Contact mechanics for layered materials with randomly rough surfaces

The contact mechanics model of Persson is applied to layered materials. We calculate the M function, which relates the surface stress to the surface displacement, for a layered material, where the top layer (thickness d) has different elastic properties than the semi-infinite solid below. Numerical results for the contact area as a function of the magnification are presented for several cases. As an application, we calculate the fluid leak rate for laminated rubber seals.     

Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties

In this paper we extend the theory of contact mechanics and rubber friction developed by one of us (B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)) to the case of surfaces with anisotropic surface roughness. As an application we calculate the viscoelastic contribution to the rubber friction. We show that the friction coefficient may depend significantly on the sliding direction, while the area of contact depends weakly on the sliding direction. We have carried out experiments for rubber blocks sliding on unidirectionally polished steel surfaces. The experimental data are in a good qualitative agreement with the theory.     

Elastic contact mechanics: Percolation of the contact area and fluid squeeze-out

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.     

Rubber friction: Comparison of theory with experiment

We have measured the friction force acting on a rubber block slid on a concrete surface. We used both unfilled and filled (with carbon black) styrene butadiene (SB) rubber and have varied the temperature from −10 °C to 100 °C and the sliding velocity from 1 μm/s to 1000 μm/s. We find that the experimental data at different temperatures can be shifted into a smooth master-curve, using the temperature-frequency shifting factors obtained from measurements of the bulk viscoelastic modulus. The experimental data has been analyzed using a theory which takes into account the contributions to the friction from both the substrate asperity-induced viscoelastic deformations of the rubber, and from shearing the area of real contact. For filled SB rubber the frictional shear stress σ_f in the area of real contact results mainly from the energy dissipation at the opening crack on the exit side of the rubber-asperity contact regions. For unfilled rubber we instead attribute σ_f to shearing of a thin rubber smear film, which is deposited on the concrete surface during run in. We observe very different rubber wear processes for filled and unfilled SB rubber, which is consistent with the different frictional processes. Thus, the wear of filled SB rubber results in micrometer-sized rubber particles which accumulate as dry dust, which is easily removed by blowing air on the concrete surface. This wear process seams to occur at a steady rate. For unfilled rubber a smear film forms on the concrete surface, which cannot be removed even using a high-pressure air stream. In this case the wear rate appears to slow down after some run in time period.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

用于测量ICF靶丸内氚活度的电离室的设计

设计了一种可测量ICF靶内氚含量的圆柱电离室。密封部件的设计抛弃了传统的橡胶密封而采用全金属密封, 以消除橡胶、 塑料对氚的强吸附性产生的电离室污染。为防止氚扩散污染电离室的内壁, 内壁镀上一层2 μm的Au膜。在中心电极和外电极间引入保护电极以降低低水平放射性测量时的电极漏电流。保护电极和中心电极间的绝缘材料, 以及保护电极和外电极间的绝缘材料分别选择绝缘性好、 耐高温的蓝宝石和Al2O3陶瓷。另外, 基于对ICF靶参数测量的特殊要求, 在电离室中设计了一个压碎靶丸释放氚的装置。最后, 通过物理建模和复合损失计算, 得到了优化的电离室参数。A cylindrical ionization chamber was designed for the measurement of the tritium at the level enclosed in inertial confinement fusion(ICF) targets. In stead of the conventional rubber seals, the metallic seals was adopted to reduce the chamber contamination caused by the strong tritium absorption of rubber and plastics. A 2 μm thick Au layer was plated on the inner wall of the chamber to avoid the contamination due to tritium diffusion in the chamber. The protective electrode was introduced to reduce the leakage current when measuring the low level radioactivity. Sapphire was employed as an insulator between the protective electrode and central electrode, while Al2O3 ceramic was used in between the protective electrode and the external electrode. In addition, to meet the specific requirements on the measurement of ICF targets’ parameters, a component used to crash the target to release tritium was designed in the chamber. Finally, the optimal chamber parameters were obtained in terms of physics modeling and combination loss computation.     

Molecular dynamics study of contact mechanics: contact area and interfacial separation from small to full contact

We report a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. We study the contact area and the interfacial separation from small contact (low load) to full contact (high load). For small load the contact area varies linearly with the load and the interfacial separation depends logarithmically on the load. For high load the contact area approaches the nominal contact area (i.e., complete contact), and the interfacial separation approaches zero. The present results may be very important for soft solids, e.g., rubber, or for very smooth surfaces, where complete contact can be reached at moderate high loads without plastic deformation of the solids.     

Slip dynamics at a patterned rubber/glass interface during stick-slip motions

We report on an experimental study of heterogeneous slip instabilities generated during stick-slip motions at a contact interface between a smooth rubber substrate and a patterned glass lens. Using a sol-gel process, the glass lens is patterned with a lattice of parallel ridges (wavelength, 1.6 μm, amplitude 0.35 μm). Friction experiments using this patterned surface result in the systematic occurrence of stick-slip motions over three orders of magnitude in the imposed driving velocity while stable friction is achieved with a smooth surface. Using a contact imaging method, real-time displacement fields are measured at the surface of the rubber substrate. Stick-slip motions are found to involve the localized propagation of transverse interface shear cracks whose velocity is observed to be remarkably independent on the driving velocity.     

玻璃-橡胶混合颗粒体系的弹性行为研究

废旧橡胶制品颗粒与砂土颗粒混合物作为建筑填充材料具有环保、轻质、减震效果好等特点.软硬组分的混合比例可以调制体系力学性能从而实现兼顾材料柔韧性与强度的需求,但细观层面上材料性能改变的原因尚不明确.本文主要研究玻璃-橡胶混合颗粒体系的弹性行为及其微观机制.利用飞行时间法测量混合材料等效动弹性模量,发现随着橡胶颗粒增加,体系逐渐从类玻璃刚性行为转变为类橡胶柔性行为.离散元模拟结果与实验结果类似.此外,模拟显示低橡胶颗粒占比样品内主要由玻璃颗粒构成主力链结构,而橡胶颗粒基本不参与强力链的构成.当橡胶颗粒占比较大时,玻璃颗粒和橡胶颗粒共同构成主力链网络结构,但颗粒间法向接触力分布相对更为均匀,可视为玻璃颗粒悬浮于橡胶颗粒中.基于上述结果,提出了改进的等效介质理论,用于描述混合颗粒体系的弹性行为.研究认为:橡胶颗粒占比较小时内部颗粒的变形相对均匀,材料近似满足等应变假设,视为并联弹簧模型;橡胶颗粒占比较大时混合材料近似满足等应力假设,视为串联弹簧模型.两种模型得到的结果与模拟结果一致.上述结果有利于从微观角度揭示混合颗粒材料弹性行为的变化机制.     

Analysis of the Wrinkle of an Automobile Weather-Strip Seal in Bending

Weather-strip seals in automotive door systems play a major role in determining the door closing effort, isolating the passenger compartment from water and reducing the wind noise inside the vehicle. The phenomenon of a wrinkle often occurs in weather-strips when they are assembled on the door surfaces which have bent or twisted profiles. Wrinkles in automobile weather-strip seals will affect the closing effort and noise isolation characteristics of the automotive door system. The wrinkle of anethylene-propylene-diene (EPDM) automobile weather-strip seals when bent and the critical conditions for a wrinkle to develop were characterized in this study. The hyperelastic material behavior of the EPDM sponge and EPDM dense rubber in the seal were modeled using the Foam model and Mooney–Rivlin model, respectively. Then a finite element analysis (FEA) model of the automobile weather-strip seal in assembly was developed and analyzed using then on linear FEA software Marc. The deformation of the seal and the thickness decrease in the critical region where it was prone to wrinkle were obtained by this FEA method. Finally the critical criterion of wrinkling was determined by analysis of the reaction forces in the critical region. The proposed analysis method can shorten the product design cycle and decrease the design and trial-product cost considerably.     

接触式机械密封流固耦合模型及性能分析

为研究不同密封压力下接触式机械密封的密封性能,考虑密封端面的压力变形和表而微凸体接触,建立了密封端面的流同力耦合模型,给出了数值求解方法.通过实例分析了密封压力对御封关键性能指标的影响.该模型分析结果表明;随着密封压力的增大,端面间液膜厚度,泄漏率明显增加,密封压力对液膜压力、接触压力的分布影响较大.该模型能较好地用于接触式机械密封流田耦合问题的分析和密封的优化设计.     

Identifying the viscoelastic properties of soft matter from the indentation response of a hard film-soft substrate system

The indentation technique is widely used in measuring the mechanical properties of soft matter at the microscale or nanoscale,but still faces challenges by these unique properties as well as the consequent strong surface adhesion, including the strong nonlinear effect, unclear judgment of the contact point, difficulties in estimating the contact area, and the risk of the indenter piercing the sample. Here we propose a two-step method to solve these problems: lay a hard film on a soft matter, and obtain the viscoelastic properties of this soft matter through the indentation response of this composite structure. We first establish a theoretical indentation model of the hard film-soft substrate system based on the theory of plates, elastic-viscoelastic correspondence principle and Boltzmann superposition principle. To verify the correctness of this method, we measure the mechanical properties of the methyl vinyl silicone rubber(MVSR) covered by a Cu nanofilm. Finally, we test the effectiveness and error sensitivity of this method with the finite element method(FEM). The results show that our method can accurately measure the mechanical properties of soft matter, while effectively circumventing the problems of the traditional indentation technique.     

Buckling instability in liquid crystalline physical gels

In a nematic gel we observe a low-energy buckling deformation arising from soft and semisoft elastic modes. We prepare the self-assembled gel by dissolving a coil-side-group liquid-crystalline polymer-coil copolymer in a nematic liquid crystal. The gel has long network strands and a precisely tailored structure, making it ideal for studying nematic rubber elasticity. Under polarized optical microscopy we observe a striped texture that forms when gels uniformly aligned at 35 degrees C are cooled to room temperature. We model the instability using the molecular theory of nematic rubber elasticity, and the theory correctly captures the change in pitch length with sample thickness and polymer concentration. This buckling instability is a clear example of a low-energy deformation that arises in materials where polymer network strains are coupled to the director orientation.     

Investigation of Carbon Black Network in Natural Rubber with Different Bound Rubber Contents

A new method was applied to modify the surface activity of virginal carbon black (VCB). LA‐57, one kind of hindered amine light stabilizer, was adsorbed onto the carbon black surface through a strong shear force induced by the screws of a HAAKE internal mixer. The modified carbon black (MCB) was characterized by FT‐IR and thermogravimetric analysis (TGA). The bound rubber content of the natural rubber (NR) compounded with MCB and VCB varied with the fraction of LA‐57 on the MCB surface. The nonlinear effect at small strains, generally referred as the Payne effect, was investigated in the rubber compounds based on the different bound rubber contents. The NR compound containing the lowest bound rubber content had an obvious Payne effect. Based on the bound rubber content, the types of filler network varied from direct contact mode to the joint rubber shell mechanism.     

A three-level non-deterministic modeling methodology for the NVH behavior of rubber connections

Complex built-up structures such as vehicles have a variety of joint types, such as spot-welds, bolted joints, rubber joints, etc. Rubber joints highly contribute to the nonlinear level of the structure and are a major source of uncertainties and variability. In the general framework of developing engineering tools for virtual prototyping and product refinement, the modeling of the NVH behavior of rubber joints involve the computational burden of including a detailed nonlinear model of the joint and the uncertainties and variability typical of that joint in a full-scale system model. However, in an engineering design phase the knowledge on the joint rubber material properties is typically poor, and the working conditions a rubber joint will experience are generally not known in detail. This lack of knowledge often do not justify the computational burden and the modeling effort of including detailed nonlinear models of the joint in a full-scale system model.Driven by these issues a non-deterministic numerical methodology based on a three-level modeling approach is being developed. The methodology aims at evaluating directly in the frequency domain the sensitivity of the NVH behavior of a full-scale system model to the rubber joint material properties when nonlinear visco-elastic rubber material behavior is considered. Rather than including directly in the model a representation of the rubber nonlinear visco-elastic behavior, the methodology proposes to model the material nonlinear visco-elastic behavior by using a linear visco-elastic material model defined in an interval sense, from which the scatter on the full-scale system NVH response is evaluated. Furthermore the development of a multi-level solution scheme allows to reduce the computational burden introduced by the non-deterministic approach by allowing the definition of an equivalent linear interval parametric rubber joint model, ready to be assembled in a full-scale system model at a reasonable computational cost.By using a commercial finite element code the developed methodology is illustrated through a numerical case-study: the low-frequency dynamic analysis of automotive door weather-strip seals.     

Local friction at a sliding interface between an elastomer and a rigid spherical probe

This paper reports on spatially resolved measurements of the shear stress distribution at a frictional interface between a flat rubber substrate and a glass lens. Silicone rubber specimens marked close to their surface by a colored pattern have been prepared in order to measure the surface displacement field induced by the steady-state friction of the spherical probe. The deconvolution of this displacement field then provides the actual shear stress distribution at the contact interface. When a smooth glass lens is used, a nearly constant shear stress is achieved within the contact. On the other hand, a bell-shaped shear stress distribution is obtained with rough lenses. These first results suggest that simple notions of real contact area and constant interface shear stress cannot account for the observed changes in local friction when roughness is varied.     

Implicit Versus Explicit Renormalization of the NN Force: An S-Wave Toy Model

We use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalization through a flow equation which integrates out the high momentum components. By fitting the low-momentum interaction with a new contact theory, we show that the running of the contact strengths in both original and fitted contact theories match over a wide cutoff range.     

交错式迷宫密封的动力特性分析

本文针对交错式迷宫密封的结构特点,提出了一种全新的多控制体模型,从流体力学的基本方程出发,建立起一组描述气体流动的偏微分方程,并将其在静态解基础上线性化,从而导出了这种密封的动力特性计算公式,该方法具有简单、方便、实用的特点。计算结果与国外文献所给出的实验结果基本吻合。     

Acoustic field evaluation of asphalt mixtures with crumb rubber

The aim of this study is to characterize the acoustical behavior of bituminous mixtures fabricated with recycled rubber crumb. Acoustic field measurements of the tire/pavement interaction in close proximity to the contact patch were carried out with a trailer with a protective chamber (TiresonicMk4-LA²IC). The survey was conducted on a test track with several experimental sections paved with a gap-graded mixture. Different methods of incorporating crumb rubber in the mixture were used: (i) into binder and (ii) with the aggregate materials. Close proximity sound levels are assigned to the gap-graded mixtures containing rubber and compared to that of a reference mixture without rubber. It is shown that asphalt mixtures fabricated with the addition of crumb rubber to the aggregate material (dry process) managed to reduce the noise from the tire/pavement interaction up to 2 dB(A).