Effective strain–fatigue life data for variable amplitude fatigue

The usual analysis procedure for variable amplitude fatigue calculates fatigue damage based on constant amplitude strain controlled fatigue tests of smooth specimens. The resulting predictions are typically nonconservative due to a load interaction effect in variable amplitude fatigue. This paper reviews recent work which shows that large loads in a service load history decrease the crack opening stress and as a result increase the effective strain range for subsequent small cycles. A new strain–life fatigue test is introduced in which periodic large strain cycles reduce the crack opening stress for subsequent smaller cycles. The overloads are applied frequently enough that closure free fully open crack growth is achieved for the small cycles in the long life regime. An effective strain–life curve is derived and a crack opening stress equation calibrated by comparison of constant amplitude and effective strain ranges at given fatigue lives. The use of the effective strain–life curve in predicting fatigue lives is illustrated for service strain histories and for a variable amplitude load sequence applied to notched specimens. The predictions are good but somewhat conservative.     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

Derivation of crack closure and crack growth rate data from effective-strain fatigue life data for fracture mechanics fatigue life predictions

This study deals with the behavior of short cracks growing out of notches. Three types of load histories are used: (a) a fully-reversed constant amplitude history; (b) a periodic compressive overload history consisting of repeated load blocks containing one fully-reversed constant amplitude yield–stress magnitude cycle (the overload) followed by a group of smaller constant amplitude cycles having the same maximum stress as the overload cycle; (c) and a service strain history. Procedures are presented for deriving crack closure data and crack growth rate vs effective stress intensity factor range data from data obtained by subjecting a small number of smooth laboratory specimens to simple periodic compressive overload tests to obtain closure-free strain-life data. These procedures are illustrated in an example in which fatigue life predictions are made for a service strain history applied to notched plate specimens. The fatigue life predictions based on the measured and the derived crack closure and crack growth rate data are in good agreement with the experimentally determined fatigue lives.     

Damage tolerance reliability analysis of automotive spot-welded joints

This paper develops a damage tolerance reliability analysis methodology for automotive spot-welded joints under multi-axial and variable amplitude loading history. The total fatigue life of a spot weld is divided into two parts, crack initiation and crack propagation. The multi-axial loading history is obtained from transient response finite element analysis of a vehicle model. A three-dimensional finite element model of a simplified joint with four spot welds is developed for static stress/strain analysis. A probabilistic Miner's rule is combined with a randomized strain-life curve family and the stress/strain analysis result to develop a strain-based probabilistic fatigue crack initiation life prediction for spot welds. Afterwards, the fatigue crack inside the base material sheet is modeled as a surface crack. Then a probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction for spot welds. Both methods are implemented with MSC/NASTRAN and MSC/FATIGUE software, and are useful for reliability assessment of automotive spot-welded joints against fatigue and fracture.     

Fatigue life prediction for stainless steel welded plate CCT geometry based on Lawrence''s local-stress approach

In the present study, the effect of welding process and procedure on fatigue crack initiation from notches and fatigue crack propagation in AISI 304L stainless steel welds was experimentally investigated. Full penetration, double-vee butt welds have been fabricated and CCT type specimens were used. Lawrence's local-stress approach (a two-stage model) is used to predict the fatigue life. The notch-root stress method was applied to calculate the fatigue crack initiation life, while the fatigue crack propagation life was estimated using fracture mechanics concepts. The fatigue notch factor is calculated using Lawrence's approach. Constant amplitude fatigue tests with stress ratio, R=0 were carried out using 100 kN servo-hydraulic DARTEC universal testing machine with a frequency of 30 Hz. The predicted lives were compared with the experimental values. A good agreement has been reached. It is found that the weld procedure has a stronger effect on lives to initiation than on propagation lives.     

Effects of mean stress and crack closure on fatigue life of spot welds

The effects of mean stress and crack closure on fatigue life of spot welds were investigated. A review showed that several of the previously proposed mean stress corrections give similar results. Fatigue tests on shear and peel loaded specimens were carried out, and the results agreed with the corrections reviewed. The present study shows that crack closure explains the mean stress effects observed. The crack opening force for spot welds was obtained, both experimentally from F–N curves with different load ratios and analytically from the available mean stress corrections. This was verified with detailed finite element simulations. Finally, the experiments and simulations indicate that the use of linear damage accumulation in fatigue life prediction of spot welds can be non‐conservative.     

Fatigue of spot-welded lap joints

The fatigue properties of spot-welded lap joints under a constant mean load made from 1.2 and 3 mm sheet thickness stainless steel with one, two or three-spot welds in series are reported. A log plot of cyclic load range versus fatigue life shows that for given sheet thickness and fixed load range, fatigue life increases with the number of spot welds. Oil has a beneficial effect by increasing the fatigue life of the welded joints. A fracture mechanics analysis is carried out on the data by treating the spot weld as a crack. A log plot of initial stress intensity factor range versus fatigue life is a straight line which is independent of the number of spot welds. However, increasing the sheet thickness shifts the straight line upwards in the log plot, thus indicating a longer fatigue life for the same applied initial stress intensity factor range.     

LONG LIFE SPECTRUM FATIGUE OF CARBON AND STAINLESS STEEL WELDS

Abstract— Fatigue tests of non-load carrying carbon and stainless steel fillet welds have been performed using spectrum loading typical for rail vehicles. The proportion of spectrum cycles exceeding the constant amplitude fatigue limit ranged between 0.86% and 100% and cycles to failure ranged from 4.2 ± 10⁵ to 2.1 ± 10⁷. For the longest tests, the majority of fatigue damage was contributed by cycles with stress ranges less than the constant amplitude fatigue limit. For the carbon steel welds a significant portion of fatigue damage was produced by cycles with stress ranges less than 50% of the fatigue limit but only a small fraction of damage was produced by cycles of this size for the stainless steel welds. The carbon steel welds had slightly better fatigue strength at lives less than 10⁷ cycles but results suggest that stainless steels may have superior long-life variable amplitude fatigue strength when a greater portion of life is spent in the early stages of crack nucleation and growth.     

Fatigue tests and life prediction of 16 Mn steel butt welds without crack-like defect

Fatigue test results of 16 Mn steel butt welds without crack-like defect under both constant and variable amplitude loads are reported and new procedures are used to predict fatigue crack initiation (FCI) life, fatigue crack propagation (FCP) life and total life of the butt welds. The results indicate that the FCI life and FCP life should be calculated separately and the total life is the sum of the FCI life and FCP life. For the butt welds investigated, stress cycles to initiate a crack of engineering size may occupy more than 70 percent of the total life of the butt welds and it is more suitable to express the total life as a power function of the equivalent stress amplitude {ie275-1}. In predicting the FCI life, the expression of FCI life obtained from the test results of notched specimens is used but the effects of microstructure, surface condition, macro- and micro-geometrical discontinuities at weld toe should be taken into account. In predicting the FCP life, the formula developed by Zheng and Hirt is used and the stress ratio is taken as 0.6 to account for the residual stresses effect on the FCP rate. Because overload produced by the maximum load in a load spectrum has no effect on the FCI life of 16 Mn steel and weldment of the steel, according to the procedures outlined in the paper, one can use the FCI life expression mentioned and the linear damage accumulation rule proposed by Miner to predict the FCI life of 16 Mn steel butt welds under variable amplitude loads. A good agreement is achieved between the predicted results and the test data.     

Variable amplitude crack growth in notched specimens

Predictions of variable amplitude fatigue crack growth in notched tensile specimens at an elevated temperature and relative high loads were conducted. The predictions were based on constant amplitude fatigue data and mean crack growth rates were calculated. Crack closure levels were calculated by comparison of crack closure free experimental data obtained with the so called constant K_I,max-method and nominal data. Also, numerical simulations of the closure level throughout the specimens were performed. Although experimental data showed rather large a scatter it was concluded that variable amplitude crack growth rates can be predicted with reasonable agreement using constant amplitude fatigue data. Also, crack growth rates cannot be predicted by LEFM in the inelastic notch affected zone, even if absence of crack closure is assumed.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

Fatigue crack growth in 7249‐T76511 aluminium alloy under constant‐amplitude and spectrum loading

Fatigue crack growth tests were conducted on compact, C(T), specimens made of 7249‐T76511 aluminium alloy. These tests were conducted to generate crack growth rate data from threshold to near fracture over a wide range of load ratios (R). Four methods were used to generate near threshold data: (1) ASTM E‐647 load reduction (LR), (2) compression pre‐cracking constant‐amplitude (CPCA), (3) compression pre‐cracking LR, and (4) constant crack mouth opening displacement LR method. A crack closure analysis was used to develop an effective stress‐intensity factor range against rate relation using a constraint factor (α = 1.85). Simulated aircraft wing spectrum tests were conducted on middle crack tension, M(T), specimens using a modified full‐scale fatigue test spectrum. The tests were used to develop the constraint‐loss regime (plane strain to plane stress; α = 1.85 to 1.15) behaviour. Comparisons were made between the spectrum tests and calculations made with the FASTRAN life prediction code; and the calculated crack growth lives were generally with ±10% of the test results.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

Fatigue life prediction based on natural frequency changes for spot welds under random loading

Fatigue tests were carried out on tensile-shear spot-welded specimens under random loading; at the same time, natural frequencies at different life stages were measured. Test results were compared with that under constant amplitude loading. The relationship between damage and natural frequency change ratio established under constant amplitude loading is here modified. The nonlinear damage evolution equation was established using the damage represented by frequency change for spot welds. The fatigue life of spot welds under random loading was predicted with this damage evolution relationship using the rainflow counting method results, as well as other life prediction methods with different counting methods. Comparison of life prediction results showed that the method using changes of natural frequency can be an on-line approach and the predicted lives have a good agreement with the experimental data.     

Fatigue life prediction based on equivalent stresses for laser beam welded 6156 Al‐alloy joints under variable amplitude loading

In the present work, a simple fatigue life prediction approach is proposed using fracture mechanics for laser beam welded Al‐alloy joints under variable amplitude loading. In the proposed approach, variable amplitude loading sequence is transformed into an equivalent constant amplitude loading using the root mean square model. The crack growth driving force K^* is chosen to describe the fatigue crack growth rate. The influences of residual stress and its relaxation on fatigue life are taken into account in the proposed approach. The fatigue lives are also predicted using the traditional approach based on the S‐N curves and the rainflow counting method. The predicted results show that the proposed approach is better than the traditional approach.     

Fatigue life prediction based on crack closure for 6156 Al-alloy laser welded joints under variable amplitude loading

A fatigue prediction approach is proposed using fracture mechanics for laser beam welded Al-alloy joints under stationary variable amplitude loading. The proposed approach was based on the constant crack open stress intensity factor in each loading block for stationary variable amplitude loading. The influence of welding residual stress on fatigue life under stationary variable amplitude was taken into account by the change of crack open stress intensity factor in each loading block. The residual stress relaxation coefficient β = 0.5 was proposed to consider the residual stress relaxation for the laser beam welded Al-alloy joints during the fatigue crack growth process. Fatigue life prediction results showed that a very good agreement between experimental and estimated results was obtained.     

Fatigue life predictions of spot welds using coarse FE meshes

A new engineering method for fatigue life prediction of spot welds is presented. The method starts with a coarse finite element representation of each spot weld using shell elements and one beam element. Forces and moments at the spot weld are calculated using the finite element method and used in an analytical calculation of the stresses around the spot weld. Mode I and II stress intensity factors are calculated from these stresses. Thereafter, an equivalent stress intensity factor is calculated and the fatigue life prediction is made using one unique K N curve for spot welds. Good agreement is found between a K N curve derived from the Paris law and several experimental results from the literature, although in order to achieve this, a shear correction factor is required. This factor is discussed in relation to results from the literature.     

PREDICTION OF THE FATIGUE LIMIT OF CRACKED SPECIMENS BASED ON THE CYCLIC R-CURVE METHOD

Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R -curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R -curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.     

Failure modes and fatigue life estimations of spot friction welds in cross-tension specimens of aluminum 6061-T6 sheets

Failure modes of spot friction welds (SFWs) in cross-tension specimens of aluminum 6061-T6 sheets are investigated. Micrographs of the SFWs before and after failure under quasi-static and cyclic loading conditions are examined. Two different nugget pullout failure modes can be seen. A fatigue crack growth model based on the paths of the dominant kinked fatigue cracks is adopted to estimate the fatigue lives of SFWs. The computational stress intensity factors for finite kinked cracks and the Paris law for fatigue crack propagation are considered. The fatigue life estimations based on this model agree well with the experimental results.