Improved tri-layered interfacial stress model with the effect of different temperatures in the layers

The study of thermal mismatch induced stresses and their role in mechanical failure is one relevant topic to composite materials and electronic packages. An understanding of the nature of the interfacial stresses under different temperature conditions is necessary in order to minimize or eliminate the risk of mechanical failure. An accurate estimate of thermal stresses in the interfaces plays an important role in the design and reliability studies of micro-electronic devices. In the microelectronic industry, from a practical point of view, there is a need for simple and powerful analytical models to determine interfacial stresses in layered structures quickly and accurately. In the present paper, a model is proposed for the shearing and peeling stresses occurring at the interface of three bonded thin plates of dissimilar materials to account for different uniform temperatures in the layers by incorporating two temperature ratios. The model is then further upgraded to accommodate the effect of thickness wise linear temperature gradients in the layers by incorporating three linear temperature gradients at the interfaces. This upgraded model can be viewed as a more generalized form to take care of different temperature conditions which may occur in a tri-layered structure. The improved uniform temperature model of tri-material assembly provided by Sujan (Int Microelectron Packag Soc JMEP 5(1):37–42, 2008) is utilized to develop the proposed tri-layered model. The selected shearing stress results are presented for the case of die, die attach and substrate as commonly found in electronic packaging.     

Nickel doped zinc oxide nanoparticles produced by hydrothermal decomposition of nickel-doped zinc hydroxide nitrate

Zinc hydroxide nitrate, an anionic exchanger layered material, undoped as well as doped with 2–10% nickel, was synthesized by using a pH-controlled precipitation method. The layered materials were then used to produce the undoped and nickel-doped zinc oxides by hydrothermal-treatment. X-ray diffraction, Fourier transform infrared spectroscopy and scanning electron microscopy confirmed the formation of pure phase undoped and nickel-doped layered materials, as well as the products of the hydrothermal-treated materials, nanostructured zinc oxides. Optical studies of the nanostructured zinc oxides showed a decrease in band gap with increasing content of the doping agent, nickel.     

Probabilistic character of the microcrack growth in brittle layered materials

Characteristics of microcrack initiation, multiplication and saturation in layered materials are discussed. A probabilistic-analytical method, the ‘characteristic curve method (CCM)’ is developed to correlate the initial defects and the microcrack evolution under static and cyclic loadings. The ‘equivalent applied loading’ and the ‘equivalent crack density’ concepts are introduced to describe different microcrack multiplication features in different layered materials. Microcrack multiplication processes in many layered materials with brittle matrices subjected to static and cyclic loadings can be easily predicted.     

SH波在压电材料条中垂直界面裂纹处的散射

研究了SH波在压电材料条中裂纹处的散射.压电材料条两侧涂有相同梯度参数的两个半无限大功能梯度材料,裂纹垂直于界面.通过Fourier变换,利用边界条件把问题转化为柯西核奇异积分方程,然后利用Chebyshev多项式对奇异积分方程进行数值求解.通过数值计算,分析讨论了压电条的几何参数和SH波频率对标准动应力强度因子的影响.     

磁敏智能软材料及磁流变机理

磁敏智能软材料是一类将微米或纳米尺度的磁性颗粒分散在不同基体中制备而成的多功能复合材料.由于其流变性能在外磁场的调控下可以实现连续、快速、可逆的改变,因此在建筑、振动控制和汽车工业等领域得到了广泛地应用.本文首先介绍了磁敏智能软材料发展历史及分类,分析了不同种类的磁敏智能软材料的特点和存在的科学问题;然后从实验和理论两个方面讨论了磁流变机理的研究现状;最后从实际应用的角度对这类材料未来的发展方向进行了展望.      

A note on failure conditions for layered materials

Summary Some failure conditions for heterogeneous layered media, formed by two alternating homogeneous materials, are presented. The failure criteria have been obtained by a homogenization procedure, on the basis of the criteria of the materials forming the layered medium. The paper deals with layers formed by Mohr-Coulomb's type materials (the cases of cohesionless materials or materials provided by the same friction angle are discussed), as well as with layers undergoing the maximum tensile stress criterion. Theoretical predictions are in good agreement with the experimental results obtained by other authors on layered sands and laminated rocks.

---

Sommario Vengono presentati alcuni criteri di rottura per materiali stratificati eterogenei, caratterizzati da regolare altenanza di due materiali omogenei. Tali criteri sono stati ottenuti mediante una procedura di omogeneizzazione, sulla base delle condizioni di rottura dei materiali che compongono il continuo stratiflcato. Sono stati considerati strati formati da materiali del tipo di Mohr-Coulomb (per i casi in cui i materiali sono o privi di coesione, oppure sono dotati dello stesso angolo d'attrito), o da materiali che obbediscono al criterio della massima trazione. Le pre-dizioni teoriche mostrano un buon accordo con i risultati di prove sperimentali eseguite da altri autori su sabbie e rocce stratificate.

     

Scattering of a plane harmonic SH wave by multiple layered inclusions

Scattering of a plane harmonic SH wave by an arbitrary number of layered inclusions in a half-space is investigated by using a direct boundary integral equation method. The inclusions of arbitrary shape and placement are embedded within an elastic half-space. The effects of multiple scattering, the geometry, and the impedance contrast of the materials for layered inclusions and pipes are considered in detail.     

Estimate of energy consumption in fracture of solids

The problem of determining the loading conditions under which the maximum softening of materials is attained with minimal fracture energy consumption is posed in many practical applications (in building, explosion, drilling, grinding, metal processing by cutting, domestic and industrial waste processing, food industry, drug production, and pulp-and-paper industry). Nowadays, in many of these areas, the fracture energy consumption is rather large and ill grounded. Comparison of energy consumption by different loading programs allows one to distinguish energy saving loading conditions which can be recommended to improve the structures and operation modes of various equipment, in particular, in the field of grinding of hard materials. In the present paper, it is proposed to estimate the energy consumption according to the damage summation law expressed in terms of relative energy consumption indices.     

层状地基中单桩扭转振动特性分析

采用积分变换和Muki的方法求解了层状地基中单桩的扭转振动问题.在分析过程中,首先对基本控制方程进行Hankel变换,建立了单层地基的初参数解答和刚度矩阵,得到层状地基的递推矩阵;然后利用递推矩阵、边界条件和桩-土变形协调条件建立了层状地基中单桩扭转振动问题的基本积分方程并进行数值求解.文末数值算例给出了退化的层状地基中刚性单桩的扭转变形,其结果与已有经典解答吻合良好.同时,并研究了两层地基中单桩的扭转动力响应,分析了桩-土参数对动力响应的影响,所得结论对工程实践和桩基扭转波检测有一定的指导意义.     

EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS 1)

两种或多种不同性质材料组成的层状结构可以满足工业发展的需求. 然而, 材料属性在接触面的突变问题, 容易导致层间界面处产生应力集中、裂纹以及分层等问题. 功能梯度材料利用连续变化的组分梯度来代替突变界面, 可以消除界面处的物理性能突变, 提高结构的粘结强度. 本文以一维准晶功能梯度层合圆柱壳为研究对象, 利用类Stroh公式和传递矩阵方法, 建立了材料参数沿径向呈现幂函数变化的层合圆柱壳模型, 获得了简支边界条件对应的一维准晶功能梯度层合圆柱壳的热电弹性精确解. 数值算例中讨论了层合圆柱壳内外表面承受温度载荷时, 功能梯度指数因子对温度场、电场、声子场和相位子场的影响, 尤其是对层合圆柱壳内外表面的影响. 结果表明, 指数因子改变了材料参数的空间分布情况, 进而对温度场、电场、声子场和相位子场都有影响; 增加功能梯度指数因子, 可减小温度载荷引起的内表面变形, 进而提升结构强度. 本文得到的结果可以为功能梯度准晶层合圆柱壳的设计和制造提供可靠的理论依据.     

一维准晶功能梯度层合圆柱壳热电弹性精确解

两种或多种不同性质材料组成的层状结构可以满足工业发展的需求.然而,材料属性在接触面的突变问题,容易导致层间界面处产生应力集中、裂纹以及分层等问题.功能梯度材料利用连续变化的组分梯度来代替突变界面,可以消除界面处的物理性能突变,提高结构的粘结强度.本文以一维准晶功能梯度层合圆柱壳为研究对象,利用类Stroh公式和传递矩阵方法,建立了材料参数沿径向呈现幂函数变化的层合圆柱壳模型,获得了简支边界条件对应的一维准晶功能梯度层合圆柱壳的热电弹性精确解.数值算例中讨论了层合圆柱壳内外表面承受温度载荷时,功能梯度指数因子对温度场、电场、声子场和相位子场的影响,尤其是对层合圆柱壳内外表面的影响.结果表明,指数因子改变了材料参数的空间分布情况,进而对温度场、电场、声子场和相位子场都有影响;增加功能梯度指数因子,可减小温度载荷引起的内表面变形,进而提升结构强度.本文得到的结果可以为功能梯度准晶层合圆柱壳的设计和制造提供可靠的理论依据.     

Modeling of Two Phase Flow in a Hydrophobic Porous Medium Interacting with a Hydrophilic Structure

Transport in Porous Media - Fluid flow through layered materials with different wetting behavior is observed in a wide range of applications in biological, environmental and technical systems....     

Mo-ZrC梯度金属陶瓷的冲击响应行为

分层梯度材料特定的梯度变化能有效增强材料性能。为研究梯度结构、冲击方向对分层梯度材料冲击响应的影响,利用分离式霍普金森压杆结合高速摄影技术对Mo-ZrC分层梯度金属陶瓷进行了动态压缩实验,基于数字图像相关技术讨论了梯度结构、冲击方向对金属陶瓷材料破坏模式的影响,利用Mori-Tanaka理论计算得到金属陶瓷等效性质,结合应力波理论研究波在分层梯度复合材料中的传播规律。结果表明：(1)相同加载条件下,梯度结构对材料的强度、韧性和破坏产物的完整性具有重要影响,在冲击过程中,样品响应可以分为压紧阶段、裂纹成核发展阶段和贯穿阶段,对于不同梯度结构和冲击方向,样品在加载过程中呈现出不同的破坏时序和失效模式;(2)利用数字图像相关方法跟踪分层梯度陶瓷的局部变形发展,分析发现局部增量达到临界状态后,局部变形发展转化为微裂纹的形成和累积,最终导致整体性破碎失效;(3)通过分层梯度材料一维应力波传播理论推导得到,改变冲击梯度方向对应力波透反射系数存在一定影响,不同梯度结构设计对改变冲击梯度方向敏感性不同,且存在极值情况。     

Analysis and calculation of stresses and displacements in layered elastic systems

The general formulae for the stresses and displacements in layered elastic systems subjected to external loads are derived in this paper. On the basis of these formulae the practical formulae for calculation of the stresses and displacements in layered elastic systems under the action of vertical, centripetal-horizontal, unidirectional-horizontal and rotational-horizontal loads distributed on circular areas and compressed by rigid circular plates are further derived, and the corresponding computer programs have been worked out.     

Wave propagation in magneto-electro-elastic multilayered plates

An analytical treatment is presented for the propagation of harmonic waves in magneto-electro-elastic multilayered plates, where the general anisotropic and three-phase coupled constitutive equations are used. The state-vector approach is employed to derive the propagator matrix which connects the field variables at the upper interface to those at the lower interface of each layer. The global propagator matrix is obtained by propagating the solution in each layer from the bottom of the layered plate to the top using the continuity conditions of the field variables across the interfaces. From the global propagator matrix, we finally obtain the dispersion relation by imposing the traction-free boundary condition on the top and bottom surfaces of the layered plate. Dispersion curves, modal shapes, and natural frequencies are presented for layered plates made of orthotropic elastic (graphite–epoxy), transversely isotropic PZT-5A, piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄ materials. While the numerical results show clearly the influence of different stacking sequences as well as material properties on the field response, the general methodology presented in the paper could be useful to the analysis and design of layered composites made of smart piezoelectric and piezomagnetic materials.     

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.     

Preparation of Materials for Composite Photoelastic Models

For composite structural problems, modulus of elasticity may vary appreciably for different material zones. For example, a concrete dam founded on faulted or layered rock, a steel-framed building resting on a soil foundation or the bone-flesh interaction problem in biomechanics. For the exact representation of a composite structure, photoelastic materials of the same modular ratios as in the prototype should be used, provided such materials are available.     

Broadband optimization of a pentamode-layered spherical acoustic waveguide

Transformational acoustics offers the theoretical possibility of cloaking obstacles within fluids, provided metamaterials having continuously varying bulk moduli and densities can be found or constructed. Realistically, materials with the proper, continuously varying anisotropies do not presently exist. Discretely layered cloaks having constant material parameters within each layer are a viable alternative, but due to their discrete nature, may become ineffective outside of narrow frequency ranges. Because of such limitations, there is interest in finding discretely layered systems that can be effective in as wide as possible bandwidth without the need for unrealizable material properties within each layer. The present work introduces a novel methodology for finding optimal material parameters for use in such layered cloaks. In principle, the technique could be applied to any acoustic or electromagnetic scattering problem, but for purposes of demonstration, this paper considers a fluid-loaded acoustically hard sphere with a cloak that comprised layered pentamodes, whose material properties are constrained to lie within reasonable ranges relative to the density and bulk modulus of water.     

广义Rayleigh波的频谱特性分析

本文导出了在加层半空间中广义Ｒａｙｌｅｉｇｈ波的谱函数方程，研究了不同的材料组合对其频率特性的影响，并给出了广义Ｒａｙｌｅｉｇｈ波的相速度随频率变化的计算曲线。     

Compaction of a double-layered metal foam block impacting a rigid wall

The propagation of compaction waves in layered metal foam materials subjected to impact loading is analysed in order to examine the mechanism of compaction and reveal the phenomena that develop at the interface between the foam layers. The analysis is focused on double-layered configurations in which the individual materials exhibit strain hardening in the quasi-static regime of loading.