Effect of interfacial stiffness on the stretchability of metal/elastomer bilayers under in-plane biaxial tension

Flexible electronic devices are often subjected to large and repeated deformation, so that their functional components such as metal interconnects need to sustain strains up to tens of percent, which is far beyond the intrinsic deformability of metal materials(～1%). To meet the stringent requirements of flexible electronics, metal/elastomer bilayers, a stretchable structure that consists of a metal film adhered to a stretchable elastomer substrate, have been developed to improve the stretch capability of metal interconnects. Previous studies have predicted that the metal/elastomer bilayers are much more stretchable than freestanding metal films. However, these investigations usually assume perfect bonding between the metal and elastomer layers. In this work, the effect of the metal/elastomer interface with a finite interfacial stiffness on the stretchability of bilayer structures is analyzed. The results show that the assumption of perfect interface(with infinite interfacial stiffness) may lead to an overestimation of the stretchability of bilayer structures. It is also demonstrated that increased adhesion between the metal and elastomer layers can enhance the stretchability of the metal layer.     

Stretchable hydrophobic surfaces and droplet heating

Silicon elastomer surface is treated towards achieving the hydrophobic state. Functionalized nano-silica units are coated onto elastomer surface and resulting texture characteristics are examined prior to stretching, stretched and after stretching. The droplet heating of the hydrophobic elastomer surface is carried out when the surface is subjected to unstretching, stretching and stretch releasing conditions. The thermal-flow field in the liquid is simulated and validated incorporating high speed recording system. Nano-size silica units coated elastomer surface demonstrates the hydrophobic wetting state. The hydrophobic wetting state changes slightly for stretched and stretched released surface. The contact angle is about 154° ± 2° for unstretched surface while it is 152° ± 2° for the stretched released surface; hence, stretch relaxing provides reversible change of the surface wetting state of the elastomer surface. The contact angle reduces to 142° ± 2° when surface is under stretched, which is related to increased pillar spacing on the surface. The droplet heating results in development of Marangoni current in the fluid, which significantly affects the flow and temperature fields and it becomes more apparent for the large size droplets. The maximum flow velocity increases almost 9% in 45 µL as the surface is stretched. The Nusselt number increases with droplet size and the Bond number has the values less than unity; hence, stretching increases the Nusselt number by 60% for droplet of 45 µL.     

Heating analysis of a droplet on stretchable hydrophilic surface

Heating of a droplet on a stretchable hydrophilic surface is investigated and fluid dynamics in the droplet under the heating load is assessed. Elastomer wafers are considered as the sample material and the fixture is designed and manufactured to assure uniform stretching of the droplet located elastomer surface. Droplet adhesion and possible slipping/sliding of the droplet are evaluated during stretching of the sample surface. Numerical simulations are carried out to predict thermal and flow response of the droplet fluid before and after stretching. The effect of droplet volume on heating enhancement is also included in the numerical simulations. Experiments are carried out using a high-speed recording system towards comparing the flow predictions. Findings reveal that predictions are in agreement with their counterparts of experiments. Stretching of sample surface increases wetting area and lowers height of the droplet while influencing thermal flow structures in the fluid. The Nusselt and the Bond numbers increase with enlarging stretching, which becomes more visible for large droplet volume (80 µl). Hence, stretching corresponding to 80% extension of elastomer surface gives rise to 60% improvement in the Nusselt number.     

A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions

A combined necking and shear localization analysis is adopted to model the failures of two aluminum sheets, AA5754 and AA6111, under biaxial stretching conditions. The approach is based on the assumption that the reduction of thickness or the necking mode is modeled by a plane stress formulation and the final failure mode of shear localization is modeled by a generalized plane strain formulation. The sheet material is modeled by an elastic-viscoplastic constitutive relation that accounts for the potential surface curvature, material plastic anisotropy, material rate sensitivity, and the softening due to the nucleation, growth, and coalescence of microvoids. Specifically, the necking/shear failure of the aluminum sheets is modeled under uniaxial tension, plane strain tension and equal biaxial tension. The results based on the mechanics model presented in this paper are in agreement with those based on the forming limit diagrams (FLDs) and tensile tests. When the necking mode is suppressed, the failure strains are also determined under plane strain conditions. These failure strains can be used as guidances for estimation of the surface failure strains on the stretching sides of the aluminum sheets under plane strain bending conditions. The estimated surface failure strains are higher than the failure strains of the forming limit diagrams under plane strain stretching conditions. The results are consistent with experimental observations where the surface failure strains of the aluminum sheets increase significantly on the stretching sides of the sheets under bending conditions. The results also indicate that when a considerable amount of necking is observed for a sheet metal under stretching conditions, the surface failure strains on the stretching sides of the sheet metal under bending conditions can be significantly higher.     

粗糙薄层弹性体接触刚度分析

薄层弹性体功能结构表面在工程领域有着广泛的应用前景,薄层弹性体的接触特性分析对功能结构表面设计与应用非常重要.采用随机粗糙表面模拟生成技术和有限元分析技术建立了粗糙薄层弹性体表面的接触刚度确定性分析模型,研究了薄层弹性体的接触特性,对基于半数值确定性分析方法的粗糙层-基体层串联模型用于粗糙薄层弹性体接触刚度计算的适用性进行了讨论,进一步分析了粗糙薄层弹性体串联模型接触刚度的误差来源.研究结果表明:当薄层弹性体的基体层厚度小于10倍表面均方根粗糙度时,由传统粗糙层-基体层串联模型分析获得的粗糙薄层弹性体刚度误差将超过15%,误差主要来源于粗糙峰的大变形和基体层的局部变形不均匀的共同作用.     

表面加工塑性层对金属柱壳剪切带自组织单旋起始的影响

在外爆加载金属柱壳高速坍塌过程中, 发生塑性变形失稳形成的剪切带具有高度的自组织特征, 甚至出现剪切带排列的单旋现象—剪切带在顺时针和逆时针两个方向呈现一个方向占优的现象. 柱壳在坍塌时, 最大剪切应力位于柱壳内表面, 剪切带的形核及扩展行为受内表面材料介观状态的影响显著. 本文通过选材和控制柱壳加工工艺, 获得了内表面具有不同厚度塑性层的20钢柱壳, 采用厚壁圆筒实验技术, 研究了表面加工塑性层对金属柱壳绝热剪切带自组织单旋现象起始的影响规律及其物理机制. 研究结果表明, 金属柱壳内表面加工塑性层显著改变了试样剪切带的起始条件, 沿顺时针或逆时针方向排列的剪切带形核数量在总剪切带数量中所占比例取决于表面加工塑性层的厚度和晶粒取向, 具有单一晶粒拉伸方向的较厚塑性层样品更容易形成单向螺旋剪切带结构. 在相同变形条件下, 随着塑性层厚度增加, 剪切带平均形核速率和扩展速率增大, 剪切带平均间距减小. 结果可为理解金属柱壳在高速塌陷过程中绝热剪切带占优取向现象提供有价值的参考.      

Deformability of thin metal films on elastomer substrates

Recent applications in flexible electronics require that thin metal films grown on elastomer substrates be deformable. However, how such laminates deform is poorly understood. While a freestanding metal film subject to tension will rupture at a small strain by undergoing a necking instability, we anticipate that a substrate will retard this instability to an extent that depends on the relative stiffness and thickness of the film and the substrate. Using a combination of a bifurcation analysis and finite element simulations, we identify three modes of tensile deformation. On a compliant elastomer, a metal film forms a neck and ruptures at a small strain close to that of a freestanding film. On a stiff elastomer, the metal film deforms uniformly to large strains. On an elastomer of intermediate compliance, the metal film forms multiple necks, deforms much beyond the initial bifurcation, and ruptures at a large strain. Our theoretical predictions call for new experiments.     

The electro-mechanical response of elastomer membranes coated with ultra-thin metal electrodes

This paper presents experimental and theoretical analyses of the electro-mechanical response of metal/elastomer multilayers. A novel test has been devised to determine the relationship between the mechanical response of clamped elastomer membranes, coated on both sides with metal electrodes, and an applied electric field. The load-deflection response of the multilayers subjected to different voltages was measured using an instrumented spherical indenter having dimensions comparable to the freestanding span. The measurements are used with closed-form solutions for membrane deflection to determine the effective plane-strain modulus of cracked multilayers and electrically induced in-plane strains. The experiments demonstrate that: (i) electrically induced strains vary with the square of the electric field, as expected from electrostatic models of parallel plate capacitors, (ii) the transverse stiffness of membranes can be controlled using applied electric fields, (iii) analytical models accurately predict the relationship between electrode crack spacing, layer properties and effective moduli. Finally, we estimate the toughness of the sub-micron metal electrodes, using cracking models that relate crack spacing, imposed strain and the energy release rate governing channel crack formation.     

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.     

Constitutive relation of viscoelastic dielectric elastomer

In this paper, we present a modified model describing the constitutive relation of viscoelastic dielectric elastomer (DE). The uniform uniaxial tension-recovery experiment was carried out at different stretching rates. Based on Yeoh hyper-elastic model, model-fitting approach is put forward to obtain the relationship between parameters of Yeoh model and stretching rate, thus the modified model was obtained. From the approximate relationship between harmonic motion and uniform reciprocating motion, the stress–strain curve in the recovery process was also identified through the hysteresis between stress and strain. The modified model, with concise form and evident physical concept, can describe the strong nonlinear behavior between deformation and mechanical stress of the material in a common stretching rate range (from 0.01s^?1 to 0.8s^?1 at least). The accuracy and reliability of the modified model was examined.     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

Effect of non-uniform heat source on MHD heat transfer in a liquid film over an unsteady stretching sheet

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a laminar liquid film over a flat impermeable stretching sheet in the presence of a non-uniform heat source/sink. The basic unsteady boundary layer equations governing the flow and heat transfer are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformation. Numerical solutions of the resulting boundary value problem are obtained by the efficient shooting technique. The effects of magnetic and the non-uniform heat source/sink parameters on the dynamics are discussed. Findings of the paper reveal that non-uniform heat sinks are better suited for effective cooling of the stretching sheet. Skin friction coefficient and the local Nusselt number are also explored for typical values of magnetic and non-uniform heat source/sink parameters. The results are in excellent agreement with the earlier published works, under some limiting cases.     

Periodic necking instabilities in layered plastic composites

A bifurcation analysis of a solid composed of alternating material layers is carried out. We study the conditions under which periodic incremental deformations (eigenmodes), consistent with an overall homogeneous stretching, can emerge when the solid is subjected to plane strain, uniaxial tension parallel to the layer interfaces. These undulatory eigenmodes are in competition with shear localization, taken here to be signaled by a loss of ellipticity of the governing incremental equations. The influence of various material parameters on this competition is discussed and contact is made with previous work.     

用损伤理论方法预测铝合金薄板成型极限

应用各向异性损伤理论研究2024-T3铝合金薄板的成形极限,通过构造有限元单胞模型预测薄板结构的极限应变.单胞模型由两相材料组成:铝合金基体和金属强化物.基体采用全耦合弹塑性-损伤本构方程描述,而金属强化物则视为弹脆性材料.采用所提出的缩颈准则,得到了双轴拉伸状态下铝合金薄板的极限应变,和实验结果比较两者吻合较好.研究结果揭示有限元单胞模型可以提供铝合金的细观损伤机理信息,当忽略材料的损伤影响,采用金属薄板成型理论的研究结果将过高估计薄板的极限应变.     

胶接体系的胶接强度、粘结能及损伤破坏研究

胶接是指一种用粘合剂实现连接和固持的方法,胶接形式的金属薄板在汽车工业,建筑业以及航空航天领域有着广泛的应用.论文采用有限元模拟方法,研究了该胶接体系在受载状态下的滑剪破坏行为,重点关注了胶层粘结能,搭接长度,胶层厚度对胶接接头承载能力的影响,同时初步探讨了胶层的界面损伤情况.胶层粘结能的提高能够显著提高接头的承载能力.此承载能力受搭接长度和胶层粘结能的共同影响,较大的粘结能情况下,提高搭接长度能够显著提高接头的承载能力.胶层厚度对接头的承载能力也存在影响,在论文考虑的厚度范围内,提高厚度能够增强接头的承载能力.最后初步考虑了接头在达到载荷峰值时刻的胶层损伤情况.     

On axisymmetric flow of Sisko fluid over a radially stretching sheet

This study presents an analysis of the axisymmetric flow of a non-Newtonian fluid over a radially stretching sheet. The momentum equations for two-dimensional flow are first modeled for Sisko fluid constitutive model, which is a combination of power-law and Newtonian fluids. The general momentum equations are then simplified by invoking the boundary layer analysis. Then a non-linear ordinary differential equation governing the axisymmetric boundary layer flow of Sisko fluid over a radially stretching sheet is obtained by introducing new suitable similarity transformations. The resulting non-linear ordinary differential equation is solved analytically via the homotopy analysis method (HAM). Closed form exact solution is then also obtained for the cases n=0 and 1. Analytical results are presented for the velocity profiles for some values of governing parameters such as power-law index, material parameter and stretching parameter. In addition, the local skin friction coefficient for several sets of the values of physical parameter is tabulated and analyzed. It is shown that the results presented in this study for the axisymmetric flow over a radially non-linear stretching sheet of Sisko fluid are quite general so that the corresponding results for the Newtonian fluid and the power-law fluid can be obtained as two limiting cases.     

Computational modeling of heat transfer over an unsteady stretching surface embedded in a porous medium

The present paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of an incompressible viscous fluid over an unsteady stretching sheet which is placed in a porous medium in the presence of viscous dissipation and internal absorption or generation. Similarity transformations are used to convert the governing time dependent nonlinear boundary layer equations into a system of non-linear ordinary differential equations containing Prandtl number, Eckert number, heat source/sink parameter, porous parameter and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the parameters which determine the velocity and temperature fields are discussed in detail.     

The Evolution of Effective Elastic Properties of a Cold Formed Stainless Steel Sheet

In accordance with the great importance given to the subject of stiffness degradation, in particular with regard to metal forming, this work experimentally investigates the anisotropic elastic properties of plastically prestrained cold-rolled sheet metal (stainless steel EN 1.4301, also AISI 304). From the experiments performed, two main conclusions regarding stiffness degradation can be extracted. First, since under specific stretching the intensity of the normalized Young’s moduli degradation in both directions remains approximately similar, it may be concluded that the potential initial elastic anisotropy tends to be preserved during loading. Second, as the evidenced stiffness degradation has proved to be strongly correlated with the stretching direction of the sheet metal, it can be concluded that the stiffness evolution in the cold rolled sheet steel is path dependent. These interesting discoveries also provide some answers for modelling the kinetic damage evolution laws in damage mechanics.     

Dynamic Analysis of the Non-Linear Behavior of a Composite Sandwich Beam with a Magnetorheological Elastomer Core

This work deals with the active control of the vibrations of mechanical structures incorporating magnetorheological elastomer. The damping coefficient and shear modulus of the elastomer increase when exposed to a magnetic field. Compared with the vibration control where the elastomer is permanently exposed to a magnetic field, the control of this process through time reduces vibrations more effectively. The experimental study for the vibrations of a sandwich beam filled with an elastomer is conducted, followed by a numerical study using the Abaqus code.The vibration damping is found to be dependent on the loading rate of micro-size ferromagnetic particles in the elastomer.     

Effects of thermal stratification on flow and heat transfer past a porous vertical stretching surface

The aim of this paper is to present the boundary layer flow of viscous incompressible fluid due to a porous vertical stretching surface with a power-law stretching velocity in a thermally stratified medium. Using a special form of Lie group transformations viz. scaling group of transformations, similarity solutions for this problem are obtained. The equations are then solved numerically. With increasing values of the stratification parameter, the velocity as well as temperature decreases. At a particular point of the porous stretching sheet, the velocity decreases with the increasing suction parameter. The dimensionless temperature at a point of the sheet decreases due to suction but increases due to injection. The findings of this study reveal that stratification and suction can be used as means of cooling the boundary layer flow region.