Stress concentration around a nano-scale spherical cavity in elastic media: effect of surface stress

Influence of surface effect on stress concentration around a spherical cavity in a linearly isotropic elastic medium is studied on the basis of continuum surface elasticity. Following Goodier's work, a close form solution of the elastic field created by biaxial uniform load is presented. The stress concentration factors under different load combinations are obtained. It is concluded that consideration of surface effect leads to dependence of stress concentration factors on cavity size. Besides, numerical result indicates that stress concentration factors around the cavity are mainly affected by residual surface tension. The result is significant in the understanding of relevant mechanical phenomena in solids with nano-sized cavities.     

Plasticity Effects in the Hole-Drilling Residual Stress Measurement in Peened Surfaces

The incremental hole-drilling technique (IHD) is a widely established and accepted technique to determine residual stresses in peened surfaces. However, high residual stresses can lead to local yielding, due to the stress concentration around the drilled hole, affecting the standard residual stress evaluation, which is based on linear elastic equations. This so-called plasticity effect can be quantified by means of a plasticity factor, which measures the residual stress magnitude with respect to the approximate onset of plasticity. The observed resultant overestimation of IHD residual stresses depends on various factors, such as the residual stress state, the stress gradients and the material’s strain hardening. In peened surfaces, equibiaxial stresses are often found. For this case, the combined effect of the local yielding and stress gradients is numerically and experimentally analyzed in detail in this work. In addition, a new plasticity factor is proposed for the evaluation of the onset of yielding around drilled holes in peened surface layers. This new factor is able to explain the agreement and disagreement found between the IHD residual stresses and those determined by X-ray diffraction in shot-peened steel surfaces.     

梯形应力脉冲在弹性杆中的传播过程和几何弥散

在应力波传播过程中,几何弥散效应往往难以避免.对应力波在弹性杆中传播的几何弥散效应进行解析分析,对于基础波动问题研究以及材料动态力学行为表征等课题,显得至关重要.本文简单说明了弹性杆中考虑横向惯性修正的一维 Rayleigh-Love应力波理论,概述了其波动控制方程的变分法推导过程;针对 Hopkinson杆实验中常用的梯形应力加载脉冲,建立了相应的偏微分方程初边值问题的求解模型,并运用 Laplace变换方法研究了脉冲在杆中传播的几何弥散现象;根据留数定理进行 Laplace反变换,给出了杆中不同位置和时刻的应力波的级数形式解析解,分析了计算项数对结果收敛性的影响;将解析计算结果与采用三维有限元数值模拟的计算结果进行对比,两者吻合程度良好,从而证明 Rayleigh-Love横向惯性修正理论可以有效地表征典型 Hopkinson杆实验中的几何弥散效应.在此基础上围绕梯形加载脉冲的弥散效应进行参数研究,定量描述了传播距离、泊松比、脉冲斜率等参数的影响.本文给出的 Rayleigh-Love杆在梯形加载条件下的解析解,揭示了几何弥散效应的本质规律,可以用于实际实验的弥散修正过程.      

A method for reconstruction of residual stress fields from measurements made in an incompatible region

A method is introduced by which the complete state of residual stress in an elastic body may be inferred from a limited set of experimental measurements. Two techniques for carrying out this reconstruction using finite element analysis are compared and it is shown that for exact reconstruction of the stress field via this method, the stress field must be measured over all eigenstrain-containing regions of the object. The effects of error and incompleteness in the measured part of the stress field on the subsequent analysis are investigated in a series of numerical experiments using synthetic measurement data based on the NeT TG1 round-robin weld specimen. It is hence shown that accurate residual stress field reconstruction is possible using measurement data of a quality achievable using current experimental techniques.     

Scattering of elastic waves in an elastic matrix containing an inclusion with interfaces

Based on the theory of elastic dynamics, the scattering of elastic waves and dynamic stress concentration in fiber-reinforced composite with interfaces are studied. Analytical expressions of elastic waves in different medium areas are presented and an analytic method of solving this problem is established. The mode coefficients are determined by means of the continuous conditions of displacement and stress on the boundary of the interfaces. The influence of material properties and structural size on the dynamic stress concentration factors near the interfaces is analyzed. It indicates that they have a great influence on the dynamic properties of fiber-reinforced composite. As examples, numerical results of dynamic stress concentration factors near the interfaces are presented and discussed. This paper provides reliable theoretical evidence for the study of dynamic properties in fiber-reinforced composite. Project supported by the National Natural Science Foundation of China (No. 19972018).     

Thermal Stress Measurement in Continuous Welded Rails Using the Hole-Drilling Method

The absence of expansion joints in Continuous Welded Rail has created the need for the railroad industry to determine the in-situ thermal stress levels for rail buckling and breakage prevention. This paper explores the hole-drilling method as a possible solution to this problem. A new set of calibration coefficients to compute the stress field relieved by fine hole depth increments required by the high strength steel was determined. The new calibration coefficients were experimentally validated on an aluminum plate subjected to a known uniaxial load. The thermal stress levels of constrained rails were estimated after compensation for the residual stress components, based on statistical relationships developed experimentally between the longitudinal and the vertical residual stresses. The results showed that the hole-drilling procedure, with appropriate calibration coefficients and residual stress compensation, can estimate the in-situ rail thermal stresses with an expected accuracy that is within the industry acceptable levels.     

复合材料层合板粘弹性固化残余应力分析

基于Ｓｃｈａｐｅｒｙ积分型粘弹性本构关系，推导了考虑横向剪切效应的复合材料层合板线性热粘弹性有限元分析列式，对层合板的粘弹性响应和加工成型过程中的残余应力进行了分析，给出一些有意义的结果     

Elastic wave scattering and dynamic stress in composite with fiber

IntroductionTheproblemofscatteringofelasticwavesinsolidstructureshasnotonlytheoreticalsignificancebutalsowideoutlookinengineering .Thisproblemhasabsorbedmanypeople’sattentionsinmanyfieldssuchasaeronautics,compositemechanics,civilengineeringandearthquakeengineering[1～ 3 ] .Thepropagatingvelocityanddirectionofelasticwaveareinvariableasitpropagatesinaninfiniteuniformmedium .Butscatteringofelasticwavescanoccurifthereexistsincontinuitysuchasinclusion ,crackandcavityinelasticmedium .Fiber_reinfor…     

Crack-compliance method for assessing residual stress due to loading/unloading history: Numerical and experimental analysis

The understanding of how materials fail is still today a fundamental research problem for scientist and engineers. The main concern is the assessment of the necessary conditions to propagate a crack that will eventually lead to failure. Nevertheless, this kind of analysis tends to be more complicated, when a prior loading history in the material is taken into consideration and it will be extremely important to recognize all the factors involved in this process. In this work, a numerical simulation and experimental evaluation of the induction of residual stresses, which change the crack initiation conditions, in a modified compact tensile specimen is presented. Several analyses were carried out; an initial evaluation (numerical and experimental) was performed in a specimen without a crack and this was used for the estimation of a residual stress field produced by an overload; three more cases were simulated and a crack was introduced in each specimen (1 mm, 5 mm and 10 mm long, respectively). The overload was then applied to set up a residual stress field into the component; furthermore, in each case the Crack Compliance Method (CCM) was applied to measure the induced residual stress field. By performing this numerical simulation, the accuracy of the CCM can be evaluated and later corroborated by experimental procedure. On the other hand, elastic-plastic finite element analysis was utilized for the residual stress estimation. The analyses were based on the mechanical properties of a biocompatible material (AISI 316L). The obtained results provided significant data about diverse factors, like; the manner in which a residual stress field could modify the crack initiation conditions, the convenient set up for the induction of a beneficial residual stresses field, as well as useful information that can be applied for the experimental implementation in this research. Finally, some beneficial aspects of residual stresses are discussed.     

Validation of Mechanical Strain Relaxation Methods for Stress Measurement

Most validation studies of mechanical strain relaxation (MSR) methods for residual stress measurement rely on using the saw-tooth residual stress distribution resulting from four point bending and elastic–plastic deformation. Validation studies using simple applied stress profiles in rectangular steel beams are used in this work, together with beams subjected to elastic–plastic bending. Two MSR methods are explored, deep-hole drilling (DHD) and incremental centre hole drilling (ICHD). As well as a series of experiments, finite element analyses are conducted to determine the accuracy in the inversion of measured deformation to reconstruct stress. The validation tests demonstrated that apart from the applied stresses, the initial residual stresses also contribute even when samples are expected to be stress free. The uncertainty in measurement for the two MSR methods is determined, with the uncertainty in near surface measurement found to be significantly larger than uncertainty for interior measurement. In simple loading cases (and simple stress profiles) the uncertainty in measurement and hence the degree of validation is shown to be within about ±50 MPa for steel for “known” stress up to about 140 MPa. However, if the residual stress distribution is more complex there arises increased uncertainty in the predicted residual stress and lack of confidence between measurements methods.     

Contact laws between solid particles

This paper presents a comprehensive study for the contact laws between solid particles taking into account the effects of plasticity, strain hardening and very large deformation. The study takes advantage of the development of a so-called material point method (MPM) which requires neither remeshing for large deformation problems, nor iterative schemes to satisfy the contact boundary conditions. The numerical results show that the contact law is sensitive to impact velocity and material properties. The contact laws currently used in the discrete element simulations often ignore these factors and are therefore over-simplistic. For spherical particles made of elastic perfectly plastic material, the study shows that the contact law can be fully determined by knowing the relative impact velocity and the ratio between the effective elastic modulus and yield stress. For particles with strain hardening, the study shows that it is difficult to develop an analytical contact law. The same difficulty exists when dealing with particles of irregular shapes or made of heterogeneous materials. The problem can be overcome by using numerical contact laws which can be easily obtained using the material point method.     

A Procedure to Measure Biaxial Near Yield Residual Stresses Using the Deep Hole Drilling Technique

Deep Hole Drilling (DHD) is a mechanical strain relief technique used to measure residual stresses within engineering components. Such techniques measure strains or displacements when part of the component is machined away and typically assume elastic unloading. However, in components containing high levels of residual stress, elastic–plastic unloading can occur which may introduce substantial error. For the case of the DHD technique, a modification to the technique referred to here as the incremental or iDHD technique has been developed to allow such high levels of residual stress to be measured. Previous work has demonstrated the accuracy of the iDHD technique, although only for axisymmetric residual stress distributions. In the present investigation, the application of the iDHD technique has been extended to the general case of biaxial residual stress fields. Finite element simulations are first carried out to demonstrate the ability of the iDHD technique to measure biaxial residual stress. Experimental measurements were then made on shrink fit components and ring welded components containing biaxial residual stress to investigate the performance of the technique in practice. Good agreements between iDHD measurements, neutron diffraction measurements and FE predictions of the residual stresses were obtained, demonstrating the generally improved accuracy of the iDHD technique compared to the standard DHD approach.     

Enhancing water level prediction through model residual correction based on Chaos theory and Kriging

Hydrodynamic models based on the physical processes are indispensable tools for predicting water levels in ocean environment. Nonetheless, their accuracies are limited by various factors such as simplifying assumptions, complex ocean bathymetry, and so on. Residual correction, as one of the data assimilation techniques, can extract information from observation and assimilate it into a numerical model to correct the model output directly. Such correction is often performed in two steps: prediction of the model residuals at measured stations followed by spatial distribution at non‐measured locations. For long‐term residual forecast, the accuracy of prediction usually deteriorates with the forecast horizon. In addition to the residual correction at measurement locations, in this paper, we address the critical question as to how to effectively update outputs for computational points without measurements. We develop a hybrid data assimilation procedure, which combines a modified local model (MLM) and an approximated ordinary kriging (AOK). This technique improves the forecasts over a long horizon over the entire computational domain. Using the proposed residual correction technique, the hybrid procedure is examined on a case study of Singapore Regional Model for correcting the water level outputs at locations with and without measurements. In order to provide a comparison, the analysis is carried out throughout prediction horizon of model residuals, tidal residuals, and sea level anomaly, respectively. The comparisons show that the proposed method can successfully assimilate and forecast all variables. Results indicate that resulting prediction accuracy can be significantly improved for all locations of interest independently of the forecast horizon. Copyright © 2014 John Wiley & Sons, Ltd.     

颗粒增强复合材料中微观热应力和残余应力分析

运用空间配位体密堆模型和球对称分析单元，分析计算了颗粒增强复合材料经历温度变化后产生的微观热应力和残余应力。分析结果表明，温度升高时界面产生径向张应力，降温时产生压应力。存在一个基体开始发生塑性变形的临界温差ｔ＿ｐ，其值随增强体体积分数Ｖ＿ｐ增加而降低。除组元间热膨胀系数差和弹性常数外，基体材料本构关系和屈服强度对热应力和残余应力均有很大影响。随Ｖ＿ｐ增加，微观应力和水静宏观应力幅值上升。但粒子周围塑性区尺寸近似与Ｖ＿ｐ无关。给出了不同变温条件下残余应力的确定方法。     

Full field methods and residual stress analysis in orthotropic material. I Linear approach

This work analyzes the problem of residual stress determination in an orthotropic material using the hole drilling technique combined with non-contact, full field optical methods. Due to the complex behavior of the material, first a solution algorithm for the isotropic case is analyzed, then the procedure is extended to solving the more complex problem. In the first part of the work, the simplified Smith–Schajer solution to the through-hole problem for an orthotropic material is analyzed, showing that the same linear least square approach used in the isotropic case applies to a large set of orthotropic materials; based on this analysis a simple residual stress measurement algorithm is developed using either analytical or numerically estimated calibration coefficients.In the second part of the work, the general solution is discussed: since in this case the simplified Smith–Schajer solution cannot be used, the Lekhnitskii’s analysis of the through-hole plate in tension is introduced and extended to handle residual stresses. On this basis a solution algorithm using the nonlinear fit of the theoretical displacement field capable of treating all the orthotropic materials at the cost of a more complex numerical procedure is proposed. The performances of both algorithms are tested against numerically generated noisy fields and experimental ones and show a good reliability and accuracy.     

Stress concentration factors in finite anti-plane shear: numerical calculations and analytical estimates

In two recent papers [1, 2], an analytical approach for obtaining bounds on elastic stress concentration factors in the theory of finite anti-plane shear of homogeneous isotropic incompressible materials was presented. For the problem of an infinite slab, with a traction-free circular or elliptical cavity, subject to a state of finite simple shear deformation, explicit estimates for the stress concentration factor were obtained in terms of the cavity geometry, applied stress at infinity and constitutive parameters. In this paper, numerical results for these stress concentration factors are obtained using a finite-difference scheme and the analytical and numerical results are compared.     

Numerical modeling of viscoelastic counter flows using the pressure correction method

Counter flows of a viscoelastic fluid described by the rheological Oldroyd model in crossshaped channels are investigated. The modeling is based on the pressure correction method in a convenient-in-use form and with a simple topology of the computation grid and formally proved convergence. It is shown that, starting from certain threshold values of the Weissenberg numbers, the flow pattern in the stabilization stage exhibits considerable changes following two different mechanisms, depending on the Reynolds number. In particular, at low Reynolds numbers (less than 0.1) the flows involve vortex-like structures near the central point, where at the same time anomalies in normal stress distributions are observable. The similarity of these structures with the elastic instability phenomena, which were previously observed in the experimental realizations of the counter flows of this type and in other processes, is shown. To demonstrate the numerical procedure convergence, the results of calculations with different computation grid steps varied on a wide range are presented. In the context of the problem considered the general features of elastic instability are discussed.     

An experimental/computational approach to identify moduli and residual stress in MEMS radio-frequency switches

In this paper, we identify the Young's modulus and residual stress state of a free-standing thin aluminum membrane, used in MEMS radio-frequency (rf) switches. We have developed a new methodology that combines a membrane deflection experiment (MDE) and three-dimensional numerical simulations. Wafer-level MDE tests were conducted with a commercially available nanoindenter. The accuracy and usefulness of the MDE is confirmed by the repeatability and uniformity of measured load-deflection curves on a number of switches with both wedge and Berkovich tips. It was found that the load-deflection behavior is a function of membrane elastic properties, initial residual stress state and corresponding membrane shape. Furthermore, it was assessed that initial membrane shape has a strong effect on load-deflection curves; hence, its accurate characterization is critical. Through an iterative process and comparison between MDE data and numerical simulations, the Young's modulus and residual stress state, consistent with measured membrane shape, were identified. One important finding from this investigation is that variations in membrane elastic properties and residual stress state affect the load-deflection curve in different regimes. Changes in residual stress state significantly affect the load-deflection slope at small values of deflection. By contrast, variations in Young's modulus result in changes in load-deflection slope at large deflections. These features are helpful to decouple both effects in the identification process.     

Constitutive Model Calibration for Powder Compaction Using Instrumented Die Testing

Calibration procedures for constitutive models for powder compaction are presented. A practical calibration method based on a die compaction experiment is presented. A newly developed apparatus consisting of a die instrumented with radial stress sensors is described. The paper proposes two contributions to account for errors present in instrumented die testing, which are due to 1) elastic compliance of the testing frame, influencing the measurement of axial strain and 2) the presence on non-homogeneous stress state in the test specimen. It is shown that system compliance is important for generating an accurate stress-strain curve for compression. The effect of different compliance correction methods is evaluated with regard to the accuracy of models predicting pressing forces. The system compliance becomes more significant during unloading in the die; this information is used to determine the elastic properties. A new compliance correction method is introduced following a detailed analysis of the forces and deformations of different parts of the loading frame. In instrumented die compaction the axial and radial stresses are measured at fixed locations and the specimen is subject to non-homogeneous stresses and strains due to the effect of friction between the powder and die wall. Starting from the Janssen-Walker method of differential slices a method to account for non-homogeneous stress and strain is developed.