Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.     

Multi-axial fatigue behaviour of a severely notched carbon steel

The paper deals with multi-axial fatigue strength of notched specimens made of C40 carbon steel (normalised state), subjected to combined tension and torsion loading, both in-phase and out-of-phase (Φ=0 and 90°). V-notched specimens have been tested under two nominal load ratios, R=−1 and 0, while keeping constant and equal to the unity the biaxiality ratio, λ=σ_a/τ_a. All specimens have the same geometry, with notch tip radius and depth equal to 0.5 and 4 mm, respectively, while the V-notch angle is equal to 90°. The results determined are discussed together with those deduced under pure tension or torsion loading on plain and notched specimens as well as on small shafts with shoulders. The application of an energy-based approach allows all the fatigue data obtained from the notched specimens to be summarised in a single scatter band, in terms of the total strain energy density evaluated at the notch tip against cycles to failure.     

Fatigue crack growth from small defects under out-of-phase combined loading

A modified linear elastic fracture mechanics analysis is presented for the evaluation of the crack growth and threshold behavior of small cracks initiated from small defects under combined loading fatigue. For the detailed evaluation of the behavior of small fatigue cracks, the Kitagawa effect, the elastic–plastic behavior of cracks in biaxial stress fields and crack closure effects are taken into account. In-phase and out-of-phase combined tension and torsion fatigue tests were conducted using annealed carbon steel specimens containing small holes. The direction of crack propagation, S–N curves and fatigue limits were found to be in good agreement with the theoretical predictions.     

Multiaxial fatigue of a short glass fibre reinforced polyamide 6.6 – Fatigue and fracture behaviour

The multiaxial fatigue behaviour of a short glass fibre reinforced polyamide 6.6 (PA66-GF35) is investigated on hollow tubular specimens in the range of fatigue lives between 10² and 10⁷ cycles. Fatigue experiments included pure tension, pure torsion, combined tension–torsion at different biaxiality ratios and phase shifting angles between the stress components. Tests were carried out with load ratio R = 0 and R = −1 at room temperature as well as at 130 °C. The influence of biaxiality ratio, phase angle between load components and load ratio is discussed.An extensive analysis of the fracture behaviour is performed on the specimens to recognise the crack nucleation and propagation mechanisms; failure modes were evaluated via optical and scanning electron microscopy.     

Low‐cycle fatigue/high‐cycle fatigue interactions in notched Ti‐6Al‐4V*

Combined low‐cycle fatigue/high‐cycle fatigue (LCF/HCF) loadings were investigated for smooth and circumferentially V‐notched cylindrical Ti–6Al–4V fatigue specimens. Smooth specimens were first cycled under LCF loading conditions for a fraction of the previously established fatigue life. The HCF 10⁷ cycle fatigue limit stress after LCF cycling was established using a step loading technique. Specimens with two notch sizes, both having elastic stress concentration factors of K_t = 2.7, were cycled under LCF loading conditions at a nominal stress ratio of R = 0.1. The subsequent 10⁶ cycle HCF fatigue limit stress at both R = 0.1 and 0.8 was determined. The combined loading LCF/HCF fatigue limit stresses for all specimens were compared to the baseline HCF fatigue limit stresses. After LCF cycling and prior to HCF cycling, the notched specimens were heat tinted, and final fracture surfaces examined for cracks formed during the initial LCF loading. Fatigue test results indicate that the LCF loading, applied for 75% of total LCF life for the smooth specimens and 25% for the notched specimens, resulted in only small reductions in the subsequent HCF fatigue limit stress. Under certain loading conditions, plasticity‐induced stress redistribution at the notch root during LCF cycling appears responsible for an observed increase in HCF fatigue limit stress, in terms of net section stress.     

Notch fatigue behaviour of low-temperature gaseous carburised 316L austenitic stainless steel

ABSTRACT

The influence of low-temperature gaseous carburisation on notch fatigue behaviour of 316L steel under cyclic axial loading was investigated. After carburisation, the carburised case was well distributed at the surface region and was not influenced by the notch geometry. Low-temperature carburisation considerably enhanced the notch fatigue performance, which led to 32% and 44% increase in the endurance limits for the specimens with stress concentration factors K _t?=?1.91 and 3.91, respectively. The notch sensitivity of 316L steel reduced after carburisation. Irrespective of the applied stress amplitude, the fatigue crack nucleation sites were always at the notch root surface for the untreated specimens. For the carburised specimens, fatigue cracks nucleation changed from surface at high-level stress to subsurface at low-level stress.     

Mixed-Mode Crack Propagation in Cruciform Joint using Franc2D

The focus of this research was on determining the cracking behavior when parameter such as the biaxiality ratio was varied. The crack propagation under mixed-mode loading was simulated by means of finite element method. The stress intensity factors have been calculated by the linear elastic fracture mechanics approach using fracture analysis code-2D (Franc2D). The crack growth under opening mode-I was considered because the crack growth occurs mainly along the direction where the mode-I stress component becomes the maximum. The numerical integration of Paris’ equation was carried out. The effect of normal and transverse applied load (σ _x, and σ _y, respectively) on crack propagation was presented. It was found that the fatigue crack growth was faster at a smaller biaxial stress ratio (λ), i.e., higher σ _y on the horizontal crack plan. Moreover, fatigue strength values decrease as λ decreases. The results confirm the use of fracture mechanics approach in biaxial fracture.     

Fatigue assessment of arc welded automotive components using local stress approaches: Application to a track control arm

The applicability of the structural and notch stress approach is examined on the basis of arc welded and dynamically loaded steel structures, taken from the automotive sector. In detail, this is a transverse control arm. Components and specimens with critical regions of failure are tested under cyclic loading with constant and variable amplitudes. With the help of strain gauges, the crack initiation is determined. The specimens are the basis for the application and evaluation of the different approaches for the assessment of fatigue life. The numerical determination of the nominal, structural and notch stresses is performed with finite-element models. Finally the experimental and computational results allow the derivation of structural and notch Woehler S-N curves.     

Fatigue strength of laser beam welded automotive components made of thin steel sheets considering size effects

The applicability of and the quality of assessment using the nominal stress, structural stress and notch stress approaches for calculating the fatigue strength of laserbeam welded components made of thin steel sheets has been investigated. For this purpose, the fatigue lives of a longitudinal carrier, an injector and two tube-flange specimens have been determined by tests under constant amplitude loading. Fatigue cracks initiated at sharp root notches on all of these components. While the nominal stress is derived by theory of structural mechanics, the determination of structural and notch stresses is performed using 3D finite element models and solid elements. The structural stress is derived by an extrapolation of surface stress to the fatigue critical notch and the notch stresses by rounding the sharp root notch with a reference radius of r_ref = 0.05 mm. For all of the concepts used, the endurable stresses have been compared to the design SN-curves recommended by the International Institute of Welding (IIW).On comparing the quality of assessment of the different concepts, the notch stress approach shows the highest scatter. The highest endurable notch stresses occur in specimens with crack initiation at weld ends. These specimens have a very small highly loaded weld length. The lowest endurable stresses are determined for specimens with a long, equally loaded weld. The reason for these findings can be explained by statistical size effects. For an improved fatigue assessment, an easily applicable method is introduced, which takes into account the highly stressed weld length.     

Behaviour of short cracks in alloy 800HT under biaxial fatigue

Biaxial in phase fatigue tests were carried out on thin walled tube specimens of alloy 800HT at ambient temperature. The loading modes included tension, torsion, and combined tension—torsion with a tensile/shear plastic strain range ratio Δ?p/Δγp = 3^1/2. The influence of effective strain amplitudes and biaxiality on the initial growth of fatigue cracks was investigated using the replica technique. The results indicated that the loading conditions strongly affected the growth rates of short cracks. In torsion the cracks grew significantly more slowly than under axial or biaxial loading. A mean tensile stress perpendicular to the shear crack promoted its growth and reduced the fatigue life. The growth of the cracks could be described by the ΔJ integral for axial and biaxial loading; the integration predicted the fatigue life under axial and biaxial loading correctly. However, significantly conservative lifetime predictions were obtained for pure torsional loading since ΔJ does not include crack closure and crack surface rubbing.

MST/3234     

High-temperature fatigue behaviour of a second generation near-γ titanium aluminide sheet material under isothermal and thermomechanical conditions

The high-temperature deformation behaviour of a second generation γ-TiAl sheet material with near-γ microstructure was characterised under tensile, creep, isothermal and thermomechanical fatigue (TMF) loading conditions. Test temperature ranged from 500 to 750 °C in isothermal tests and these temperatures were also used as minimum and maximum temperature of in-phase (IP) and out-of-phase (OP) thermomechanical fatigue tests. Under tensile loading, a ductile-to-brittle transition temperature (DBTT) of about 650 °C was observed. At this temperature the material experiences a temperature dependent change in the fracture morphology. Creep tests carried out in the temperature range from 650 to 800 °C under true constant stress conditions revealed a temperature and stress dependence of the Norton stress exponent n and the apparent activation energy for creep Q_app. With increasing temperature, isothermal fatigue life at constant strain amplitude decreased in vacuum, but increased in air indicating an abnormal (inverse) environmental effect. Under IP loading, fatigue is characterised by cyclic softening due to dynamic recrystallisation. OP loading drastically reduces fatigue life and turned out to be an extremely critical loading situation for γ-TiAl alloys.     

Crack growth behavior of 7075-T6 under biaxial tension–tension fatigue

Crack growth behavior of aluminum alloy 7075-T6 was investigated under in-plane biaxial tension–tension fatigue with stress ratio of 0.5. Two biaxiality ratios, λ (=1 and 1.5) were used. Cruciform specimens with a center hole, having a notch at 45° to the specimen’s arms, were tested in a biaxial fatigue test machine. Crack initiated and propagated coplanar with the notch for λ = 1 in L–T orientation, while it was non-coplanar for λ = 1.5 between L–T and T–L orientations. Uniaxial fatigue crack growth tests in L–T and T–L orientations were also conducted. Crack growth rate in region II was practically the same for biaxial fatigue with λ = 1 in L–T orientation and for the uniaxial fatigue in L–T or T–L orientations, while it was faster for biaxial fatigue with λ = 1.5 at a given crack driving force. However, fatigue damage mechanisms were quite different in each case. In region I, crack driving force at a given crack growth rate was smallest for biaxial fatigue with λ = 1.5 and for uniaxial fatigue in T–L orientation, followed by biaxial fatigue with λ = 1 and uniaxial fatigue in L–T orientation in ascending order at a given crack growth rate.     

Fatigue cracking simulation based on crack closure effects in Al-based sheet materials subjected to biaxial cyclic loads

Fatigue crack growth experiments have been carried out on cruciform specimens in the range of thickness 1.2–10 mm of Al-based alloys, loaded under constant (regular) and variable (irregular) amplitudes of uniaxial and biaxial loads, including sequences of various overloads. Different cases for crack closure effects are considered because of shear lips development, crack-growth direction re-orientation after multiparameters change of cyclic loads, by examining plastic blunting effect at a crack tip during an overload and interaction effects analyzing the crack retardation length and associated parameters together with their relationships. Crack closure effect because of rotation instability of material mesovolumes under biaxial compression–tension has suggested to analyse semi-elliptical cracks. Under biaxial cyclic loads in the range of load ratio-1.4 < λ < +1.5, and R-ratios from 0.05 to 0.8, for frequency variations ?, fatigue striation formation takes place beyond a crack-growth rate close to 4 × 10⁻⁸ m/cycle. The striation spacing and the crack-growth rate increase as the ?-angle of the out-of-phase biaxial loads increases (in the range of ? from 0° to 180°). Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF(λ,R,?,?). The values of F(λ,R,?,?) are determined. The calculated crack growth period (predicted using F(λ,R,?,?)) in regular and irregular cases of cyclic loads, including material cracking after overloads, is correlated with the experimental data, and the error is of the order of 15%.     

FATIGUE CRACK GROWTH IN D16T A1-ALLOY SHEET SUBJECTED TO BIAXIAL OUT-OF-PHASE LOADING

Abstract— Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under out-of-phase biaxial tension and tension-compression. In the range of the biaxial load ratios λ from ?0.5 to +0.5 and an R-ratio of 0.3, fatigue striation formation took place beyond a crack growth rate near to 4 × 10^?8 m/cycle. The striation spacing and the crack growth rate increase as the φ-angle of the out-of-phase biaxial loads increases in the range of φ-angles from 0° to 180°. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1 to 1 when da/dN is greater than 4 × 10^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 10^?6 m/cycle (N_d), and the crack growth period, N_P, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ ratios and φ angles. The value of N_d decreases as the φ angle is increased in the range from 0° to 1807deg;. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF₁(λ, R)F₂(φ). The values of F₂(φ) were determined. The calculated fatigue crack growth period, N_c, applicable up to and including the stage of fatigue striation formation (predicted by using both of the F₁(λ, R) and F₂(φ) functions) is correlated with the experimental data and the error is of the order of 15%.     

Analytical study of fatigue crack growth in AA7050 notched specimens under spectrum loading

An analytical study of fatigue crack growth in aluminium alloy 7050-T7451 notched specimens under a fighter aircraft wing root bending moment spectrum was conducted. The crack growth data were measured by quantitative fractography for three groups of specimens with different stress concentration geometrical features. Under spectrum loading and for each spectrum peak stress level, a minimum of five specimens were tested. Based on the analysis of the measured spectrum crack growth data using linear elastic fracture mechanics, it was found that the concept of geometry factors formulated in the stress intensity factor could not collapse the crack growth rate data derived from each stress concentration feature, particularly near the small crack growth region. In order to investigate the possible reasons for this, three-dimensional elastic-plastic finite element analysis was used to determine notch plastic zone sizes for each stress concentration geometry. As a consequence, an alternative crack growth driving force by considering both notch elastic-plastic stress field and gross net-section stress field was proposed and used to interpret the fatigue crack growth data under spectrum loading. It was found that the predictions of crack growth under spectrum loading for different stress concentration factors at different peak load levels agree reasonably well with the experimental results.     

Assessment of fatigue crack closure under in-phase and out-of-phase thermomechanical fatigue loading using a temperature dependent strip yield model

In this paper fatigue crack closure under in-phase and out-of-phase thermomechanical fatigue (TMF) loading is studied using a temperature dependent strip yield model. It is shown that fatigue crack closure is strongly influenced by the phase relation between mechanical loading and temperature, if the temperature difference goes along with a temperature dependence of the yield stress. In order to demonstrate the effect of the temperature dependent yield stress, the influence of in-phase and out-of-phase TMF loading is studied for a polycrystalline nickel-base superalloy. By using a mechanism based lifetime model, implications for fatigue lives are demonstrated.     

Influence of load ratio on the biaxial fatigue behaviour and damage evolution in glass/epoxy tubes under tension–torsion loading

An extensive experimental campaign was carried out to understand the influence of the multiaxial stress state and load ratio on the matrix-dominated damage initiation and evolution in composite laminates under fatigue. Tubular glass/epoxy specimens were tested under combined tension–torsion loadings with different values of the load ratio and biaxiality ratio (shear to transverse stress ratio). Results are reported in terms of S–N curves for the first crack initiation and Paris-like diagrams for crack propagation, showing a strong influence of both parameters. Fracture surfaces were also analysed to identify the damage mechanisms at the microscopic scale responsible for the initiation and propagation of transverse cracks. Eventually, a crack initiation criterion presented by the authors in a previous work is applied to the experimental data showing a good agreement.     

FATIGUE-CRACK ARREST IN MILD STEEL SPECIMENS UNDER CONSTANT AMPLITUDE LOADING

Abstract— Unexpected arrest of long fatigue cracks was observed in mild steel single edge notch three-point bend specimens tested under constant amplitude loading. Arrest was associated with a low, but still positive, slope of the crack length against stress intensity factor curve, and can be explained using the R -curve concept for fatigue-crack growth. At a stress ratio of 0.1, the fatigue threshold was 6.6, 7.3 or 8.0 MN/m^3/2 depending on the definition of threshold used. This has obvious implications for both the development of a standard test method for the fatigue threshold and the application of data to practical problems.     

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.     

Review of the fatigue strength of welded joints based on the notch stress intensity factor and SED approaches

Several approaches exist for the fatigue strength assessment of welded joints. In addition to the traditional nominal stress approach, various approaches were developed using a local stress as fatigue parameter. In recent times, the N-SIF based approaches using the notch stress intensity at the weld toe or root have been developed. Based on this, the more practical strain energy density (SED) and the Peak Stress approaches were proposed. This paper reviews the proposed design S–N curves of the N-SIF and SED approaches questioning in particular the consideration of misalignment effects, which should be included on the load side of local approaches in order to consider them individually in different types of welded joints. A re-analysis of fatigue tests evaluated for the effective notch stress approach leads to slight changes of the design S–N curves and of the radius of the control volume used for averaging the SED at the notches. Further, on purpose fatigue tests of artificially notched specimens show that the fatigue assessment using a single-point fatigue parameter might be problematic because the crack propagation phase, being part of the fatigue life, is strongly affected by the stress distribution along the crack path that may vary considerably between different geometries and loading cases.