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

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

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.     

The effect of notch geometry on critical distance high cycle fatigue predictions

A critical distance method for predicting the fatigue limit stresses of notched specimens was implemented for notched specimens with a wide range of notch dimensions. Circumferentially notched cylindrical specimens (k_t=1.97–4.07) taken from Ti–6Al–4V forged plate were cycled to failure (R=0.1 and 0.5) using a step loading method for estimating the 10⁶ cycle fatigue limit stresses. These experimental data were used in combination with finite element solutions for all specimen geometries to determine a ‘critical distance’, a quantity or parameter determined from the stress distribution surrounding the notch in combination with fatigue limit stress data from unnotched specimens. A unique parameter was not found for all of the specimen geometries. However, predictions for the fatigue limit stresses of the larger notch geometries may be made with some amount of accuracy using a single value of the critical distance parameter, while reasonable predictions for the specimens with the smallest notch dimensions may be made upon the recognition of an apparent size effect.     

Two methods for predicting the multiaxial fatigue limits of sharp notches

In this paper the problem of the multiaxial fatigue limit estimation of sharply notched components has been addressed using two different methods: a critical distance method and a method involving modified Wöhler curves. These two methods had been previously developed by the authors, but required modification for use in conjunction with finite element stress analysis of sharply notched specimens subjected to multiaxial loadings. Initially, it was demonstrated mathematically that these methods are equivalent in terms of multiaxial stresses near the notch tip. Subsequently, by employing some well‐known uniaxial notch fatigue concepts, some assumptions have been made in order to extend the use of these methods to in‐phase multiaxial notch fatigue situations. Experimental data were obtained from tests conducted on V‐notched specimens subjected to in‐phase mixed Mode I and Mode II loadings. Both methods were successful in giving fatigue limit predictions with an error usually less than 15%. This is interesting because the two methods make quite different assumptions about the nature of fatigue crack growth in the vicinity of the notch.     

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.     

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

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

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.     

Fatigue strength of sharp V-notched specimens made of ductile cast iron

In the present, the high cycle fatigue strength of notched ductile cast iron is investigated. Experimental tests under axial loading, has been carried out on sharp V-notched specimens taken from heavy section casting considering nominal load ratios (R = 0). All specimens, taken from a heavy section casting, are characterized by a notch tip radius less than 0.1 mm, a notch depth of 10 mm and a notch opening angle = 90°. In order to evaluate the influence of chunky graphite morphology on fatigue life, fatigue tests were carried out also on a second set of specimens without that microstructural defect.Metallurgical analyses were performed on all the samples and some important microstructural parameters (nodule count and nodularity rating, among others) were measured and compared. It was found that a mean content of 40% of chunky graphite in the microstructure (with respect to total graphite content) does not influence significantly the fatigue strength properties of the analysed cast iron.     

High-cycle fatigue crack paths in specimens having different stress concentration features

This paper summarises an attempt to study the high-cycle fatigue cracking behaviour in specimens of low carbon steel weakened by U-notches. The specimens were tested under uniaxial fatigue loading with a load ratio equal to 0.1, and the considered K_t values, calculated with respect to the gross area, ranged from 3.8 up to about 25. The generated crack paths were quite irregular showing a propagation occurring in alternate trans- and intra-crystalline mode: in many cases, this made difficult to unambiguously measure orientation and length of Stage 1 planes. In spite of these experimental difficulties, the observed material cracking behaviour seemed to suggest that a Stage 1-like process could always be assumed to be representative of the crack initiation phenomenon, and this held true independently of the notch sharpness. In light of the fact that, at a mesoscopic level, crack initiations never occurred on material planes parallel to the notch bisector, we attempted to investigate whether it was possible to use a critical plane approach to estimate high-cycle fatigue damage in notched components under uniaxial fatigue loading. In more detail, the generated results have initially been re-analysed by using the Modified Wöhler Curve Method re-interpreted in terms of the Theory of Critical Distances [Susmel L. A unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings. Fatigue Fract Eng Mater Struct 2004;27:391–411]. The accuracy in predicting the high-cycle fatigue behaviour of the considered multiaxial fatigue method was then compared to the accuracy of two other uniaxial approaches: the classical one by Smith and Miller [Smith RA, Miller KJ. Prediction of fatigue regimes in notched components. Int J Mech Sci 1978;20:201–206] and the one recently proposed by Atzori and co-workers [Atzori B, Lazzarin P, Meneghetti G. A unified treatment of the mode I fatigue limit of components containing notches or defects. Int J Fract 2005;133:61–87] and based on the use of some classic LEFM concepts. In particular, this comparison was performed considering virtual specimens having the same geometries as the ones investigated in the present study, but assuming that they were made of materials having mechanical properties known from the literature. This exercise allowed us to see that the high-cycle fatigue damage in notched specimens under uniaxial fatigue loading can satisfactorily be predicted not only using Mode I-crack based methods, but also using multiaxial fatigue criteria modelling the crack initiation phenomenon.     

Notch effect on creep–fatigue life for Sn–3.5Ag solder

This paper studies the creep–fatigue crack initiation and failure lives of Sn–3.5Ag solder notched specimens focused on the multiaxial strain at the notch root. Push–pull creep–fatigue tests were performed using three circumferential notched specimens using four kinds of creep–fatigue strain waveforms. Multiaxial strains at the notched section were calculated by finite element (FE) analysis under four kinds of creep–fatigue loading. Creep–fatigue damage laws were applied for evaluating the crack initiation and failure lives using the multiaxial strains obtained by the FE analysis. von Mises equivalent strain at the notch root estimated the crack initiation lives with a large scatter as well as the failure lives. Instead, the mean value of von Mises equivalent strain over the cross section of the notch root estimated the crack initiation and failure lives with a small scatter.     

Fatigue assessment of laserbeam‐welded aluminium joints under multiaxial loading

This paper presents the results and evaluation of the multiaxial fatigue behaviour of laserbeam‐welded overlapped tubular joints made from the artificially hardened aluminium alloy AlSi1MgMn T6 (EN AW 6082 T6) under multiaxial loadings with constant and variable amplitudes. Several fatigue test series under pure axial and pure torsional loadings as well as combined axial and torsional proportional and non‐proportional loadings have been carried out in the range of 2·10⁴ to 2·10⁷ cycles. The assessment of the investigated thin‐walled joints is based on a local notch stress concept. In this concept the fatigue critical area of the weld root is substituted by a fictitious notch radius r_ref = 0.05 mm. The equivalent stresses in the notch, considering especially the fatigue life reducing influence of non‐proportional loading in comparison to proportional loading, were calculated by a recently developed hypothesis, which is called the Stress Space Curve Hypothesis (SSCH). This hypothesis is based on the time evolution of the stress state during one load cycle. In addition, the fatigue strength evaluation of multiaxial spectrum loading was carried out using a modified Gough‐Pollard algorithm.     

Multiaxial fatigue behaviour of a short‐fibre reinforced polyamide – experiments and calculations

This paper deals with the fatigue behaviour of a short fibre reinforced thermoplastic under multi‐axial cyclic stress. Based on experimental results on notched and plain specimens, limits of existing methods for the fatigue life estimation in the design process of components exposed to complex multi‐axial loads were investigated. During the manufacturing process of short fibre reinforced thermoplastic components, a moderately anisotropic behaviour in stiffness and strength arises. Because of the material's anisotropy, classical failure hypotheses for the assessment of multiaxial load cases do not apply. In this study, a fatigue failure hypothesis was implemented that assesses the stress components in accordance with the correlating fatigue strengths in the material coordinate system, considering potential interaction between the stress components. Striving for a verified multi‐usable fatigue life assessment method, multiaxial load cases were examined experimentally. The experimental results on unnotched and notched specimens and the fatigue life estimation on the basis of the Tsai‐Wu‐failure hypothesis will be presented.     

Notch sensitivity of multidirectional carbon fibre-reinforced polyimides in fatigue loading as a function of stress ratio

Multidirectional laminates of carbon fibre-reinforced bismaleinimide with a central hole as a notch were examined in a fatigue loading test using various stress ratios (R). In the case of R= −1, an increase in the number of load cycles was found to diminish the notch influence on fatigue strength. At R = 0.1 no complete failure was observed when the maximum stress was less than or equal to the static tensile strength up to a load cycle range of 2 × 10⁶. Damage observed that would affect mechanical behaviour in fatigue loading by a faster decrease of notch sensitivity was more pronounced than in that reported for notched multidirectional carbon fibre-reinforced epoxy resin specimens.     

Study on creep mechanical behaviour of P92 steel under multiaxial stress state

The creep mechanical behaviour of P92 steel at 650°C has been studied by experimental research and finite element analysis. During the creep of P92 steel, there existed the notched strengthening effect, which was influenced by the shapes of the notch and the nominal stress. Under the condition of the same notch depth, the creep life enhancement factor increased with decreasing notched radius or the increase of stress. The multiaxial stress caused by the notch effect had a significant influence on the evolution of the microstructure and resulted in a transforming tendency from ductile to brittle at the root of the notch. The fracture position varied with the shapes of the notch: the U shaped notch started to fracture at the root of the notch, while the C shaped notch in the centre of the specimen. The creep process of notched specimens was simulated by embedding Kachanov–Rabotnov creep damage constitutive model into the interface program of finite element software. The result showed that damage distribution of notched specimens varied during the process of creep. The maximum damage location at the end of creep depended on the notch shape: with larger notch radius the maximum damage location was in the centre, while smaller radius of notch specimens was near the notch root, which was consistent with the analysis of the fracture morphology.     

Fatigue properties of notched specimens made of FeP04 steel

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

Numerical prediction of notch bluntness effect on fracture resistance of SM490A carbon steel

The present work investigates the notch radius effect on fracture resistance using the finite element (FE) damage analysis based on the multiaxial fracture strain model. The damage model was determined from experimental data of notched bar tensile and fracture toughness test data using a sharp‐cracked compact tension specimen. Then, the FE damage analysis was applied to simulate fracture resistance tests of SM490A carbon steel specimens with different notch radii. Comparison of simulated results with experimental data showed good agreement. Further simulation was then performed to see effects of the specimen size, thickness, and side groove on J‐R curves for different notch radii. It was found that effects of the specimen size and thickness became more pronounced for the larger notch radius. Furthermore, it was found that without side groove, tearing modulus for notched specimens was similar to that for cracked specimens, regardless of the notch radius.     

Fracture investigation of U‐notch made of tungsten–copper functionally graded materials by means of strain energy density

The averaged strain energy density over a well‐defined control volume was employed to assess the fracture of U‐notched specimens made of tungsten–copper functionally graded materials under prevalent mode II loading. The boundary of control volume was evaluated by using a numerical method. Power law function was employed to describe the mechanical properties (elasticity modulus, Poisson's ratio, fracture toughness and ultimate tensile stress) through the specimen width. The effect of notch tip radius and notch depth on notch stress intensity factors and mode mixity parameter χ were assessed. In addition, a comparison based on fracture load between functionally graded and homogeneous W–Cu was made. Furthermore, in this research, it was shown that the mean value of the strain energy density over the control volume can be accurately determined using coarse meshes for functionally graded materials.     

Fatigue life evaluation of tension‐compression asymmetric material using local stress–strain method

In this paper, the low‐cycle fatigue characteristics of cold‐drawn steel were investigated under strain‐controlled uniaxial fatigue load. Cyclic softening was observed throughout fatigue life except for the initial relatively short period which exhibited cyclic hardening. Positive mean stress was found under fully reversed strain loading, indicating that there was a significant cyclic asymmetry. A modified local stress–strain method was proposed to estimate fatigue life of notched tension‐compression asymmetric material. In order to verify this method, fatigue experiments on two kinds of notched specimens with different notch radius were carried out under constant and block load spectrum. It was found that the modified local stress–strain method was more accurate than the traditional ones, the maximum relative error between predicted and experimental fatigue life was less than 6%.     

Foreword – Materialwissenschaft und Werkstofftechnik 10/2011

Load controlled fatigue tests were performed up to 10⁷ cycles on flat notched specimens (K_t = 2.5) under constant amplitude and variable amplitude loadings with and without periodical overloads. Two materials are studied: a ferritic‐bainitic steel and a cast aluminium alloy. These materials have a very different cyclic behaviour: the steel exhibits cyclic strain softening whereas the Al alloy shows cyclic strain hardening. The fatigue tests show that, for the steel, periodical overload applications reduce significantly the fatigue life for fully reversed load ratio (R_σ = –1), while they have no influence under pulsating loading (R_σ = 0). For the Al alloy overloads have an effect (fatigue life decreasing) only for variable amplitude loadings. The detrimental effect of overloads on the steel is due to ratcheting at the notch root which evolution is overload's dependent.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.