A Phenomenological Discrete Brittle Damage-Mechanics Model for Fatigue of MEMS Devices With Application to LIGA Ni

Fatigue initiation and failure of various microelectromechanical systems (MEMS) is of significant importance as they gain widespread acceptance in sensors and electronics. This paper presents an approach for utilizing available experimental fatigue data to evaluate the fatigue lives of MEMS components. The approach is based on a phenomenological discrete material representation in which a domain is represented by a collection of rigid elements that interacts via springs along their boundaries. The principles of continuum damage mechanics are used to degrade the spring stiffnesses as brittle damage occurs when the domain is subjected to fatigue loading. The model utilizes experimental stress–life data for LIGA Ni to identify the material properties used in the model. The proposed model captures the statistical distribution of material properties and geometrical randomness of the microstructure commonly observed in a wide variety of MEMS. Consequently, simulations that account for the variability in fatigue life can be readily performed. The model is applied to a dog-bone-shaped specimen to evaluate the influence of material heterogeneity and material flaws on fatigue crack initiation life and scatter. The ability of the model to predict the fatigue life of different types of MEMS devices and loading conditions is also demonstrated by simulating the fatigue stress–life behavior of a MEMS resonator support beam. $hfill$[2008-0087]      

High-cycle fatigue of single-crystal silicon thin films

When subjected to alternating stresses, most materials degrade, e.g., suffer premature failure, due to a phenomenon known as fatigue. It is generally accepted that in brittle materials, such as ceramics, fatigue can only take place in toughened solids, i.e., premature fatigue failure would not be expected in materials such as single crystal silicon. The results of this study, however, appear to be at odds with the current understanding of brittle material fatigue. Twelve thin-film (~20 μm thick) single crystal silicon specimens were tested to failure in a controlled air environment (30±0.1°C, 50±2% relative humidity). Damage accumulation and failure of the notched cantilever beams were monitored electrically during the "fatigue life" test. Specimen lives ranged from about 10 s to 48 days, or 1×106 to 1×1011 cycles before failure over stress amplitudes ranging from approximately 4 to 10 GPa. A variety of mechanisms are discussed in light of the fatigue life data and fracture surface evaluation     

Statistical analysis and predictions of fracture and fatigue of micro-components

A number of materials typically used in MEMS technology exhibit brittle fracture behaviour which leads to a scatter in strength and a size effect as a consequence. Furthermore, some of these materials, e.g. polycrystalline silicon, show fatigue effects which limit the lifetime under cyclic loading conditions. Probabilistic methods based on the Weibull theory have been established successfully in predicting the strength of micro-components under static loading. However, the consequence of fatigue on reliability predictions has not yet been studied extensively. We present strength as well as lifetime predictions for poly-silicon components with stress concentrations based on experimental data published in the literature. Our results show that while strength predictions for components with stress concentrations based on scaling procedures works well, lifetime prediction is a challenging task associated with large prediction uncertainties. Finally, we relate the crack propagation approach used for our lifetime predictions with micro-mechanical fatigue models that are discussed for poly-silicon.     

A Numerical Fatigue Damage Model for Life Scatter of MEMS Devices

This paper presents a fatigue damage model to estimate fatigue lives of microelectromechanical systems (MEMS) devices and account for the effects of topological randomness of material microstructure. For this purpose, the damage mechanics modeling approach is incorporated into a new Voronoi finite-element model (VFEM). The VFEM developed for this investigation is able to consider both intergranular crack initiation (debonding) and propagation stages. The model relates the fatigue life to a damage parameter "D" which is a measure of the gradual material degradation under cyclic loading. The fatigue damage model is then used to investigate the effects of microstructure randomness on the fatigue of MEMS. In this paper, three different types of randomness are considered: (1) randomness in the microstructure due to random shapes and sizes of the material grains; (2) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus; and (3) the randomness in the material properties considering a normally distributed resistance stress, which is the experimentally determined material property controlling the ability of a material to resist the damage accumulation. Thirty-one numerical models of MEMS specimens are considered under cyclic axial and bending loading conditions. It is observed that the stress-life results obtained are in good agreement with the experimental study. The effects of material inhomogeneity and internal voids are numerically investigated.     

Fatigue Life Prediction Criterion for Micro–Nanoscale Single-Crystal Silicon Structures

This paper describes fatigue damage evaluation for micro–nanoscale single-crystal silicon (SCS) structures toward the reliable design of microelectromechanical systems subjected to fluctuating stresses. The fatigue tests, by using atomic force microscope (AFM), nanoindentation tester, and specially developed uniaxial tensile tester, have been conducted under tensile and bending deformation modes for investigating the effects of specimen size, frequency, temperature, and deformation mode on the fatigue life of SCS specimens. Regardless of frequency and temperature, the fatigue life has correlated with specimen size. For example, nanoscale SCS specimens with 200 nm in width and 255 nm in thickness have showed a larger number of cycles to failure, by a factor of $10^{5}$, at the same stress level, as compared to microscale specimens with 48 $muhbox{m}$ in width and 19 $muhbox{m}$ in thickness. Deformation mode has also affected the lifetime; however, no frequency and temperature dependences have been observed unambiguously in the $S{-}N$ curves. The stress ratio parameter corresponding to the ratio of peak stress to average fracture strength has enabled us to estimate the lifetime for each deformation mode. To predict the fatigue life of SCS structures regardless of deformation mode and specimen size, we have proposed an empirical parameter that includes the resolved shear stress. The mechanism of fatigue failure of SCS structures is discussed from the viewpoint of dislocation slip, crack nucleation, growth, and failure through observations using AFM and scanning electron microscope.$hfillhbox{[2008-0072]}$      

Ultra thin chips for miniaturized products

The demand to miniaturize products especially for mobile applications and autonomous systems is continuing to drive the evolution of electronic products and manufacturing methods. One key to miniaturization developed in the past was the use of unpackaged, bare dice. Saving the volume and weight of the package, significant reduction in footprint was achieved. A next step conceived to further the miniaturization is the integration of functions on miniaturized subsystems, i.e. System-in-Package (SiP), in contrast to a full silicon integration (System-on-Chip, SoC). The use of recent manufacturing methods allows to merge the SiP approach with a volumetric integration. Up to now, most of the systems utilize single- or double-sided populated system carriers. Embedding of passive components was a first step forward. A new challenge is to incorporate not only passive components, but active circuitry (IC's) and the necessary thermal management as well. Ultra thin chips (i.e. silicon dies thinned down to 50 m total thickness) lend themselves to reach these goals. Chips with that thickness can be embedded in the dielectric layers of modern laminate PCB's. Micro via technology allows to connect the embedded chip to the outer faces of the system circuitry. As an ultimate goal for microsystem integration, the embedding of optical and fluidical system components can be envisioned. This paper presents the first approach to embed thin silicon dies in to polymeric system carriers. The aspects of embedding and making the electrical contact as well as the thermal management are highlighted. To reach the goal of a vertically stackable box-of-bricks type of ultra thin (UT) package, thin silicon chips are embedded and interconnected on a peripheral UT BGA.The authors would like to thank the team of the 3D-CSP and the ChiP task force at IZM Berlin/Munich and TU Berlin as well as the colleagues from the PCB industry having supported this feasibility study with activity and discussion. Part of the work shown here is done in of the BMBF Project Systemintegration in polymere Schaltungsträger, No.02PP2051, co-ordinated by the FZK-PFT. The support is gratefully acknowledged.This paper was presented at the Conference of Micro System Technologies 2001 in March 2001     

The critical role of environment in fatigue damage accumulation in deep-reactive ion-etched single-crystal silicon structural films

The importance of service environment to the fatigue resistance of n/sup +/-type, 10 /spl mu/m thick, deep-reactive ion-etched (DRIE) silicon structural films used in microelectromechanical systems (MEMS) was characterized by testing of electrostatically actuated resonators (natural frequency, f/sub 0/, /spl sim/40 kHz) in controlled atmospheres. Stress-life (S-N) fatigue tests conducted in 30/spl deg/C, 50% relative humidity (R.H.) air demonstrated the fatigue susceptibility of silicon films. Further characterization of the films in medium vacuum and 25% R.H. air at various stress amplitudes revealed that the rates of fatigue damage accumulation (measured via resonant frequency changes) are strongly sensitive to both stress amplitude and, more importantly, humidity. Scanning electron microscopy of high-cycle fatigue fracture surfaces (cycles to failure, N/sub f/>1/spl times/10/sup 9/) revealed clear failure origins that were not observed in short-life (N/sub f/<1/spl times/10/sup 4/) specimens. Reaction-layer and microcracking mechanisms for fatigue of silicon films are discussed in light of this empirical evidence for the critical role of service environment during damage accumulation under cyclic loading conditions.     

Notch Root Oxide Formation During Fatigue of Polycrystalline Silicon Structural Films

This paper investigates the fatigue behavior of n⁺-type 2-mum- thick polycrystalline silicon films that exhibit an initially thin (~2-3 nm) native oxide layer. The testing of kilohertz-frequency resonators provided accurate stress-life fatigue data at 30 and 50% relative humidity (RH) in the low (< 10⁶)and high (up to 10¹¹) cycle regimes. Long fatigue life specimens were associated with larger decreases in the natural frequency of the resonator and very smooth failure origins (at the notch) that encompassed several grains. Additional testing at various humidity levels highlighted the critical influence of humidity on the fatigue damage accumulation rate, which was measured via changes in the natural frequency. Finally, Auger electron spectroscopy (AES) characterized the formation of a nanometer-scale oxygen-rich reaction layer during cyclic loading. Although AES revealed a thin 2-3-nm initial oxide layer on a control specimen, measurements on a long-life fatigued specimen revealed an increased oxygen concentration over the first 10 nm of the material at the notch root. These findings demonstrate that the reaction-layer fatigue mechanism for silicon structural films operates even when reaction layers are initially very thin.     

Determination of mechanical properties of slip cast, micro powder injection moulded and microcast high aspect ratio microspecimens

In a project of the German Research Council (DFG) Collaborative Research Centre (SFB) 499 Development, production and quality assurance of moulded micro-components made of metallic and ceramic materials [SFB03] three-point bending-specimens (dimension: 1.2 × 0.2 × 0.2 mm) made of slip cast [BAU02] or micro powder injection moulded ZrO₂ [RUP03] as well as tensile specimens (dimension of the gauge length: 0.78 × 0.26 × 0.13 mm) made of the micro-cast AuAgCu-alloy Stabilor G [BAU03] were investigated with respect to their behaviour under quasi-static loading.The support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. The authors appreciate the co-operation of all the project partners within the SFB 499.     

Micro-ECM for production of microsystems with a high aspect ratio

The most used processes for production of microsytem components are basically from the semiconductor technology. The material properties of used silicon often dont achieve the demands of for example: micro-surgery, biotechnology life science, fluidics or high temperature environment. For microstructuring of highly stressed metals, like stainless and heat resisting steels, cold work tool steels, hot work tool steels and nickel-base-alloys and a variety of metals there is no manufacturing-process. An interesting possibility for structuring this type of materials are the electrochemical machining processes (ECM). Some new developed ECM-sinking-processes are working with oscillating tool-electrode, to improve shape accuracy.     

多因素耦合下剥落损伤随机分布特性对轴承疲劳寿命的影响

以控制力矩陀螺的角接触球轴承为研究对象,考虑环境温度、摩擦热、对流换热、轴向力和转速等复杂多应力耦合作用及剥落损伤特征,推导其传热模型、接触应力仿真模型和疲劳寿命仿真模型。对比轴承有疲劳剥落损伤和无疲劳剥落损伤2种情况,分别给出典型工况下的温度、应力和疲劳寿命结果,讨论轴向力和转速对温度和应力的影响,总结疲劳损伤的特征尺寸随机分布对应力和疲劳寿命的影响。结果表明：在同样的条件下,剥落损伤引起的应力集中效应很明显,并且会引起区域温度升高;分别改变转速和轴向力,转速对温度和应力影响更明显;随着轴向力和转速增加,损伤轴承的最高温度和最大应力的大小和增长率均大于无损伤轴承;应力和疲劳寿命对剥落区域的直径更敏感,最大应力随直径增大呈先增大后减小的抛物线形关系,并随着深度增加而减小;虽然当剥落区域取最小直径且最大深度、最小深度且最大直径这2种情况下轴承疲劳寿命大于0,但是在剥落区域直径和深度的大部分取值范围内轴承疲劳寿命均为0。     

基于数字疲劳传感器的疲劳监测系统及寿命评估

疲劳寿命计是电阻-疲劳响应记忆元件,其电阻值随疲劳而增加,栽荷卸除后电阻变化值保留.通过设计适用于桥梁疲劳栽荷检测的数字式传感器和监测系统,对大桥实施长期实时监测和定期技术状态评估,考察大桥在服役期内完成设计预定功能的能力,提高桥梁的安全性.为解决疲劳损伤及寿命评估问题,通过编制的疲劳评估系统,对东海大桥48个危险截面测点进行疲劳分析,得到实际损伤及损伤度,并进行寿命评估.成功地建立了东海大桥疲劳损伤及寿命评估系统,并可推广应用于其他桥梁.     

轿车设计中的焊点疲劳寿命预测方法

介绍一种焊点疲劳寿命预测的工程计算方法. 用有限元分析中的CWELD单元模拟焊核,用壳单元模拟连接板,根据CWELD单元传递力和力矩计算焊核附近连接板和焊核周围的"结构应力";然后通过一组焊点S-N曲线估计焊点的疲劳寿命. 通过分析预测焊点疲劳寿命以及相应位置,发现白车身薄弱环节.     

Interactive scenarios—building ubiquitous computing concepts in the spirit of participatory design

The amount of information technology in our everyday lives is increasing and getting more and more ambient in our daily environments. The environments are supposed to be intelligent, adaptive, intuitive and interactive in the future. User participation for future concept building is essential, but challenging, when designing appliances that might be unfamiliar in their appearance, functionality and impressiveness compared to the users current everyday life. New allocated methods and viewpoints are needed for user experience design and evaluation of intelligent environments to build systems that naturally support the users in their daily life. We present interactive scenario building together with potential users (including role-playing, drama and improvisational aspects) as one promising tool for early concept definition phase.     

The SQUID approach to defining a quality model

This paper describes an attempt to use the approach developed by the SQUIDproject, which was part of the ESPRIT 3 programme, to define the software quality requirements of the Telescience project. The SQUID project developed its approach to quality modelling in parallel with ongoing feedback from testing that approach on the Telescience project, which was both large and software intensive. As part of this exercise we used the ISO software quality standard ISO 9126. It was an assessment of this and other existing quality models that caused us to re-assess what was meant by a quality model and led to a decomposition of existing quality models into a composite model reflecting the different aspects of the model and its mapping onto a specific project or product. We break existing quality models into components which reflect the structure and content of the model. This composite model must then be customized for an individual product/project, we call this customized model a Product Quality Model. Application of this approach to the Telescience project identified a number of practical problems that the SQUID project needed to address. It also indicated a number of problems inherent in the current version of ISO 9126.     

Application of a model to the evaluation of flood damage

This paper presents the initial results of a common methodology for the evaluation of damage produced by a flood. A model has been developed for flood damage estimation based on a geographic information system (GIS). It could be used by land administration bodies and insurance companies to manage flood-related damage data. The model simulates flood scenarios and evaluates expected economic losses from the impact of floodwaters on exposed elements, through the application of a computational model elaborated by GIS. During the development of the model, the Boesio Stream, a small watercourse flowing into Lake Maggiore (Lombardy, northern Italy) which was recently affected by a flash flood, was used as case study to test and calibrate the methodology. The method could be used either as a forecasting tool to define event scenarios, utilizing data from events simulated with a hydraulic model, or for real-time damage assessment after a disaster. The approach is suitable to large-area damage assessment and could be appropriate for land use planning, civil protection and risk mitigation.

The mechanical properties, dimensional tolerance and microstructural characterization of micro-molded ceramic and metal components

Metal and ceramic micro-components with 10 m features were fabricated by molding nano-powder-binder mixtures in micro-molds produced from LiGA-formed masters and then sintering to achieve the desired density and properties. The mechanical properties of the metals nickel and 316L stainless steel were measured in tension using miniature dog bone shaped, micro-molded test specimens. The sintering temperature controlled yield stress (YS), the ultimate tensile strength (UTS) and the ductility of the nickel with the YS and the UTS decreasing and the ductility increasing with increasing sintering temperature. For the stainless steel, the YS was nearly 400 MPa, UTS was 650 MPa and the ductility was 3%. The mechanical properties of aluminum oxide ceramics were determined using 4-point bending on miniature micro-molded bend bars. The average modulus of rupture (MOR) was 260 MPa. Careful measurements were made of the dimensional tolerance of the micro-molded parts both before and after sintering using automated optical metrology. The variability in the dimensions of a sintered SS gear after sintering was <3 m. Finally microscopic examination of the micromolded components indicated that the final grain size was generally less than 1 m with minimal residual porosity.This work was performed at Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-ACO4–94AL85000. The authors wish to thank Linda Domeier for developing the replicated PMMA molds and Dale Zschiesche, Ralph Tissot, Joe Ceramuga, Paul Hlava and Dave Schmale for technical support.     

Optimal design of machine components using notch correction and plasticity models

Shape optimization computational technology is used in order to maximize life time of notched machine/structural components in low cycle fatigue regime. The present approach is composed of three steps: (i) stress–strain calculation using notch correction and plasticity models, (ii) estimation of critical plane to asses fatigue lives, (iii) formulation of the optimization problem with constraint set on the number of cycles corresponding to crack initiation. The optimal design procedure is a combination of the computer aided geometrical design mathematical methods for the shape definition, the boundary element method used for analysis of the response quantities, assisted by the sequential linear programming method with move limits. Numerical examples display significant increase in the number of cycles corresponding to crack initiation phase in comparison to traditional (regular) notch shapes.