Influence of hardening type on self-heating of metallic materials under cyclic loadings at low amplitude

For several years, some authors have worked on the rapid estimation of the High-Cycle Fatigue (HCF) properties of metallic materials based upon temperature measurements under cyclic loadings. This method is so-called “self-heating tests”. More recently, the development of a two-scale probabilistic model has shown that self-heating tests permit to identify, not only, the mean fatigue limit, but also, the scatter of classical fatigue results. So, it is proposed, in this paper, to extend the previous approach for materials with different kinds of hardening and different kinds of hardening evolution (i.e., cyclic hardening or cyclic softening) and to show the influence of the hardening type on self-heating and on the partition of the plastic energy (i.e., dissipated and stored energies). The identification and the validation of the proposed approach have been performed on two different metallic materials (i.e., a dual-phase steel and a chrome–cobalt alloy).     

A micromechanical explanation of the mean stress effect in high cycle fatigue

A micro–macro approach of multiaxial fatigue in unlimited endurance is presented in this study, as an extension of a previous model recently proposed by the authors [Monchiet, V., Charkaluk, E., Kondo, D., 2006. A plasticity–damage based micromechanical modelling in high cycle fatigue. C.R. Mécanique 334 (2), 129–136]. It allows to take into account coupling between polycrystalline plasticity and damage mechanisms which occur at the scale of persistent slip bands (PSB) during cyclic deformation. The plasticity–damage coupled model is obtained by adapting the Gurson [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth: part I – yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15] limit analysis to polycrystalline materials to take into account microvoids growth along PSBs. The macroscopic fatigue criterion corresponds to microcracks nucleation at the PSB–matrix interface. It is shown that this criterion accounts for the effect of the mean stress and of the hydrostatic pressure in high cycle fatigue. Such features of HCF are related to the damage micro-mechanisms. Finally, some illustrations concerning the particular case of cyclic affine loadings are presented and comparisons of the predictions of the fatigue criterion with experimental data show the relevance of this new approach.     

Contribution of Kinematical and Thermal Full-field Measurements for Mechanical Properties Identification: Application to High Cycle Fatigue of Steels

The purpose of this work is to extend the use of unconventional tests and full field measurements (kinematical and thermal) to the identification of the effect of a wide plastic pre-strain range on the high cycle fatigue properties of a dual-phase steel. An unconventional specimen is designed. The geometry of this specimen permits a constant gradient of pre-strain to be obtained after a monotonic tensile test. Then, a self-heating test under cyclic loading is carried out on the pre-strained specimen. During this cyclic test, the thermal field is measured using an infrared camera. Finally, a suitable numerical strategy is proposed to identify a given thermal source model taking into account the influence of plastic pre-strain. The results show that, with the unconventional test and the procedure developed in this work, the influence of a plastic pre-strain range on fatigue properties can be identified by using only one specimen when, for a classical fatigue campaign, a great number of specimens is required.     

一种基于耗散能计算的高周疲劳参数预测方法

在热力学框架下,基于薄板假设,建立金属材料薄板试样在高周疲劳载荷作用下的热传导方程,将试样温度场数据和实时载荷信号导入,准确计算与高周疲劳损伤相关的单个循环内耗散能. 基于该方法,以316L不锈钢材料为例,通过实时监测试样不同应力水平下高周疲劳破坏全过程中耗散能的变化,拟合出耗散能-疲劳寿命曲线,呈现与传统的应力-疲劳寿命曲线相同的规律;提出一种新的预测高周疲劳极限的能量法,确定的疲劳极限与实验值相近.     

Frequency-dependent random fatigue of panel-type structures made of ceramic matrix composites

The panel-type structures used in aerospace engineering can be subjected to severe highfrequency acoustic loadings in service. This paper evaluates the frequency-dependent random fatigue of panel-type structures made of ceramic matrix composites(CMCs) under acoustic loadings. Firstly, the high-frequency random responses from the broadband random excitation will result in more stress cycles in a deinite period of time. The probability density distributions of stress amplitudes will be different in different frequency bandwidths, though the peak stress estimations are identical. Secondly, the fatigue properties of CMCs can be highly frequency-dependent. The fatigue evaluation method for the random vibration case is adopted to evaluate the fatigue damage of a representative stiffened panel structure. The frequency effect through S-N curves on random fatigue damage is numerically veriied. Finally, a parameter is demonstrated to characterize the mean vibration frequency of a random process, and hence this parameter can further be considered as a reasonable loading frequency in the fatigue tests of CMCs to obtain more reliable S-N curves.Therefore, the inluence of vibration frequency can be incorporated in the random fatigue model from the two perspectives.     

STUDY ON THE SURFACE CRACK GROWTH BEHAVIOR IN 14MnNbq BRIDGE STEEL

Three-dimensional crack closure correction methods are investigated in this paper.The fatigue crack growth tests of surface cracks in 14MnNbq steel for bridge plate subjected to tensile and bending loadings are systematically conducted.The experimentally measured fatigue crack growth rates of surface cracks are compared with those of through-thickness cracks in detail.It is found that the crack growth rates of surface cracks are lower than those of through-thickness cracks.In order to correct their differences in fatigue crack growth rates, a dimensionless crack closure correction model is proposed.Although this correction model is determined only by the experimental data of surface cracks under tensile loading with a constant ratio R=0.05, it can correlate the surface crack growth rates with reasonable accuracy under tensile and bending loadings with various stress ratios ranging from 0 to 0.5.Furthermore, predictions of fatigue life and crack aspect ratio for surface cracks are discussed, and the predicted results are also compared with those obtained from other prediction approaches.Comparison results show that the proposed crack closure correction model gives better prediction of fatigue life than other models.     

Fatigue damage in polycrystals – Part 1: The numbers two and three

The fundamental difference between the cyclic yield stress and the fatigue limit is scale. The basic rate of slip mismatch towards a saturated condition, representing polycrystalline behaviour, is a material property embedded into the grain size distribution. Deviations from its basic rate will depend on the shape of the crack and the selected crack path. This work concludes that during the first loading cycle, and for stresses equal and above the fatigue limit, the surface will always been deformed plastically.     

Theoretical analysis of the spatial variability in tillage forces for fatigue analysis of tillage machines

This paper presents a new theoretical model to describe the spatial variability in tillage forces for the purpose of fatigue analysis of tillage machines. The proposed model took into account both the variability in tillage system parameters (soil engineering properties, tool design parameters and operational conditions) and the cyclic effects of mechanical behavior of the soil during failure ahead of tillage tools on the spatial variability in tillage forces. The stress-based fatigue life approach was used to determine the life time of tillage machines, based on the fact that the applied stress on tillage machines is primarily within the elastic range of the material. Stress cycles with their mean values and amplitudes were determined by the rainflow algorithm. The damage friction caused by each cycle of stress was computed according to the Soderberg criterion and the total damage was calculated by the Miner’s law. The proposed model was applied to determine the spatial variability in tillage forces on the shank of a chisel plough. The equivalent stress history resulted from these forces were calculated by means of a finite element model and the Von misses criterion. The histograms of mean stress and stress amplitude obtained by the rainflow algorithm showed significant dispersions. Although the equivalent stress is smaller than the yield stress of the material, the failure by fatigue will occur after a certain travel distance. The expected distance to failure was found to be d_f = 0.825 × 10⁶ km. It is concluded that the spatial variability in tillage forces has significant effect on the life time of tillage machines and should be considered in the design analysis of tillage machines to predict the life time. Further investigations are required to correlate the results achieved by the proposed model with field tests and to validate the proposed assumptions to model the spatial variability in tillage forces.     

Two scale damage model and related numerical issues for thermo-mechanical High Cycle Fatigue

On the idea that fatigue damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), a three-dimensional two scale damage model has been proposed for High Cycle Fatigue applications. It is extended here to anisothermal cases and then to thermo-mechanical fatigue. The modeling consists in the micromechanics analysis of a weak micro-inclusion subjected to plasticity and damage embedded in an elastic meso-element (the RVE of continuum mechanics). The consideration of plasticity coupled with damage equations at microscale, altogether with Eshelby–Kröner localization law, allows to compute the value of microscopic damage up to failure for any kind of loading, 1D or 3D, cyclic or random, isothermal or anisothermal, mechanical, thermal or thermo-mechanical. A robust numerical scheme is proposed in order to make the computations fast. A post-processor for damage and fatigue (DAMAGE_2005) has been developed. It applies to complex thermo-mechanical loadings. Examples of the representation by the two scale damage model of physical phenomena related to High Cycle Fatigue are given such as the mean stress effect, the non-linear accumulation of damage. Examples of thermal and thermo-mechanical fatigue as well as complex applications on real size testing structure subjected to thermo-mechanical fatigue are detailed.     

Micromechanical modeling of low cycle fatigue under complex loadings — Part II. Applications

Motivated by the effect of the different loading paths (uniaxial and multiaxial) and the mean stress or strain effects, fatigue life is qualitatively evaluated by employing a micromechanical approach developed in the first part of this paper. Taking into account these loading conditions, a number of numerical tests are carried out to demonstrate the ability of this model to describe the inelastic-damaged behavior of low cyclic fatigue. Theoretically, the internal variables evolution on the Crystallographic Slip Systems (CSS) are recorded under these loadings up to the final fracture of the Representative Volume Element (RVE). The predicted macro-damage D^T as well as the applied macro-stress Σ are recorded and analyzed during fatigue life. It is demonstrated that, at least qualitatively, the developed model gives successful results describing the fatigue lives under employed loading paths. Quantitatively, after the identification of the material constants of the over-aged Waspaloy, two examples are taken into consideration representing the uniaxial and biaxial cyclic behavior of this alloy. It is shown that the predicted responses are in good agreement with the experimental results.     

Mechanical Behaviors of Saturated Sand under Complicated Loading

The different physical states of saturated sand, including shear elasticity, positive dilatancy, and negative dilatancy (preliminary negative dilatancy, secondary negative dilatancy and reversal negative dilatancy) are revealed based on the pore water pressure response of saturated sand in undrained dynamic torsional tests of thin cylinder samples and also checked by the drained cyclic triaxial tests under a given mean effective normal stress. According to the effective stress path of different physical states under the undrained cyclic torsional tests the physical state transformation surface, stress history boundary and yield surface are determined, and the state boundary surface is also determined by the range of effective frictional stress state movement. Based on the moving yield surface without rotation, and the expanding stress history boundary surface relevant to the stress path variations under different physical states in 3D stress space, a physical state model is proposed to provide a new app     

基于能量法的多轴疲劳寿命预测方法

摘 要：有效的疲劳寿命预测方法是确保处于多轴循环载荷作用下的工程构件安全性的关键。结合临界平面思想,提出了一种基于能量法的多轴疲劳寿命预测模型;该模型针对不同的疲劳失效形式采用不同的临界面上能量参数作为损伤参量,可体现多轴加载条件下的平均应力效应以及临界面上各方向参量对材料疲劳损伤的影响。通过六种材料的多轴疲劳试验数据对所提出的模型及其它三种经典能量模型进行了评估与验证,结果显示所提出的模型相较于其他模型具有更好的寿命预测精度及工程适用性。     

An Investigation of Fatigue Characteristics of Copper Film

Tensile and fatigue behaviors of the copper film coated by tin (Sn) were investigated considering S-N relationships and scanning electron microscope (SEM) observation of fracture surfaces. The fatigue behavior was investigated considering the effect of load ratio, R. The specimen of 2000 μm width, 8000 μm length and 15.26 μm thickness was fabricated by etching process. Tensile properties were measured using the micro-tensile testing system and in-plane electronic speckle pattern interferometric (ESPI) system for measuring the tensile strain during the test. The fatigue tests of the film were carried out in load-control mode with 40 Hz at three different stress ratios of 0.05, 0.3 and 0.5. The S-N curves, including the slope of the curve and fatigue limit, at the respective stress ratios were obtained. These curves were dependent on the load ratio. Empirical relationships indicating the dependency of the fatigue limit and S-N curve on the load ratio were suggested in this study. SEM observation of the tensile fracture surface showed that the cross-sectional area of the testing section was necked in the direction of the film thickness (i.e. parallel to the substrate surface normal) and some ductile dimples in the fracture surface were present. The fracture of the copper film under cyclic loading was progressed in the transgranular fracture mode.     

随机载荷下疲劳裂纹的闭合和扩展估算模型

本文分析了裂尖前,后方塑性区对闭合性能的影响,提出从裂尖塑性钝化量和尾迹区残余塑性变形两个方面来确定裂纹面的残余变形,并讨论了压缩载荷对闭合应力的影响,由此建立了一个疲劳裂纹闭合模型,然后通过模型“有限记忆”性质的假定将它应用到随机加载情况。用此模型对铝合金2219——T851受飞机谱载荷的CCT平面应力试件进行了疲劳寿命估算,估算值与实验结果接近。     

Cyclic behavior of unidirectional and cross-ply titanium matrix composites

Relatively simple and efficient micromechanical models are used to obtain the uniaxial response of SCS-6/Timetal 21S with [0]₄ and [0/90]_s laminates when subjected to isothermal and thermomechanical fatigue (TMF) loadings. Features of the modeling that are required to obtain the accurate deformation behavior for this class of materials under these loadings are highlighted. To this end, a comparison is made between the concentric cylinder model and the uniaxial stress model for representing the [0] laminate. The axial stresses from the two models are very similar under mechanical loading. The greatest differences appear under thermal loading alone. The differences on the composite response between a time-independent elastic-plastic and a viscoplastic matrix constitutive model are also examined. The latter is based on the Bodner-Partom unified constitutive model. The [0/90] laminate is treated by adding a parallel element with smeared [90] ply properties to the [0] model and invoking axial strain compatibility as well as stress equilibrium. The proposed constitutive law for the [90] ply includes both matrix viscoplasticity and fiber/matrix separation damage and is based on damage mechanics concepts. The effect of cyclic frequency on TMF behavior is examined. The in-phase TMF life is shown to be very sensitive to frequency due to the relaxation of matrix stress and the attendant increase in fiber stress.     

The effect of frequency and sample shape on fatigue behaviors of DZ125 superalloy

The effect of frequency and sample shape on fatigue behaviors of DZ125 superalloy are systematically studied. The results show that fatigue fracture still occurs above the cycle of 10⁸ for tests carried out at the frequency of f = 20 kHz and stress ratio R = ?1, so the traditional fatigue limit at cycle of 10⁷ is not appropriate for fatigue design. Fatigue fracture surfaces are perpendicular to stress axis for cylindrical and plate specimens, and the fatigue cracks originate from the extra surface of the specimens. Fatigue crack is apt to propagate from cutting direction to forward direction, which occurs mainly in the second propagation stage at higher stress amplitude. There is an obvious frequency effect for DZ125 superalloy. The higher the test frequency is, the more serious the effect of frequency on fatigue behaviors of the alloy. After the frequency correction, the ultra-high cycle fatigue S-N curve well coincide with the traditional fatigue S-N curve.     

金属材料疲劳行为的应力场强法描述

基于近年来发展的应力场地对金属材料的多种疲劳行为作了系统的描述，给出了缺口疲劳系Ｋｆ，疲劳尺寸系数ε，疲劳加载方式因子ＣＬ，多轴疲劳极限方程，缺口件Ｓ－Ｎ曲线的预测等多方面的定量描述，并引用了大量的实验数据加以验证，由此表明应场强法是一种很好的抗疲劳设计方法。     

TC21钛合金显微组织对超长寿命疲劳行为的影响

本文主要研究钛合金的网篮尺寸对于超声疲劳行为的影响。研究发现,对于TC21钛合金,高应力下疲劳裂纹萌生于试样表面;低应力下疲劳裂纹萌生于试样亚表面。最大应力-循环次数(S-N)曲线显示,在两段连续下降的曲线之间有一个表面萌生向内部萌生的转变平台。对于网篮尺寸为60μm的钛合金,转变平台对应的应力幅为540MPa,疲劳极限为430MPa。网篮尺寸为40μm的转变平台应力幅为600MPa,疲劳极限为530MPa。分析得知网篮尺寸为60μm的TC21钛合金疲劳性能低于网篮尺寸为40μm的TC21钛合金。     

透平转子的可靠性设计

介绍透平转子的可靠性设计方法。该方法以传统的转子强度和振动的设计方法为基础,把透平转子的静应力、材料静强度、应力幅、尺寸系数、表面加工系数、应力集中系数、材料疲劳极限、热疲劳累积损伤程度、材料低周疲劳程度、蠕变寿命、固有频率、激振力频率、不平衡响应等处理为随机变量,使用机械概率设计法确定转子设计的可靠度。文中给出了透平转子静强度、疲劳强度、热疲劳、蠕变寿命、避开弯曲共振、避开扭转共振和限制不平稳响