rig has been designed in order to perform the experimental fatigue tests, taking advantage of two hydraulic actuators. The experimental fatigue results have been compared with fatigue lifetime estimations performed using the automated PSM tool.

Compliance-Based Determination of Fatigue Design Curves for Elastomeric Adhesive Joints

A compliance-based method for the determination of fatigue design curves for elastomeric adhesive joints is developed and validated. Fatigue experiments are conducted on elastomeric adhesives (a polyurethane and a silane-modified polymer) under different stress ratios (R = 0.1/0.5/−1) and conditions (23 °C/50% r.h. and 40 °C/60% r.h.). The investigation focused on butt and thick adherent shear test joints. Fatigue tests are recorded with cameras to identify the stages of crack initiation and propagation. For each fatigue test, the stiffness and compliance per cycle are calculated until final failure. The proposed method identifies a transition point that distinguishes regions under stable and unstable compliance growth. Fatigue design curves are then built based on the transition point and on the number of cycles to reach different degrees of initial stiffness (90%, 80%, 70% and 60%). The failure ratio, i.e., the lifetime for reaching a given approach divided by the total lifetime, is introduced to evaluate the data in terms of average values and standard deviation. The results indicate that the proposed method can yield fatigue design curves with a high coefficient of determination (accuracy) and high failure ratio (avoiding over-conservative design). Moreover, the method is robust, as the failure ratio for different adhesives, stress ratios, conditions and geometries is highly consistent.

Statistical estimation of fatigue design curves from datasets involving failures from defects

In the present paper, two methodologies for the estimation of the design curves of datasets with failures originating from defects are proposed. With the first methodology, the Likelihood Ratio Confidence Bound of a specific quantile P-S-N curve is considered. The second method is based on the bootstrap approach, with a large number of datasets simulated starting from the stress life and the defect size distributions estimated from the experimental data. The two approaches have been validated on literature datasets covering also the Very High Cycle Fatigue (VHCF) life region, proving their effectiveness.

Numerical Fatigue Life Evaluation With Experimental Results for Type III Accumulators

Abstract Type III accumulator is widely used in hydrogen stations. A high-cost pressure cycle test is mandatory to ensure the safety of the accumulator in present regulations. To reduce the high cost, the aim is to develop a methodology of numerical fatigue life prediction, where an axisymmetric finite element model for the Type III accumulator is created precisely and actual loading process including autofrettage pressure is simulated. The alternating stress intensity is evaluated based on the instructions in KD-3 of 2015 ASME Boiler & Pressure Vessel Code, Section VIII, Division 3. By comparing stress amplitude distributions with the leak positions after the pressure cycle test, and plotting the results in the design fatigue curve, it could be shown that fatigue life prediction of Type III accumulator can be done by precise finite element analysis of the liner including dome part, where the principal axes of stress change in pressure cycle.

The influence of printing strategies on fatigue crack growth behavior of an additively manufactured AISI 316L stainless steel

AbstractSelective laser melting (SLM) is an additive manufacturing powder‐bed fusion process that allows producing complex metallic parts with a relative density of up to 99.9%. Nevertheless, the mechanical properties of these components depend on numerous process variables, and there is a lack of systematic studies focused on SLM stainless steels. In the work herein presented, three specific printing strategies were X‐Y patterned to manufacture Compact Tension specimens transversally, longitudinally, or chess‐oriented, without any post‐processing heat treatment. The specimens were made of AISI 316L austenitic stainless steel. Thereafter, fatigue crack growth rate (FCGR) tests were carried out at room temperature, at constant amplitude loading (R = 0.2), to determine the fatigue crack propagation constants of the Paris Law associated with each print strategy. It was possible to conclude that transversal additively manufactured specimens showed the lowest FCGRs, and all results were well below the fatigue design curve given in ASME BPVC, Section XI.

Mechanical behavior of additively and conventionally manufactured 316L stainless steel plates joined by gas metal arc welding

Combining several additive manufactured (AM) parts to larger parts by welding may be required due the limited building volume of powder bed AM methods. Laser powder bed fusion (LPBF) has a great potential because it enables the production of nearly full-density components through AM processes; however, additional residual stresses and production defects are induced by LPBF. These residual stresses affect the residual stress state of welded AM parts. In combination with the production related defects, both alter the mechanical and—in particular—the fatigue behavior of these welded joints. In this study, various tests are performed to characterize the butt joints of 316L AM steel plates made by gas metal arc welding. To this goal, joints are produced with weld seams parallel and vertical to the layer orientation of AM plates. The results are compared to joints of conventionally rolled steel plates produced with the same welding parameter. The residual stress states in initial (unloaded) condition and after cyclic loading were determined by X-ray diffraction techniques for AM and rolled plates. Complex residual stress states were determined at the welds made of AM steel plates compared to the welds made of rolled steel plates; however, the residual stress level in the heat affected zone of the butt-welded AM steel plates was similar to the welds made of hot-rolled steel plates. After cyclic loading with a high load level, high residual stress relaxations were observed in the parent materials. The fatigue design curve for butt joints from international standards is exceeded by all three test series, but the fatigue strength of the butt joints made by LBPF and hot rolling vary significantly. This is thought to be related to differences between the AM and conventional joints in microstructure, static strength, residual stress level, and small crack-like defects that partially interact with stress concentrations at the weld transition.

General Reference and Design S–N Curves Obtained for 1.2709 Tool Steel

At present, due to advanced fatigue calculation models, it is becoming more crucial to find a reliable source for design S-N curves, especially in the case of new 3D-printed materials. Such obtained steel components are becoming very popular and are often used for important parts of dynamically loaded structures. One of the commonly used printing steels is EN 1.2709 tool steel, which has good strength properties and high abrasion resistance, and can be hardened. The research shows, however, that its fatigue strength may differ depending on the printing method, and may be characterized by a wide scatter of the fatigue life. This paper presents selected S-N curves for EN 1.2709 steel after printing with the selective laser melting method. The characteristics are compared, and conclusions are presented regarding the resistance of this material to fatigue loading, especially in the tension-compression state. A combined general mean reference and design fatigue curve is presented, which incorporates our own experimental results as well as those from the literature for the tension-compression loading state. The design curve may be implemented in the finite element method by engineers and scientists in order to calculate the fatigue life.

Implementation of the Peak Stress Method for the automated FEA-assisted design of aluminium welded joints subjected to constant amplitude multiaxial fatigue loads

The Peak Stress Method (PSM) is a FE-oriented local approach to the fatigue strength assessment of welded structures subjected to fatigue loading. Starting from the peak stresses calculated at the V-notch tip nodes defining weld toes or the weld roots, the PSM defines an equivalent peak stress which allows to estimate the fatigue failure location and fatigue lifetime of welded structures, in compliance with appropriate fatigue design curves. An Ansys® Mechanical extension has been developed to achieve full automated implementation of the tasks and calculations necessary to apply the PSM to welded structures. The tool allows to identify and analyse all the V-notch tip edges of the structure and perform fatigue life estimation on each analysed node. As an output, fatigue life results can be visualized through dedicated tabular data, graphs and contour results generated over the edges of the model. In this work, common-to-complex 3D geometries taken from the literature and related to aluminium alloys welded joints subjected to uniaxial as well as multiaxial fatigue loads have been analysed by comparing two design approaches: (i) manual application of the PSM, (ii) automated implementation of the PSM. The tool developed in Ansys® Mechanical allows to significantly contain the time and effort required to analyse welded structures according to the PSM.

Fatigue life assessment of wire arc additively manufactured ER100S-1 steel parts

The aim of this work was to examine uniaxial, torsion, and multi-axial fatigue characteristics of ER100S-1 low carbon steel specimens fabricated with wire arc additive manufacturing (WAAM) technique, a subcategory of directed energy deposition (DED). Two distinct specimen orientations were tested—vertical and horizontal, extracted perpendicular and parallel to the WAAM deposited layers, respectively. Fracture surfaces of the tested specimens were analysed under scanning electron microscope (SEM) to observe fracture mechanisms corresponding to different specimen orientations, different fatigue loading conditions, and to interpret the fatigue results obtained from the tests. Finally, the obtained stress–life results were compared with the fatigue data available in the literature for a series of wrought and WAAM-built structural steel specimens. Moreover, the S–N curves obtained in this study were evaluated against the fatigue design curve recommended for offshore marine welded structures in DNV standard. Test results have shown advantageous characteristics of WAAM-built ER100S-1 specimens compared with behaviours of other structural steels and conservative prediction of its fatigue life by the design curve available in the DNV standard.

High-cycle fatigue properties of explosion bonded titanium-clad bimetallic steel

Titanium-clad (TC) bimetallic steel is a new type of high-performance laminated structural steel, of which the high-cycle fatigue properties were experimentally studied in this paper. The test coupons were manufactured from explosion bonded TA2 + Q355B TC bimetallic steel plate, and their fracture features after fatigue failure were analysed through a sets of scanning electron microscope (SEM) micrographs. Besides, their basic mechanical properties were obtained by the tensile coupon tests and bonding interface shear tests. Based on the test results, the fatigue stress-life curve (S–N curve) of the explosion bonded TC bimetallic steel was obtained, and it was subsequently compared with that of the uniform material law estimates as well as the codified S–N curves provided by four national standards for steel structure design. It demonstrates that the fatigue performance of TC bimetallic steel studied in this paper is much higher than that of standard single-metal structural steel (by over 20 % compared with the low-alloyed steels with similar tensile strength), and the fatigue design curves for conventional structural steel are conservative in predicting the fatigue life of the TC bimetallic steel herein. In addition, fatigue cracks tend to initiate from the bonding interface and exhibit considerably different propagation phenomena in the cladding titanium alloy and substrate structural steel regions.

Fretting Fatigue Test and Simulation Analysis of Steam Generator Heat Transfer Tube

In a steam generator, the heat transfer tubes are supported by the contact with support plates and anti-vibration bars. The two-phase flow flows over the tubes and causes a vibration when operating. In fatigue analysis, the heat transfer tube is simplified to a beam model, and the contacts with the support plates and the anti-vibration bars are simplified as simple-supported boundary conditions. This linear simplification improves the computational efficiency but cannot simulate the actual situation of the contact area. In consideration of this situation, in the actual analysis, a downwards modified S–N fatigue curve is used to envelop the fretting. For different materials and contact pressure, this modification needs to be obtained through experimental and computational analysis. In this paper, the effect of fretting on fatigue performance of heat transfer tube material 690 alloy is discussed by means of high cycle fretting fatigue test of tube specimen in room temperature air, low cycle fretting fatigue test of sheet specimen in high temperature water environment, and SWT (Smith–Watson–Topper) fretting fatigue predicting simulation, and the conservatism of design fatigue curve is discussed. It is shown that, in range of low cycle and high cycle, the fatigue strength is lower than the mean curve, but it can still be enveloped by the design curve of ASME (the American Society of Mechanical Engineers). However, under the condition of ultra-high cycle, the design curve of ASME can no longer envelop the effect of fretting on fatigue performance, so a further downward modification is necessary to ensure the safety of design.

Numerical and Analytical Studies of Low Cycle Fatigue Behavior of 316 LN Austenitic Stainless Steel

Abstract Mechanical components are frequently subjected to severe cyclic pressure and/or temperature loadings. Therefore, numerical and analytical low cycle fatigue methods become widely used in the field of engineering to estimate the design fatigue lives. The primary aim of this work is to evaluate the accuracy of the most commonly used numerical and analytical low cycle fatigue life methods for specimens made of 316 LN austenitic stainless steel and subjected to fully reversed uniaxial tension–compression loading, in the room temperature condition. It was found that both maximum shear strain and Brown–Miller criterions result in a very conservative estimation for uniaxially loaded specimens. However, maximum shear strain criteria provide better results compared to the Brown–Miller criteria. The total strain energy density approach was also used, and both the Masing and non-Masing analysis were adopted in this study. It is found that the Masing model provides conservative fatigue lives, and non-Masing model results in a more realistic fatigue life prediction for 316 LN stainless steel for both low and high strain amplitudes. The fatigue design curves obtained from the commonly used analytical low cycle fatigue equations were reexamined for 316 LN SS. The obtained design curves from Langer model and its modified versions are nonconservative for this type of material. Consequently, the authors suggest new optimized parameters to fit the given test data. The obtained curve using the currently suggested parameters is in better agreement with the experimental data for 316 LN SS.

Evaluation of local stress‐based fatigue strength assessment methods for cover plates and T‐joints subjected to axial and bending loading

AbstractThis study aims to find suitable fatigue assessment methods for welded structures (cover plates and T‐joints) subjected to axial and bending loading. The Hot Spot Stress (HSS), 1‐mm stress (OM), Theory of Critical Distances (TCD), Stress Averaging (SA), and Effective Notch Stress (ENS) methods are evaluated in terms of accuracy and reliability. The evaluation is based on fatigue test data extracted from the literature and carried out in this study. It is found that the SA method can be used to assess the fatigue strength of cover plate joints under axial loading with relatively good accuracy and low scatter, followed by the ENS method. The HSS, TCD, SA, and ENS methods are conservative estimation methods for T‐joints under bending, while the accuracy is low. Furthermore, fatigue design curves applicable for T‐joints under bending are discussed, which can be used in the TCD method and SA method.

Microstructure based cracking behavior and life assessment of titanium alloy under very-high-cycle fatigue with elevated temperatures

High and very high cycle fatigue tests for TC11 titanium alloy were performed to clarify the interior cracking behavior under fully reversed and pulsating tension at three service temperatures. According to the estimation of threshold values for small and long crack growth, the fatigue design curves are established. Combined with electron backscatter diffraction and fracture mechanics analysis, the interior cracking is closely related to grain strength and size, and microtexture. The interior failure is attributed to the facet formation caused by larger αp phase fracture. Based on FIP model, a temperature-based method is proposed to predict the crack nucleation life.

High Cycle Fatigue Life of Ti-6Al-4V Titanium Alloy Processed by Electron Beam Welding

Fatigue is the most important failure mode of welded structures in engineering applications. However, unlike steel and aluminum alloy welds, the fatigue design guideline of titanium-welded structures are still limited. In this study, Ti-6Al-4V titanium alloy welds with butt joint were produced by electron beam welding (EBW). We examined the suitability of related design codes and established an optimal fatigue-life analysis method for titanium structures. Fatigue tests with constant amplitude loading and variable amplitude loading were performed. Two mean stress correction methods usually adopted in high cycle fatigue analysis, Goodman and Gerber, were evaluated. The results showed that the fracture site of the EBW fatigue sample was located in the base metal. The EBW butt joints of the Ti-6Al-4V alloy apparently illustrated a higher fatigue strength compared to the corresponding fatigue design curve in the AWS D1.9 standard. Under constant amplitude loading with tensile mean stress, the experimental fatigue life fell between the Gerber and Goodman curves. The Miner rule combined with the Goodman mean stress correction approach was recommended to obtain a better fatigue life prediction in the case of variable amplitude loading with tensile or slightly compressive mean stress. All predicted fatigue lives fell within a three-fold change boundary for both SAE transmission and bracket histories.

A fatigue life prediction approach to interior cracking induced high cycle and very high cycle fatigue for surface‐carburized steels

AbstractHigh cycle fatigue and very high cycle fatigue tests with pulsating tension for three surface‐carburized steels were performed to investigate interior failure behavior and life prediction method. As a result, all cracks with fine granular area and fisheye characteristics are induced from inclusions in matrix or in carburized layer. However, the later cracking morphology is smoother, which is due to the difference of plastic deformation and microstructure of the two regions. Based on estimation of threshold values for small and long crack growth, fatigue design curves are established. The maximum inclusion sizes of three carburizing steels were estimated by four statistical analysis methods. Combined with material microstructure characteristics and the critical plane theory, a failure‐based life prediction model is proposed by using fatigue indicator parameter, whose validity is verified based on good agreement between predicted and experimental ones.