Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.     

Effect of stress ratio on very high cycle fatigue properties of Ti-10V-2Fe-3Al alloy with duplex microstructure

In fatigue critical applications, Ti-10 V-2 Fe-3 Al alloy components are expected to endure cyclic loading with cycles above 109. To assess their operating safety, S-N relations of Ti-10 V-2 Fe-3 Al alloy in very high cycle fatigue(VHCF) regime are of concern and have been investigated in this work. Fatigue behavior including S-N curves and crack initiation mechanisms is reported. Two transitions of fatigue crack initiation mechanism, from internal crack initiation to surface crack initiation and from α_p cleavage to α_s/βdecohesion, occur when the stress ratio(R) and stress level are reduced. Fatigue limits exist at N_f = 6 × 10~7 cycles for all stress ratios except for 0.5. In the VHCF regime two kinds of internal crack initiation mechanisms exist, i.e., coalescence of cluster of α_p facets and α_s/β decohesion. Their mutual competition depends on the stress ratio and can be interpreted in terms of different stress character required for promotion on different internal crack initiation mechanism. Small crack propagation is discussed to be life controlling process under the stress ratio range from-0.5 to 0.1 during VHCF regime while under the stress ratio 0.5 VHCF, life almost refers to the life required for crack initiation.     

A comparative study on thermomechanical and low cycle fatigue failures of a single crystal nickel-based superalloy

The cyclic deformation and lifetime behaviors of a single crystal nickel-based superalloy CMSX-4 have been investigated under out-of-phase thermomechanical fatigue (OP TMF) and isothermal low cycle fatigue (LCF) conditions. OP TMF life exhibited less than a half of LCF life although smaller inelastic strain range and lower mean stress level during OP TMF were observed compared to those during LCF. During OP TMF cycling, the maximum tensile strain at the minimum temperature was found to accelerate the surface crack initiation and propagation. Additionally, the multiple groups of parallel twin plates near crack provided a preferential path for crack propagation.     

Multiaxial fatigue behaviour of A356‐T6

Aluminum alloy A356‐T6 was subjected to fully reversed cyclic loading under tension, torsion and combined loading. Results indicate that endurance limits are governed by maximum principal stress. Fractography demonstrates long shear mode III propagation with multiple initiation sites under torsion. Under other loadings, fracture surfaces show unique initiation sites coincidental to defects and mode I crack propagation. Using the replica technique, it has been shown that the initiation life is negligible for fatigue lives close to 10⁶ cycles for combined loading. The natural crack growth rate has also been shown to be comparable to long cracks in similar materials.     

An experimental study on fatigue characteristics of CFRP-steel hybrid laminates

This paper aims to investigate the fatigue characteristics of hybrid laminates consisting of wave carbon fiber reinforced polymer (CFRP) sheets and a thin stainless steel plate under the tension–tension loading. Different loading options (e.g. same stress and same force), layers of CFRP sheets, and lay-ups of laminates (single and double sides) were considered. A series of experimental tests were performed to determine the effectiveness of the CFRP bonding on prolonging fatigue crack initiation life, preventing fatigue crack propagation and extending fatigue life of the hybrid laminates. Three distinct failure modes, classified as delamination, delamination bending and fiber breakage, were observed in the tests. It is shown that the loading conditions and CFRP thickness are the critical parameters affecting the failure modes and fatigue resistance. The crack initiation life and fatigue life of fiber-metal laminates (FMLs) increase by factors ranging from 1.06 to 1.96 and 1.17 to 2.07, respectively, relative to monolithic steel plates under the same force condition; whereas decrease by factors ranging from 0.63 to 0.89 and 0.28 to 0.61 under the same stress condition. Moreover, the double-side bonded FMLs show better fatigue properties and more stable crack propagation than single-side counterpart with the same thickness of CFRP.     

Fatigue thresholds of holed components under in-phase and out-of-phase torsional and axial loadings

The resistance-curve ( R -curve) method was applied to the prediction of the fatigue thresholds of notched components under in-phase and out-of-phase combinations of cyclic torsion and axial loadings. The prediction was compared with the experimental data obtained from thin-walled tubular specimen of medium-carbon steel with a hole. The stress was completely reversed and the mean stress was zero. The crack nucleated at the position of the maximum range of the circumferential stress on the periphery of a hole, and propagated almost straight for all cases examined. The experimental data of the thresholds for crack initiation and fracture agreed well with the predictions for in-phase and for out-of-phase loadings with 45° phase difference. For out-of-phase loading with 90°, the threshold for fracture was close to the crack initiation limit, because of the reduction of crack closure due to crack face rubbing by mode II shear cycling.     

Experimental observation and modeling of the retardation of fatigue crack propagation under the combination of mixed-mode single overload and constant amplitude loads

It is well-known that one of the major characteristics of variable fatigue loads, especially overloads, is the retardation of the fatigue crack due to the complex interaction of many factors such as the overload ratio, the timing of overloads, the stress ratio, the yield stress of the material, the thickness of the structure, and the stress history. However, studies of the combined effect of mixed-mode I+II constant amplitude fatigue loadings and a mixed-mode I+II single overload on fatigue behavior are still scant. In this study, fatigue tests were conducted under mixed-mode I+II constant amplitude loadings with a mixed-mode I+II single overload, with reference to the variation of fatigue crack retardation. The formation of the overload plastic zone (OPZ) ahead of the crack tip under a mixed-mode I+II single overload is studied experimentally by the measurement of the shape and size of the OPZ. The behavior of fatigue crack propagation under mixed-mode loading conditions is examined by changing the loading mode of a single overload, and the relationship between the mixed-mode I+II single overload and the behavior of fatigue crack propagation in terms of the characteristics of the OPZ is evaluated. The empirical modeling of the fatigue life under mixed-mode I+II constant amplitude loadings is proposed by considering the characteristics of both the OPZ and the combination of the mode-mixity of mixed-mode I+II constant amplitude loadings and a mixed-mode I+II single overload.     

Evaluation of corrosion fatigue crack propagation life at low-pressure steam turbine rotor groove

The corrosion fatigue crack propagation life of Christmas-tree type rotor groove with three hooks is studied. Each corner of the hook can be a candidate for crack initiation site therefore the condition where cracks initiate and propagate simultaneously at several hook corners must be considered. When a blade is inserted in the rotor groove, narrow gap is introduced unavoidably between the rotor groove and the blade root. The effect of this narrow gap on the crack behavior must also be considered. A procedure was presented to assess the crack initiation and propagation behavior under such a condition. Using the procedure, crack initiation and propagation behavior was evaluated for several gap conditions. It was revealed that the gap condition had little effect on the relation between crack depth at the third hook corner and life consumption ratio (ratio of loading cycle to final failure life). A corrosion fatigue test was performed using a rotor groove model specimen, and the results were compared with the evaluation results.     

Cyclic stress–strain response and crystal plasticity finite element analysis of AISI 9310 steel in biaxial fatigue loading

There are still many gaps in the research on the multiaxial fatigue failure mechanism of the gear shaft. In this paper, cyclic stress–strain response and biaxial fatigue damage characteristics of gear steel AISI 9310 were investigated. The specimens showed obvious cyclic softening characteristics at all phase angles, and the softening rate was directly associated with the initiation and propagation of cracks. The fractographies at different phase angles revealed that the specimens under out-of-phase loading suffered fatigue failure caused by a single crack source on the surface, while the fatigue crack under in-phase loading was gathered together by the propagation of different crack sources. Finally, the established crystal plastic finite element model showed a good prediction of the plastic strain energy density at different phase angles, and the maximum error was 13.03%. Furthermore, a biaxial fatigue life prediction method was proposed, with a maximum error of 39.5%.     

Low cycle fatigue life of Ti–6Al–4V alloy under non-proportional loading

Multiaxial low cycle fatigue life of Ti–6Al–4V under non-proportional loading was studied. Strain-controlled multiaxial fatigue tests at room temperature were carried out using tubular specimens. The strain paths employed were push–pull loading, reversed torsion loading, and two kinds of 90° out-of-phase loadings. The former two loadings are proportional loading tests where the principal directions of stress and strain are fixed in the cycle. The latter two are non-proportional loading tests where there is a 90° phase difference between axial and shear loadings, and the principal directions are cyclically rotated continuously. Failure lives are reduced obviously by non-proportional loadings in comparison with those in proportional loading tests. This paper focuses on determining a suitable fatigue model for evaluating the failure lives of Ti–6Al–4V under multiaxial loading.     

An analytical study on cracking directions and damage in thermal fatigue crazing subjected to variable amplitude loadings

In this paper, the effects of biaxial mean stress, mainly contributed by the weld residual stress, and thermal loading conditions on cracking directions and damage in high cycle thermal fatigue crazing subjected to variable amplitude loadings are investigated by a combined analytical and computational approach. The cracking directions are related to the orientation of the critical plane defined by the maximum damage. Analytical solutions of the critical plane orientation under constant amplitude biaxial tension/compression loadings are first derived and then employed to study the effects of biaxial mean stress on the critical plane orientation. The critical plane orientation appears to strongly depend on the dominant direction defined by the larger maximum stress. The developed analytical solution of the critical plane orientation and the analytical solution of the thermal stress from the literature are employed to study the effects of thermal loading conditions on the critical plane orientation. The critical plane orientation does not seem to significantly depend on the frequency, the amplitude and the mean value of the fluid temperature fluctuations, and the heat transfer film coefficient between the fluid and the pipe wall. The critical plane orientation under variable amplitude loadings is also studied, and an approximate solution is proposed for convenient engineering applications. The critical plane orientations are used to partially explain the observed cracking directions in the high cycle thermal fatigue crazing in the old residual heat removal system of a nuclear power plant. Finally, the effects of biaxial mean stress and thermal loading conditions on the fatigue crack initiation life are discussed.     

Lifetime prediction of cast iron materials under combined thermomechanical fatigue and high cycle fatigue loading using a mechanism-based model

In this paper the fatigue life of three cast iron materials, namely EN-GJS-700, EN-GJV-450 and EN-GJL-250, is predicted for combined thermomechanical fatigue and high cycle fatigue loading. To this end, a mechanism-based model is used, which is based on microcrack growth. The model considers crack growth due to low frequency loading (thermomechanical and low cycle fatigue) and due to high cycle fatigue. To determine the model parameters for the cast iron materials, fatigue tests are performed under combined loading and crack growth is measured at room temperature using the replica technique. Superimposed high cycle fatigue leads to an accelerated crack growth as soon as a critical crack length and thus the threshold stress intensity factor is exceeded. The model takes this effect into account and predicts the fatigue lives of all cast iron materials investigated under combined loadings very well.     

A FATIGUE LIFE PREDICTION METHOD BASED ON A MESOSCOPIC APPROACH IN CONSTANT AMPLITUDE MULTIAXIAL LOADING

The aim of this paper is to present a high cycle multiaxial fatigue life prediction method for metallic materials based on Papadopoulos' previous works and limited to constant amplitude loading. The initiation process of a crack is treated as a mesoscopic phenomenon taking place on a scale of the order of a grain or a few grains. The damage variable chosen is the accumulated plastic strain at this mesoscopic scale. Its estimation requires a macro-meso passage and the location of the plane subjected to maximum damage. Initiation is achieved as soon as a critical value of the accumulated plastic mesostrain is reached in these grains, so-orientated that their easy glide directions coincide with a particular direction of the critical plane. The detrimental effect of out-of-phase loading on damage accumulation is taken into account through a newly defined coefficient estimated from mechanical loading parameters; no adjustable parameter is required. A good agreement has been found between the predicted and experimental results for in-phase and out-of-phase sinusoidal constant amplitude loadings by examining a large amount of experimental data.     

加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟

采用不同应力比条件下的16MnR钢紧凑拉伸试样,设计了三种有限元分析模型,即不考虑加载历史效应的静态裂纹扩展模型,同时考虑加载历史和裂纹闭合的动态裂纹扩展模型以及仅考虑加载历史的伪动态裂纹扩展模型,对疲劳裂纹闭合过程、裂纹尖端的应力-应变迟滞环、疲劳损伤和裂纹扩展速率进行了数值模拟与分析,进而着重探讨了加载历史和裂纹闭合影响疲劳裂纹扩展行为的交互作用机制。结果表明:对于同类分析模型,应力比越大越不容易产生裂纹闭合;而在应力比相同的情况下,加载历史引起的残余压应力对裂纹闭合有明显的促进作用。裂纹闭合效应阻碍了平均应力的松弛,减小了裂纹尖端附近的应力-应变场强度、疲劳损伤和裂纹扩展速率,而加载历史引起的残余压应力则加快了平均应力的松弛和抑制了棘轮效应。与实验结果比较发现,只有同时考虑了裂纹闭合效应和加载历史影响的动态裂纹扩展模型,才能对疲劳裂纹扩展行为进行准确、定量的模拟。     

Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes

This paper is focused on the VHCF behavior of aeronautical titanium alloy under tensile and torsion fatigue loadings. Tensile tests were carried out with two different stress ratios: R = −1 and R = 0.1. Both surface and subsurface crack initiations were observed. In the case of subsurface crack initiation several fatigue life controlling mechanisms of crack initiation were found under fully-reversed loading conditions: initiation from (1) strong defects; (2) ‘macro-zone’ borders; (3) quasi-smooth facets and (4) smooth facets. Tests with stress ratio R = 0.1, have shown that initiation from the borders of ‘macro-zones’ becomes the dominant crack initiation mechanism in presence of positive mean stress. Like for the tensile results, surface and subsurface crack initiations were observed under ultrasonic torsion in spite of the maximum shear stress location on the specimen surface. But the real reason for the subsurface crack initiation under torsion was not found.     

Cyclic loadings and crystallization of natural rubber: An explanation of fatigue crack propagation reinforcement under a positive loading ratio

Natural rubber is known to have excellent fatigue properties. Fatigue crack propagation studies show that, under uniaxial tension loading, fatigue crack growth resistance increases with the loading ratio, even if the peak stress increases. Studies dealing with crack initiation confirm this trend. If strain induced crystallization is believed to play a major role in this reinforcement process, it is not clear yet by which mechanism this reinforcement takes place. Using SEM investigation, it is shown here that the reinforcement process is associated with strong crack branching in the crack tip region. From experimental results it is shown that under particular reinforcing loading condition a cyclic strain hardening process can be observed on the natural rubber which is able to overcome classically observed softening effects. A cumulative strain induced crystallization process is proposed to explain the stress ratio effect on fatigue crack initiation and propagation properties of natural rubber.     

Crack initiation and growth path under multiaxial fatigue loading in structural steels

In real engineering components and structures many accidental failures occur due to unexpected or additional loadings, such as additional bending or torsion. There are many factors influencing the fatigue crack paths, such as the material type (microstructure), structural geometry and loading path. It is widely believed that fatigue crack nucleation and early crack growth are caused by cyclic plasticity. This paper studies the effects of multiaxial loading paths on the cyclic deformation behaviour, crack initiation and crack path. Three types of structural steels are studied: Ck45, medium carbon steel, 42CrMo4, low alloy steel and the AISI 303 stainless steel. Four biaxial loading paths were applied in the tests to observe the effects of multiaxial loading paths on the additional hardening, fatigue crack initiation and crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It is shown that these materials have different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non-proportional loading. Theoretical predictions of the damage plane were conducted using the critical plane approaches, either based on stress analysis or strain analysis (Findley, Smith–Watson–Topper, Fatemi–Socie, Wang–Brown–Miller, etc). Comparisons of the predicted crack orientation based on the critical plane approaches with the experimental observations for the wide range of loading paths and the three structural materials are shown and discussed. Results show the applicability of the critical plane approaches to predict the fatigue life and crack initial orientation in structural steels.     

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 growth behavior for surface crack in welding joints under combined compressive and bending stresses

It has been demonstrated by experiments that crack can grow under cyclic compressive loading. However, it is difficult to observe and describe accurately by mathematical methods. In addition, cracks may close under compressive loading, which also increases the complexity of the problem. The fatigue growth behavior for surface cracks under biaxial loadings was studied by fatigue tests of HTS-A steel. According to experimental evidences, it is concluded that the transverse compressive stress not only changes the fracture morphology but also affect crack propagation life. Considering the influence of the compressive stress, this paper proposed an equivalent SIF and crack growth model subjected to compressive and bending stresses on the basis of McEvily formula. Finally, comparisons are made between prediction results and experimental data.     

A novel accumulative fatigue damage model for multiaxial step spectrum considering the variations of loading amplitude and loading path

In this paper, based on the process of the fatigue crack initiation and the critical plane theory, a continuous stress parameter was proposed to quantify the driving force of the fatigue crack initiation for the fully reversed multiaxial fatigue loading. In this stress parameter, the shear stress amplitude and normal stress amplitude on the critical plane were combined with the variable coefficients which were affected by the normalized fatigue life and the loading non‐proportionality. Owing to these coefficients, for the multiaxial loadings with different non‐proportionalities, the driving force of the fatigue crack initiation during the whole life could be described. After that, a novel accumulative fatigue damage model was established for the multiaxial two‐stage step spectrum. In this model, the accumulative damage was calculated according to the variation of the proposed stress parameter on the critical plane. Considering the directionality of the multiaxial fatigue damage, for the spectrum in which the loading path was variable, the damage accumulation was carried out on the critical planes of the both loadings, and the larger one was chosen as the final accumulative fatigue damage. In order to verify the new model, up to 41 different multiaxial two‐stage step spectrum loading tests on 2024‐T4 aluminium alloy were collected. The new model, as well as other five commonly used models, was applied to calculate the accumulative fatigue damage. The final results showed that, compared with other commonly used models, the new model had the most accurate results with the smallest scatters.