两接触粗糙表面的椭圆弹塑性模型

视两单峰的接触区为椭圆,给出了两接触相糙表面的椭圆弹性通解.根据两单峰塑性接触时单个相糙峰的椭圆抛物面体积守恒推导了椭圆塑性通解.临界弹性干涉量随有效半径比增加而减小.塑性指数越小,临界弹性干涉量减小量越大.临界弹性干涉量随表面粗糙度增加、材料硬度减小而减小.椭圆、GW模型的临界弹性干涉量之比随有效半径比增加而减小.GW模型高估了临界弹性干涉量.椭圆、GW模型的塑性指数之比随有效半径比增加而增加.GW模型低估了塑性指数.有效半径比越大,偏差量越大.     

热障涂层平头压痕蠕变研究

研究典型热障涂层(thermal barrier coating,TBC)系统在圆柱形平头压痕下的蠕变响应。考虑刚性压头、弹性压头和弹性磨损压头作用下,压头压痕深度随时间的变化规律和压头前方的Mises应力分布,分析压头尺寸和外载荷变化对压痕深度和Mises应力分布的影响．可以得出结论,平头压痕下TBC系统的蠕变在较短时间内即达到稳态,压痕深度随外载荷和压头半径的增大而增大;在相同载荷和压头半径下,压痕深度的影响表现为弹性磨损心头大于弹性压头,弹性压头大于刚性压头;对于弹性磨损压头,在相同载荷和压头半径下,压痕深度随磨损圆角半径的增大而增大。     

基于残余应力应变关系的压痕法测试技术

根据压痕法测量原理,建立了有限元分析模型,构造了残余应力范围σres/σy为-0.7~+0.7,分析了在不同载荷下压痕位移量,压痕接触应力分布规律,建立了不同位置处残余应力应变标定关系,在测试中根据不同位置处所得的应变量,代入到相应的标定关系式,计算得出残余应力。研究结果表明:残余拉、压应力程度大,压痕等效应力值大,弹塑性边界c宽。残余压应力程度越大,抗变形能力大,变形量小,接触应力分布范围窄;反之成立。在一定条件下根据所标定的残余应力应变关系所计算得到残余应力,与预先设定应力其吻合程度较高,说明标定关系可行;但也存在一定的偏差,在L=3mm处最大偏差范围在1%~31%。因此,合理的测试位置和测试技术的进一步研究对于提高残余应力测试精度尤为重要。     

残余应力影响压痕尺寸和隆起量的研究

残余应力的存在直接影响材料的力学性能,在压痕法中影响其压痕形状大小、压入载荷-位移曲线和隆起量,因此通过比较压痕形状大小、压入载荷-位移曲线和隆起量的大小,可以推断出构件内部残余应力,再通过有限元研究不同程度的残余应力对压痕形状、压入载荷-位移曲线和隆起量的影响.研究结果表明, 残余压应力使压痕尺寸变小,残余拉应力使压痕尺寸变大,不同性质和大小分布的残余应力使压痕形状为椭圆形,压入载荷-位移曲线斜率和隆起量高度随着残余压应力的增加而增加,随着拉应力的减小而减小,当构件内部存在一定程度的残余拉应力时,随着压入载荷的继续增加出现负隆起量(沉降量),沉降量的大小与压入载荷的大小和残余拉应力的程度有关.     

残余应力对球形压入响应的影响研究

针对残余应力影响仪器化球形压入响应的问题,测试了两种常用工程材料(硬铝LY12和钛合金TC4)的力学参数,建立了相应的有限元仿真模型,并采用球形压入试验验证了模型的可靠性;在此基础上,对材料在不同残余应力状态下压入载荷、凸起/凹陷和压入接触塑性区域半径等压入响应问题进行了系统研究。研究结果表明:随着残余压应力的增加,压入载荷变大,压入接触区域周围易于产生凸起现象,塑性区域半径增大;随着残余拉应力的增加,压入响应的影响情况相反;这些现象可以为判断材料内部残余应力的状态和冲击压入试验中敏感元件的布置提供依据和指导。     

重载下调心滚子轴承接触应力分析及凸形设计

基于弹性接触理论,应用数值方法编制FORTRAN程序计算了调心滚子轴承的接触应力。轻载下其接触应力计算值和Hertz理论的计算结果相差仅为0.11%,从而验证了程序的正确性。并据此计算了其他更高载荷水平下的轴承接触应力。当轴承施加0.15Cr载荷时滚子有效长度利用率过低;载荷增加到0.3Cr时滚子的有效长度能被有效利用;当载荷进一步增加时开始出现边缘应力集中。通过改变滚子、滚道的密合度和优化滚子端部修形半径,以充分利用滚子全长,可在极重载下球面滚子-滚道接触区域中间应力增加很小的情况下大大减小边缘的应力集中。     

不同种类光学玻璃的纳米压痕测试分析

以探索不同光学玻璃在纳米压痕条件下的机械特性,分析塑性去除的能力为目的,为后续机械加工质量的改善提供技术支撑,采用纳米压痕测试技术,测得BK7玻璃、石英玻璃及微晶玻璃表面的载荷与压入深度变化关系。在最大加载力为10 mN、50 mN和100 mN时,对光学玻璃的机械特性进行研究,得出三种材料在法向载荷作用下的变形和断裂行为。结果表明光学玻璃的弹性回复量、最大压深和残余深度随最大加载力的加大而上升,但相对弹性回复率基本稳定。石英玻璃、微晶玻璃和BK7玻璃的硬度依次减小,而弹性模量值依次增加。当表征材料的弹塑性特性时,相对弹性回复率这个参量兼具很强的参考意义,可推测加工时塑性去除的能力。这将有助于机械加工时表面质量的分析,并为研究加工机理提供保障。     

纳米压痕理论在残余应力检测方面的技术进展

介绍了纳米压痕理论以及2种典型的测量残余应力的理论模型,这2种模型都假设表面存在等双轴残余应力。其中Suresh和A．E．Giannakopoulos模型测量残余应力是由存在残余应力时和没有残余应力时的接触面积之比来确定;随后Y．H．Lee和D．Kwon对该模型进行了修正,根据载荷与硬度的对应关系,将接触面积转换成载荷的函数;最后的残余应力计算仅与载荷有关。本文还详细综述了用纳米压痕理论检测残余应力的应用实例,最后提出用纳米压痕技术检测残余应力的可能性还有待更深入的研究。     

利用LS-DYNA的微尺度球面-平面接触模型力学行为有限元分析

球面-平面接触模型是研究接触问题的基础.首先,分析了LS-DYNA有限元接触算法的基础理论,然后利用LS-DYNA有限元分析软件,分析了微尺度球面-平面接触模型的力学行为.研究表明,微尺度球面与平面以不同接触深度接触时,接触应力场以球面顶部位置为中心,呈圆形分布在接触位置区域,并且随着接触深度增加,合应力明显增大.接触过程中首先在基体表层产生弹性变形,然后进入塑性变形,并随接触深度增加,塑性变形区进一步扩大.比较接触区域不同位置的接触应力,在接触区域底部、中下部接触应力最大,而在上部、中上部的接触应力要小.随着接触深度的加深,局部发生以塑性变形为主的变形,材料失效,接触区域各位置的接触应力反而变小,且大致相同.     

焊接残余应力对弹塑性接触应力场的影响

对接触应力场的力学分析,以前发表的文章都是在弹性或理想弹塑性的假设下作出的。由于实际材料在屈服后的加工硬化,以上假设显然有较大的近似性。运用弹塑性力学的原理和数值计算方法,考虑了材料的加工硬化,讨论了焊接残余应力对弹塑性接触应力场的影响,并给出了亚表面塑性区随循环周次的变化。还用实验证明了焊接残余应力对工件的接触疲劳寿命的危害性。     

Application of spherical indentation mechanics to reversible and irreversible contact between rough surfaces

A probabilistic model for the deformation mechanics of the interface between randomly rough metal surfaces, which is geometrically and mechanically more realistic than previous models, is derived and numerically evaluated. The model is based on the premise that the contact of two nominally plane engineering surfaces is in general equivalent to loading their sum against a smooth plane. The “sum surface” is assumed to be Gaussian and isotropic; thus the height and curvature of its peaks are correlated random variables. By using an idealized peak shape which is paraboloidal only at its vertex, the surface height distribution of the population of peaks is also made Gaussian. The upper load limit of the model is estimated, beyond which the microcontacts can no longer be assumed to be geometrically discrete and mechanically independent. Each microcontact is assumed to grow by mutual spherical indentation, thus enabling the entire deformation range, from Hertzian elastic to fully plastic, to be described by previously determined empirical functions. A two-stage linear/power law stress-strain curve is assumed. By summing over all microcontacts the total contact area and load are obtained as functions of the separation of the mean surfaces. For elastic deformation both normal loading and sliding friction are treated. For plastic flow two cases are considered: (1) identical materials; (2) one surface remains elastic. The mechanics of unloading are also investigated. After enough microcontacts have yielded to cause significant deviation from totally elastic behavior, the contact mechanics depend principally on the strain hardening exponent, the ratio of the yield stress to the Young's modulus, and the measurable ratio of the mean peak radius to the r.m.s. height of the sum surface.     

局部载荷下压入响应与材料性能的关系

采用量纲分析法,建立了在载荷作用下压入响应与材料硬度/弹性模量(H/E)之间的无量纲函数,并基于有限元分析结果,分析了材料性能对于压入响应的影响,建立了在一定载荷下,材料性能H/E从0.005到0.025范围内,压入响应参数即压痕深度h、压痕接触半径a、塑性隆起量δ与材料H/E为基本物理量之间近似函数表达式。研究结果表明:材料H/E比值小,压入响应参数变化率随着载荷增加而加快,材料H/E比值大,其变化率慢;在压入响应过程中,压痕周围均产生隆起量;压入响应参数与H/E之间函数表达式拟合精度高达99%以上,在实测中根据压痕参数可计算材料的H/E值。     

Elastic recovery of a scratch in a polymeric surface: experiments and analysis

A scratch may be regarded as a tangential indentation. Hence standard indentation laws can be used to analyse the geometry of the scratches left by a moving tip on the surface of a viscoelastic viscoplastic body such as a commercial grade of cast polymethylmethacrylate (PMMA). This paper presents experimental results and an analysis of the elastic recovery of a scratch after contact with a tip. The experimental data were obtained with a new scratch apparatus fitted with a built-in microscope, which allows in situ analysis of the contact area and the groove left on the surface. The elastic plastic total penetration depth h_ep is split into its plastic part h_p and elastic part h_e. In the case of full plasticity around the tip during scratching, which for an elastic plastic material implies a sufficiently high value of the contact strain, the elastic law describes the depth relaxation and experimental data agree with the analysis. In the case of a purely elastic response of the material, corresponding to low values of the contact strain, the rear contact radius is equal to the front contact radius. At intermediate levels of strain, an analysis of the elastic recovery must take into account the contribution of the plastic term to the elastic plastic response of the material.     

Micro-contact analysis for the initial contact in nanoindentation tests

The force-depth behavior of initial contact between a Berkovich indenter and S45C steel specimens has been examined. The indenter is considered as a rigid sphere with a radius of 300 nm since the blunt tip is dominant under initial contact. The S45C steel specimens were prepared to have different surface characteristics. The specimen surface profile was decomposed by Fourier cosine series; then the statistical evaluation for force and area of micro-contact was proposed. The influence of surface roughness on the real contact area and thus the contact pressure arising in the indentation test can be investigated from the proposed analyses. The force-depth responses obtained by the proposed method revealed good agreement with the experimental results for the prepared specimens with their different surface characteristics. The evaluated results of the force fractions in the elastic, elastoplastic, and plastic deformation regions showed that the S45C steel specimens had fully plastic deformation under the initial contact load of 5 μN. The average values of real contact pressure evaluated by the current method rapidly reached the hardness value. Through the proposed method, the dominant radii of summits were evaluated and their relation to the indentation depth was demonstrated.     

Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces

The paper suggests a revision to the asperities plastic to elastic mode transition in the elastic–plastic contact model of fractal rough surfaces, offered by Majumdar and Bushan [A. Majumdar, B. Bushan (MB model) J. Tribol. 113 (1991) 1–11.]. According to the MB model, the contact mode of a single fractal asperity transfers from plastic to elastic when the load increases and the growing contact area exceeds a certain critical value, which is scale independent. This surprising result of the MB model is in contrast with classical contact mechanics where increasing contact area due to increased load is associated with a transition from elastic to plastic contact. The present study describes a revised elastic–plastic contact model of a single fractal asperity showing that, contrary to the MB model prediction, the critical contact area is scale dependent. The revised model also shows that a fractal asperity behaves as would be expected from classical contact mechanics namely, as the load and contact area increase a transition from elastic to plastic contact mode takes place in this order.     

Universal dependences between parameters of deformation and the load during plastic-elastic implementation of a spherical indentation into a semi infinite elastic medium

Processing the great amount of experimental data concerning the implementation of a spherical indentation into a semi infinite elastic medium with universal load dependences for total and residual deformation parameters, depth of penetration, radius of contact area, and mean pressure have been obtained.     

Investigation of sharp contact at rigid–plastic conditions

Sharp contact problems are examined theoretically and numerically. The analysis is focused on elastic–plastic material behaviour and in particular the case when the local plastic zone arising at contact is so large that elastic effects on the mean contact pressure will be small or negligible. It is shown that, save for the particular case of a rigid–plastic power-law material, at such conditions, there is no single representative value on the uniaxial stress-strain curve that can be used in order to evaluate the global parameters at contact. However, the present numerical results indicate that good accuracy predictions for the mean contact pressure can be achieved when this variable is described by two parameters corresponding to the stress levels at, approximately, 2 and 35% plastic strain. Regarding the size of the contact area, it is shown that this quantity is very sensitive to elastic effects and any general correlation with material properties is complicated at best. The numerical analysis is performed by using the finite element method and the theoretical as well as the numerical results are compared with relevant experimental ones taken from the literature. From a practical point of view, the presented results are directly applicable to material characterization or measurements of residual mechanical fields by sharp indentation tests, but also for situations such as contact in gears or in electronic devices.     

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.     

Subsurface characteristics of an abraded low carbon steel

Ductile metals commonly exhibit plastic deformation at and near the worn surface and their flow behaviour at large strains has a clear effect on wear resistance. In this study, the characteristics of the near-surface region of a ferritic-pearlitic steel (0.2% C, 1.2% Mn), subjected to abrasive wear tests, were examined. Wear tests were performed under different loads by rubbing the specimens on sliding 60 mesh Al₂O₃ abrasive band. The metallographic technique used to determine the magnitude of plastic deformation was based on measurement of the displacements of pearlite bands. The hardness of the plastic deformation zone was determined by performing ultramicrohardness tests along ferrite bands with a Vickers indenter. Microscopic examinations of the near-surface regions revealed the wear mechanism to be ploughing and the deformation mechanism to be cross-slip. It was observed that plastic strain (more than 6) occurred on the abraded surface, and increased the hardness to about 1.5 times the original value. The strain and hardness gradient extended to a larger depth into the bulk with increasing wear test load. It is concluded that the wear resistance of the investigated steel increases by work hardening of the near-surface region which is required to consume high energy for abrasion, during sliding. Ultramicrohardness measurements performed on worn specimens revealed high hardness, as the indent size decreased. The indentation size-hardness relation was explained by a dislocation model incorporating geometrically necessary dislocations due to the presence of strain gradients in the deformation region around the indent.     

考虑硬度变化的结合面法向接触刚度分形模型*

基于分形几何理论,考虑微凸体因应变硬化而造成弹塑性变形阶段硬度随变形量变化而变化,建立结合面第一、第二弹塑性变形阶段单次加载刚度分形模型。推导出在计入硬度变化的情况下,单个微凸体在弹塑性变形阶段法向接触刚度与接触面积之间的关系式,进而得出结合面在弹塑性变形阶段法向接触刚度与接触面积、接触载荷之间量纲为一的关系式,并通过仿真分析得出相关参数对结合面法向接触刚度的影响。仿真结果显示:考虑硬度变化时,结合面量纲一法向接触刚度的值与法向实际接触载荷、实际接触面积之间存在关系;结合面法向接触刚度随着分形维数D的增大而增大;分形维数一定时,结合面法向接触刚度随表面长度尺度参数G值增大而增大。