Accelerated fatigue testing method

A method for accelerated fatigue testing of materials, based on a cumulative damage rule, is developed and examined. The method is based on monotonically increasing the stress amplitude with the number of cycles, until failure. When the initial stress amplitude is above the endurance limit, two tests are needed to determine the S/N curve; another test, with an initial stress amplitude below the endurance limit, is needed to determine the fatigue endurance limit. It is shown how to choose the right loading rate and starting level. This method minimizes the number of tests needed for the determination of the fatigue strength endurance limit, and also shortens these tests by reducing the number of cycles, (as each test ends with specimen failure).     

Threshold crack growth behavior of shear and tensile cracks

Crack-face interference-free mode I and mode II crack-growth data was combined with smooth axial (λ = ε_xy/ε_xx = 0) and torsional (λ = ∞) endurance limit data to develop unified crack growth models that incorporate both shear and tensile cracking. The crack growth models incorporated growth from a slip band (including short crack behavior) size crack until the final failure of a long crack, and the ability to switch between crack growth on shear planes to growth on tensile planes. The models successfully predicted smooth specimen crack-face interference-free fatigue lives and gave reasonable estimates of the smooth specimen endurance limits of crack-face interference free tubular tests run at intermediate strain ratios (λ = 3/4, 3/2, and 3). The series of Kitigawa–Takahashi (threshold fatigue) diagrams developed from the models help illustrate the competition between shear and tensile cracking at the fatigue limit under crack-face interference-free crack growth.     

Modelling curved S–N curves

The fatigue limit distribution is estimated using fatigue data and under the assumption that the fatigue limit is random. The stress levels for the broken and unbroken specimens are used. For the broken specimen the number of cycles to failure is also used. By combining the finite life and fatigue limit distribution it is possible to get the probability of not surviving a certain life. This probability is used to estimate a curved S–N curve by using the method of likelihood. The whole S–N curve is estimated at the same time. These curves show the predictive life given a certain stress level. The life and the quantile of the fatigue limit distribution are also predicted by using profile predictive likelihood. In this way the scatter around the S–N curve as well as the uncertainty of the S–N curve are taken into account.     

Fatigue of hybrid composites by a cohesive micromechanic model

A cohesive micromechanic fatigue model (CMFM) which identifies a nonconservative bonding reaction between a broken molecular chain and its neighbor as the main microscale source of fatigue damage accumulation has been recently developed for a unidirectional material constructed from a parallel set of chain-like elements. The successive breakages in each cycle are controlled by the statistical strength distribution of the elements and the probability and amount of interference which a broken element causes to its neighbors. The model gave a physically sound explanation to the fatigue power law S—N curve and the endurance limit phenomena by direct interpretations of microstructure parameters.

In this study the model is expanded by considering a material which have two components with different mechanical and statistical properties and are mixed to give a hybrid composite. The main target is to find the best combination for fatigue resistance, or more specifically, to explore the possibility of making a composite which is more fatigue resistant than each of its two components. It is found that mixing a brittle component (high modulus and low failure strain) with a soft one (low modulus and high failure strain) having a specific microstructure gives the desired effect if some requirements on the structural and mechanical properties are met.

The two materials are mixed in a form of bundles, so that the composite microstructure and fatigue resistance are controlled by their relative volume faction (a macro property) as well as the number of elements in each bundle (a micro property).     

Fatigue behaviour of clinched joints in a steel sheet

Clinch joining has been used in sheet metal work owing to its simplicity and because it facilitates the joining dissimilar metal sheets. In this study, monotonic and fatigue tests were conducted using coach‐peel and cross‐tension type specimens to evaluate the fatigue strength of clinch joints in a cold‐rolled mild steel sheet. The monotonic experimental results reveal that the coach‐peel specimen exhibits the lowest monotonic strength among the three specimen configurations. The coach‐peel and cross‐tension specimen geometries exhibit very low fatigue ratios, compared with the tensile‐shear specimen. The maximum von Mises and principal stresses at the fatigue endurance limit are much higher than the engineering tensile strengths of the steel sheet used to determine the three specimen geometries. Compared with the effective stress and maximum principal stress, the Smith–Watson–Topper fatigue parameter can be used for an appropriate prediction of the current experimental fatigue life. With regard to the coach‐peel specimen geometry, all samples exhibit pull‐out failure mode in the fatigue testing range. However, for the cross‐tension specimen geometry, mixed (pull‐out and interface) and interface failure modes occurred, depending on the number of cycles to failure.     

A cohesive micromechanic fatigue model. Part I: Basic mechanisms

A model which identifies a cohesive (bonding) reaction between a broken element (molecule, or chain) and its neighbor as the main micro-scale source of fatigue failure, is proposed. By applying statistical laws, the macro response is revealed. Three types of macro damage accumulation functions emerge, in agreement with known experimental, as a direct result of different values for the micro-material parameters. The reference type shows secondary and tertiary stages, the second type includes an additional primary stage, and the third type, exhibiting an endurance limit, has a primary stage only.

A very well known empirical power law relationship between the fatigue stress and the number of cycles to failure is obtained analytically for the reference type, when a Weibull strength distribution function for the micro-elements is used. The micro-scale roots of the model enables the use of physical internal variables for the damage evolution equations. Thus, a clear insight of the macro response, including the existence of an endurance limit, is achieved through basic mechanism on the micro-scale.

Experimental correlations with available fatigue data for different materials, including metals, plastics and composites, show the general validity of the model, in spite of the diversity of their micro-structures.

It may be proposed that in each material type, the physical “element” is different (i.e. molecules for plastics, grains for metals, etc.), but their response towards fatigue is similar: a non-reversible bonding between a broken element and its neighbor.     

Crack initiation: the choice of tests available to calibrate Dang Van's criterion

ABSTRACT Dang Van has proposed a method for predicting fatigue life under high cycle fatigue conditions, where the time for a crack to propagate to the critical length is negligible compared to the time it takes for it to initiate. His argument is that if shakedown is achieved at the grain level, a crack will never initiate. Since the exact stress state at the grain level is very difficult to quantify, the determination of the fatigue limit is achieved using calibration experiments. These experiments need not be restricted to bending and torsion as is common practice. Indeed, any form of specimen geometry and loading path may be used to estimate fatigue life. The comparison of many such tests can not only lead to a more accurate definition of the fatigue limit, but also indicates the suitability of the criterion. Moreover, by ensuring that calibration and specimen data lie close together on the fatigue locus, a better prediction of initiation conditions is achieved.     

Corrosion-fatigue resistance of steel in cyclic bending and torsion

Summary As a result of the action of corrosive media the ratio of the fatigue limit in torsion to that in bending (in the long endurance range) is increased to k=1, as compared with k=0.5–0.6 recorded in air. In other words, the torsional fatigue strength of steel in corrosive media is reduced much less than the fatigue strength in bending.In the low endurance range, a liquid corrosive medium may increase the fatigue strength as a result of its cooling action. Tests in corrosive and neutral media supported the view that the fatigue strength at high overloads depends to a large extent on the thermal effect associated with the internal friction of the specimen material.     

Influence of surface integrity on fatigue strength of 40CrNi2Si2MoVA steel

Influence of surface integrity (including surface roughness, residual stresses, and microstructure in surface) on fatigue limit of 40CrNi2Si2MoVA steel specimens is investigated comprehensively in this work according to a systematic consideration. The surface integrity of specimens is changed due to several widely used manufacturing procedures: heat-treatment, grinding, electro-polishing, hard chromium plating and shot peening. In comparison with specimen electro-polished after grinding, the specimen without polishing has 10% lower fatigue limit due to higher surface roughness; while shot peening improves the fatigue limit for about 36% due to inducing of compressive residual stress field in the surface and transferring the fatigue crack source from surface to interior. The fatigue limit of specimen with decarburized layer after grinding is lower about 13%, but the shot peening can eliminate its detrimental effect. Hard chromium plating decreases the fatigue limit dramatically. The shot peening carried before plating can improve the fatigue limit of specimen and cause it to get to a level even higher than that of specimen without plating.     

Further trials of a strain hardening index of fatigue damage

Previous cyclic-strain, smooth-specimen fatigue tests of α–β titanium alloys displayed an anomolous endurance enhancement for some of the alloy conditions. This could be explained by associating resistance to fatigue damage directly with the stress-normalized plastic strain hardening rate at the point of maximum cyclic tensile stress. Since this rate also controls the extent of stress-relaxation-induced tensile creep strain in each cycle, it was thought that fatigue damage might be associated with it. To test this hypothesis, data with varied load hold time, and over a full range of cyclic life, is reported here for some of the previously reported alloys of Ti-6A1-4V, as well as for an A36 steel plate. Notch fatigue tests of the A36, combined with those of Yoder et al. for the titanium alloys, are compared to the smooth specimen data. Results tend to support the damage-inhibiting role of the plastic strain hardening rate, but not of the creep strain portion of each cycle. Notch fatigue data agrees with smooth specimen trends if Neuber's rule is used to characterize the stress concentration factor, particularly with the A36 steel. As with Yoder's notch fatigue results, smooth specimen LCF life, though quite different in the range less than 10³ cycles, tends to converge near the endurance limit, thus mitigating adverse effects of alloy conditions which favor resistance to fatigue crack propagation in α-β titanium alloys.     

The effect of stress transients on the HCF endurance limit

Constant amplitude fatigue of a material at a fixed stress ratio, R, and at some limiting stress level, may produce high cycle fatigue (HCF) lives in excess of some large number, typically 10⁷ or higher, which can be treated as an endurance limit. Under vibratory loading, stress transients can exceed this endurance limit amplitude and cause damage that accumulates with repeated transient loading. These HCF transients normally occur at lower stress amplitudes than those needed to cause low cycle fatigue (LCF) where lives, N, are typically in the range N < 10⁴–10⁵. Therefore, the HCF transient stresses produce cycles to failure beyond the normal LCF regime but correspond to amplitudes that are above the fatigue limit stress. In this investigation, a titanium alloy, Ti-6Al-4V, is subjected to HCF stress transients while being cycled under constant amplitude HCF. The HCF transients correspond to blocks of loading above the fatigue limit stress applied for a specified fraction of their expected life. A step-loading procedure is used to determine the fatigue limit stress at a frequency of 420 Hz. Stress transients applied at stresses up to 40% above the endurance limit for cycle counts up to 25% of expected life are found to have little or no effect on the fatigue limit stress. Simple calculations of the propagation life in a test specimen show that most of the life at these transient stress levels is spent in the nucleation phase. Fractography, aided by heat tinting, was unable to detect any prior cracks due to the HCF stress transients on the fractured specimens.     

金属材料低温疲劳性能的预测方法

本文总结了作者近来研究金属低温疲劳取得的进展,主要内容包括:疲劳极限的热激活模型、应变疲劳公式、疲劳始裂寿命和裂纹扩展速率的定量预测方法、疲劳裂纹扩展机制脆转模型。当室温下的疲劳极限和门槛植ΔK_(th)确定后,应用本文的方法可根据拉伸性能定量预测材料在低温下的疲劳极限、应变疲劳寿命、疲劳始裂寿命和裂纹扩展速率,并且不需要低温疲劳试验和经验修正。     

Tensile fatigue behaviour of ultra-high performance fibre reinforced concrete (UHPFRC)

The tensile fatigue behaviour of ultra-high performance fibre reinforced concrete (UHPFRC) under constant amplitude fatigue cycles is presented. Three series of uniaxial tensile fatigue tests up to a maximum of 10 million cycles were conducted with the objective to determine the endurance limit of UHPFRC that was supposed to exist for this material. The fatigue tests reveal that an endurance limit exists in all three domains of UHPFRC tensile behaviour at S-ratios ranging from 0.70 to 0.45 with S being the ratio of the maximum fatigue stress to the elastic limit strength of UHPFRC. Rather large variation in local specimen deformations indicates significant stress and deformation redistribution capacity of the UHPFRC bulk material enhancing the fatigue behaviour. The fatigue fracture surface of UHPFRC shows features of the fatigue fracture surfaces of steel, i.e. fatigue crack propagation is identified by a smooth surface while final fracture leads to rather rough surface. Various fatigue damaging mechanisms due to fretting and grinding as well as tribocorrosion are identified.     

Probabilistic approach in high-cycle multiaxial fatigue: volume and surface effects

The stress gradient and the size of a component are known to influence the fatigue strength of metallic components. Indeed, in high‐cycle fatigue, experiments prove that the stress distribution as well as the size of the loaded specimen can be responsible for changes in the fatigue limit (for instance, the fatigue limits in tension and bending are different, and decrease with the size of the specimen). When dealing with multiaxial load conditions, those effects still act but a relevant criterion must be used to account for the complex state of stress. The weakest‐link concept together with a multiaxial endurance criterion based on a microplasticity analysis are then combined to describe the fatigue limit distribution of different metallic materials. Several load conditions are analysed: tension–compression, torsion, rotating bending and plane bending. By means of the proposed model, all the known effects on fatigue strength can be reflected. First, the endurance probability can be adequately predicted for any complex load conditions knowing some reference data from uniaxial fatigue tests. It can be linked to the probability of finding a defect with a critical size. The weakest‐link theory also accounts for the decrease of multiaxial fatigue limit with the stressed volume. For the same load condition (i.e. for the same stress distribution in the volume), the probability of finding a critical defect increases with the component size and then according to the weakest‐link theory the fatigue strength drops. A second model, based only on the damage developed at the surface, is also proposed. While the original Weibull theory makes no distinction between potential initiation sites at the free surface and in the volume and can lead to unsatisfactory predictions when applied to materials containing defects such as nodular cast iron, the new surface approach distinguishes between surface and volume effects.     

A method for modelling of fatigue life for rubbers and rubber isolators

A method for modelling fatigue life of rubbers and rubber isolators is presented in this paper. Firstly, a fatigue experiment is carried out for a rubber dumbbell cylindrical specimen and a rubber isolator. Based on the finite element analysis, the damage parameters including the strain energy density, the maximum principal Green–Lagrange strain and the effective stress are calculated and discussed. Secondly, three fatigue life prediction models are established by using the three damage parameters and using the relation between the measured fatigue life of a dumbbell cylindrical specimen and the computed value of the damage parameters. Thirdly, three proposed prediction models are used to investigate which one can be best used to predicting fatigue life of rubber isolators, taking a typical powertrain rubber isolator as studying example. The fatigue lives of the rubber isolator predicted by the three models are compared with the experimental life. The results demonstrate that the predicted fatigue lives of the rubber isolator using the three fatigue models agree well with the experimental fatigue life within a factor of four, and the model using the effective stress as the damage parameter can predict the fatigue life within a factor of two, which has the best accuracy among the three models.     

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.     

FATIGUE STRENGTH EVALUATION FROM SURFACE YIELDING DATA

Surface yielding was detected by X-ray diffraction. The surface yield strength _sy was significantly less than the bulk yield strength, and depends on the physical state and roughness of the surface. However _sy does not change with changes in surface residual stress. Determination of surface yielding, measured under static loading, indicates that a remarkable number of grains have been plastically deformed at the _sy stress level, which will result in damage accumulation under cyclic loading. Crack initiation predominates at the level of the fatigue endurance life for smooth parts and experiments indicate that _sy equals the smooth specimen fatigue limit, particularly that associated with a high survival probability.     

The nature of initiation and propagation S-N curves at and below the fatigue limit

The traditional stress-life method of life prediction relies on an S – N curve of stress versus total life. However, the total life of a sample can be divided into two phases—an initiation phase and a propagation phase that leads to ultimate failure. Although this break-up of total life into two phases has been recognized in theory, there has been no experimental method to generate initiation and propagation S – N curves. In this paper a methodology to generate initiation and propagation S – N curves is presented. Acoustic emission technology is used to detect the transition from the initiation phase to the propagation phase. The phenomenon of fatigue limits is also explored and it is shown that the fatigue limit of the traditional S – N curve corresponds to the fatigue limit of the initiation phase and that initiated cracks continue to propagate at stress levels below the initiation endurance limit. It is also shown that no damage is accrued at stress levels below the fatigue limit. A method to extend the propagation life curve below the initiation endurance limit is also presented. The proposed two-phase S – N curve will greatly extend the life-predicting capability of the stress-life method and can explain some of the contradictions observed in experiments.     

Fatigue life and endurance limit prediction of asphalt mixtures using energy-based failure criterion

Fatigue cracking is one of the major types of distress in asphalt mixtures and is caused by the accumulation of damage in pavement sections under repeated load applications. The fatigue endurance limit (EL) concept assumes a specific strain level, below which the damage in hot mix asphalt (HMA) is not cumulative. In other words, if the asphalt layer depth is controlled in a way that keeps the critical HMA flexural strain level below the EL, the fatigue life of the mixture can be extended significantly. This paper uses two common failure criteria, the traditional beam fatigue criterion and the simplified viscoelastic continuum damage model energy-based failure criterion (the so-called G^R method), to evaluate the effect of different parameters, such as reclaimed asphalt pavement (RAP) content, binder content, binder modification and warm mix asphalt (WMA) additives, on the EL value. In addition, both failure criteria are employed to investigate the impacts of these parameters in terms of the fatigue life of the study mixtures. According to the findings, unlike an increase in RAP content, which has a negative effect on the mixtures’ fatigue resistance, a higher binder content and/or binder modification can significantly increase the EL value and extend the fatigue life as was proved before by other researchers, whereas WMA additives do not significantly affect the mixtures’ fatigue behaviour. A comparison of the model simulation results with the field observations indicates that the G^R method predicts the field performance more accurately than the traditional method.