On the accurate determination of contact compliance for impact test modelling

To model the specimen interaction with supports during an impact test, simple formulas for indentation–contact force relation between a beam specimen and a rigid cylindrical indenter have been derived using a mixed analytical/numerical approach. Two types of boundary conditions for the specimen (i) support by a frictionless rigid foundation and (ii) conventional three-point bending have been considered. The first scheme of loading (the compression indentation test, CIT) is sometimes used for quasi-static estimation of the specimen–striker or specimen–support contact compliance instead of the second scheme, which more closely corresponds to the real loading conditions of the specimen during an impact test. It has been found that the indentation (and, therefore, the contact compliance) of the specimen loaded according to the first scheme is up to 19% higher than for the second one. A simple correction of the results of CIT, which allows to estimate the contact compliance accurately has been proposed. Approximate formulas for the linearized contact compliance have been derived for both schemes of loading using three different methods of linearization. The best result has been obtained by the method of the equality of work done by nonlinear and linearized contact forces. An example of modelling of the three-point-bending test using the computed contact stiffness of the anvil is presented.     

Numerical and Experimental Studies of a Conical Striker Application for the Achievement of a True and Nominal Constant Strain Rate in SHPB Tests

The problem of ensuring both nominal and true constant strain rate in the split Hopkinson pressure bar experiment was considered through the application of the conical striker for 316 L steel specimen. The experimentally confirmed results from numerical analyses indicate that the application of a conical striker with the determined apex angle for the given experimental conditions is a good method for achieving a constant value of the strain rate. Moreover, the results of the study showed that the value of the striker apex angle has the greatest influence on the mechanical response of the specimen material. In turn, the impact velocity slightly affects the value of the striker apex angle.     

690合金管在室温干态下的冲击微动磨损特性研究

采用小载荷冲击试验机研究了690合金传热管与405不锈钢块在室温干态不同载荷条件下的微幅冲击磨损行为.其中管采用悬臂梁式固定,与冲击配副采取线接触方式,冲击频率为10 Hz,循环次数为106次,试验载荷选取5、10、20和40 N.结果表明:在室温干态条件下,随着载荷的增加,690合金管的磨损体积增大;加工硬化效应增强,磨损表面硬度增加越大.冲击磨损过程中材料表面发生摩擦氧化行为,690合金管的冲击磨损机制主要是磨粒磨损、剥落,且随着载荷增加,磨粒磨损及氧化行为加剧.     

受轴向撞击复合材料管的渐进破坏

玻璃—环氧圆柱壳 (管 )的撞击试验表明它的破坏是渐进过程。在低加载速率范围假定圆柱壳与均质圆柱杆具有相同的轴向破坏过程基础上 ,通过建立它们之间的刚度等效关系 ,复合材料圆柱壳的破坏问题简化为一维碰撞问题。根据一维应力波传播的理论 ,提出了圆柱壳受轴向撞击破坏的简化模型 ,分析了这一破坏过程中的能量变化。结果表明本文所提模型能较好地描述圆柱壳受轴向撞击渐进破坏。     

Measurement of Torsionally Induced Shear Stresses in Shrink-Fit Assemblies

Shear stresses along the shaft/hub interface in shrink-fit components, generated by torsional loads, can drive premature failure through fretting mechanisms. It is difficult to numerically predict these shear stresses, and the associated circumferential slip along the shaft/hub interface, due to uncertainties in frictional behaviour and the presence of steep stress gradients which can cause meshing problems. This paper attempts to provide validation of a numerical modelling methodology, based on finite element analysis, so the procedure may be used with confidence in fitness-for-purpose cases. Very few experimental techniques offer the potential to make measurements of stress and residual stress interior to metallic components. Even fewer techniques provide the possibility of measuring shear stresses. This paper reports the results of neutron diffraction measurements of shear stress and residual shear stress in a bespoke test specimen containing a shrink-fit. One set of measurements was made with a torsional load ‘locked-in’. A second set of measurements was made to determine the residual shear stress when the torsional load had been applied and removed. Overall, measurement results were consistent with numerical models, but the necessity for a small test specimen to allow penetration of the neutron beam to the measurement locations meant the magnitude of shear stresses was at the limits of what could be measured experimentally.     

Properties of rocks tested in one-dimensional compression

An apparatus has been developed and used to obtain static stress-strain data on rock and soil samples in one-dimensional compression. This paper describes the design and method of use, and reports test results obtained on several types of rock and sand specimens. A 4-in.-diam specimen with height up to 2 in. is contained in a thin-walled steel cylinder. This cylinder is contained in the main pressure vessel which has a pressure cavity surrounding the specimen. Load is applied through a load cell on top of the specimen by a hydraulic press. An operator maintains a constant zero balance on strain gages bonded to the thin, steel cylinder containing the specimen by pumping hydraulic fluid into the pressure cavity, thus nullifying the tendency of the test specimen to expand laterally as it is compressed axially. Axial load and deflection are recorded on anx?y plotter from signals received from the load cell and a deflectometer mounted on the load cell. This apparatus has been successfully used to obtain data on rocks to axial stresses of 75,000 psi and on sand to 30,000 psi. Test data for both rocks and sand are presented in this paper.     

On indentation and initiation of fracture in glass

The influence of indenter elasticity on Hertzian fracture initiation at frictional dissimilar elastic contact has been examined experimentally and numerically. In flat float glass specimens initiation of cone cracks has been observed and fracture loads measured with steel and tungsten carbide indenters at monotonically increasing loading and during a load cycle. The observed effect of indenter elasticity on fracture loads was found to be qualitatively different from the one predicted by the Hertz contact theory. This discrepancy may be explained by the presence of interfacial friction. The friction coefficient between the indenters and the specimen was measured and a contact cycle at finite Coulomb friction has been analyzed numerically. The influence of the indenter elasticity and the friction coefficient on the surface maximum tensile stress has been investigated and the results concerning the influence of these parameters on the fracture loads as given based on a critical stress fracture criterion. The obtained computational results were found to be in better agreement with experimental findings as compared to the predictions based on the frictionless contact theory. A remaining quantitative discrepancy was attributed to the well-known fact that a Hertzian macro-crack initiates from pre-existing defects on the specimen’s surface. In order to account for the influence of the random distribution of these defects a Weibull statistics was introduced. The predicted critical loads corresponding to the 50% failure probability were found to be in close agreement with experimentally observed ones.     

Interfacial slip and creep in rolling contact incorporating a cylinder with an elastic layer

A systematic approach for investigating the interfacial behaviour of tyred systems is proposed. A two-dimensional contact model of an elastic strip, shrink-fitted onto a wheel, and subjected to different rolling contact conditions, has been adopted to illustrate the method. The model combines existing techniques to explore individual elastic contact problems and it enables us to characterise the behaviour at the strip/substrate interface caused by loads induced by a quasi-static application of stationary and moving loads on the surface of the layer. The solution is compared to the stationary load case and regimes of local slip, full stick, separation and frictional creep are identified and collated for a variety of loading conditions, materials and geometries. Further, this article presents an investigation of frictional shakedown for layered systems subjected to periodic contact loading. The term shakedown is here referred to as the possibility of developing interfacial residual stresses at the layer/substrate interface such that frictional slip, originally activated by the applied external contact load, ceases after a few loading cycles. The possible applicability of the Melan’s theorem for elastic frictional system is investigated and preliminary results presented.     

钢管混凝土纯压拱失稳临界荷载计算的等效柱法

在双重非线性有限元分析的基础上,进行了钢管混凝土纯压拱失稳临界荷载的简化计算方法——等效柱法的研究,提出了等效柱法中考虑矢跨比影响的稳定系数K₁ 以及考虑初始几何缺陷影响的折减系数K₂及其与现有规范相对应的计算公式。与有限元计算结果的对比表明,采用考虑矢跨比因素的稳定系数的等效柱法能较精确地估算钢管混凝土纯压拱的非线性失稳临界荷载,且计算精度受含钢率和钢材种类变化的影响较小。     

基于双剪统一强度理论的复式钢管混凝土轴压承载力计算

考虑内、外钢管对混凝土的双重约束作用, 分析复式钢管混凝土的轴压应力状态, 采用双剪统一强度理论分析混凝土和钢管各自的极限轴压强度, 得出复式钢管混凝土轴压承载力公式; 通过推导钢管在极限状态的强度折减系数及钢管与混凝土之间的紧箍力值, 计算出的轴压承载力与试验数据进行对比, 吻合较好, 验证了双剪统一强度理论在复式钢管混凝土轴压承载力计算中的适用性; 并给出了内圆钢管的径厚比和直径与轴压承载力提高系数的关系, 为复式钢管混凝土的优化设计提供理论依据.     

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．     

Finite element modeling of interfacial forces and contact stresses of pneumatic tire on fresh snow for combined longitudinal and lateral slips

Significant challenges exist in the prediction of interaction forces generated from the interface between pneumatic tires and snow-covered terrains due to the highly non-linear nature of the properties of flexible tires, deformable snow cover and the contact mechanics at the interface of tire and snow. Operational conditions of tire-snow interaction are affected by many factors, especially interfacial slips, including longitudinal slip during braking or driving, lateral slip (slip angle) due to turning, and combined slip (longitudinal and lateral slips) due to brake-and-turn and drive-and-turn maneuvers, normal load applied on the wheel, friction coefficient at the interface and snow depth. This paper presents comprehensive three-dimensional finite element simulations of tire-snow interaction for low-strength snow under the full-range of controlled longitudinal and lateral slips for three vertical loads to gain significant mechanistic insight. The pneumatic tire was modeled using elastic, viscoelastic and hyperelastic material models; the snow was modeled using the modified Drucker-Prager Cap material model (MDPC). The traction, motion resistance, drawbar pull, tire sinkage, tire deflection, snow density, contact pressure and contact shear stresses were obtained as a function of longitudinal slip and lateral slip. Wheel states - braked, towed, driven, self-propelled, and driving - have been identified and serve as key classifiers of discernable patterns in tire-snow interaction such as zones of contact shear stresses. The predicted results can be applied to analytical deterministic and stochastic modeling of tire-snow interaction.     

Microbuckling of a doublewalled carbon nanotube embedded in an elastic matrix

Microbuckling of a doublewalled carbon nanotube (DWCNT) in an elastic (polymer) matrix is studied. The investigations are made within the scope of the piecewise homogeneous body model by utilizing the three-dimensional linearized theory of stability of deformable bodies. Flexural and axisymmetric microbuckling modes are considered. The DWCNT is modeled as concentrically-nested two circular hollow cylinders between which there is free space. It is assumed that on the inner surface of the outer tube (cylinder) and on the outer surface of the inner tube (cylinder) of the DWCNT full slipping conditions occur. At the same time, it is assumed that the difference between the radial displacements of the adjacent surfaces of the tubes resists with the van der Waals forces. On the interface between the matrix and DWCNT complete contact conditions are satisfied. Numerical results on the influence of the problem parameters on the critical deformation are presented and discussed. Also, numerical results related to the cases where the interlayer space is ignored and where full contact between the tubes is assumed are presented and compared with the mentioned results. In particular, it is established that full slipping between the tubes causes the values of the critical deformation to decrease significantly with respect to those obtained in the case where complete contact conditions occur between the tubes. Moreover, it is established that an increase in the values of the van der Waals forces also causes a decrease in the values of the critical compressing strain and the magnitude of this decrease depends on the thicknesses of the tubes of the DWCNT.     

含非理想空间棱柱铰的多体系统接触分析

传统的接触分析方法通过物体间的相对运动确定接触位置. 将这种方法用于多体系统中铰内的接触分析时, 无论铰内间隙是否十分微小都必须解除铰的运动学约束, 从而导致求解效率和求解精度方面的诸多弊端. 基于铰约束反力与铰内接触力之间的力系等效关系, 以及铰内可能接触点运动之间内在的运动学关系, 以矩形截面的棱柱铰为例, 提出了一种对空间棱柱铰进行摩擦接触分析的方法, 可在不解除铰的运动学约束的前提下得到铰内接触模式和接触力. 数值算例验证了方法的可行性.      

Non-steady-state elastic–plastic behavior of metal forming (rolling) with a generalized friction law

An analytical and generalized friction law is formulated and a three-dimensional large-strain non-steady-state elastic–plastic finite element analysis has been performed for rolling process. The contact/friction problem at the interface between the workpiece and the rolls is treated rigorously by using this new friction law. The numerical results, including the evolutions of roll torque and roll forces, and the interfacial normal and shear stresses, are presented and discussed.     

The ability of agricultural tyres to distribute the wheel load at the soil-tyre interface

Bigger tyres with lower inflation pressure at equivalent wheel loads are expected to reduce the stresses transmitted to the soil. We measured the contact area and the vertical stress distribution near the soil-tyre interface for five agricultural implement tyres at 30 and 60 kN wheel load and rated inflation pressures. Seventeen stress transducers were installed at 0.1 m depth in a sandy soil at a water content slightly lower than field capacity and covered with loose soil. The recently developed model FRIDA was successfully fitted to the experimental stress data across the footprint. The contact area reflected the size of the tyres. The small tyres had identical contact area at the two loads, while it increased with load for the two biggest tyres. The small tyres presented uneven stress distributions with high peak stresses. Across the tests, the tyre inflation pressure described well the measured peak stress as well as the modelled maximum stress. The latter seems to be appropriate in evaluating vehicle trafficability. We found significant differences among tyres for the slope of a linear regression between the mean ground pressure and the inflation pressure, while the tyres displayed the same interception on the mean ground pressure axis. Our results therefore suggest that the slope of this relation is the most sensitive expression of tyres’ ability to deflect and transfer stresses to the soil. The two small tyres performed poorer in this respect than the larger tyres. Tests were limited to one soil strength, with future research directed toward a broader spectrum of soil strengths.     

The stability of a finitely inflated cylindrical elastic membrane under axial compression

The stability under overall axial compression of a finitely inflated cylindrical membrane composed of highly elastic material is investigated. The critical loads for inflated tubes with closed ends and with either simply-supported or fixed ends are determined in terms of the material properties of the membrane. For long tubes the results are compared with the Euler formulae for the buckling load for struts in compression. An equivalent Young's modulus is derived, and it is shown that the critical loads can be obtained from the Euler formulae by using the dimensions of the inflated state and the equivalent Young's modulus.     

不同材料交界面上接触应力的有限元分析

工程中有许多不同材料组成的结构。对这类复合结构，正确计算材料交界面上的接触应力是非常重要的。通常的位移有限元法得到的应力是不连续且欠准确的。本文提出了一种新的用于不同材料交界面处的接触单元。应用虚位移原理和结合考虑材料交界面上的约束条件，文章建立了接触单元的刚度矩阵和等效荷载向量。该单元具有算法简单，程序容易实现的优点。计算实例证实了该单元的实用性和可靠性。     

The effect of the irregular interface geometry in deformation and fracture of a steel substrate–boride coating composite

Presented in this paper is a computational analysis of the mechanisms involved in plastic deformation and fracture of a composite with coating under compressive and tensile loading. Using a steel specimen surface-hardened by diffusion borating, a role of the irregular geometry of the interface between the base material and hardened surface layer is investigated. In order to describe the mechanical behavior of the steel substrate and brittle coating, use is made of a plastic flow model including isotropic strain hardening and a fracture model, respectively. Using the Huber fracture criterion, the model takes into account the difference in the critical strength values for different types of local compressive and tensile states. It is shown that the irregular, serrated shape of the substrate–coating interface retards propagation of a longitudinal crack into this coating and prevents it from spalling under external compression of this composite. It is found out that even in the case of a simple uniaxial compression of the mesovolumes of this composite the boride “teeth” are subjected to tensile stresses, whose values are comparable with those of the external compressive load, and the direction of crack propagation and the general fracture behavior largely depend on the external loading conditions.     

Simulation of impacts in geartrains using different approaches

Gear hammering in diesel engines is a well-known phenomenon in geared drives, exhibiting not only noise but also influencing the performance and durability of diesel engines. Gear hammering is characterised by flanks in contact that lift off and cause impacts when the contact reestablishes, which induces high, sharp dynamic loads. The knowledge of these contact forces is very important for the design of gears. Since contact forces in meshing gears are extremely difficult and expensive to measure, the simulation of these forces plays an important role. Nowadays, these contact simulations are usually carried out within overall models of entire engines using commercial multibody programs that provide submodels for gear contacts, usually based on rigid-body models. However, to reduce inertia effects, gears in geartrains are often designed with very thin bodies, whose elastic compliance influences the contact behaviour to a large extent. For a closer insight into the dynamic behaviour, and especially the influence of thin gear bodies during impact, a typical gear pairing is selected and impacts between one tooth pair are investigated for different boundary and initial conditions with three different models. Besides a multibody model, similar to those used in commercial multibody programs, a fully nonlinear finite-element model and a modally reduced model in combination with a local force law is used. The results of the different approaches are benchmarked in terms of accuracy and numerical effort.