The effect of loaded volume and stress gradient on the fatigue limit

In this paper an investigation of multiaxial stress based criteria and evaluation methods is presented. The criteria are used with the point, gradient and volume methods. The purpose is to determine the combination of criteria and methods that is best suited for design against the fatigue limit. The evaluation is based on elastic FE-analysis of 15 geometries for which the fatigue limit loads are known. The point method is based on the maximum values of the fatigue stress in each specimen. With the gradient method, the fatigue stress is adjusted with the relative or absolute gradient of the fatigue stress itself. With the volume method, a statistical size effect is considered, by use of a weakest link integral. Thus, the probability of fatigue depends on the fatigue stress distribution. Also, the gradient and volume methods are combined. The results show that the point and gradient methods are not good for prediction of the fatigue limit. It is recommended to use the volume method in fatigue design. It is accurate enough for prediction of the fatigue limit, straightforward to use and easy to interpret. The choice of method is much more important than the choice of criteria.     

A GENERALIZED FATIGUE LIMIT CRITERION AND A UNIFIED THEORY OF LOW-CYCLE FATIGUE DAMAGE

Abstract— A generalized fatigue limit criterion for multiaxial stress state conditions of isotropic materials is presented. This criterion includes four material parameters and uses two invariants of stress amplitudes and furthermore two invariants of mean stresses. It is shown that the fatigue criteria of Sines and Crossland are particular cases of the formulated criterion. Practical recommendations for the use of different fatigue limit criteria are established. Theoretical predictions are compared with experimental data. Finally a continuum damage mechanics theory for low cycle fatigue of isotropic materials is proposed. This theory describes simultaneously the influence of the stress amplitude and the mean stress on the fatigue damage suffered by materials. The proposed theory is based on four material parameters. Special damage theories with a smaller number of material parameters are obtained. Practical recommendations for the use of these fatigue damage theories are presented.     

Approach to Formulation of Nondestructive Quality Assessment Criterion of High-Strength Steel Lifting Hooks

The present investigation attempts to formulate the analytical quality assessment criteria of lifting hooks made of 4140 grade (400 °C temper) high-strength steel using linear elastic fracture mechanics (LEFM) procedures. According to the existing standard specifications, the proof load test is mandatory for the acceptance/rejection of these components. Also, there is a provision that the hooks should be checked by nondestructive testing (NDT) techniques and must be free from obvious defects, but there is no stipulation of acceptance limit of defect, if any. It is therefore not realistic and is insufficient, because sometimes tested hooks are found to fail in actual service. In the present paper, acceptance limit that is, the maximum allowable defect sizes for dynamic loads with various stress ratios are quantitatively estimated from the computed defect growth curves. The maximum allowable operating cycles for nondestructively detectable minimum defects are tabulated, from which a logical quality assessment criteria has been formulated for the assessment of the fatigue life of the hooks. This investigation is helpful for the safe operation of the hooks.     

A unified statistical model for S‐N fatigue curves: probabilistic definition

In recent years, experimental tests exploring the gigacycle fatigue properties of materials suggest the introduction of modifications in well‐known statistical fatigue life models. Usual fatigue life models, characterized by a single failure mechanism and by the presence of the fatigue limit, have been integrated by models that can take into account the occurrence of two failure mechanisms and do not consider the presence of the fatigue limit. The general case, in which more than two failure mechanisms coexist with the fatigue limit, has not been proposed yet. The paper presents a unified statistical model which can take into account any number of failure mechanisms and the possible presence of the fatigue limit. The case of S‐N curves with different fatigue life distributions coexisting for the entire stress range covered by fatigue tests is also considered. The adaptability of the statistical model to the S‐N curves proposed in the open literature is demonstrated by qualitative numerical examples.     

Three energy-based multiaxial HCF criteria for fatigue life determination in components under random non-proportional stress fields

The prominent high cycle fatigue (HCF) criteria have been generally proposed based on definition of an equivalent stress that is mainly a modified version of a static failure criterion or a static yield function. One or more effects including the mean normal and shear stresses, different phase shifts or random frequencies of the stress components, relative instantaneous time variations of the stress components, relative time locations of the extrema of the time histories of the stress components, etc. have not been considered by many of the previously proposed criteria. In the present paper, based on the proposed instantaneous stress amplitude and mean stress concepts, three new energy-based HCF criteria are proposed to overcome the mentioned shortcomings. A relevant fatigue life assessment algorithm is proposed and results of the prominent criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are examined for components with complicated geometries under proportional, non-proportional and random loadings. Results confirm the efficiency and accuracy of the proposed criteria. Furthermore, it is deduced that the Liu–Zenner type criteria which include the hydrostatic stress implicitly are more accurate than the Papadopoulos-type criteria that consider the hydrostatic stress explicitly.     

Mean stress and plasticity effect prediction on notch fatigue and crack growth threshold,combining the theory of critical distances and multiaxial fatigue criteria

In the present work, we propose a robust calibration of some bi‐parametric multiaxial fatigue criteria applied in conjunction with the theory of critical distances (TCD). This is based on least‐square fitting fatigue data generated using plain and sharp‐notched specimens tested at two different load ratios and allows for the estimation of the critical distance according to the point and line method formulation of TCD. It is shown that this combination permits to incorporate the mean stress effect into the fatigue strength calculation, which is not accounted for in the classical formulation of TCD based on the range of the maximum principal stress. It is also shown that for those materials exhibiting a low fatigue‐strength‐to‐yield‐stress ratio σ_fl,R = ?1/σ_YS, such as 7075‐T6 (σ_fl,R = ?1/σ_YS = 0.30), satisfactorily accurate predictions are obtained assuming a linear‐elastic stress distribution, even at the tip of sharp notches and cracks. Conversely, for any materials characterized by higher values of this ratio, as quenched and tempered 42CrMo4 (σ_fl,R = ?1/σ_YS = 0.54), it is recommended to consider the stabilized elastic‐plastic stress/strain distribution, also for plain and blunt‐notched samples and even in the high cycle fatigue regime still with the application of the TCD.     

Relation between fatigue threshold and fatigue limit for surface-rolled specimens

After cylinder notch fatigue specimens of 40 CrNiMo steel were rolled, their fatigue limit increased by 41%. The rolled specimens did not fracture, even though they had been loaded for 10⁷ cycles under fatigue limit stress, but a non-propagating fatigue crack was generated. Thus the value of the fatigue limit depends on the fatigue threshold value ΔK_th of the metal of the rolled layer. Plastic deformation increased ΔK_th in these experiments. It can be inferred that ΔK_th of the rolled layer increases from the occurrence of plastic deformation and microvoids on the layer. Calculation of the effect of residual stress in the crack wake on the stress intensity factor ΔK indicates that residual compression stress decreases ΔK by 21.5 MPa √M. It was calculated that rolling induced both the length of the non-propagating crack and the increase of fatigue limit. The calculated values are in accord with experiment. Analysis and calculations indicate that the non-propagating crack is generated on the rolled layer. Thus the fatigue limit is improved because rolling produces residual compression stress in the layer (which decreases the stress intensity factor), and increases ΔK_th of the layer.     

Cumulative fatigue damage of stress below the fatigue limit in weldment steel under block loading

To investigate the cumulative fatigue damage below the fatigue limit of multipass weldment martensitic stainless steel, and to clarify the effect of cycle ratios and high‐stress level in the statement, fatigue tests were conducted under constant and combined high‐ and low‐stress amplitude relative to stress above and below the fatigue limit. The outcomes indicate that neither modified Miner's nor Haibach's approach provided accurate evaluation under repeated two‐step amplitude loading. Moreover, effect of cycle ratios has been determined. Additionally, the cumulative fatigue damage saturated model is established and validated. Cumulative fatigue damage contributed by low‐stress below the fatigue limit in high stress of 700 MPa is higher than that with 650 MPa at identical conditions (fatigue limit 575 MPa). Thus, high stress affects fatigue damage behaviour below the fatigue limit. A new predicted approach has been proposed based on Corten‐Dolan law, whose accuracy and applicability have been proven.     

一种新的多轴高周疲劳模型

将疲劳强度以上加载等效为塑性应变,建立了塑性应变与加载应力呈线性关系的表达式,由此得到循环加载的塑性应变能。该塑性应变能使材料微观组织结构发生不可逆变化而引起等效宏观应力。假定该应力符合一种特定的分布函数,导出其最大应力与外加应力叠加达到材料本征断裂应力时的裂纹成核寿命,从而并由微裂纹引起上述两部分应力变化,得到继续加载直至宏观裂纹出现的疲劳寿命。所建立的多轴疲劳寿命公式由3个材料参数表达,并通过单轴疲劳试验数据确定。初步研究表明：该模型对所引用的多轴疲劳试验数据有很好的预测能力。     

An improved multiaxial high‐cycle fatigue criterion based on critical plane approach

Several groups of fatigue damage parameters are discussed and then an improved multiaxial high‐cycle fatigue criterion based on critical plane defined by the plane of maximum shear stress range is presented in this paper. A compromising solution to consider the mean normal stress acting on the critical plane is also proposed. The new fatigue criterion extends the range of metallic materials which is valid for the ratio 1.25 < f_?1/t_?1 < 2. The predictions based on the presented model show a good agreement with test data.     

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.     

Fretting fatigue under variable loading below fretting fatigue limit

The fatigue limit diagram provides the critical condition of non‐failure against fatigue under constant amplitude loading. The fatigue limit diagram is usually considered to give the allowable stress if every stress component is kept within the fatigue limit diagram. In the case of variable amplitude fretting fatigue, however, this study showed that fatigue failure could occur even when all stresses were within the fatigue limit diagram. An example of such a condition is a repeated two‐step loading such as when the first step stress is R=?1 and the second step stress has a high mean value. The reason why such a phenomenon occurs was investigated. A non‐propagating crack was formed by the first step stress even when well below the fatigue limit. The resultant non‐propagating crack functioned as a pre‐crack for the second step stress with a high mean value. Consequently, fatigue failure occurred even when every stress was within the fatigue limit diagram of constant amplitude loading. The fatigue limit diagram obtained in constant amplitude fatigue test does not necessarily guarantee safety in the case of variable amplitude loading in fretting fatigue.     

The effect of adherent thickness on fatigue life of adhesively bonded joints

The effect of adherent thickness on the fatigue performance, fatigue limit, and failure mode of adhesively bonded thin aluminum single lap joint (SLJ) was experimentally and numerically investigated. High‐cycle fatigue tests were performed, and fatigue life was estimated using various fatigue criteria and finite element modeling. Based on the experimental results, increase in adherent thickness leads to increase in fatigue limit. In addition, failure location changes from adhesive to adherent by increasing the adherent thickness. It seems that in adherent failure, selecting a sheet with higher fatigue strength is required to achieve higher fatigue life. Also, based on the analysis of different fatigue criteria, Smith‐Watson‐Topper criterion could predict the joint fatigue life more accurately by considering the mean stress effect and the plastic strain. Finally, as an important result, an unsymmetrical SLJ specimen was evaluated as an industrial case study, and the empirical estimated life was consistent with the experimental results.     

Determining fatigue limits with thermal analysis of static traction tests

This work evaluates the limit stress of the thermo‐elastic phase of deformation by thermo‐analysing the surface of a specimen during a static traction test. By adding a temperature curve measured over a small area of the surface to the classical stress–strain curve, it is possible to evaluate a limit temperature T₀ that is coincident with the beginning of the curve's nonlinear trend. The corresponding stress value is as estimation of the fatigue limit of the component under analysis. The authors derive an expression to evaluate temperature during a mono‐axial static traction test. As an example, temperature curves recorded during traction tests performed on two notched steel specimens are reported and compared with this proposed expression. The change to the linearity in the temperature curve during the static traction test is evident in these examples and the corresponding stress value is an estimation of the fatigue limit of the component under analysis.     

Long fatigue life critical crack lengths*

A model based on surface strain redistribution and crack closure is presented for prediction of the endurance or fatigue limit stress by determining the threshold stress and critical length of short cracks that develop under microstructural control. The threshold stress first decreases with crack size to a local minimum then increases to a local maximum corresponding to the fatigue limit stress. This occurs at the critical crack length corresponding to about four grain diameters. The model is capable of determining the threshold stress range and depth of propagating and non‐propagating surface cracks as a function of stress ratio, material and grain size. The microstructure is shown to be particularly significant in the very long life regime (N_f ≈ 10⁹ cycles). When the surface cracks become non‐propagating, internally initiated cracks continue growing slowly, eventually reaching the critical crack length with failure occurring after a very high number of cycles (10⁷ < N_f < 10⁹ cycles).     

A non-local theory applied to high cycle multiaxial fatigue

ABSTRACT The stress gradient effect on the fatigue limit is an important factor which has to be taken into account for an efficient transfer of fatigue data from laboratory tests to design of industrial components. A short review of some multiaxial high cycle fatigue criteria considering this effect is presented. On the basis of the two local mesoscopic approaches of Papadopoulos, two new non‐local high cycle multiaxial fatigue criteria are developed. These proposals are based on the concept of volume influencing fatigue crack initiation. Their predictions are compared with experimental multiaxial fatigue data on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron). The accuracy of the two local Papadopoulos criteria and of the non‐local proposals are compared and discussed, together with the physical interpretation of the threshold defining the volume influencing fatigue crack initiation.     

Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field Part I: Slit and elliptical cracks under uniaxial tensile loading

Predictions for the angle of crack extension, critical load and unstable crack paths based on the criteria of maximum tangential stress (MTS), maximum tangential strain (MTSN) and strain energy density (SED) for angled slit and elliptical cracks under uniaxial tensile loading are compared. The tangential stress associated with the MTS criterion need not be a principal stress and a new approach to this criterion is suggested. A criterion based on maximum tangential principal stress (MTPS) is proposed. Predictions by these two criteria are compared. Some difficulties associated with the application of the SED criterion are indicated. A new basis, which permits a unification of all the criteria in respect of prediction of critical load, is suggested. Some of the results have been compared with data available in the literature.     

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.