微结构片外弯曲测试装置及试样设计

硅是微电子机械系统（简称微机电系统）中最常见的功能结构材料,可靠性是制约硅微构件小尺度加工和大规模制造的瓶颈问题．为研究硅微构件的力学特性,本文开发了一套以压电驱动、微力测量、位移检测为核心组件的片外测试系统．设计了一种将四个弯曲测试梁集于一体的微结构,借助有限元方法确定其尺寸,并用理论方法验证有限元分析的合理性．本文着重确保了四个关键设计目标：一、每根测试梁最大应力应位于其与外框架结合处;二、未断裂测试梁的最大应力受其他梁的断裂的影响应足够小;三、各个测试梁的最大应力的差别应足够小;四、支撑梁的最大应力应明显小于测试梁．最后测试了试样的弯曲强度,实验加载曲线和有限元分析基本吻合,表明测试装置和试样设计是合理的,为后续的硅微构件可靠性测试奠定了基础．     

Experimental stress analysis of loaded boundries in two-dimensional second-boundary value problems

The application of in-plane displacements to the boundaries of two-dimensional specimens is frequently associated with out-of-plane restraints. The state of strain developed at the boundaries when the displacements are applied mechanically, or thermally, is analyzed for several typical cases. The stresses associated with a knife-edge device used to eliminate out-of-plane restraints are also analyzed.     

Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring

A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost complete overview of residual stress states in the component during each production step. To reduce the measurement time in the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process. Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well.     

A highly sensitive noncontacting electromagnetic device for detecting dynamic stress in structures

A highly sensitive, noncontacting electromagnetic device has been developed to detect stress waves in structures. It is shown that for detecting an induced strain this device is over 500 times more sensitive than conventional bonded strain gages. The principle of detecting the strain by this device is based on the fact that dynamic stresses in a structure induce similar stresses in a bonded piezoelectric material. This, in turn, creates a magnetic field which extends beyond the material itself. An electromagnetic device has been built to detect this magnetic field and thus monitor the dynamic stresses. This method provides a noncontacting means of measuring strain in structures with improved sensitivity.     

Exact three-dimensional interface stress and electrode-effect analysis of multilayer piezoelectric transducers under torsion

In this paper, exact three-dimensional analysis for torsion of multilayer piezoelectric transducers is presented to highlight the remarkable effects of electrode and size effects on interface stresses and deformation. A generalized formulation is introduced for torsion of an arbitrarily layered cross section. In order to reach an advanced and better device, multilayer piezoelectric materials with different properties are formulated while axis of torsion and the polarization axes of each layer make different orientations with respect to each other. An exact formulation for n-layer piezoelectric device with rectangular cross section is presented to compensate considerable deviation of previous studies’ results from exact solution due to the assumption of linear distribution for the electric potential. In order to improve the performance of the transducers, being utilized in industry, several case studies are presented in order to investigate the influence of different parameters, e.g. thickness and material properties of electrodes over shear and peel stresses. Besides, a correction factor is introduced to completely compensate the effect of ignoring electrodes.     

Thermal stresses in functionally graded materials caused by a laser thermal shock

 Mathematical simulation of a thermal shock method for reliability testing of functionally graded material (FGM) is performed with the end to determine operating parameters of the testing device (power of a laser, laser beam radius, duration of heating) and to investigate the effect of the composition of FGM on a magnitude of thermal stresses in a coating. An analytical method for solution of the thermal elasticity problem is developed whereby the approach of a multilayer plate is used for determining temperature and thermal stresses distributions in a coating. We considered the limiting case of the obtained solution when the thickness of a layer is infinitesimally small and the number of layers tends to infinity. This procedure allowed us to obtain the thermal stresses distribution in a FGM coating. The results for the FGM coating composed of WC (tungsten carbide) ceramics and HS-steel are presented. It is showed that variation of the volume content of ceramics strongly affects thermal stresses in a coating and they decrease significantly in the case of the uniform spatial distribution of ceramics. Received on 21 November 2000 / Published online: 29 November 2001     

Experimental Evaluation of Residual Stresses in Pipes Manufactured by UOE and ERW Processes

Pipes are basic elements used in the construction of pipelines for the long-distance transportation of oil and gas and their derivatives. They can be manufactured by cold forming processes such as UOE and ERW, both widely used in the oil and gas industry. These processes produce high levels of non-uniform plastic deformation, which introduce a new state of residual stress into the material. In some cases, these stresses combine with mechanical stresses generated by external loads leading to service failures, interrupting the transmission line and increasing the risk of accidents. Therefore, determining in advance the residual stress distribution in pipes is an important task which involves the evaluation of the structural integrity. Six pipe samples obtained by the UOE and ERW processes were measured and evaluated using a portable optical device that combines radial in-plane digital speckle pattern interferometer (DSPI) with the incremental hole-drilling technique to measure residual stresses. The experimental results indicate a distinct residual stress distribution for each manufacturing process, while the measured residual stress distributions in the longitudinal and circumferential directions were similar at all measurement locations along an individual pipe.     

Transparency enhancement for an active knee orthosis by a constraint-free mechanical design and a gait phase detection based predictive control

This paper proposes a novel mechanical design of a lower limb exoskeleton device which prevents the residual stresses due to arthro-kinematics movements of synovial joints and by the way allows effective compensation for dynamic disturbances in osteo-kinematic movements of the wearer. Here, the exoskeleton is only actuated at the knee joints to provide assistive torques, which are required to assist the anatomical joint motion and to increase the transparency of the device. Dynamic simulations of a virtual human equipped with this exoskeleton are used to quantify the disturbances induced by the device during locomotion and to show the benefit of passive mechanisms introduced in the mechanical attaches as well. The authors also demonstrated how the device’s transparency can be improved by providing the motor torques in order to compensate the inertial and gravitational effects. This can be done rely on the knowledge of the locomotion movement phases. A robust gait phase detection method was implemented on the experimental device in order to identify specific gait phases in real time. This method exploits the K-nearest neighbors algorithm to identify the k-closest trained vectors, coupling with a discrete time Markov chain to determine the phases shift probability during the gait cycle. This gait detection algorithm was tested with a percentage of success of more than 95% when the subjects walked with constant and variable stride lengths.     

Ultra High Speed DIC and Virtual Fields Method Analysis of a Three Point Bending Impact Test on an Aluminium Bar

This paper deals with the analysis of an aluminium beam impacted in a three point bending configuration using a Hopkinson bar device. Full-field deformation measurements were performed using Digital Image Correlation on images captured with an ultra high speed camera (16 frames at a time resolution of 10 μs). The performance of the deformation and strain measurements were evaluated and the data were then used quantitatively to analyse the very complex dynamic behaviour of the beam. It was shown that the deformation of the beam was controlled by the interaction between the striker and the flexural bending wave triggered by the initial impact. The principle of virtual work was used to reconstruct the impact force from the shear strains and to analyze how this impact force relates to the acceleration of the specimen (inertia forces) and the development of the bending stresses. The results are in good agreement with expectations. This opens up new perspectives in the quantitative use of full-field measurements to extract elasto-plastic constitutive parameters from such impact tests.     

Explicit algebraic Reynolds stress model for shock-dominated flows

Shock waves drastically alter the nature of Reynolds stresses in a turbulent flow, and conventional turbulence models cannot reproduce this effect. In the present study, we employ explicit algebraic Reynolds stress model (EARSM) to predict the Reynolds stress anisotropy generated by a shockwave. The model by Wallin and Johansson (2000) is used as the baseline model. It is found to over-predict the post-shock Reynolds stresses in canonical shock turbulence interaction. The budget of the transport equation of Reynolds stresses computed using linear interaction analysis shows that the unsteady shock distortion mechanism and the pressure–velocity correlations are important. We propose improvement to the baseline model using linear interaction analysis results and redistribute the turbulent kinetic energy between the principle Reynolds stresses. The new model matches DNS data for the amplification of Reynolds stresses across the shock and their post-shock evolution, for a range of Mach numbers. It is applied to oblique shock/boundary-layer interaction at Mach 5. Significant improvements are observed in predicting surface pressure and skin friction coefficient, with respect to experimental measurements.     

Photoelastic analysis of a thin-walled compressor housing

The fabrication, testing, and analysis of a full-sized photoelastic model of a thin-walled compressor housing are presented. The conical model and connecting bolts were stress frozen under axial and bending loads to simulate severe in-flight manoeuver loads of a jet aircraft sufficient to cause flange separation. Results and discussion are presented for stresses in and near the flange, for stresses experienced by the bolts, and for the fabrication techniques used.     

Design and stress evaluation of a nonsymmetric pressure vessel

Presently, the large variation in demand for electrical power at different periods of the day imposes new considerations in the evaluation of pressure components in large steam-generating equipment. In the past, pressure components such as valve bodies have been designed for static pressure conditions against bursting with sufficient stiffness to assure operation ability. In today's plant operation, the response of the valve body to thermal transients will have a major influence on the life of the valve. Since the valve body is a compact nonsymmetric body, the direct calculation of stresses is very complex. The evaluation of the behavior of nonsymmetric pressure components under the loads imposed by various operational modes requires information from both analytical and experimental methods of analysis. The contributions from modern computer-calculation programs and three-dimensional photoelasticity are discussed as applied to the evaluation of a valve body used in a large, supercritical steam generator. In the analysis, computer procedures are used to develop the preliminary geometry for pressure loading. Because of the close proximity of the nonsymmetrical openings, a three-dimensional photoelastic analysis is used to calibrate the computer model. Once a satisfactory computer model has been developed for pressure loading, it is used to calculate the thermal stresses. Since stresses have little meaning in themselves, a design basis is necessary to evaluate the significance of the calculated stresses. The design basis must consider the types of failures which are possible and is thus dependent on the temperature at which the valve must operate. A design basis is discussed for the evaluation of pressure components in a boiler system.     

Detection and study of compressor-blade vibration

The many compressor blades in modern axially staged gas turbines are susceptible to vibration. The energy exciting the vibrations comes from many sources which are discussed. The vibratory stresses generated must be experimentally determined. A new device capable of detecting rotor-blade vibration without contact is described.     

A Bayesian Calibration–Prediction Method for Reducing Model-Form Uncertainties with Application in RANS Simulations

Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example, Reynolds-Averaged Navier-Stokes (RANS) simulations are increasingly used in the design, analysis, and safety assessment of mission-critical systems involving turbulent flows. However, for many practical flows the RANS predictions have large model-form uncertainties originating from the uncertainty in the modeled Reynolds stresses. Recently, a physics-informed Bayesian framework has been proposed to quantify and reduce model-form uncertainties in RANS simulations for flows by utilizing sparse observation data. However, in the design stage of engineering systems, when the system or device has not been built yet, measurement data are usually not available. In the present work we extend the original framework to scenarios where there are no available data on the flow to be predicted. In the proposed method, we first calibrate the model discrepancy on a related flow with available data, leading to a statistical model for the uncertainty distribution of the Reynolds stress discrepancy. The obtained distribution is then sampled to correct the RANS-modeled Reynolds stresses for the flow to be predicted. The extended framework is a Bayesian calibration–prediction method for reducing model-form uncertainties. The merits of the proposed method are demonstrated on two flows that are challenging to standard RANS models. By not requiring observation data on the flow to be predicted, the present calibration–prediction method will gain wider acceptance in practical engineering design and analysis compared to the original framework. While RANS modeling is chosen to demonstrate the merits of the proposed framework, the methodology is generally applicable to other complex mechanics models involving solids, fluids flows, or the coupling between the two (e.g., mechanics models for the cardiovascular systems), where model-form uncertainties are present in the constitutive relations.     

有限元表面应力计算

用有限元[1]通用程序进行结构计算时,最常用的是位移法,因而计算得到的位移有较高的精度。由位移计算应力时,有限元法应用的是应力-应变关系和应变-位移关系,其中应变-位移是微商关系。在数值计算中,微商只能转化为差商等用插值近似处理。这样,虽然位移精度高,但应力的计算精度就被大打折扣。本文应用弹性力学辛体系理论[2],解析求解了位移和应力的影响函数。利用有限元程序计算得到的位移,由功互等定理,不需要微分插值,就可以得到指定点的应力,应力精度大大提高。工程实际中有许多问题的最大应力往往发生在构件表面。针对表面应力问题,本文给出了半平面表面应力的影响函数,进行了数值算例计算。计算结果表明,用本文提出的影响函数法求解一点的应力,其精度明显提高,并且计算结果有很好的稳定性。用本文的影响函数法编制成子程序,可作为有限元软件应力计算的一个模块,可以更好地发挥有限元程序的功效。     

A two-dimensional continuum theory for angle-ply laminates

A two-dimensional continuum theory of microstructure is developed for stress analysis of angle-ply laminates under in-plane loading. An example problem is used to evaluate the results of the theory against a reference solution obtained by the finite element method. The results are in satisfactory agreement; they also show that the in-plane stresses reach somewhat higher peak values than reported in previous literature.The theory is also presented in a simplified version, which is found to be adequate for predicting interlaminar stresses and in-plane stress resultants, but does not give acceptable results for the variation of in-plane stresses through the thickness of the laminations.     

Generalized coordinate for warping of naturally curved and twisted beams with general cross-sectional shapes

This paper presents an efficient procedure for analyzing naturally curved and twisted beams with general cross-sectional shapes. The hypothesis concerning the cross-sectional shapes of the beams is abandoned in this analysis, and relatively general equations are derived for the analysis of such a structure. Solving directly such equations for various boundary conditions, which take into account the effects of torsion-related warping as well as transverse shear deformations, can yield the solutions to the problem. The solutions can be used to calculate various internal forces, stresses, strains and displacements of the beams. The present theory will be used to investigate the stresses and displacements of a cantilevered curved beam subjected to action of arbitrary load. The numerical results are very close to the FEM results.     

Embedded markers to measure strain in extremely soft materials

This paper presents an experimental method for measuring the displacement fields in extremely soft materials and the subsequent analysis of the data to yield the stress field. The stresses in soft materials are difficult to measure by transducers because the measurement device can easily alter the quantity to be measured. In this study, strains in seat cushions and in the buttock model are indicated by lead markers and recorded on X-ray films. The method is different from previous grid methods in that the strains can be measured in any plane inside a three dimensional model. The lead-ball matrix gives a clear picture of the overall displacement field and areas of high strain. The displacement data are converted to a digital form and analyzed on a computer. Two separate aspects of the computer analysis are discussed in detail in this paper. First, by curve fitting, the hydrostatic pressure gradient is obtained. Second, a finite-element model with the displacement data as input yields a set of stress contours.     

激光加热金属薄膜的热弹性研究

基于电子-声子相互作用的双曲两步热传导模型的超快热弹性理论,计及晶格的热传导效应,利用有限元方法研究了无限大金属薄膜在短暂激光冲击下诱导的位移、应力、应变和温度等物理量的演化特点,与已有文献比较,说明该方法的合理性与正确性.比较了计及电子热爆发力与不计电子热爆发力对位移、应力等物理量的影响,说明计及电子热爆发力的必要性...     

Embedded piezoelectric sensors to measure peel stresses in adhesive joints

Although peel stresses are believed to be responsible for failure in many adhesive joint geometries, the measurement of these peel stresses has been elusive. In this work, embedded poly(vinylidene fluoride) piezoelectric sensors were used to measure peel stresses in adhesively bonded joints. Piezoelectric KYNAR^® film was etched to produce multi-area stress sensors which were bonded into adhesive joints. Calibration results and results for single-lap and elastomeric butt joints are presented. The elastomeric butt joint was compared to an analytical solution for the bond-normal stresses, and the single-lap joint results were compared to finite-element analysis. Promising features and liminations of this technique are discussed.