连接结构接触界面非线性力学建模研究

连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因.由于连接界面的力学行为的复杂性,以及难以对连接界面进行直接试验观测,连接界面的力学建模一直是非常具有挑战性的科学问题.本文首先从分析结合面的跨尺度物理机理入手,将名义的光滑平面视作凹凸不平的粗糙面,考虑单个微凸体的黏滑摩擦行为,建立接触载荷与变形的非线性关系,然后采用GW(Greenwood and Williamson)模型数理统计方法建立整个粗糙界面的跨尺度力学模型,并与公开文献中试验结果进行对比.考虑连接界面具有典型非线性特征,提出一种改进的Iwan唯象模型,利用精细有限元方法获得非线性特征结果,采用系统辨识理论建立连接结构的降阶力学模型,并利用有限元结果进行模型验证.结果表明,本文提出的粗糙界面跨尺度模型在法向载荷较小时与试验结果吻合较好,改进的Iwan模型能够较好描述连接界面的非线性特征,并与有限元结果吻合较好.     

弹性波在螺栓搭接结构中传播行为的数值模拟

为了建立有效的基于弹性波的螺栓连接损伤检测方法,研究弹性波在连接结构中的传播行为至关重要。本文针对典型单螺栓搭接薄梁,采用非线性多物理场耦合有限元仿真方法,研究弹性波在连接结构中的传播行为。采用ANSYS中压电耦合单元建模MFC压电传感器,非线性接触单元建模螺栓连接结构,将接触面之间考虑为考虑摩擦接触的非线性关系。依次对螺栓施加预紧载荷,对结构施加模拟电压激励,进行非线性瞬态波传播分析。同时,本文对仿真结果进行了实验验证。结果表明,本文建立的有限元模型和分析方法能够有效地模拟弹性波在连接结构中的传播过程,数值预测的响应电压和实验结果吻合较好。针对非线性模型计算耗费大的问题,本文对非线性模型进行了线性化改进。具体为采用准静态接触有限元分析确定对接面有效接触面积的大小,然后将接触面积上对应节点绑定,进行线性瞬态波传播分析。结果表明:本文的线性方法能够有效模拟波传播过程,并能有效降低计算耗费;弹性波在连接梁中传播时,经过连接界面和螺栓位置时,传播路径、波形、幅值都发生了较大的变化。     

螺栓连接大变形梁振动特性的实验与数值研究

螺栓连接的柔性梁既有非线性又有几何非线性,本文针对其动力学建模和振动特性开展了实验与数值研究。首先,搭建了含螺栓连接的柔性大变形梁的实验台架,并开展敲击和正弦激振的实验测试。实验结果表明:螺栓连接的柔性梁较(无螺栓连接的)连续梁的模态频率降低,阻尼增加,呈现出随着激励能量增大,模态频率降低的非线性模态特征。其次,为了建立大变形柔性梁的有效计算模型,采用了动坐标迭代法,并采用改进Iwan模型和库仑摩擦模型刻画连接部件的力学特性。最后,开展了数值计算,通过与实验测试结果对比表明:数值计算结果与实验测试结果误差在7%以内,所建立的柔性连接梁的计算模型能够有效准确地模拟含连接部件柔性梁的非线性模态和动力学响应特征。     

考虑弹塑性变形阶段的干气密封接触模型

为探究干气密封摩擦界面在变形全阶段的接触特性,基于分形接触理论及微观接触力学理论,充分考虑微凸体变形的3个阶段,通过余弦函数构建干气密封全阶段接触模型,并分别与GW模型、KE模型和ZMC模型三种经典接触模型及相关文献的试验数据作对比,验证本文中接触模型的合理性与正确性. 最后对干气密封摩擦界面接触特性的主要影响因素进行探究. 模型研究结果表明:干气密封摩擦界面的接触特性与分形维数、特征尺度及两表面的真实接触面积有关. 接触特性与分形维数和两表面真实接触面积呈正相关,与特征尺度呈负相关. 分形维数越大,接触载荷与接触刚度的数量级就越大,且接触载荷变化范围相对较大. 当特征尺度每次以1个数量级递增时,接触载荷与接触刚度的变化范围较小,都在1个数量级内.      

缝合式C/SiC复合材料非线性本构关系及断裂行为研究

C/SiC复合材料具有高比强度、高比模量和优良的热稳定性能等一系列优点, 广泛应用于航空航天领域中. 裂纹扩展进而引起的脆性断裂是其主要失效形式之一, 因而材料的断裂性能分析对材料的结构设计和应用有重要的指导意义. 本文开展了缝合式C/SiC复合材料简单力学试验和断裂试验, 研究了材料在不同载荷下的力学响应及断裂特征. 基于缝合式C/SiC复合材料简单力学试验, 建立了材料宏观非线性损伤本构方程, 并模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 本构方程采用简单函数描述了材料在复杂应力状态下的非线性应力-应变曲线, 并考虑了反向加载过程中造成的裂纹闭合. 基于商业有限元软件ABAQUS, 通过编写UMAT子程序实现非线性损伤本构方程, 采用单个单元验证了建立的本构方程的有效性. 在此基础上, 采用线弹性损伤本构和非线性损伤本构分别模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 采用非线性损伤本构方程模拟的力-位移曲线结果与试验结果更为吻合, 非线性损伤本构预测的失效载荷与试验失效载荷更为接近, 验证了所建立的非线性损伤本构方程的准确性, 为C/SiC复合材料断裂行为的研究提供了借鉴, 为缝合式C/SiC复合材料结构的设计和应用提供了理论基础.      

基于微凸体接触压力分布的粗糙表面法向接触建模

提出一种考虑微凸体弹塑性接触变形影响的粗糙表面法向接触力学模型。采用有限元模拟微凸体弹塑性接触过程,分析不同塑性屈服条件对微凸体接触载荷和实际接触面积的影响。再根据微凸体接触面上压力分布的变化规律,将微凸体的接触状态分为完全弹性接触阶段、弹塑性接触阶段、完全塑性接触阶段。分析接触面压力变化规律对微凸体法向接触载荷-变形的影响,再利用GW模型的数理统计分析的方法得到粗糙表面的法向接触载荷。将本文提出的模型与完全弹性模型、CEB模型、ZMC模型、KE模型、JG模型进行对比,并且研究了塑性指数对粗糙面接触载荷-平均高度距离的影响。结果表明,本文提出的模型能够更好地描述微凸体法向接触载荷与接触变形的变化趋势,模型预测粗糙表面法向载荷与ZMC、KE模型具有较好的一致性;粗糙面接触载荷随着平均接触距离增加而减少,随着塑性指数的增加,不同模型预测的法向接触载荷差异逐渐增大。     

平面编织混杂铺层层合板单钉连接拉伸性能

对平面编织混杂铺层层合板单钉连接结构的挤压性能进行试验研究,分析了铺层比例和试件尺寸对其挤压强度和破坏形式的影响.基于ANSYS平台建立了该层合板单钉连接结构的三维损伤累积有限元模型,对其非线性挤压破坏行为进行了数值计算,预测了初始挤压破坏载荷;同时提出并验证了适合该类型层合板的损伤判据和衰减准则.计算得出的初始挤压破坏载荷与试验结果吻合良好,说明该模型能准确预测层合板单钉连接的初始挤压破坏载荷.     

STUDY ON NONLINEAR CONSTITUTIVE RELATIONSHIP AND FRACTURE BEHAVIOR OF STITCHED C/SiC COMPOSITES$^{\bf 1)}$

C/SiC复合材料具有高比强度、高比模量和优良的热稳定性能等一系列优点, 广泛应用于航空航天领域中. 裂纹扩展进而引起的脆性断裂是其主要失效形式之一, 因而材料的断裂性能分析对材料的结构设计和应用有重要的指导意义. 本文开展了缝合式C/SiC复合材料简单力学试验和断裂试验, 研究了材料在不同载荷下的力学响应及断裂特征. 基于缝合式C/SiC复合材料简单力学试验, 建立了材料宏观非线性损伤本构方程, 并模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 本构方程采用简单函数描述了材料在复杂应力状态下的非线性应力-应变曲线, 并考虑了反向加载过程中造成的裂纹闭合. 基于商业有限元软件ABAQUS, 通过编写UMAT子程序实现非线性损伤本构方程, 采用单个单元验证了建立的本构方程的有效性. 在此基础上, 采用线弹性损伤本构和非线性损伤本构分别模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 采用非线性损伤本构方程模拟的力-位移曲线结果与试验结果更为吻合, 非线性损伤本构预测的失效载荷与试验失效载荷更为接近, 验证了所建立的非线性损伤本构方程的准确性, 为C/SiC复合材料断裂行为的研究提供了借鉴, 为缝合式C/SiC复合材料结构的设计和应用提供了理论基础.     

考虑粗糙结合面弹塑性接触的黏滑摩擦建模

提出一种同时考虑粗糙面上微凸体弹性变形和塑性接触的切向黏滑摩擦建模方法。采用Hertz弹性理论和Mindlin解描述弹性接触微凸体的切向载荷和相对变形的关系;采用AF(Abbott-Firstone)塑性理论和Fujimoto模型描述塑性接触微凸体切向载荷和相对变形的关系。再利用GW(Greenwood-Williamson)模型统计分析方法建立粗糙表面切向载荷和相对变形之间的关系。将模型与仅考虑微凸体弹性接触情况的模型进行对比,并研究了不同塑性指数对切向载荷和相对变形关系的影响。结果表明：与完全弹性接触模型相比,本文模型引入了塑性接触理论,能够更好地描述粗糙表面切向载荷和相对变形关系,并且考虑不同接触条件下弹性变形微凸体和塑性变形微凸体对切向接触载荷的贡献,在微滑移阶段,主要由弹性接触变形影响,而在进入宏观滑移阶段之后,切向行为主要由塑性变形影响。界面切向载荷由黏着和滑移接触作用共同决定,随着切向变形的增加,滑移接触力逐渐增加,而黏着接触力先增加后减少,反映了界面由微滑移逐渐向宏滑移演化的过程。随着塑性指数的增加,粗糙面上发生塑性接触的微凸体数目逐渐增加,切向黏滑行为主要受到塑性接触特征的控制。     

2.5维自愈合C/SiC复合材料的压缩力学行为

试验研究了2.5维自愈合C/SiC复合材料的压缩力学行为,根据材料的细观结构特点,建立了压缩载荷下的损伤力学模型,得到了经纬向压缩的非线性应力应变关系,预测结果与试验值吻合较好。结果表明,经向和纬向的力学行为不同,纬向的压应力逐渐增大时,切线模量逐渐增大,压缩强度为270.05MPa,而经向压应力逐渐增大时,层间损伤逐渐发生,经纱承受的弯矩越来越大,切线模量逐渐降低,破坏强度为128.66MPa。     

On the Iwan models for lap-type bolted joints

The paper presents mathematical modeling of the non-linear constitutive relation for bolted joints in the framework of the Kragelsky-Demkin theory of rough contact. It is shown that this approach, which maintains the tribology-related features of bolted joint interfaces, leads to a singular Iwan distribution density. In particular, we show that the Iwan density is expressed in terms of the height distribution density of the surface asperities, whereas its singular exponent is determined by the shape exponent of the surface asperities. Following this, constitutive relations for lap joints and the corresponding backbone (force-deflection) curves are obtained. Finally, Masing's hypothesis is applied and Goodman's relation for energy dissipation is recovered in order to describe the effects of cyclic loading. The two cases of a rough surface in contact with a flat surface and of two contacting rough surfaces are treated separately.     

包含几何误差的机械结合面法向刚度研究

对包含几何误差的机械结合面进行离散化,离散后的微表面的基准平面高度满足结合面几何误差分布.每个微表面内,微凸体的高度只受粗糙度的影响.基于接触理论建立了微表面的法向刚度模型,通过对微表面模型集成获得了结合面的法向刚度模型.通过对所建模型的数值仿真,揭示了结合面法向刚度与间隙的非线性关系,几何误差的幅值和波长对法向刚度的影响以及非线性刚度对结合面振动特性的影响.计算结果表明:法向刚度随着间隙的减少而迅速增加,几何误差会导致结合面宏观上的局部接触和应力集中;在相同干涉量下,法向刚度随着几何误差幅值的增加而增加,但与结合面的波长没有关系;非线性刚度会导致结合面固有频率的下降和振动位移的不对称.     

单峰接触研究及其在分形表面接触中的应用

基于有限元方法,建立了弹塑性单峰的接触模型.粗糙峰为理想的弹塑性材料,为了考虑不同的材料特性对微凸体变形的影响,分别对9种不同的材料进行了分析.根据有限元计算结果,分析了接触面积,平均接触压力和接触力与变形干涉量之间的关系,并进行了经验公式的拟合.单峰接触所经历的4个不同的阶段,以及不同阶段之间的转化点均作了明确的表达.然后,根据分形理论,将单峰接触模型扩展到了三维的粗糙表面的接触,并提出了一个计算接触表面法向刚度的模型.通过与实验数据和以往模型的结果对比,证明本文中所提出的模型具有较高的精度.     

机械结合面切向接触阻尼计算模型

针对两粗糙表面在法向力和切向力共同作用下相互接触时结合面切向阻尼的问题进行了研究。首先,根据KE模型对单个微凸体在弹性、弹塑性、塑性变形阶段的切向接触行为进行了分析,获得了微凸体在三个变形阶段的黏滑特性;然后,基于GW统计模型建立了一种在微凸体法向弹性、弹塑性和塑性变形机制基础上,考虑微凸体黏滑摩擦行为的机械结合面切向接触阻尼统计模型;最后,分别讨论了机械结合面的法向预载荷、切向激振频率和切向动态位移幅值对机械结合面切向阻尼的影响。研究表明:结合面切向接触阻尼系数随着结合面法向载荷的增大而增大,随着切向激振频率和切向动态位移幅值的增大而减小;在高频率、大幅值下,结合面切向接触阻尼系数几乎与动态位移幅值和激振频率无关。为了验证模型的准确性,构建了动态切向力作用下的结合面切向阻尼试验,其试验结果与理论仿真变化规律与量级基本一致,从而证明了本文所提出的切向阻尼模型的有效性。      

Hysteretic linear and nonlinear acoustic responses from pressed interfaces

An analysis of the linear and nonlinear acoustic responses from an interface between rough surfaces in elastoplastic contact is presented as a model of the ultrasonic wave interactions with imperfect interfaces and closed cracks. A micromechanical elastoplastic contact model predicts the linear and second order interfacial stiffness from the topographic and mechanical properties of the contacting surfaces during a loading–unloading cycle. The effects of those surface properties on the linear and nonlinear reflection/transmission of elastic longitudinal waves are shown. The second order harmonic amplitudes of reflected/transmitted waves decrease by more than an order of magnitude during the transition from the elastic contact mode to the elastoplastic contact mode. It is observed that under specific loading histories the interface between smooth surfaces generates higher elastoplastic hysteresis in the interfacial stiffness and the acoustic nonlinearity than interfaces between rough surfaces. The results show that when plastic flow in the contacting asperities is significant, the acoustic nonlinearity is insensitive to the asperity peak distribution. A comparison with existing experimental data for the acoustic nonlinearity in the transmitted waves is also given with a discussion on its contact mechanical implication.     

A friction contact stiffness model of fractal geometry in forced response analysis of a shrouded blade

To investigate the nonlinear vibration behavior of a shrouded blade with friction dynamic contact interface, a friction contact stiffness model is proposed to describe the friction force at different rough interfaces and different normal loads. In the proposed model, the friction contact interface is discretized to a series of friction contact pairs and each of them can experience stick, slip, or separate states. Fractal geometry is used to simulate the topography of contact surfaces. The contact stiffness is calculated using the Hertz contact theory and fractal geometry, which is related to contact interfaces parameters including normal load, roughness, Young??s modulus, and Poisson??s ratio. The trajectory tracking method is used to predict the friction force and it is not necessary to judge the transition condition among stick, slip, and separate states. It is suitable for complicated periodic motion of the contact interfaces. The forced response of a real shrouded blade is predicted using the proposed model and the multi-harmonic balance method. The effect of surface roughness, initial normal load, and contact area on the forced response of a shrouded blade is studied. It is shown that contact stiffness increases with normal load and fractal dimension. The resonant amplitude is sensitive to the initial normal load and contact surface roughness. The response can be influenced by the contact area, which is an important parameter for blade designers.     

考虑接触应力非线性分布的接触力元模式及其验证分析

在作者提出的非连续变形计算力学模型中,采用接触力元模型描述多体接触界面上的接触特性．由于这种模型中假定接触应力沿接触界面为线性分布,从而得到的接触界面应力分布往往出现跳跃等非光滑性特征,该文对此进行了改进,采用具有高阶光滑性的非线性函数建立了能够考虑界面上接触应力非线性分布的接触力元模式,以期合理地揭示多体系统中界面的接触特性．对某一典型算例进行了数值计算,通过与大型通用非线性有限元结构分析软件ABASQUS的计算结果对比,验证了所建议计算模型的合理性与有效性．两种方法计算得到的界面接触对上的接触力基本相同;而由于采用的应力分布模式的假定不同,接触应力有所差别,由于在该文计算模型中接触对上的接触应力是按照未知量直接求得的,因此按照所建议的非线性接触力元模式所得到的接触应力更为合理．     

Nonlinear Parameter Identification of a Mechanical Interface Based on Primary Wave Scattering

We study stress-wave propagation in an impulsively forced split Hopkinson bar system incorporating a threaded interface. We first consider only primary transmission and reflection and reduce the problem to a first-order, strongly nonlinear ordinary differential equation governing the displacement across the interface, called the primary-pulse model. The interface is modeled as an adjusted-Iwan element, which is characterized by matching experimental and numerical eigenfrequencies as well as primary pulse amplitudes. We find that the adjusted-Iwan element parameters are dependent on preload and impact velocity (input force). A high-order finite element model paired with the identified adjusted-Iwan element is used to simulate multiple transmissions and reflections across the interface. We find that the finite element simulation reproduces the experimental results in both the wavelet and Fourier domains, validating the identification method. Our findings demonstrate that the primary-pulse model can be used for experimental parameter identification of nonlinear interfaces in waveguides.     

A methodology to model the complex morphology of rough interfaces

A methodology is proposed to model the complex morphology of rough interfaces using Fourier techniques and image analysis. It allows an optimal representation of a rough interface so as to enable a realistic calculation of the local stress and strain fields in the interface vicinity using finite element techniques. The methodology is illustrated through a sensitivity analysis carried out on a thermal barrier coating system. Typical bi-material interfaces with different levels of morphological complexity are described in 2D and 3D using both periodic (sinusoidal) and Fourier functions. The results are discussed in terms of their relative accuracy.     

Modeling interface shear behavior of granular materials using micro-polar continuum approach

Recently, the authors have focused on the shear behavior of interface between granular soil body and very rough surface of moving bounding structure. For this purpose, they have used finite element method and a micro-polar elasto-plastic continuum model. They have shown that the boundary conditions assumed along the interface have strong influences on the soil behavior. While in the previous studies, only very rough bounding interfaces have been taken into account, the present investigation focuses on the rough, medium rough and relatively smooth interfaces. In this regard, plane monotonic shearing of an infinite extended narrow granular soil layer is simulated under constant vertical pressure and free dilatancy. The soil layer is located between two parallel rigid boundaries of different surface roughness values. Particular attention is paid to the effect of surface roughness of top and bottom boundaries on the shear behavior of granular soil layer. It is shown that the interaction between roughness of bounding structure surface and the rotation resistance of bounding grains can be modeled in a reasonable manner through considered Cosserat boundary conditions. The influence of surface roughness is investigated on the soil shear strength mobilized along the interface as well as on the location and evolution of shear localization formed within the layer. The obtained numerical results have been qualitatively compared with experimental observations as well as DEM simulations, and acceptable agreement is shown.