Characterization of fatigue damage for paving asphaltic materials*

This study investigates the fatigue characteristics of typical bituminous materials used in road applications. Fatigue testing was performed in a four‐point bending beam test apparatus under controlled strain and stress conditions. Fatigue life was defined using the classical approach as the number of cycles, N_f, to 50% reduction in the initial stiffness modulus. It has also been defined in terms of macro‐crack initiation, N₁. A different approach, based on the linear reduction in stiffness during a particular stage of a fatigue test, was introduced to define a damage parameter, and the evolution of this damage parameter with number of cycles was used to characterize fatigue life. Furthermore, refinements to the linear damage model were introduced to take into account the difference in the evolution of dissipated energy between controlled strain and stress testing modes. These modifications have enabled the identification of a unique fatigue damage rate for both controlled strain and stress test modes.     

A fatigue damage model of composite materials

The mechanical properties of composite materials degrade progressively with the increasing of the number of cyclic loadings. Based on the stiffness degradation rule of composites, a phenomenological fatigue damage model is presented in this paper, which contains two material parameters. They are proportional to the fatigue life of materials and inversely proportional to the fatigue loading level. Thirteen sets of experimental data of composite stiffness degradation were employed to verify the presented model, and the statistical results showed that this model is capable of describing the damage evolution of composite materials. The characteristics of damage development and accumulation of composite materials subjected to variable loading were studied in this paper. Four sets of two-level loading experimental data were cited to verify the damage model, and the results showed that the predicted life is in good agreement with the experimental ones.     

基于劲度模量分析的橡胶沥青混合料疲劳寿命研究

变幅加载下沥青的疲劳损伤累积具有明显的非线性特征,传统的Miner’s线性疲劳损伤累积准则无法表征不同变幅加载次序下沥青的非线性疲劳损伤累积(NLFDA)。该研究旨在建立考虑加载次序影响的NLFDA模型,准确表征加载次序对沥青疲劳损伤累积的影响。通过开展应力控制的沥青恒幅加载疲劳试验,采用耗散伪应变能(DPSE)表征沥青疲劳损伤,分析恒幅加载下沥青的疲劳损伤累积规律;采用低-高和高-低两种加载次序,开展应力控制的沥青变幅加载疲劳试验,分析变幅加载下沥青的疲劳损伤累积规律;基于损伤等效准则,建立考虑加载次序影响的NLFDA模型,分析加载次序对疲劳损伤累积的影响。结果表明：应力控制模式下的沥青疲劳损伤,呈先缓慢后急剧的非线性增加演化趋势;恒幅加载下沥青疲劳损伤服从Miner’s准则发生线性累积,且累积寿命分数等于1;变幅加载下沥青疲劳损伤不服从Miner’s准则而发生非线性累积。低-高和高-低变幅加载次序下,沥青累积疲劳寿命随一级寿命分数的增大而分别增加和减小,累积寿命分数分别大于1和小于1;建立的NLFDA模型可克服Miner’s准则缺陷,并较为准确地表征加载次序对沥青疲劳损伤累积的影响。

     

Corrosion fatigue life prediction of a steel shaft material in seawater

Corrosion fatigue behaviour of a medium strength structural material was studied in air and in 3.5% NaCl solution. Emphasis was placed on the study of corrosion pit formation and the development of cracks from pits. Pitting and crack propagation were quantified throughout the fatigue loading thereby allowing a model to be developed that included the stages of pitting and the pit-to-crack transition in order to predict the fatigue life. The results showed that a large number of corrosion pits with small size form at a very early stage in the fatigue lifetime. The number of pits and subsequent cracks was found to be higher at higher stress levels leading to multiple crack development and coalescence. When compared to air, fatigue life in a corrosive environment was significantly reduced at low stress levels due to pitting damage, indicating a dominant role of corrosion over that of mechanical effects. The corrosion fatigue model proposed shows good agreement with the experimental test data at lower stress levels but predicts more conservative lifetimes as the stress increases. Kitagawa–Takahashi diagram was produced for both test environments where it is indicated that the fatigue limit can be eliminated in a corrosive environment.     

Cumulative fatigue damage and life prediction of elastomeric components

Elastomeric components are widely used in many applications due to their good damping and energy absorption characteristics. The type of loading normally encountered by these components in service is variable amplitude cyclic loading. Therefore, fatigue failure is a major consideration in their design. In this work capabilities of Rainflow cycle counting procedure, maximum principal strain as a damage criterion, and Miner's linear cumulative damage rule are evaluated with both specimen and component tests. An automotive cradle mount is used as an illustrative component. Comparison of predicted and experimental fatigue lives in both specimen and cradle mount variable amplitude load tests indicate satisfactory predictions in both cases.     

Stochastic fatigue damage assessment of metro switch blade

Stochastic fatigue damage of a metro switch blade is studied with a combination of explicit finite element model (FEM), multiaxial fatigue criterion, and statistical analysis. The explicit FEM is used to reproduce dynamic procedure and to provide detailed stress/strain state variation. A multiaxial fatigue criterion proposed recently is extended to 3D conditions for fatigue prediction. The influence of stochastic impact position is considered by statistical analysis. After analysis, the formation of the serious unstable crack (continuous bites) on the switch blade can be revealed. From the perspective of service life, increasing traction coefficient and decreasing friction coefficient between wheel flange and switch blade gauge surface are beneficial but not significant. However, a speed increase from 36 to 54 km/h can lead to 40% reduction in service life. This work enhances the cognition of damage mechanism on switch blade and provides theoretical foundation for service life design and maintenance operation.     

A statistically consistent fatigue damage model based on Miner’s rule

With Monte Carlo sampling method, a statistically consistent fatigue damage model under constant and variable amplitude loadings based on linear Miner’s rule is proposed, which can quantitatively depict the probabilistic properties of fatigue damage and life. Numerical simulation shows that linear Miner’s damage criterion is statistically inconsistent; through some modification from a probabilistic point of view, a statistically consistent damage criterion is first established. To validate the statistical model, numerical verification of a supposed two-level cyclic loading and experimental verification of fatigue tests for Al-alloy straight lugs available in the literature are successfully conducted. The model predictions coincide quite well with both engineering hypotheses and experimental observations, compared with Miner’s model, indicating that the model can be regarded quantitatively accurate for engineering application.     

Study of the fatigue behavior of a synthetic rubber undergoing cumulative damage tests

Fatigue damage tests were carried on polychloroprene rubber using a loading sequence with alternate blocks of two force amplitudes, one being damaging and the other not, and carried until the failure of the dumbbell-shaped samples. The duration of the blocks was investigated and chosen to be higher than 20% of the fatigue life of the damaging loading. The presence of cracks was assured by preliminary micro-tomography measurements on samples undergoing constant amplitude fatigue tests at the damaging solicitation. It was observed that the sum of cycles to failure at this damaging loading was more than 5 times the fatigue life at constant amplitude. The behavior of the hysteresis area, the maximal and the minimal strain hinted that the explanation of such an improvement of the fatigue characteristic was caused by the relationship between the crack growth, the strain-induced crystallized area at the tip of those cracks and the self-heating.     

锻锤基础的冲击疲劳损伤分析

用损伤力学的概念提出了一种研究由锻锤锻打引起锻锤基础系统的疲劳损伤增长和疲劳寿命估计的方法。该方法通过定义,引入锻锤基础系统中减振垫与基础块的损伤状态寿命因子,能够估计出锻锤基础系统的减振垫和基础块的损伤疲劳寿命上、下限。通过分析发现,长期的重复冲击载荷会引起锻锤基础系统发生疲劳微损伤积累,疲劳损伤积累的宏观损伤又引起锻锤基础的动力响应随宏观损伤发展而增大,动力响应的增大又加剧基础系统的损伤发展。因此,为减少周围环境的振动以及保护周围环境免受锻锤冲击损伤,在锻锤基础系统设计中需考虑吸振和损伤控制。     

Cumulative fatigue damage dynamic interference statistical model

After studying in depth the statistical characteristics of cumulative fatigue damage D(t) and its critical value D_c, a new dynamic interference statistical model for fatigue reliability analysis is presented in this paper. Because the non-linearity of fatigue damage accumulation has been taken into account, this model is able to predict the fatigue reliability for random spectrum loading. To verify the predicted results, two fatigue experiments were conducted in which the numbers of specimens were more than 100, using fighter spectrum loading (FALSTAFF spectrum) and constant-amplitude loading respectively. It is shown that the new model is reliable, practicable and better than existing models.     

A continuum damage model applied to high-temperature fatigue lifetime prediction of a martensitic tool steel

High‐temperature operational conditions of hot work tool steels induce several thermomechanical loads. Depending on the processes, (i.e. forging, die casting or extrusion), stress, strain, strain rate and temperature levels applied on the material are nevertheless very different. Thus, lifetime prediction models need to be able to take into account a broad range of working conditions. In this paper, a non‐isothermal continuum damage model is identified for a widely used hot work tool steel AISI H11 (X38CrMoV5) with a nominal hardness of 47 HRc. This investigation is based on an extensive high‐temperature, low‐cycle fatigue database performed under strain rate controlled conditions with and without dwell times in the temperature range 300–600°C . As analysis of experimental results does not reveal significant time‐dependent damage mechanisms, only a fatigue damage component was activated in the model formulation. After normalization, all fatigue results are defined on a master Woehler curve defined by a nonlinear damage model, which allows the parameter identification. Last, a validation stage of the model is performed from thermomechanical fatigue tests.     

A stochastic theory of cumulative fatigue damage

A Stochastic theory for the cumulative fatigue damage of structural component with random fatigue strength under random loading is proposed on the basis of the Stratonovich-Khasminskii theorem. The analytical solutions for the probability densities of the cumulative fatigue damage and fatigue life and for the reliability function are given for steel and reinforced concrete components, with constant fatigue strength subject to narrow band stationary Gaussian stress process with zero mean. The results agree very well with those of digital simulation. It is noted that the theory can be applied, in principle, to metallic and some nonmetallic materials, to both narrow band and wide band stress process, and can be adapted to a sequence of n stationary stress process or quasi-stationary stress process. The scatter and degradation of fatigue strength can also be incorporated into the theory.     

Reconsideration of the fatigue tests for asphalt mixtures and binders containing high percentage RAP

When applying reclaimed asphalt technology in a flexible pavement project, most performance concerns are related to low temperature and fatigue cracking since the stiffness of the HMA mixture could dramatically increase through adding a high percentage of reclaimed asphalt pavement (RAP) material. The purpose of this study is to evaluate asphalt mixtures with high RAP contents, prepared using two RAP addition methods, for their performance based on fatigue-cracking resistance rather than relying on volumetric properties. Asphalt mixture samples were prepared with three RAP binder content replacement percentages (30, 40 and 50%) using two preparation methods: the as-is RAP gradation (traditional method) and the splitting of the RAP gradation into coarse and fine fractions (fractionated method). Asphalt mixture beam fatigue and binder fatigue time-sweep tests were performed. Beam fatigue samples also underwent freeze–thaw cycling for freeze–thaw damage evaluation. Rather than basing the performance based solely on S–N_f curves to illustrate the fatigue performance, the beam fatigue test data was analysed through a dissipated energy approach. Faster fatigue degradation was observed for the 40% RAP binder and beam mixture when subjected to repeated loading. From a morphology aspect, this can be explained by the binder’s phase separation and physical hardening effects.     

High cycle fatigue analysis in presence of residual stresses by using a continuum damage mechanics model

This study attempts to predict the high cycle fatigue life of steel butt welds by numerical method. At first, FE simulation of plate butt welding is carried out to obtain the weld-induced residual stresses employing sequentially coupled three-dimensional (3-D) thermo-mechanical FE formulation. Then, a nonlinear damage cumulative model for multiaxial high cycle fatigue based on continuum damage mechanics (CDM), which can incorporate the effect of welding residual stresses, is derived using FE technique. The high cycle fatigue damage model is applied to the butt welds subjected to cyclic fatigue loading to calculate the fatigue life considering the residual stresses, and the computed total fatigue life which takes into account the fatigue crack initiation and the propagation is compared with the test result. In addition, the fatigue life prediction of the welds without considering the residual stresses is implemented to investigate the influence of welding residual stresses on the fatigue performance. The FE results show that the high cycle fatigue damage model proposed in this work can predict the fatigue life of steel butt welds with high accuracy, and welding residual stresses should be taken into account in assessing the fatigue life of the welds.     

Fatigue damage discrepancies,the intrinsic fatigue damage map locus and the multiple stages of the similitude concept

The work demonstrates how the theory of the fatigue damage map (FDM) can be used in order to define a closed form locus where fatigue crack growth can be sought. The Intrinsic FDM Locus depending only on readily material properties represents a tool able to accurately predict crack growth of polycrystals. If the Locus is expressed in terms of a surface plot after triangulation of the data, it concludes into visualization of the potential for multiple similitude stages. The stages are defined as a function of the maximum far field stress and ΔK. Multiple similitude stages are found to dominate the short and near threshold area (Stage I growth) and represent direct result of the effect of polycrystalline behaviour to flow resistance. The work concludes that interrogation of the points defining the Intrinsic FDM Locus and related to the three thresholds can provide potential characteristics in the quest for an ideal damage tolerance material.     

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.     

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.     

An anisotropic damage model for tensile fatigue

Fatigue damage in materials is considered to be the effect of material degradation, and the dispersion in fatigue life is attributed to variability in microstructure. This paper presents a numerical model to simulate fatigue damage evolution using continuum damage mechanics to characterize material degradation. An explicit microstructure topology representation is achieved using Voronoi tessellations. Unlike conventional models which use a scalar approximation for damage, this model treats the damage variable as an anisotropic tensor. The model is used to simulate tensile fatigue failure in thin steel specimen. The fatigue life estimations from the model compares well with published experimental results. The results predict a high variability in fatigue life that is characteristic of metals and alloys, as compared with the existing isotropic damage models available in the literature. The model was also used to study the influence of material inhomogeneity on fatigue life dispersion.