Micro‐indentation fracture from flat‐ended cylindrical indenter

Unlike a Hertzian ring crack induced by a spherical indenter in absence of a singular stress field, a ring crack generated by a rigid flat cylindrical indenter can be explicitly linked to a K‐dominant singular stress field at the perimeter of the flat indenter. This means microcrack initiation induced by a flat indenter and relevant properties such as the critical indentation load and fracture toughness can be formulated explicitly using the fracture mechanics approach. It is shown in this paper that the indentation stress intensity factor, , for such a stress field is similar to that of a mode I crack. Based on the energy‐releasing rate and the Griffith's theorem, a flat indentation cracking model has been proposed; the critical load and critical cracking angle for crack initiation are derived. A new concept of fracture toughness for negative mode I singular stress field,, has been defined and a relationship between and the traditional K_IC has been derived. The experimental investigation validates the existence of such , from which the K_IC value of the glass had been determined to be 0.772 ± 0.003 MPa m^1/2, agreeing well with the literature data. This analysis for indentation fracture or crack initiation due to surface contact of a flat indenter is particularly useful in determining K_IC of brittle materials with dimensions in micro/nanoscales, e.g. thin films and other microstructures as flat micro/nano‐indenters are available and can be used on various nano‐indentation machines.     

基于Newmark法敏度计算的刚架结构动力优化

提出一种有效的求解结构最小质量设计,同时满足动位移和动应力约束的二阶优化设计方法。在有限元法和纽马克法基础上导出一种高效的动应力、动位移对设计变量一阶导数和二阶导数的算法。建立含时间参数,以结构质量最小化为目标,同时满足动位移、动应力和设计变量约束的优化数学模型,通过积分型内点罚函数将含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题。利用动位移、动应力对设计变量一阶导数和二阶导数的信息计算内点罚函数的梯度和海森矩阵,利用梯度和海森矩阵构造求解优化设计问题高效有效的二阶优化算法。算例结果表明该文的优化设计方法能获得刚架结构的局部最优设计,优化的效率高于增广拉格朗日乘子法。     

基于Hertz接触模型的柔性梁碰撞振动分析

首先研究两弹性体碰撞振动中的接触力，用多项式逼近具有分数指数的Ｈｅｒｔｚ模型来实现近似解析分析，然后讨论与碰撞有关的各因素对两柔性梁受迫碰撞振动的影响。当耦合模态解增加时，碰撞强度增大，系统呈现典型的非线性     

Micro and macro contact mechanics for interacting asperities

Contact of rough surfaces at micro and macro scales is studied in this paper. The asperities at micro scale are characterised by small radius of curvature whereas the waviness is characterised by large radius of curvature. When two rough surfaces come in contact, on the micro scale, of asperities contacts in a very small area leave large gaps between the surfaces; whereas on the macro scale the surfaces conform to each other under the application of load without gaps. Contact at micro scale is modelled by superposition of Hertzian stress fields of individual asperity contacts and the waviness at macro scale is modelled as a mixed boundary problem of rough punch indentation where displacements of uneven profile are prescribed along the region of contact. In both the cases for simplification the roughness is assigned to one surface making the other surface perfectly flat an assumption often made in contact mechanics of rough bodies. The motivation for modelling the asperities at micro scales comes from the preliminary results obtained from photoelastic experiments. Numerical results are presented based on the analytical results available for Hertzian contacts. The motivation for modelling the asperities at macro scales comes from the results available in literature for flat contacts from solving mixed boundary elasticity problems. A condition of full stick is assumed along the contact which is a common assumption made for rough contacts. The numerical results are presented for both the cases of rough contact at micro and macro scales.     

Combination of Newmark method and natural element method for elastodynamics

The natural element method (NEM) is a meshless method. The trial and test functions of the NEM are constructed using natural neighbor interpolations which are based on the Voronoi tessellation of a set of nodes. The NEM interpolation is linear between adjacent nodes on the boundary of the convex hull, which makes imposition of essential boundary conditions easy to implement. We investigate the performance of the NEM combined with the Newmark method for problems of elastodynamics in this article. Applications are considered for a cantilever beam with different initial load conditions. The NEM numerical results are compared with the finite element method. NEM shows promise for these applications.     

Experimental observation and numerical modeling of formation of local plastic zones in hardened surface layers due to contact overloading

The problem of formation of plastic zones in case-hardened metallic bodies due to contact overloading is studied both experimentally and numerically. Metallic materials exposed to surface hardening demonstrate spatial variation of the material hardness and yield strength with a decreasing profile with depth and belong to the class of so-called plastically graded materials. The presented experimental program employs micro-Vickers hardness tests to map the variation in material hardness and corresponding yield strength for both virgin and loaded case-hardened specimens made of a chromium tool steel. It is shown that, depending on the profile of the yield strength in the near-surface zones and contact parameters, a plastic deformation can originate underneath the hardened layer. The distribution of the effective plastic strain extracted from the micro-hardness increment measurements are found in good agreement with the results of finite element simulations of a plastically graded material subjected to similar loading conditions. Numerical analysis reveals significant perturbations in the stress field distribution within the hardened layer due to formation of a closed-shaped plastic zone in the gradient layers, including development of a tensile stress on the boundary between the elastic and plastic zones as well as an overall increase in the effective stress intensity. It is shown that the hardened layer behaves similar to an elastic beam on a compliant foundation. These stress field perturbations in the hardened layers with low deformation capacity can greatly affect the durability and serviceability of surface treated mechanical parts.     

非线性分数阶微分振子的动力学研究

本文结合Zhang—Shimizu法与Newmark法，解决了二次非线性的Riemann—Liouville分数导数中奇异性问题，从而得到了非线性分数微积分求解的单步数值积分算法。在此基础上对某型非线性分数阶微分振子的动力学行为进行研究，分别讨论了振子自由振动及强迫振动下参数变化对振子非线性特性的影响。数值计算结果表明，该数值方法具有较好的稳定好，收敛速度快，精度较高，编程简单容易等优点。     

Low velocity impact analysis of composite sandwich shells using higher-order shear deformation theories

In the present investigation, higher-order and conventional first-order shear deformation theories are used to study the impact response of composite sandwich shells. The formulation is based on Donnell’s shallow shell theory. Nine-noded Lagrangian elements are used for the finite element formulation. A modified Hertzian contact law is used to calculate the contact force. The results obtained from the present investigation are found to compare well with those existing in the open literature. The numerical results are presented to study the changes in the impact response due to the increase of core depth from zero to some specified value and the changes in core stiffness for a particular core depth.     

往复荷载作用下的改进动接触力方法

该文基于与中心差分显式时间积分法相结合的动接触力方法,引入主、从节点的相对速度作为判断接触状态转变的标准,提出了一种能够适用于求解往复荷载作用的改进动接触力方法。改进方法能够准确地模拟分离、静接触、滑动接触以及反向滑动四种不同接触状态间的转变,为地震等往复荷载作用下结构动力分析提供了有力工具。数值算例验证了该文方法的正确性。     

Effects of weak boundary phases (WBP) on the microstructure and mechanical properties of pressureless sintered Al2O3/h-BN machinable composites

Al₂O₃/h-BN machinable composites were fabricated by pressureless sintering at 1750 °C for 2 h in nitrogen atmosphere. The relative density of the sintered composites decreased, while the porosity increased with increasing h-BN content. By adding 20 vol.% h-BN to the composites, the porosity increased up to 16.7%. The effects of weak boundary phases (WBP), including h-BN and pores, on the microstructure, mechanical properties and machinability of the composites were investigated. The flexural strength, fracture toughness, Young's modulus and hardness of the composites decreased with increasing WBP content. When WBP content increased up to 18.8 vol.%, the composites can be machined easily by cemented carbide drills. Furthermore, the machining mechanisms of the composites were investigated using Hertzian contact tests.     

ON STRESS SINGULARITIES INDUCED BY THE DISCRETIZATION IN CURVED RECEDING CONTACT SURFACES: A BEM ANALYSIS

This paper is concerned with the effects of the piecewise approximation of the geometry of contacting solids, in which a discontinuity of the normal outward boundary vector is, in general, implied. This discontinuity is shown to be of particular relevance when contact takes place on a curved surface, and sliding occurs. Only load-independent receding contact problems are considered. The behaviour of a sliding contact zone having a corner inside is investigated first, by means of a particular problem. Then, it is shown that using curved elements, a meshing refinement process can reduce the effects of unreal corners, whereas discretizations based on flat elements may produce unacceptable results regardless of the performed meshing refinement. Chances to overcome this drawback are recognized for some special flat boundary elements, but others are to be discarded for these kinds of problems. A parameter to quantify the error due to unreal stress concentrations is proposed. Two-dimensional examples discretized using boundary elements are presented for illustration purposes. © 1997 John Wiley & Sons, Ltd.     

储液容器流固耦合动力响应分析计算

本文采用交替解法对地震条件下储液容器的动态响应问题进行了实例分析和计算。首先推导出流固耦合系统在地震条件下的有限元模型。然后,对在水平地震激励条件下的圆柱形储液容器,采用交替解法进行了计算,并将其与整体解法进行了比较。结果表明交替解法具有更好的计算效率。