Three‐dimensional modelling of intergranular fatigue failure of fine grain polycrystalline metallic MEMS devices

This paper presents a 3D finite element model to investigate intergranular fatigue damage of microelectromechanical systems (MEMS) devices and to account for the effects of topological randomness of material microstructure on fatigue lives. The topology of MEMS material grain structures is modelled using randomly generated 3D Voronoi tessellations. Continuum Damage Mechanics is used to model progressive material degradation due to fatigue. A new 3D micro‐grain debonding procedure is developed to consider both intergranular crack initiation and propagation stages. The fatigue damage model is then used to investigate the effects of microstructure randomness on the variability in fatigue life of cantilever MEMS devices. Three different types of randomness are considered: (1) topological disorder due to random shapes and sizes of the material grains, (2) variation in material properties considering a normally (Gaussian) distributed elastic modulus and (3) material defects or internal voids. The stress–life results obtained are in good agreement with experimental data. The progression of damage and the overall crack pattern obtained from the microcantilever beam model are consistent with empirical observations.     

Experimental and numerical investigation of fatigue of thin tensile specimen

This paper presents the results of experimental and numerical investigation on fatigue of thin 304 stainless steel tensile specimens. In order to achieve the experimental aspects of this investigation a Micro Fatigue Test Rig (MFTR) was designed and developed to evaluate fatigue life and failure mechanism of tensile specimen. A 3D finite element model was also developed to investigate the fatigue damage of thin tensile specimen and to account for the effects of topological randomness of material microstructure on fatigue lives. The topology of the material grain structure was modeled using randomly generated 3D Voronoi tessellations corresponding to the measured grain size. Continuum damage mechanics was used to model the progressive material degradation. The damage parameters were obtained from the experimentally obtained S–N curve. A 3D mesh partitioning procedure was developed to consider both crack initiation and propagation stages considering the predominant transgranular, non-planar crack growth observed in the experiments. The stress–life results obtained from the fatigue damage model are in good agreement with the experimental data. The progression of damage and the proportion of life spent in crack initiation obtained from the model are consistent with empirical observations. The fatigue damage model was used to assess the influence of microstructure randomness accompanied by material inhomogeneity and internal voids on fatigue life dispersion.     

A discrete damage mechanics model for high cycle fatigue in polycrystalline materials subject to rolling contact

Fatigue behavior of polycrystalline materials is significantly influenced by their microstructural topology. The microstructural heterogeneity is one of the primary reasons for dispersion in high cycle fatigue lives of such materials. In this work, a damage mechanics based fatigue model that incorporates gradual material degradation under cyclic loading is presented in conjunction with a discrete material representation that takes the material microstructural topology into account. Microstructures are generated stochastically through the process of Voronoi tessellation. Micro-crack initiation, coalescence and propagation stages are modeled using damaged zones in a unified framework. The model is applied to study high cycle fatigue in rolling contacts. The effect of material topological disorder and inhomogeneity on fatigue life dispersion is studied. Fatigue damage is found to originate sub-surface and propagate towards the surface. Sub-surface damage patterns from the model are consistent with experimental observations. Propagation life is found to constitute a significant fraction of total life. Lives are found to follow a 3-parameter Weibull distribution. The relative proportion of lives spent in the initiation and propagation stages are in good quantitative agreement with experiments.     

Stacking Sequence Effects on Fatigue Intra-laminar Damage Progression in Composite Joints

In this paper the effects of the stacking sequence on the fatigue intra-laminar damage accumulation in pinned composite joints is investigated. A fatigue damage propagation numerical model based on gradual material degradation rules and Hashin fatigue failure criteria is formulated, implemented in a finite element platform and then used to simulate the intra-laminar fatigue damage evolution in the analysed composite joints. The model has been preliminary validated against literature experimental data in terms of s-n curves providing confirmation of its effectiveness in predicting the joints fatigue life. Different stacking sequences: zero-dominated, quasi-isotropic, cross-ply with different 0 ° and 90 ° plies distributions, have been considered when investigating the influence of the stacking sequence on the fatigue behaviour of the joints. The simulation of the joints’ fatigue life provided detailed information on the intra-laminar damage mechanisms on-set and evolution related to fatigue gradual degradation of material stiffness and strength for different values of the applied maximum stresses.     

复合材料疲劳寿命预测

在疲劳载荷作用下,复合材料的弹性模量会随着载荷循环数的增加而不断下降,而材料中的内部损伤则不断增大。为此,本文提出复合材料的疲劳模量和累积应变的概念,并由此定义出三种预测复合材料疲劳寿命的疲劳损伤模型。文中应用这三种模型对单应力水平和多应力水平下的玻璃纤维增强环氧树脂复合材料的疲劳寿命进行了估算,并同实验结果进行了比较。     

金属材料和结构的疲劳寿命预测概率模型及应用研究进展

疲劳过程的不确定性以及影响疲劳寿命的不确定性因素较多,导致疲劳寿命的分散性难以预测,在疲劳寿命预测模型中采用统计学和概率论的概念和方法是描述疲劳过程不确定性和疲劳寿命分散性的一种重要手段。本文针对疲劳寿命预测概率模型进行综述,总结和介绍了疲劳寿命经验公式和参数的随机化模型、表征疲劳寿命离散性的统计模型、基于材料微结构和疲劳物理机制的疲劳寿命预测概率模型以及研究广布疲劳损伤的概率模型,并对金属材料与结构的疲劳寿命预测方法进行了展望。     

Fatigue life prediction of composite laminates by FEA simulation method

This paper is to simulate the fatigue damage evolution in composite laminates and predict fatigue life of the laminates with different lay-up sequences on the basis of the fatigue characteristics of longitudinal, transverse and in-plane shear directions by finite element analysis (FEA) method. In FEA model, considering the scatter of the material’s properties, each element was assigned with different material’s properties. The stress analysis was carried out in MSC Patran/Nastran, and a modified Hashin’s failure criterion was applied to predict the failure of the elements. A new stiffness degradation model was proposed and applied in the simulation and then a strength degradation model was deduced, which is coupled with the presented stiffness degradation model. The reduced or discounted elastic constants were determined based on the failure mechanism of the laminates and the restrictive conditions of orthotropic property. The fatigue behavior and fatigue life of six kinds of E-glass/epoxy composite laminates with different lay-up sequences were experimentally studied, and the S–N curves and stiffness degradation models in longitudinal, transverse and in-plane shear direction were obtained. These fatigue data were adopted in the simulation to simulate fatigue behavior and estimate life of the laminates. The simulation results, including the fatigue life predicted and the residual stiffness, were coincident with the experimental results well except for the quasi-isotropic laminate for the lack of consideration of the out-of-plane fatigue character in the simulation.     

复合材料单钉接头疲劳累积损伤破坏分析

基于时间增量原理 , 推导了层合板接头疲劳加载累积损伤应力2应变分析的虚功方程。同时 , 引入Hashin三维疲劳失效准则进行材料的损伤判定 , 并结合建立的疲劳加载材料退化模型、 4种基本损伤机制相互关联作用的材料性能退化方法及复合材料接头最终失效判据 , 建立了层合板接头疲劳载荷作用下三维累积损伤分析的寿命预测方法。最后 , 对层合板接头拉2拉疲劳载荷作用下的损伤累积扩展与失效规律进行了仿真分析 , 并与试验结果进行了对比 , 结果表明 : 本文中建立的寿命预测方法能够很好地预测层合板接头的寿命以及损伤发生、扩展及最终失效。      

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.     

Development of microstructure in isothermally forged Nimonic alloy AP1

Abstract

The development of microstructure in the nickel alloy Nimonic AP1 owing to isothermal forging and subsequent heat treatment has been investigated. The microstructure initially consisted of coarse grains, which corresponded to the prior powder particles; these were surrounded by a coarse dispersion of γ′. On deformation, the volume fraction of material with a coarse γ′ dispersion increased, and this was associated with localised grain refinement following heat treatment. High volume fractions of this structural type gave some increase in tensile strength but reduced stress rupture life and increased fatigue crack growth rates. High temperature compression tests were used to develop a constitutive equation for the material which was then applied, via a finite element model, to simulate the isothermal forging process. The relationships between deformation and structural development, the modelling, and the mechanical properties are discussed. The approach is potentially useful for the design of forging operations for turbine disc production.     

基于频率变化预测玻璃纤维增强树脂复合材料层合板的剩余疲劳寿命

复合材料结构在疲劳过程中的累积损伤将导致结构刚度下降,并进一步引起结构的动态参数如频率发生衰减。因此,可以将结构疲劳状态与结构频率联系起来,基于频率预测结构的剩余疲劳寿命。本文首先基于复合材料在纵向、横向和面内剪切三个方向的疲劳特性,结合ABAQUS与Umat子程序开发了三维有限元模型模拟复合材料层合板中的疲劳损伤演变,并构建了不同疲劳状态下对应的模态分析模型,由此获得了疲劳过程中的频率衰减曲线。之后,基于疲劳过程的频率变化量训练了人工神经网络,用于预测玻璃纤维增强复合材料层合板的剩余疲劳寿命。特别地,在当前的数值模型中为每个单元分配了符合高斯正态分布的材料属性,以模拟实际情况下复合材料性能的离散性。结果表明,疲劳模型数值模拟结果与已有文献的疲劳实验数据吻合,基于频率变化量训练的人工神经网络可以成功预测玻璃纤维增强复合材料试件的剩余疲劳寿命。      

Effect of retained austenite – Compressive residual stresses on rolling contact fatigue life of carburized AISI 8620 steel

In this study the rolling contact fatigue (RCF) of case carburized AISI 8620 steel was numerically and experimentally investigated. For the numerical study, a two dimensional finite element (FE) RCF model based on the continuum damage mechanics (CDM) was developed to investigate the fatigue damage accumulation, crack propagation and final fatigue life of carburized AISI 8620 steel under various operating conditions. A randomly generated Voronoi tessellation was used to model the effects of material microstructure topology. The boundaries of the Voronoi elements were assumed to be the weak planes where damage accumulates, cracks initiate and propagate to simulate inter-granular cracks. A series of torsional fatigue tests were conducted on carburized AISI 8620 steel specimens containing 0% and 35% retained austenite (RA) to determine fatigue load (S) vs. life (N) of the material. The S–N results were then used to determine the material parameters necessary for the rolling contact fatigue model. The torsional fatigue test results indicate that the carburized AISI 8620 specimens with higher RA demonstrate higher life than the specimens with lower RA. The RCF model also indicates that the material with higher level of compressive residual stresses (RS) and retained austenite demonstrates higher RCF life. In order to corroborate the results of RCF model, a three-ball-on-rod rolling contact fatigue test rig was used to determine the RCF lives of carburized AISI 8620 steels with different amounts of RA. The fatigue life and cracks evolution pattern from the numerical and experimental results were corroborated. The results indicate that they are in good agreement.     

Comparison of fatigue life assessment by analytical,experimental and damage accumulation modelling approach for steel SAE 1045

Fatigue life assessment for two‐phase steel SAE 1045 has been carried out by experimental and simulation techniques. Analytical approach, termed as fatigue lifetime calculation, was employed making use of a load increase testing procedure and constant amplitude tests equipped with measurement techniques – plastic strain amplitude, change in temperature and change in electrical potential difference. The predicted fatigue life has been validated by constant amplitude tests and compared with fatigue life estimation by microstructure‐based simulation. Simulation has been carried out over the complete cross section of the specimen. The simulation uses damage accumulation in the gage section of the specimen culminating in the macro‐crack propagation, taking into account the inhomogeneous fatigue resistance of the material element. The results show that at the initial intervals of high cycle fatigue range at relatively higher stress amplitudes, the experimental and simulation results are in agreement; whereas in the (high cycle fatigue) region at relatively low stress amplitudes, the simulation results were found more optimistic and the corresponding fatigue scatter is also increased. Each scatter is attributed to the relatively small number of analysed models of the material structure. Scanning electron microscope was used to determine volume fraction of the microstructure for simulation. Fatigue fracture surface analysis shows that crack initiated from internal defect of material and crack propagation is driven by silicon oxide inclusion.     

Strain-based multiaxial fatigue damage modelling

A new multiaxial fatigue damage model named characteristic plane approach is proposed in this paper, in which the strain components are used to correlate with the fatigue damage. The characteristic plane is defined as a material plane on which the complex three‐dimensional (3D) fatigue problem can be approximated using the plane strain components. Compared with most available critical plane‐based models for multiaxial fatigue problem, the physical basis of the characteristic plane does not rely on the observations of the fatigue crack in the proposed model. The cracking information is not required for multiaxial fatigue analysis, and the proposed model can automatically adapt for different failure modes, such as shear or tensile‐dominated failure. Mean stress effect is also included in the proposed model by a correction factor. The life predictions of the proposed fatigue damage model under constant amplitude loading are compared with a wide range of metal fatigue results in the literature.     

Modelling of fatigue damage progression and life of CFRP laminates

A progressive fatigue damage model has been developed for predicting damage accumulation and life of carbon fibre‐reinforced plastics (CFRP) laminates with arbitrary geometry and stacking sequence subjected to constant amplitude cyclic loading. The model comprises the components of stress analysis, fatigue failure analysis and fatigue material property degradation. Stress analysis of the composite laminate was performed by creating a three‐dimensional finite element model in the ANSYS FE code. Fatigue failure analysis was performed by using a set of Hashin‐type failure criteria and the Ye‐delamination criterion. Two types of material property degradations on the basis of element stiffness and strength were applied: a sudden degradation because of sudden failure detected by the fatigue failure criteria and a gradual degradation because of the nature of cyclic loading, which is driven by the increased number of cycles. The gradual degradation of the composite material was modelled by using functions relating the residual stiffness and residual strength of the laminate to the number of cycles. All model components have been programmed in the ANSYS FE code in order to create a user‐friendly macro‐routine. The model has been applied in two different quasi‐isotropic CFRP laminates subjected to tension–compression (T–C) fatigue and the predictions of fatigue life and damage accumulation as a function of the number of cycles were compared with experimental data available in the literature. A very good agreement was obtained.     

FRP复合材料剩余刚度退化复合模型

为建立剩余刚度与材料损伤量及剩余寿命的关系, 将纤维增强树脂复合材料(FRP)层合板在拉-拉疲劳载荷作用下的失效模式划分为纤维间破坏、纤维随机断裂与分层3种类型, 分析不同失效模式与剩余刚度退化量的定量关系, 提出一个集成各失效模式影响的剩余刚度退化复合模型。该模型适用于占寿命绝大多数比例的Ⅰ、Ⅱ阶段, 避免了Ⅲ阶段刚度降不确定性的影响。剩余刚度退化曲线按时间尺度归一化, 消除了试件个体分散性影响, 分散性显著降低。对4种E-glass/Epoxy玻璃纤维复合材料层压板与3种AS-4/聚醚醚酮(PEEK)碳纤维复合材料层压板的疲劳试验结果进行了统计分析, 表明本文模型适于精确描述复合材料的剩余刚度下降规律。      

Application of nonlinear fatigue damage models in power electronic module wirebond structure under various amplitude loadings

This paper presents mean fatigue lifetime prediction of a wire-bond structure model in power electronic module using a failure physics approach that integrates high fidelity modelling and reduced order modelling.Loading current with variable amplitudes is applied to a finite element model of simplified wirebond structures.The resulting accumulated fatigue damage due to random loads is predicted by using reduced order modelling based on failure physics,a cycle counting algorithm,and various nonlinear fatigue damage models widely used in the literature.The reduced order modelling approach based on failure physics uses prediction data for the electro-thermo-mechanical behaviour of the wire-bond design of a power module obtained through non-linear transient finite element simulations,in particular for the fatigue life-time of the aluminium wire attached to the silicon chip of the wire in the module.The reduced order models that capture the black box function of the accumulated plastic strain are used in predicting the mean fatigue life time of the wire bond structure under random loads.One of the widely used cycle counting algorithms,rainflow counting algorithm,is used to count cycles of the temperature profile at the specific point of the wire bond structure in a power electronic module.The cycle data from the rainflow algorithm mean life time of the wire bond structure are predicted with various cumulative fatigue models.Non-linear cumulative fatigue models such as damage curve approach(DCA),double linear damage rule(DLDR),and double damage curve approach(DDCA),and linear cumulative fatigue damage model such as Palmgren-Miner rule are used to predict the mean fatigue life of the wire bond structure,and the results are compared.     

Non-destructive fatigue damage characterization of laminated thermosetting fibrous composites

The fatigue behaviour of the laminated thermosetting Fiberdux 6376-HTA composite material is studied experimentally for both constant and variable amplitude stress reversal loading. The fatigue-induced material degradation is correlated to non-destructive evaluation data obtained from C-scan graphs through the concept of the damage severity factor ( DSF ). The DSF is able to account for the varying severity of damage at the different specimen locations and is used to quantify the fatigue-induced damage. The concept of the DSF , introduced earlier by the authors for constant amplitude fatigue loading of thermoplastic fibrous composites, is applied to characterize fatigue damage of thermosetting fibrous composites and is extended to account for variable amplitude loading. Constant amplitude fatigue tests at various stress levels were performed to correlate fatigue damage to the change of mechanical properties, such as axial stiffness, residual tensile strength and interlaminar shear strength, and to develop expressions to relate DSF to the degradation of the mechanical properties with increasing fatigue damage. Correlation between DSF evolution and consumed fatigue life is made and fatigue damage functions involving stress amplitude dependency are formulated. These expressions together with a modified rainflow method are then used to assess fatigue life under variable amplitude fatigue loading; computed fatigue lives are compared against experimental results.     

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.