Multi-scale analyses on mechano-electric degradation of film interconnects in flexible electronics

In flexible electronics, the fatigue reliability of film interconnects will directly affect the stability of the entire device. Since the thickness of the film material is usually much smaller than its length and width, the fatigue of film interconnects exhibits significant size effects. To evaluate the reliability of film interconnects, based on the theory of continuum damage mechanics, a multi-scale damage model considering length-scale effect is established. For the convenience of the model application in damage prediction of film interconnects, a multi-scale mechano-electric degradation model is further proposed. Validation with experimental data shows that the model can predict the fatigue life and resistance changes of not pre-stretched films well. For pre-stretched films, the proposed model is also applicable to thicker films without debonding or damage localization. The proposed model is expected to provide a facile approach for fatigue life prediction of flexible electronic devices with coplanar mesh structures.     

梁结构刚度动态非概率可靠性分析

 为了定量分析在疲劳载荷作用下梁在不同寿命期内刚度的可靠性,建立梁结构物理性能退化的精确公式就十分重要.依据疲劳载荷造成的累积损伤对材料极限应力的影响,基于材料剩余强度模型,利用材料强度与弹性模量之间的关系,推导出结构弹性模量的退化表达式,并在此基础上,提出梁弹性模量退化系数的递推表达式,推导出圆截面梁剩余抗弯刚度的表达式.在对结构可靠性分析时,概率可靠性模型和模糊可靠性模型对于原始数据信息要求较高.为了充分利用结构的不确定性信息弥补原始数据的不足,将梁的初始弹性模量及所受的疲劳载荷等看作区间变量,利用区间模型建立基于刚度退化的梁刚度动态非概率可靠性模型.最后,结合工程实例的计算表明了该方法对梁的刚度退化分析及其刚度动态可靠性分析是可行、有效和合理的.     

Interval dynamic reliability analysis of mechanical components under multistage load based on strength degradation

To further study the law of strength degradation, the residual strength degradation model is established based on the definition of fatigue damage, considering the interaction of various uncertain factors and time factors in service environment. Combined with equivalent damage model, a nonlinear cumulative damage model is proposed, which takes the interaction among loading loads into account and improves the accuracy of calculation. Additionally, the equivalent transformation of multistage load is studied using interval theory. According to the interval dynamic nonprobability reliability prediction model, a dynamic reliability analysis of the interval model is carried out. Dynamic reliability of the component is analyzed under multistage load accumulation damage to verify the effectiveness of the method.     

A computationally efficient cohesive zone model for fatigue

A cohesive zone model has been developed for the simulation of both high and low cycle fatigue crack growth. The developed model provides an alternative approach that reflects the computational efficiency of the well‐established envelop‐load damage model yet can deliver the accuracy of the equally well‐established loading‐unloading hysteresis damage model. A feature included in the new cohesive zone model is a damage mechanism that accumulates as a result of cyclic plastic separation and material deterioration to capture a finite fatigue life. The accumulation of damage is reflected in the loading‐unloading hysteresis curve, but additionally, the model incorporates a fast‐track feature. This is achieved by “freezing in” a particular damage state for one loading cycle over a predefined number of cycles. The new model is used to simulate mode I fatigue crack growth in austenitic stainless steel 304 at significant reduction in the computational cost.     

岸桥起重机随机风振疲劳可靠性分析

基于时域方法研究岸桥起重机的风振疲劳可靠性问题。采用谐波叠加法给出了符合Davenport风速谱的多维脉动风速时间历程,基于Bernoulli方程得到相应的风压时间历程,并将相应的风压荷载作用于有限元模型,采用雨流计数法处理结构关键点的应力响应。基于疲劳失效的Basquin方程、Miner线性累积损伤准则和Goodman平均应力修正方程导出疲劳累积损伤的概率模型。考虑平均风速的概率分布,提出了基于概率累积损伤机制的风振疲劳可靠度和可靠性寿命计算方法,为岸桥起重机的风振疲劳可靠性分析作了一些有益的探索和研究。     

Fatigue reliability assessment of turbine discs under multi‐source uncertainties

Hot section components of aircraft engines like high pressure turbine (HPT) discs usually operate under complex loadings coupled with multi‐source uncertainties. The effect of these uncertainties on structural response of HPT discs should be accounted for its fatigue life and reliability assessment. In this study, a probabilistic framework for fatigue reliability analysis is established by incorporating FE simulations with Latin hypercube sampling to quantify the influence of material variability and load variations. Particularly, variability in material response is characterized by combining the Chaboche constitutive model with Fatemi‐Socie criterion. Results from fatigue reliability and sensitivity analysis of a HPT disc indicated that dispersions of basic variables must be taken into account for its fatigue reliability analysis. Moreover, the proposed framework based on the strength‐damage interference provides more reasonably correlations with its field number of flights rather than the load‐life interference one.     

Analysis of fatigue damage evolution and associated anisotropic elastic property degradation in random short-fiber composite

A theoretical analysis of cyclic fatigue damage and associated anisotropic property degradation in a random short-fiber composite is presented. The fatigue damage takes various forms of microcracking, originated from microscopic stress concentrators in the highly heterogeneous material system. A probabilistic treatment of the microcracks is introduced to evaluate the statistical nature of the microscopic fatigue damage. Damage evolution and accumulation are analyzed through the development of probabilistic density functions of microcrack length and orientation during the cyclic loading history. Constitutive equations for the damaged fiber composite are then derived on the basis of a self-consistent mechanics scheme in conjunction with a three-dimensional elliptic crack theory and the microcrack density functions. Cyclic fatigue degradation and associated damage-induced anisotropy of composite material properties are determined and checked against experiments. The tensorial nature of material damage and composite stiffness changes during fatigue are evaluated explicitly. A power-law relationship between the rate of damage growth and the fatigue loading cycle is obtained. The rate of fatigue damage growth is found to decrease exponentially with load cycles—a phenomenon unique to the random short-fiber composite. This study provides a comprehensive analytical treatment of the homogeneous fatigue damage problem for random short-fiber composites. The fundamental mechanics and mechanisms of fatigue damage evolution and associated anisotropic property degradation of the composite are elucidated.     

Thermal fatigue resistance characterization and ranking of materials using the V‐shape specimen testing method

Thermal fatigue resistance of materials is an extremely important criterion for the long‐term durability and reliability performance of very high‐temperature components and systems, such as advanced auto engine and exhaust systems. There is a broad range of material choices for thermal fatigue resistance applications. The final selection of the materials depends on the balance of engineering performance of the materials and the cost. To optimize the thermal fatigue resistance and cost of those materials, a reliable testing procedure for material thermal fatigue characterization and a material evaluation/selection matrix must be established. In this paper, the V‐shape specimen testing method in evaluating thermal fatigue resistance performance is introduced first. The influence of several factors, such as the thickness of specimens, operating temperature and hold time, on the thermal fatigue resistance is experimentally investigated. Subsequently, the statistical and probabilistic characteristics of the thermal fatigue failure data are analysed to reveal the possible failure mechanisms. Finally, a general rational approach for thermal fatigue resistance characterization and ranking is demonstrated, and a simple parameter λ = kσ_f/Eα, which combines the material strength, thermal conductivity and thermal expansion, is found to be the new breakthrough parameter, correlating to V‐shape thermal fatigue test results. Results on four currently used stainless steels verify the correlations and indicate the validity of this approach.     

A high-cycle fatigue accumulation model based on electrical resistance for structural steels

For high-cycle fatigue of metals, the DC electrical resistance is a more sensitive parameter to the initiation of micro-cracks during the irreversible fatigue damage accumulation process. This implies that the electrical resistance is a suitable parameter that can be consistent with the fatigue damage physical mechanism. The relation between the ratio of electrical resistance changes and the cyclic fraction of the fatigue specimen may reasonably represent deterioration in mechanical properties of structural steels during the high-cycle fatigue process. The high-cycle fatigue damage accumulation model based on electrical resistance for structural steels was proposed. The model was verified by some experimental data for three structural steels; normalized 45C steel, 20 Mn steel and 16 Mn steel, and good agreement was obtained. The corresponding fatigue lifetime on the basis of the electrical resistance model was also performed. The results show that the approach to fatigue lifetime prediction and failure based on the electrical resistance is a good non-destructive technique.     

Probabilistic modeling of threshold stress intensity factor for fatigue endurance reliability prediction

This study develops a probabilistic model for the threshold stress intensity factor range, which is a critical parameter in infinite fatigue life design under material flaws. The model is based on the proposed concept of probability of propagation in the probabilistic framework, allowing for deriving the probability density function of the threshold intensity factor range. The uncertainty in fatigue crack growth can naturally be incorporated into the resulting distribution. By further introducing the derived distribution into the Kitagawa–Takahashi diagram, the fatigue endurance reliability model can be established in a rational manner. With the first-order asymptotic approximation, the analytical form of fatigue endurance reliability index is obtained. The usefulness of the overall method is demonstrated using realistic engineering application examples.     

Microstructure based fatigue analysis of cast components under variable amplitude loading

Reliable numerical fatigue life analyses are becoming increasingly important given the need to reduce the time and costs for product development and the need to evaluate large and single components. Stress‐based approaches as well as the local strain approach and its fracture mechanics based extension (P_J model) are in use for that. Both the local strain approach and the P_J model require the supply of pure material data. This requirement for input data that are not component‐specific makes such approaches interesting for widespread application. The accuracy of numerical fatigue life analyses is an essential criterion for the acceptance and the spread in industrial application. In the local strain approach, accuracy is determined on one hand by the transferability of material data for the fatigue life analysis of components and on the other by the damage accumulation rule. In this paper, the local strain approach and the P_J model are used to analyse fatigue life under both constant and variable amplitude loading. These analyses are based on the experimental results obtained from tests of a commercial vehicle component made of nodular cast iron EN‐GJS‐400‐15. Aspects of transferability and damage accumulation are considered. Results obtained from using an elastic‐plastic fracture mechanics based approach to estimate a P_SWT‐N curve, taken into account the inhomogeneities in the microstructure of the cast iron, are also presented.     

Damage evolution with growing cyclic creep and life prediction of MDYB‐3 PMMA

The influence of cyclic creep accumulation rate on the damage evolution of MDYB‐3 polymethyl methacrylate (PMMA) was experimentally investigated. Fatigue tests were carried out at four stress levels by stress control mode. The steady cyclic creep accumulation stage was observed occupying a substantial proportion of all specimens fatigue processes. Cyclic creep strain growth speed and relaxed modulus degradation rate were deduced as two important indicators for describing the damage evolution characteristics. Linear evolution relations of cyclic creep strain and modulus degradation with cycle times were retrieved from different terms of hysteresis loops. A preliminary model was proposed to be able to estimate the damage extent at different cyclic stress levels. The life predictions by the proposed model were compared with the experiment results and the classical power S–N model, which were demonstrated as a good estimation for the fatigue life. It is feasible to make durability evaluations by the characteristics of steady cyclic creep for multiaxis directed PMMA material.     

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.     

Numerical Modeling of the Surface Fatigue Crack Propagation Including the Closure Effect

Presently modeling of surface fatigue crack growth for residual life assessment of structural elements is almost entirely based on application of the Linear Elastic Fracture Mechanics (LEFM). Generally, it is assumed that the crack front does not essentially change its shape, although it is not always confirmed by experiment. Furthermore, LEFM approach cannot be applied when the stress singularity vanishes due to material plasticity, one of the leading factors associated with the material degradation and fracture. Also, evaluation of stress intensity factors meets difficulties associated with changes in the stress state along the crack front circumference. An approach proposed for simulation the evolution of surface cracks based on application of the Strain-life criterion for fatigue failure and of the finite element modeling of damage accumulation. It takes into account the crack closure effect, the nonlinear behavior of damage accumulation and material compliance increasing due to the damage advance. The damage accumulation technique was applied to model the semi-elliptical crack growth from the initial defect in the steel compact specimen. The results of simulation are in good agreement with the published experimental data.     

A practical approach for predicting fatigue reliability under random cyclic loading

The purpose of this paper is to provide a simple approach for reliability analysis based on fatigue or overstress failure modes of mechanical components, and explain how this integrated method carries out spectral fatigue damage and failure reliability analysis. In exploring the ability to predict spectral fatigue life and assess the reliability under a specified dynamics environment, a methodology for reliability assessment and its corresponding fatigue life prediction of mechanical components using a supply-demand interference approach is developed in this paper. Since the methodology couples dynamics analysis and stochastic analysis for fatigue damage and reliability prediction, the conversion of the duty cycle history for the reliability study of an individual component is also presented. Using the proposed methodology, mechanical component reliability can be predicted according to different mission requirements. For an explanation of this methodology, a probabilistic method of deciding the relationship between the allowable stress or fatigue endurance limit and reliability is also presented.     

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.     

A multi‐axial low‐cycle fatigue life prediction model considering effects of additional hardening

It is generally accepted that the additional hardening of materials could largely shorten multi‐axis fatigue life of engineering components. To consider the effects of additional hardening under multi‐axial loading, this paper summarizes a new multi‐axial low‐cycle fatigue life prediction model based on the critical plane approach. In the new model, while critical plane is adopted to calculate principal equivalent strain, a new plane, subcritical plane, is also defined to calculate a correction parameter due to the effects of additional hardening. The proposed fatigue damage parameter of the new model combines the material properties and the angle of the loading orientation with respect to the principal axis and can be established with Coffin‐Manson equation directly. According to experimental verification and comparison with other traditional models, it is clear that the new model has satisfactory reliability and accuracy in multi‐axial fatigue life prediction.     

On fatigue damage accumulation and material degradation in composite materials

Phenomenological aspects of fatigue damage accumulation and material degredation in composite materials are examined. A damage variable is introduced to define phenomenologically the degree of damage, and a fatigue damage accumulation model is developed in which a power-law relationship between the rate of damage development, fatigue stress level, and the current level of damage is proposed. Evaluation of the model for a random short-fiber SMC (sheet moulding compounds) materials indicates good correlation between the present model and experimental results. The model can be used to assess the behavior of materials degradation and fatigue damage development in composite materials.     

Fatigue reliability study on T‐welded component considering load shedding

In this paper, a coupled reliability method for structural fatigue evaluation considering load shedding is first proposed based on probabilistic fracture mechanics in which the uncertainties of the structural parameters are taken into account. Then, the method is applied to predict the fatigue reliability of the T‐welded structure to the case of considering load shedding or not. The compared results show that by considering the load shedding, the structural fatigue reliability might be improved with less conservativeness. The influence rules of the load‐shedding coefficient on the fatigue failure probability of the T‐welded component are investigated, and some interesting results are obtained. That is, the influences of load‐shedding coefficient on the fatigue failure probability can be divided into three regions, namely the high, medium and low fatigue failure areas. The last area is the most intriguing when we try to design a T‐welded structure. The thickness of T‐welded structure along the crack propagation direction is found to be one of the important design variables for the design of fatigue reliability, in which the low‐fatigue failure zone is used as one of the reliability constraints. The basic design frame of T‐welded structure is established to constrain the fatigue failure probability within the low‐fatigue failure area.