A nonlinear continuous damage model based on short‐crack concept under variable amplitude loading

In this paper, a modified nonlinear damage accumulation model is proposed by using intrinsic crack size as the damage variable in the stress‐control condition. The model's development is based on the Chaboche nonlinear damage law and the short‐crack theory. The validations are confirmed by using the experimental data of Ti–6Al–4V and 2024‐T3 collected from tests and literature. The model capabilities of predicting damage accumulation and crack growth rate in the multi‐level loading condition as well as the variable amplitude loading condition with single and multiple over‐load are investigated and discussed in detail. Comparison results show that the proposed model is able to consider the loading ratio, the loading sequence and the over‐load effect on damage accumulation correctly. Meanwhile, the damage accumulation in the last stage of fatigue life can be described more clearly by the proposed model attributed to the use of crack size as the damage variable.     

Residual fatigue life prediction based on a novel damage accumulation model considering loading history

The influence of prior low‐cycle fatigue (LCF) on the residual fatigue life was investigated experimentally. A Ni‐based alloy was cyclically loaded under stress‐controlled low‐high (LH) block loading. In the first loading step, low‐amplitude loading was performed with the stress amplitude of 283.5MPa at 710°C. Different cycles of preloading were performed, varying from 100 to 10 000. Subsequently, high‐amplitude fatigue loading was carried out with the stress amplitude of 315MPa at 800°C. Experimental results show that the previous loading was beneficial to the residual fatigue life when the consumed life fraction is below 0.2 and detrimental when the consumed life fraction is larger than 0.2. A novel nonlinear fatigue damage accumulation model was proposed to estimate the residual LCF life under LH loading path considering the effects of load sequence and preloading cycles. The proposed model provided a better life prediction than some existing models, such as Kwofie‐Rahbar model, Miner' rule, Peng model, and Ye‐Wang model. Lastly, this model was further validated using various materials under LH and high‐low block loadings.     

Application of continuum damage mechanics to vibration fatigue life prediction

It is pivotal to predict the multiaxial vibration fatigue life during mechanical structural dynamics design. An algorithm of the finite element method implementation for multiaxial high cycle fatigue life evaluation is proposed, on the basis of elastic evolution model of continuum damage mechanics. By considering structural dynamic characteristics, namely, resonant frequencies and mode shapes, this algorithm includes a modal analysis and harmonic analysis, which makes this different from existing fatigue life prediction methods. A 10% decrease in the resonant frequency is regarded as the failure criterion. A critical damage value was obtained, which indicates mesocrack initiation fulfilment. To validate the effectiveness of the algorithm, auto‐phase sine resonance track‐and‐dwell experiments were conducted on notched cantilever beams made of Ti‐6Al‐4V alloy. The life predictions are conservative and in good agreements with the experimental results, which are mainly distributed within a scatter band of 2. This investigation could provide technical support for structural dynamics design and the analysis of reusable spacecraft.     

Cumulative damage model based on equivalent fatigue under multiaxial thermomechanical random loading

A new creep–fatigue damage cumulative model is proposed under multiaxial thermomechanical random loading, in which the damage at high temperature can be divided into the pure fatigue damage and the equivalent fatigue damage from creep. During the damage accumulation process, the elementary percentage of the equivalent fatigue damage increment is proportional to that of the creep damage increment, and the creep damage is converted to the equivalent fatigue damage. Moreover, combined with a multiaxial cyclic counting method, a life prediction method is developed based on the proposed creep–fatigue damage cumulative model. In the developed life prediction method, the effects of nonproportional hardening on the fatigue and creep damages are considered, and the influence of mean stress on damage is also taken into account. The thermomechanical fatigue experimental data for thin‐walled tubular specimen of superalloy GH4169 under multiaxial constant amplitude and variable amplitude loadings were used to verify the proposed model. The results showed that the proposed method can obtain satisfactory life prediction results.     

Nonlinear fatigue damage accumulation and life prediction of metals: A comparative study

Fatigue damage modelling and life prediction of engineering components under variable amplitude loadings are critical for ensuring their operational reliability and structural integrity. In this paper, five typical nonlinear fatigue damage accumulation models are evaluated and compared by considering the influence of load sequence and interaction on fatigue life of P355NL1 steels. Moreover, a new nonlinear fatigue damage accumulation model is proposed to account for these two effects. Experimental datasets of pressure vessel steel P355NL1 and four other materials under two‐block loadings are used for model comparative study. Results indicate that the proposed model yields more accurate fatigue life predictions for the five materials than the other models.     

Study on the accumulative fatigue damage rules under multiaxial two‐stage step spectra constructed by loadings with similar lives

In this paper, the influence on the multiaxial fatigue damage accumulation caused by loading path variation was studied. For 2024‐T4 aluminium alloy, the damage evolution during the entire life was first observed. On the basis of the observation, the stage I of fatigue damage evolution was further divided into two sub‐stages, and the dominant stress parameters of these two sub‐stages were proposed. Taking the dominant stress parameters into account, a phased accumulative fatigue damage model was proposed. Then, 12 multiaxial two‐stage step spectra constructed by loadings with approximately identical fatigue lives were carried out on 2024‐T4 aluminium alloy. The accumulative fatigue damage was calculated by the proposed model, and another five commonly used models and the calculated results were compared. According to the comparison, the newly proposed model had the most accurate results with the smallest scatter.     

Fatigue life prediction under variable loading based on a new damage model

To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T 6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This paper contains the results of mono-axial random load fatigue tests with different mean and amplitude values performed on 6082 T 6 aluminium alloy specimens. Cycles were counted with rainflow algorithm and damage was cumulated with a new model proposed in this paper and with the Palmgren–Miner model. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.     

Prediction of short fatigue crack growth of Ti‐6Al‐4V

It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti‐6Al‐4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.     

Effect of carbon fibres on the static and fatigue mechanical properties of fibre metal laminates

It is crucial to understand the characteristic fatigue crack initiation and its growth mechanisms, as well as the relationship between the mechanical properties and the fatigue damage evolution in fibre metal laminates (FMLs). Two types of FML were studied in this work: a polyacrylonitrile‐based carbon fibre epoxy matrix composite sandwiched by Ti‐6Al‐4V (Ti‐alloy) sheets (IMS60‐Ti) and a pitch‐based carbon fibre epoxy matrix composite sandwiched by Ti‐alloy sheets (K13D‐Ti). The static and fatigue mechanical properties of IMS60‐Ti and K13D‐Ti were investigated. The increased failure strain of the FML was greater than that of carbon fibre‐reinforced polymer (CFRP) matrix composites. The fatigue life of IMS60‐Ti was much longer than that of K13D‐Ti. The fatigue damage process in IMS60‐Ti was related to the fatigue creep behaviour of the Ti‐alloy face sheet and mode II cracking at the CFRP/Ti‐alloy interface, and the damage in K13D‐Ti was related to the K13D CFRP laminate.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

LOW-CYCLE FATIGUE UNDER NON-PROPORTIONAL LOADING

A series of strain-controlled, low-cycle fatigue experiments have been conducted on 42CrMo steel under various loading paths including circular, square, cruciform, and rectangular paths. Present experiments have shown that there is additional hardening under non-proportional cyclic loading. Non-proportional cyclic additional hardening also results in a shorter life for multiaxial low cycle fatigue. A non-proportionality measure of strain path based on both a physical basis and macromechanical phenomena is proposed. The loading path effect on additional hardening is also described well. Low-cycle fatigue damage accumulation and the evolution process under non-proportional loading is analysed via the Continuum Damage Mechanics Model of Chaboche. A non-proportinality measure is introduced in the damage evolution equation and a modified Coffin-Manson type formula is derived. A novel fatigue life prediction approach based on the critical-plane concept of Brown and Miller is proposed.     

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.     

A modification of UniGrow 2‐parameter driving force model for short fatigue crack growth

In this paper, a modification of the UniGrow model is proposed to predict total fatigue life with the presence of a short fatigue crack by incorporating short crack propagation into the UniGrow crack growth model. The UniGrow model is modified by 2 different methods, namely the “short crack stress intensity correction method” and the “short crack data‐fitting method” to estimate the total fatigue life including both short and long fatigue crack propagations. Predicted fatigue lives obtained from these 2 methods were compared with experimental data sets of 2024‐T3, 7075‐T56 aluminium alloys, and Ti‐6Al‐4V titanium alloy. Two proposed methods have shown good fatigue life predictions at relatively high maximum stresses; however, they provide conservative fatigue life predictions at lower stresses corresponding high cycle fatigue lives where short crack behaviour dominates total fatigue life at lower stress levels.     

Ratcheting‐fatigue behaviour of bainite 2.25Cr1MoV steel with tensile and compressed hold loading at 455°C

The ratcheting behaviour of a bainite 2.25Cr1MoV steel was studied with various hold periods at 455°C. Particular attention was paid to the effect of stress hold on whole‐life ratcheting deformation, fatigue life, and failure mechanism. Results indicate that longer peak hold periods stimulate a faster accumulation of ratcheting strain by contribution of creep strain, while double hold at peak and valley stress has an even stronger influence. Creep strains produced in peak and valley hold periods are noticeable and result in higher cyclic strain amplitudes. Dimples and acquired defects are found in failed specimen by microstructure observation, and their number and size increase under creep‐fatigue loading. Enlarged cyclic strain amplitude and material deterioration caused by creep lead to fatigue life reduction under creep‐fatigue loading. A life prediction model suitable for asymmetric cycling is proposed based on the linear damage summation rule.     

A fatigue damage accumulation model for reliability analysis of engine components under combined cycle loadings

Rotor components of an aircraft engine in service are usually subjected to combined high and low cycle fatigue (CCF) loadings. In this work, combining with the load spectrum of CCF, a modified damage accumulation model for CCF life prediction of turbine blades is first put forward to take into account the effects of load consequence and load interaction caused by high‐cycle fatigue (HCF) loads and low‐cycle fatigue (LCF) loads under CCF loading conditions. The predicted results demonstrate that the proposed model presents a higher prediction accuracy than Miner, Manson‐Halford model does. Moreover, to evaluate the fatigue reliability of rotor components, reliability model with the failure mode of CCF is proposed on the basis of the stress‐strength interference method when considering the strength degeneration, and its results show that the reliability model with CCF is more suitable for aero‐engine components than that with the failure mode of single fatigue.     

Energy-based time derivative damage accumulation model under uniaxial and multiaxial random loadings

A new fatigue life prediction method using the energy-based approach under uniaxial and multiaxial random loadings is proposed. The uniqueness of the proposed model is based on a time-derivative damage accumulation unlike classical cycle-based damage accumulation models. Thus, damage under arbitrary random loading can be directly obtained using time-domain integration without cycle counting. First, a brief review of existing models is given focusing on their applicability to uniaxial/multiaxial, constant/random, and high cycle fatigue/low cycle fatigue loading regimes. Next, formulation of time-derivative damage model is discussed in detail under uniaxial random loadings. Then, an equivalent energy concept for general multiaxial loading conditions is used to convert the random multiaxial loading to an equivalent random uniaxial loading, where the time-derivative damage model can be used. Finally, the proposed model is validated with extensive experimental data from open literature and in-house testing under various constant and random spectrum loadings.     

基于背应力功的疲劳能量模型及其在轮槽构件寿命预测中的应用

基于局部应力-应变法与疲劳损伤能耗结构,以疲劳过程中背应力塑性功累积为基础,建立了一种新的缺口构件疲劳寿命预测能量模型,并将其应用于某型汽轮机轮槽结构件的疲劳寿命预测.通过与试验结果相比较,初步验证了模型的预测精度(预测寿命与试验寿命误差小于20％).此外,还进一步将上述能量模型与传统疲劳寿命预测能量方法进行了比较.结...     

Fatigue life prediction based on equivalent stresses for laser beam welded 6156 Al‐alloy joints under variable amplitude loading

In the present work, a simple fatigue life prediction approach is proposed using fracture mechanics for laser beam welded Al‐alloy joints under variable amplitude loading. In the proposed approach, variable amplitude loading sequence is transformed into an equivalent constant amplitude loading using the root mean square model. The crack growth driving force K^* is chosen to describe the fatigue crack growth rate. The influences of residual stress and its relaxation on fatigue life are taken into account in the proposed approach. The fatigue lives are also predicted using the traditional approach based on the S‐N curves and the rainflow counting method. The predicted results show that the proposed approach is better than the traditional approach.     

Effect of fatigue damage on static and dynamic tensile behaviour of electro‐discharge machined Ti‐6Al‐4V

The fatigue performance of electro‐discharge machined Ti‐6Al‐4V and, more specifically, the effect of cyclic damage on the static and dynamic tensile properties of the material have been investigated. In a first step, fatigue failure was studied. Afterwards, tensile tests were performed on specimens that had been previously subjected to cyclic loading during predefined fractions of the fatigue life. In addition to conventional experiments at quasi‐static strain rate, dynamic tests were performed using a split Hopkinson tensile bar setup. The edges of some of the specimens were removed after cyclic loading to discriminate between the effects of damage at the edges and in the bulk of the material. Results revealed that early fatigue failure is due to the growth of cracks on the machined edges of the specimens. Edge cracks can randomly reduce fracture strain and energy absorbing capacity. However, cyclic damage does not affect the tensile properties of the bulk material.