Fatigue assessment methods for variable amplitude loading of welded structures

Lightweight-structural durability design by consideration of variable amplitude loading

Fatigue failure of a grid structure using bolt-sphere joints is liable to occur in a high-strength bolt due to the alternating and reciprocal actions of a suspension crane. In this study, variable amplitude fatigue tests were carried out on 20 40 Cr steel alloy M30 high-strength bolts using an MTS fatigue testing machine, and four cyclic stress amplitude loading patterns, Low-High, High- Low, Low-High-Low, and High-Low-High, were tested. The scanning electron microscope images of bolt fatigue failure due to variable amplitude stress were obtained, and the fractographic analysis of fatigue fractures was performed to investigate the fatigue failure mechanisms. Based on the available data from the constant amplitude fatigue tests, the variable amplitude fatigue life of an M30 high-strength bolt in a bolt-sphere joint was estimated using both Miner's rule and the Corten-Dolan model. Since both cumulative damage models gave similar predictions, Miner's rule is suggested for estimating the variable-amplitude fatigue life of M30 high-strength bolts in a grid structure with bolt-sphere joints; the S-N fatigue curve of the M30 high-strength bolts under variable amplitude loading was derived using equivalent stress amplitude as a design parameter.

Pulsating tension tests with constant amplitude (CA) and variable amplitude (VA) were conducted to investigate the interior failure mechanisms of a carburized Cr steel, and a cumulative damage model with the fine granular area (FGA) formation process was proposed in this study. Such a steel represents the continuously descending S‐N (stress‐number of cycles) curve characteristics associated with inclusion‐FGA‐fisheye induced failure even under variable amplitude. Due to crack growth retardations and accelerations resulted from the interaction effect between stepwise resets of the applied stress, the crack morphology under variable amplitude loading is much rougher. The interior failure mechanism was elucidated in combination with the determination of stress intensity factor values at different crack tips. Based on proposed damage model, the agreement between the predicted and experimental results is fairly good within the factor‐of‐two range.

It has been shown in several studies that methods to improve the fatigue strength of welded structures, such as high-frequency impact treatment (HFMI), can increase the fatigue life of welded joints [1–6]. The results of these investigations led to current guidelines and recommendations for the fatigue assessment of HFMI-treated welded joints. Nevertheless, in practice, there are reservations regarding the efficiency of HFMI-treated welded steel joints under variable amplitude loading. Recent results [7] from studies on transverse attachments of the material S355 and S700 under variable amplitude loading show that the fatigue strength increasing effect of the HFMI-treatment is maintained compared to the as-welded state. The aim of this study is to analyse the sequence effect on the fatigue strength of HFMI-treated transverse attachments and to validate the applicability of linear damage accumulation hypotheses for the design of as-welded and HFMI-treated welded details. In this paper, fatigue test results with random variable amplitude loading (VAL) and high-low VAL and low–high VAL with linear spectrum for the two states as-welded (AW) and HFMI-treated joints will be presented.

The aim of this study is to deal with the simulation of intralaminar fatigue damage in unidirectional composite under multi-axial and variable amplitude loadings. The variable amplitude and multi-axial loading is accounted for by using the damage hysteresis operator based on Brokate method [6]. The proposed damage model for fatigue is based on stiffness degradation laws from Van Paepegem combined with the ‘damage’ cycle jump approach extended to deal with unidirectional carbon fibres. The parameter identification method is here presented and parameter sensitivities are discussed. The initial static damage of the material is accounted for by using the Ladevèze damage model and the permanent shear strain accumulation based on Van Paepegem’s formulation. This approach is implemented into commercial software (Siemens PLM). The validation case is run on a bending test coupon (with arbitrary stacking sequence and load level) in order to minimise the risk of inter-laminar damages. This intra-laminar fatigue damage model combined efficient methods with a low number of tests to identify the parameters of the stiffness degradation law, this overall procedure for fatigue life prediction is demonstrated to be cost efficient at industrial level. This work concludes on the next challenges to be addressed (validation tests, multiple-loadings validation, failure criteria, inter-laminar damages…).

The study experimentally and analytically investigates the effects of variable amplitude (VA) load sequence and varying mean stress on the fatigue strength of welded joints made of high-strength steel. The variable amplitude load spectra were constructed according to a Gaussian normal distribution, and the test series of increasing mean stress (constant maximum stress of the VA load) and decreasing mean stress (constant minimum stress) with identical equivalent stresses were implemented. The applied load spectra incorporated a high peak stress in the beginning of the block to further study the overload and residual stress relaxation effects. In addition, a notch-based fatigue assessment approach, the 4R method, was applied to these load cases. Analyses were conducted with the 4R method to analytically compute local elastic–plastic behavior, and the sequential effect of VA load cycles were considered in the mean stress correction. The fatigue test results showed that the mean stress had a significant impact on the fatigue strength of the welded joints in spite of identical equivalent loads. The difference between the mean fatigue strengths (Δσc,50% = 130 MPa and Δσc,50% = 80 MPa) of the two-test series was approximately 63% with the higher fatigue strength corresponding to low mean stress loading conditions.

Experimental and analytical investigation of fatigue characteristics of 350WT steel under constant and variable amplitude loadings

The literature shows that variable amplitude loading can be much more severe than constant amplitude loading in a fatigue damage context. However, the underlying physical explanations for this are still unknown. Therefore, this paper investigates if the local energy release rate at each intralaminar crack tip in a tension/tension fatigue loaded multidirectional laminate can be used to determine the crack growth rate of these cracks subjected to variable amplitude loading. The local energy release rate is investigated through a developed finite element model in which any number of cracks can be included to account for their interaction. The position of the cracks is determined based on previous experimental work. The experimental results from the previous work are compared to the numerical results in this work. At similar crack density levels the energy release rates increase in the variable amplitude tests compared to constant amplitude tests, but not enough to significantly impact the crack growth rate. It is concluded that less than 5% of the increased crack density rate and crack growth rate caused by variable amplitude block loading is due to increases in local energy release rate. The primary reason is more likely found on a microstructural level.

A phenomenological stress–strain model for wrought magnesium alloys under elastoplastic strain-controlled variable amplitude loading

A detailed 3D analysis using BEM (Bounday Element Method) was performed to determine the stress distribution and SIFs of a corner crack of the fuselage to wing attachment lug of a medium range military transport aircraft.The contact pin-lug has been studied with non-linear contact analysis.Based on this study a crack growth prediction has been performed with a proper analytical model. For the above prediction, both constant and variable amplitude loads were considered. An experimental correlation has been made for both crack growth and final fracture of the component. As a result of the present work it can be concluded the industrial feasibility of fracture mechanics analyses using BEM. In fact a good agreement has been reached with the available experimental results. Also it can be concluded that the interference-fit pin installation causes a significative decrease in the stress intensity factor range and hence improvements in the fatigue crack growth life. The elasto-plastic CORPUS model will be used to predict crack growth evolution. Nomenclature : a crack depth length \i shear modulus C surface crack length V Poisson's ratio DLL design limit load Q2 Bcasy linear order element DK S.I.F. range Q38 Bcasy reduced quadratic order element E Young's modulus SIF stress intensity factor KI mode stress intensity factor DISCUSSION Structural fatigue often initiates in areas of high stress concentration caused by the bearing load of pins. The above causes a small crack initiation time and crack growth life. The main purpose of this report is to validate the Fracture Mechanics tool proposed by ALENIA. The method uses BEM for SIFs evaluation and an elasto-plastic crack propagation Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533 562 Localized Damage model for the life prediction under spectra and costant amplitude loads. A threedimensional BEM analysis using BEASY code, an engineering analysis system based on the Boundary Element Method has been performed in order to determine the stress distribution in the selected component in presence of a crack and under contact conditions. Even if a number of studies and analytical results are available in literature, the capability of a full BEM analysis gives more understanding results. Hereafter the contents, method and the results of the analysis are described. The component selected for the analysis is the fuselage to wing attachment of a medium range military transport aircraft for which results are known from an experimental test program. LUG COMPONENT DESCRIPTION Fig.l shows the detailed geometry of the component. The lug is made of 7075-T73511 forged aluminum alloy for which Young modulus is 71 GN/m^ and Poisson ratio is 0.3, with a hole diameter of 25.5 mm. The pin and the bushing are both of 155-PH steel with Young modulus equal to 210 GN/m^ and Poisson ratio to .33. The lug component has been tested with an initial corner flaw of 1.27x1.27mm under a variable amplitude spectrum coming from in service monitoring. The same test article was also tested with constant amplitude load cycles. The test apparatus used consists, mainly, of a rigid beam fixed on the ground on which both the test article and the hydraulic jack have been installed. The upper end of the test article has been constrained through fasteners to a strong back while the lug lower end has been joined to the stroke of the hydraulic jack. BOUNDARY ELEMENT MODELS BEM is an integral differential equation method based on the formulation reported below : N U'ltlS. in which I are segments in which boundary S is subdivided and C% is a costant linked to the source point, while u and t are displacements and tractions vectors. BEASY is an engineering analysis system based on this method. The surface description of the model was realized directly in BEASY-IMS, the interactive modeling environment of BEASY software, and post-processing ensures an easy way to visualize results, in particular stress intensity factors. The model was divided into three distinct zones or substructures:the main body of the lug, the lug upper side and the pin. This feature makes easier crack tip modeling as well as full model handling (see fig. 2). Different models have been realized with various crack sizes.In Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533

INCEFA-SCALE is a five-year project within the European Commission HORIZON 2020 programme starting in October 2020. Nuclear plant operators have generally observed that the number of failure events attributable to Environmentally Assisted Fatigue (EAF) are fewer than predicted by current assessment methodologies. It is recognised that a contributor to this discrepancy is the transferability of data from laboratory-scale tests to real nuclear components. This is the main knowledge gap addressed by INCEFA-SCALE. This is being achieved through the combination of testing, analysis, and materials characterisation to provide laboratory testing data, and the required meta data to understand the resulting behaviour, generated under conditions that are more representative of those experienced by plant components. The EAF assessment methodology described in NUREG/CR-6909 Rev 1 designed for use with the ASME BPVC Section III fatigue design curves (using factors of 12 on life and 2 on stress/strain) provides an international benchmark and technical justification. This benchmark has been the subject of over a decade of research defining the levels of conservatism provided and proposing alternative approaches to clearly define appropriate margins in EAF assessment methods. One such approach, initiated by the Japanese ‘Subcommittee on Design Fatigue Curve’ and further developed by Rolls-Royce, offers modifications to the design curve approach through the use of ultimate tensile strength dependent mean curves, justification of a new approach to transference factors, the use of the Smith-Watson-Topper mean stress correction approach and explicitly accounting for variable amplitude loading in the high cycle regime of fatigue. Substantial research has been conducted and improvements proposed for the low-cycle regime of the design curves (where the factor on life applies for the ASME approach). However, research data in relevant high temperature water environments relating to the transference factors influencing the factor of 2 on stress/strain is limited. Part of this value is defined by loading history and understanding how to account for this phenomenon in a fatigue assessment requires the production of research data that enables the behaviour of materials subjected to variable loading to be understood. Variable loading is known to affect hardening and mean stress behaviour. Additionally, failure modes where a crack can initiate under larger loading amplitudes and grown to failure by sub-endurance limit loading may be important. This means laboratory testing under relevant environments and variable strain amplitudes is required to advance this area and define new benchmark methods that can adequately account for such behaviours while providing an appropriate level of conservatism. This paper focuses on the presentation and analysis of test data produced by the INCEFA-SCALE project. The data investigates the effects of loading history, environment, and surface finish, through the application of single and variable amplitude waveforms to 316L stainless steel uniaxial fatigue specimens in both air and simulated Pressurised Water Reactor primary coolant environments. By altering the above variables, the aim of this paper is to provide an understanding of how the method outlined in NUREG/CR-6909 and the alternative method proposed by the Subcommittee on Design Fatigue Curve accounts for these effects. It is shown that at time of writing the data would provide support for reducing the NUREG transference factor on stress to 1.4, however a recommendation on reducing the factor on cycles requires more analysis. The reduction in the stress factor is consistent with the approach of the Japanese ‘Subcommittee on Design Fatigue Curve’. There is however inconsistency between the use of elastic pseudo stress amplitudes used in fully reversed design life predictions, and the yield stress value used to govern the boundaries of stress-based mean stress corrections which should be considered in any new design curve approaches.

Recently, the structural health monitoring becomes increasingly great important to assure the ease and safety of our life, and it is required significantly to develop non-destructive evaluation for structures such as bridges and tunnels. Some sacrificed specimens have been developed to evaluate the fatigue damage of structures such as fatigue cycles and residual lifetime, but it can be applied only when the stress history is known beforehand. These fatigue sensors need no cable and can be used at low cost in contrast to strain gage. In previous study, a smart stress memory patch was developed as a new fatigue sensor. The patch can measure simultaneously the maximum stress, stress amplitude and the number of fatigue cycles by crack length measurement and Kaiser effect of Acoustic Emission (AE). The crack growth behavior under constant amplitude (CA) loading has been investigated, and AE behavior also has been evaluated only after CA loading. However, AE characteristics after variable amplitude (VA) loading in service are extremely important. Moreover, it is very important to control AE behavior of the smart patch in order to evaluate the applied stress using Kaiser effect. In this study, fatigue test with single overload was investigated to evaluate its influence. Moreover, effect of crack length and heat treatment on AE behavior was also investigated. Finally, AE behavior of the patch was evaluated after fatigue CA loading with overload or VA loading with log-normal distribution and overload.

Modeling of fatigue crack growth (FCG) under variable amplitude (VA) loading has been a topic of intensive research for decades. This paper proposed an efficient numerical simulation procedure of the FCG process under VA loading via extended finite element method (XFEM). The procedure can describe the integrative effect of several factors (specimen thickness, stress ratio, Poisson’s ratio and so on) simultaneously with a general model. In order to improve the computation efficiency, the whole continua domain is divided into two parts by the level set functions and the global stiffness matrix is divided into four parts accordingly. Then, the inverse operation of global stiffness matrix can be calculated rapidly with the LDU decomposition and the equilibrium equation can be solved effectively. Several sets of fatigue test data in 2024-T351 and 7075-T6 aluminum alloys are used to verify the procedure, the predictions are in good agreement with the test data.

Short Fiber Reinforced Composite (SFRC) structures exhibit multiple microstructures (due to material flow during the process). They are generally subjected to variable amplitude loadings. In this context, a robust model is needed to predict fatigue life as a function of microstructure. In this paper, we propose a predictive micromechanical damage-based model allowing fatigue life prediction in the case of SFRC submitted to variable amplitude cyclic loading. An experimental study was firstly performed on Sheet Molding Compound (SMC) composite involving different microstructure configurations. Specimens were subjected to stress-controlled block loading. The influence of the order of the sequences was evaluated through Low-High amplitude (L-H) and High-Low amplitude (H-L) schemes. Damage accumulation is computed at the local scale to describe the evolution of the fiber-matrix interface damage until failure. A local failure criterion based on a critical damage state allowed predicting variable amplitude fatigue life as a function of microstructure. A good correlation was found between experimental and numerical results. Once the approach was validated, it has been used to model different useful variable amplitude loading schemes to emphasize the role of the loading sequence parameters and order.

Investigation of variable amplitude loading on fretting fatigue behavior of Ti–6Al–4V