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.     

Competing failure mechanisms of thin metal films on polymer substrates under tension

The ductility of thin metal films on polymer substrates reported in recent experiments has a huge disparity, ranging from less than 1 % up to more than 50 %. To reveal the underpinning origins for such a large variation, this paper reports a systematic computational study of two competing failure mechanisms: metal film necking and grain boundary cracking. The quantitative results suggest that strong grain boundaries and metal/polymer interfacial adhesion are keys to achieve high ductility of polymer-supported metal films.     

Effects of interfacial properties on the ductility of polymer-supported metal films for flexible electronics

Polymer-supported metal films as interconnects for flexible, large area electronics may rupture when they are stretched, and the rupture strain is strongly dependent upon the film/substrate interfacial properties. This paper investigates the influence of interfacial properties on the ductility of polymer-supported metal films by modeling the microstructure of the metal film as well as the film/substrate interface using the method of finite elements and the cohesive zone model (CZM). The influence of various system parameters including substrate thickness, Young’s modulus of substrate material, film/substrate interfacial stiffness, strength and interfacial fracture energy on the ductility of polymer-supported metal films is systematically studied. Obtained results demonstrate that the ductility of polymer-supported metal films increases as the interfacial strength increases, but the increasing trend is affected distinctly by the interfacial stiffness.     

环境水氧对纳米氮化铝/聚四氟乙烯复合材料摩擦学性能的影响

采用超声分散法制备出纳米氮化铝/聚四氟乙烯(AlN/PTFE)复合材料,使用线性往复摩擦磨损试验机在大气和干燥氩气中对比测试了该复合材料摩擦学性能. 结果表明:大气环境下,纳米氮化铝质量分数为5%时可以将聚四氟乙烯磨损率降低4个数量级[1×10?7 mm3/(N·m)]. 而在同样摩擦测试条件的干燥氩气环境中,使用纳米氮化铝只能将聚四氟乙烯磨损率降低2个数量级[1×10?5 mm3/(N·m)]. 利用三维轮廓仪、扫描电镜、红外光谱仪和光电子能谱仪对金属对偶表面形成转移膜的形貌和化学成分进行分析. 研究发现:大气环境的摩擦过程中,聚四氟乙烯与环境水氧发生摩擦化学反应生成了富含羧酸盐的转移膜,显著提高了复合材料耐磨性能;干燥氩气中,水氧的缺失使复合材料无法在摩擦中生成富含羧酸盐的转移膜,影响材料耐磨性能的进一步提高.      

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.     

Theory of necking localization in unconstrained electromagnetic expansion of thin sheets

Certain sheet metal alloys of industrial interest show a significant increase in ductility, over conventional forming methods, when high speed electromagnetic processes are used. The present work models the necking localization of a metal sheet during an electromagnetic process and examines the factors that influence this process. A Marciniak–Kuczynski “weak band” model is used to predict the onset of necking of a thin sheet under plane stress, an idealization of the local conditions in a thin sheet subjected to unconstrained electromagnetic loading. It is found that electromagnetic forming (EMF) increases ductility over quasistatic techniques due to the material’s strain-rate sensitivity, with ductility increasing monotonically with applied strain rates. The electric current also increases onset of necking strains, but the details depend on thermal sensitivity and temperature-dependence of the strain-rate sensitivity exponent. Given the insensitivity of the results to actual strain profiles, this local type analysis provides a useful tool that can be used for ductility predictions involving EMF processes.     

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.     

Stress and Moisture Effects on Thin Film Buckling Delamination

Deposition processes control the properties of thin films; they can also introduce high residual stresses, which can be relieved by delamination and fracture. Tungsten films with high 1–2 GPa compressive residual stresses were sputter deposited on top of thin (below 100 nm) copper and diamond-like carbon (DLC) films. Highly stressed films store large amounts of strain energy. When the strain energy release rate exceeds the films' interfacial toughness, delamination occurs. Compressive residual stresses cause film buckling and debonding, forming open channels. Profiles of the buckling delaminations were used to calculate the films' interfacial toughness and then were compared to the adhesion results obtained from the superlayer indentation test. Tests were conducted in both dry and wet environments and a significant drop in film adhesion, up to 100 times was noticed due to the presence of moisture at the film/substrate interface.     

Analytical and numerical analysis of sheet metal instability using a stress based criterion

Strain based Keeler–Goodwin diagrams are widely used in forming processes to predict onset of local necking. Plastic instability is determined once the forming limit strain is exceeded. Use of these diagrams requires proportional strain paths, which is not necessarily the case in sheet metal forming operations. In many forming processes, the strain path changes during deformation. This may change the forming limit curve significantly. In the paper, a stress based forming limit criterion is adopted to deal with strain path non-linearities. Comparisons with earlier published work on forming limits are made through analytical considerations. Furthermore, the criterion is implemented into the finite element code LS-DYNA and verified numerically against results from large scale bulge tests.     

Forming limit diagram prediction of tailor welded blank by modified M–K model

The Marciniak and Kuczynski (M–K) model for necking prediction in sheet metal forming was based on the in-plane forming. Bending which was resulted from out-of-plane forming was not considered in the M–K model. Whereas most of the sheet metal forming processes and also standard test of hemispherical punch for forming limit diagram are out-of-plane forming, it is important to consider bending effect in the M–K model. Therefore, in this study bending strain is added to stretching strain of M–K model and a new model is presented for forming limit diagram (FLD) prediction. This modified M–K (MM–K) model is written in the python programming language and it is used as a post-processing criterion for FLD prediction in the commercial software Abaqus. The MM–K model was used to predict FLD and weld line movement in the tailor welded blank forming. It was found that the predicted results by MM–K model are in a good agreement with experimental data.     

Computational analysis of stress-based forming limit curves

This article, through computational analyses, examines the validity of using the stress-based and extended stress-based forming limit curves to predict the onset of necking during proportional loading of sheet metal. To this end, a model material consisting of a homogeneous zone and a zone that has voids (material inhomogeneity) is proposed and used to simulate necking under plane strain and uni-axial stress load paths. Results of the in-plane loading computations are used to construct a strain-based formability limit curve for the model material. This limit curve is transformed into principal stress space using the procedure due to Stoughton [Stoughton, T.B., 2000. A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 42, 1–27]. The stress-based limit curve is then transformed into equivalent stress and mean stress space to obtain an Extended Stress-Based Limit Curve (XSFLC). When subjected to three-dimensional loading, the model material is observed to display a variety of responses. From these responses, a criterion for the applicability of the XSFLC to predict the onset of necking in the model material when it is subjected to three-dimensional loading is obtained. In the context of straight tube hydroforming, to provide support for the use of the XSFLC, it is demonstrated that the criterion is satisfied.     

聚合物/金属摩擦界面迁移过程的数值模拟

聚合物材料在与金属对偶件滑动接触时,会在摩擦界面上发生界面迁移,导致在金属对偶件表面形成一层转移膜.转移膜的存在能够有效地降低聚合物材料的磨损.本文基于离散单元法,利用二维颗粒流程序(PFC2D),对PTFE/45钢界面迁移过程进行数值模拟分析.模拟结果表明:PTFE与45钢组成摩擦副时,会在45钢表面形成一层转移颗粒层.一开始转移颗粒数逐渐增大,一段时间后随着转移颗粒层的形成与完整,转移颗粒数趋于一个定值且保持动态平衡,磨损颗粒增加速率显著下降,并维持在一个稳定的值.     

Nonisothermal analysis of extrusion film casting process using molecular constitutive equations

Extrusion film casting (EFC) is a commercially important process that is used to produce several thousand tons of polymer films and coatings. In a recent work, we demonstrated the influence of polymer chain architecture on the extent of necking in an isothermal film casting operation (Pol et al., J Rheol 57:559–583, 2013). In the present research, we have explored experimentally and theoretically the effects of long-chain branching on the extent of necking during nonisothermal film casting conditions. Polyethylenes of linear and long-chain branched architectures were used for experimental studies. The EFC process was analyzed using the 1-D flow model of Silagy et al. (Polym Eng Sci 36:2614–2625, 1996) in which the energy equation was introduced to model nonisothermal effects, and two multimode constitutive equations, namely the “extended pom-pom” (XPP, for long-chain branched polymer melts) equation and the “Rolie-Poly stretch version” (RP-S, for linear polymer melts) equation, were incorporated to account for the effects of polymer chain architecture. We show that the model does a better job of capturing the qualitative features of the experimental data, thereby elucidating the role of chain architecture and nonisothermal conditions on the extent of necking.     

Marciniak–Kuczynski type modelling of the effect of Through-Thickness Shear on the forming limits of sheet metal

The Marciniak–Kuczynski (MK) forming limit model is extended in order to predict localized necking in sheet metal forming operations in which Through-Thickness Shear (TTS), also known as out-of-plane shear, occurs. An example of such a forming operation is Single Point Incremental Forming. The Forming Limit Diagram (FLD) of a purely plastic, isotropic hardening material with von Mises yield locus is discussed, for monotonic deformation paths that include TTS. If TTS is present in the plane containing the critical groove direction in the MK model, it is seen that formability is increased for all in-plane strain modes, except equibiaxial stretching. The increase in formability due to TTS is explained through a detailed study of some selected deformation modes. The underlying mechanism is a change of the stress mode in the groove that results in a delay of the onset of localized necking.     

Analysis of sheet metal formability through isotropic and kinematic hardening models

The present paper aims at analysing the sheet metal formability through several isotropic and kinematic hardening models. Specifically, a special attention is paid to the physically-based hardening model of Teodosiu and Hu (1995), which accounts for the anisotropic work-hardening induced by the microstructural evolution at large strains, as well as to some more conventional hardening models, including the isotropic Swift strain-hardening power law, and the Voce saturation strain-hardening law, combined with a non-linear kinematic hardening described by the Armstrong–Frederick law. The onset of localized necking is simulated by an advanced sheet metal forming limit model which connects, through the Marciniak–Kuczinsky analysis, the hardening models with the anisotropic yield criterion Yld2000-2d (Barlat et al., 2003). Both linear and complex strain paths are taken into account. The selected material is a DC06 steel sheet. The validity of each model is assessed by comparing the predicted forming limits with experimental results carefully obtained on this steel. The origin of discrepancy in the predicted results using different hardening models is thoroughly analyzed.     

An extended Marciniak-Kuczynski model for anisotropic sheet subjected to monotonic strain paths with through-thickness shear

Some metal sheet forming processes may induce an amount of plastic shear over the sheet thickness. This paper investigates how formability of anisotropic sheet metal is affected by such through-thickness shear (TTS). The Marciniak-Kuczynski (MK) model framework, a commonly used analytical tool to predict the limit of sheet formability due to the onset of localized necking, is extended in this paper in order to explicitly account for TTS in anisotropic metal sheets. It is a continuation of previous work by the present authors (Eyckens et al., 2009), in which TTS is incorporated for isotropic sheet. This is achieved by the introduction of additional force equilibrium and geometric compatibility equations that govern the connection between matrix and groove in the MK model. Furthermore, in order to integrate plastic anisotropy, a material reference frame available in recent literature is incorporated, as well as a particular model for anisotropic yielding that relies on virtual testing of anisotropic properties (Facet plastic potential), since out-of-plane anisotropy related to TTS cannot be measured experimentally.It is found that formability may be increased by TTS, depending on the direction onto which it is imposed by the forming process. TTS is thus a relevant aspect of the formability in, for instance, sheet forming processes in which sliding contact with friction between sheets and forming tools occur.     

干摩擦条件下Al18B4O33晶须增强AC4C铝基复合材料的摩擦磨损特性

利用环－块磨损试验机,在干摩擦条件下研究了铸态与Ｔ６处理态Ａｌ１８Ｂ４Ｏ３３晶须增强ＡＣ４Ｃ铝基复合材料的摩擦磨损行为。结果表明：与铸态复合材料相经,Ｔ６处理态复合材料的耐磨性较差;晶须与基体间的界面化学反应影响复合材料的摩擦磨损特性,在本文试验载荷范围内,复合材料发生了由轻度磨损向严重磨损的转化;在高载荷下,除 了产生擦伤和粘着,在表层和次表层发生的应变硬化还会导致界面开裂、晶须断裂和分离;在低     

塑料SHPB实验中的端面摩擦效应

基于H.Meng的动摩擦实验结果,建立了一个端面动摩擦模型,以描述端面动摩擦因数随SHPB 塑料试样与钢压杆接触界面间最大径向相对滑动速度的关系。在SHPB实验的数值模拟中,分别考虑了该 端面动摩擦模型和以往被广泛采用的常摩擦因数模型,结果发现,选取不同的端面摩擦模型不影响通过塑料 SHPB实验的数值模拟获得的转折应变率(量级为102s-1),然而当应变率超出转折应变率以上时,不同的端 面摩擦模型会对塑料SHPB实验的数值模拟结果产生显著影响,使用提出的端面动摩擦模型可得到更准确 的塑料SHPB实验的数值模拟结果。     

Dynamic rupture of polymer–metal bilayer plates

Recent theoretical assessments of metal/polymer bilayers indicate a potentially significant delay in the onset of ductile failure modes, especially under dynamic loading, due to strain hardening of the polymer. The response of copper/polyurethane bilayers under dynamic and quasi-static loadings is investigated via static tensile, static bulge forming and dynamic bulge forming tests. Two polyurethanes PU1 and PU2 were chosen with a significant contrast in stiffness and ductility: PU1 has a glass transition temperature T_g close to ?56 °C and at room temperature it has a low modulus, low strength and a high tensile failure strain. In contrast, PU2 has a T_g of 49 °C and at room temperature it has a high modulus and strength but a much smaller tensile failure strain. In most of the tests, the polymer coatings were approximately twice the thickness of the metal layer. Under static loadings (tensile and bulge forming) the PU2 bilayer outperformed the uncoated metal plate of equal mass while the PU1 bilayer had a performance inferior to the equivalent uncoated plate. We attribute this to the fact that the PU2 retards the necking of the copper layer and thus increases its energy absorption capacity while the PU1 coating provides no such synergistic effect. The dynamic bulge forming tests indicate that on an equal mass basis, the dynamic performance of the PU2 bilayers with a weakly bonded polymer coating were comparable to the uncoated plates but intriguingly, when the PU2 was strongly adhered to the copper plates the performance of these bilayers was inferior to that of the uncoated plates. Thus, the coatings do not provide dynamic performance benefits on an equal mass basis. However, it is shown that increasing the mass of a plate by adding a polyurethane layer can improve the performance for a given total blast impulse. Given the ease of applying polyurethane coatings they may provide a practical solution to enhancing the blast resistance of existing metallic structures.     

Droplet retraction in the presence of nanoparticles with different surface modifications

We studied the influence of nanoparticles with different surface modifications on the interfacial tension and relaxation of model polymer blend after cessation of different strains. The droplet retraction experiments were carried out on a model system composed of polydimethylsiloxane (PDMS) as the suspending fluid and polyisobutylene (PIB) as droplet at room temperature in the presence of hydrophobic and hydrophilic nanosilica. Different weight fractions of particles were dispersed in the PIB droplet before forming a dispersed droplet by using a microsyringe in shear cell. We found that applied strain, nanoparticle concentration and their thermodynamically preferred localization affect both nominal interfacial tension and droplet retraction process. By addition of nanoparticles at a concentration as low as 0.2%wt, the nominal interfacial tension decreases from 3.12?±?0.15 mN/m for neat PIB-PDMS interface depending on the surface characteristics of nanosilica. Hydrophilic nanosilica has the most effect on nominal interfacial tension and decreases it as low as 0.2?±?0.21 mN/m at 1 wt.% loading under a strain of 7. The results show that the retraction process in this system is mainly controlled by interfacial phenomena rather than bulk rheological properties. Additionally, the shape evolution of droplets changes and the retraction rate slows down in the presence of nanoparticles.