Residual-stress measurement using surface displacements around an indentation

An experimental method is described which can measure the direction and magnitude of residual and applied stress in metals. The method uses optical interference to measure the permanent surface deformation around a shallow spherical indentation in a polished area on the metal specimen. The deviation from circularly symmetrical surface deformations is measured at known values of applied stress in calibration specimens. This deviation from symmetry can then be used to determine the direction and magnitude of tensile residual stress in specimens of the same material. Determination of compressive residual stress is more limited. A model of the indentation process is offered which qualitatively describes experimental results in 4340 steel for both tensile and compressive stress. The model assumes that the deformation around an indentation os controlled by stresses analogous to those around a hole in an elastic plate. Various conditions are discussed which affect the indentation process and its use to measure stress, including (a) the rigidity of support of the indentor and specimen, (b) the size and depth of the indentation, (c) the uniaxial stress-strain behavior of the specimen material.     

Surface versus bulk nucleation of dislocations during contact

The indentation of single crystals by a periodic array of flat rigid contacts is analyzed using discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modeled as line singularities in a linear elastic solid. The limiting cases of frictionless and perfectly sticking contacts are considered. The effects of contact size, dislocation source density, and dislocation obstacle density and strength on the evolution of the mean indentation pressure are explored, but the main focus is on contrasting the response of crystals having dislocation sources on the surface with that of crystals having dislocation sources in the bulk. When there are only bulk sources, the mean contact pressure for sufficiently large contacts is independent of the friction condition, whereas for sufficiently small contact sizes, there is a significant dependence on the friction condition. When there are only surface dislocation sources the mean contact pressure increases much more rapidly with indentation depth than when bulk sources are present and the mean contact pressure is very sensitive to the strength of the obstacles to dislocation glide. Also, on unloading a layer of tensile residual stress develops when surface dislocation sources dominate.     

Determination of resudual stress fields beneath a Vickers indentation using photoelasticity

Static Vickers indentation tests were performed on Homalite specimens with an intent to obtain the residual stress distribution beneath the indentation. The indented specimens were placed in a circular polariscope to view the fringe patterns corresponding to the induced residual stress. Similitude analysis was later employed to identify the functional relationship between the various parameters related to an indentation test. The analysis resulted in a unified relationship that can assist in the determination of residual stress in nontransparent materials subjected to similar geometric and loading conditions. The shear stress contours provided here can also be used as guidelines to verify constitutive models under complex three-dimensional loads.     

残余应力测定的围箍压痕法模拟

本文从同工量测方法得到启发，提出了一种新型的残余应力测试方法－围箍压痕法。采用轴对称弹塑性有限元计算模拟了围箍压痕法测量结构残余应力的力学过程，得到了围箍压痕时不同残余应力程度下材料的变形，塑性区和接触应力分布。     

Smooth static and dynamic indentation of a cantilever beam

The static and dynamic indentation of structural elements such as beams and plates continue to be intriguing problems, especially for scenarios where large area contacts are expected to occur. Standard methods of indentation analyses use a beam theory solution to obtain an overall load–displacement relationship and then a Hertzian contact solution to calculate local stresses under the indenter. However, these techniques are only applicable in a fairly limited class of problems: the stress distribution in the contact region will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. The indentation models developed herein are improvements over existing GLOBAL/LOCAL models for static and dynamic indentation of cantilever beams. Maximum contact stresses, beam displacements, and contact force time histories are obtained and compared with the predictions of current static and dynamic indentation models. The validity of the solutions presented herein is further assessed by comparing the results obtained to the predictions of modified beam theory solutions.     

A numerical analysis of spherical indentation response of thin hard films on soft substrates

In this paper, finite element simulations of spherical indentation of a thin hard film deposited on a soft substrate are carried out. The primary objective of this work is to understand the operative mode of deformation of the film corresponding to various stages of indentation. The transition from contact dominant behaviour to that governed by flexure of the film on the plastically yielding substrate is investigated from analysis of the load versus displacement curve as well as the stress distribution in the film. It is found that onset of bending deformation in the film occurs when the contact radius is about 0.2–0.3 of the film thickness. Further, distinct membrane stresses arise in the film for indentation depth greater than half the film thickness. The implications of these results on indentation fracture of the film are briefly discussed. Finally, the effects of substrate yield strength and presence of residual stresses on the indentation response are examined.     

Surface Residual Stress Measurement Using Curvature Interferometry

Surface roughness plays an important role in the delamination wear caused by rough surface contact. A recent dislocation model analysis predicts that nano-scale contacts of surface steps induce nucleation of dislocations leading to pro-load and anti-load dislocation segregation near the contact surface. Such dislocation segregation generates a sub-layer of tensile residual stress in a much thicker layer of compressive residual stress near the surface. The tensile sub-layer thickness is expected to be about 50 to 100 times the step height. In order to verify the predictions of the model analysis, contact experiments are carried out on polycrystalline aluminum surface to determine the existence of the tensile sub-layer. The variation of the residual stress along the thickness direction is measured using a newly developed high sensitivity curvature-measurement interferometer. The residual stress distribution measured with sub-nanometer spatial resolution indicates that contact loading leads to formation of a highly stressed sub-layer of tensile residual stress within a much thicker layer of compressive residual stress. Implications of tensile residual stress for delamination wear are discussed.     

Oblique indentation of creeping solids

Oblique indentation of power law creeping solids at plane strain conditions is examined with rigid-perfectly plastic material behaviour emerging as an asymptotic case. Indenter profiles are dealt with in general circumstances and represented by homogeneous functions. The core of the method developed draws on self-similarity and is based on an intermediate flat die solution. By this approach the problem of a moving contact boundary may be suppressed and the ensuing procedure becomes independent of loading, geometry, history and time. A computational method, based on the reduced procedure, is developed to obtain high accuracy solutions based on finite elements and applicable to non-linear elasticity. The originally stated problem is then solved subsequently by simple cumulative superposition and results given as a function of impression depth. The relation between contact depth and area is found to be invariant and only dependent on the power law exponent, the amount of friction, the profile and the angle of inclination of the indenter. Detailed results are given for local states of stress and deformation for flat and cylindrical dies at variation of the remaining three stated parameters. The presence of local stick and slip is given due attention and global relations between loading and indentation depth and contact area discussed for practical applications. The fundamental framework laid down may be applied to structural assemblies, joints and seals and diverse applications as flattening of rough surfaces, compaction of powder aggregates and ice-offshore structure interaction.     

On Brinell and Boussinesq indentation of creeping solids

As an alternative to traditional tensile testing of materials subjected to creep, indentation testing is examined. Axisymmetric punches of shapes defined by smooth homogeneous functions are analysed in general at power law behaviour both from a theoretical and a computational point of view. It is first shown that by correspondence to nonlinear elasticity and self-similarity the problem to determine time-dependent properties admits reduction to a stationary one. Specifically it is proved that the creep rate problem posed depends only on the resulting contact area but not on specific punch profiles. As a consequence the relation between indentation depth and contact area is history independent. So interpreted, the solution for a flat circular cylinder (Boussinesq) is not only of intrinsic interest but serves as a reference solution to generate results for various punch profiles. This is conveniently carried out by cumulative superposition and in particular ball indentation (Brinell) is analysed in depth. A carefully designed finite element procedure based on a mixed variational principle is used to provide a variety of explicit results of high accuracy pertaining to stress and deformation fields. Universal relations for hardness at creep are proposed for Boussinesq and Brinell indentation in analogy with the celebrated formula by Tabor for indentation of strain-hardening plastic materials. Quantitative comparison is made with a diversity of experimental data attained by earlier writers and the relative merits of indentation strategies are discussed.     

表面残余应力的仪器化压入检测方法研究进展

针对表面残余应力的仪器化压入检测方法, 阐释利用压入方式检测残余应力的基本原理及其力学机制, 梳理建立残余应力压入检测方法的常用技术路线, 结合残余应力压入检测方法的不同分类, 着重分析6种代表性压入检测方法的优势与局限, 讨论验证压入检测方法可靠性的常用方法, 最后总结残余应力压入检测方法的研究进展, 展望未来的发展趋势为建立无需参考试样一体化检测材料力学参数和非等轴残余应力的仪器化压入分析方法, 探讨建立方法的四个研究要领, 即机制清楚、分析可靠、技术可行、结果可信. 仪器化压入检测技术是郑哲敏先生晚年的研究兴趣之一, 作者在中科院力学所工作期间曾受到郑哲敏先生的热切关注和提问式激励, 谨以此文纪念郑哲敏先生逝世周年.      

Unloading of an elastic–plastic spherical contact under stick contact condition

The unloading process of an elastic–plastic spherical contact under stick contact condition is analyzed for various material properties. The evolution of normal and shear stress distribution at the contact area as well as the residual profile of the sphere and residual von Mises stresses inside the sphere are presented. Empirical expressions for the residual interference and for the evolution of the interference and contact area during the unloading are provided. Good agreement with experimental results is shown.     

Glass Fracture in the Region of Its Contact with Steel Balls

Results of experiments on indentation of steel balls of various diameters into glass specimens shaped as rectangular parallelepipeds are reported. The limiting load of formation of an annular crack near the contact area and the radius of this crack are experimentally determined. The field of the contact stress in the fracture region is found by using the Huber solution of the Hertz problem of ball indentation into an elastic half-space. Modeling fracture caused by contact interaction is based on using the local criterion of the maximum stress and several nonlocal criteria: average stress criterion, Nuismer criterion, and gradient criterion. For calculating the parameter that has the length dimension and is included into the nonlocal fracture criteria, the ultimate tensile stress and the critical stress intensity factor of glass are experimentally determined for beams without and with a notch. It is demonstrated that the experimental data on the annular crack radius are most adequately predicted by the gradient criterion among all criteria considered in the study. However, this criterion overpredicts the ultimate tensile stress in the course of beam bending, which is caused by the scale factor.     

Mechanics of indentation of plastically graded materials—I: Analysis

The introduction of controlled gradients in plastic properties is known to influence the resistance to damage and cracking at contact surfaces in many tribological applications. In order to assess potentially beneficial effects of plastic property gradients in tribological applications, it is essential first to develop a comprehensive and quantitative understanding of the effects of yield strength and strain hardening exponent on contact deformation under the most fundamental contact condition: normal indentation. To date, however, systematic and quantitative studies of plasticity gradient effects on indentation response have not been completed. A comprehensive parametric study of the mechanics of normal indentation of plastically graded materials was therefore undertaken in this work by recourse to finite element method (FEM) computations. On the basis of a large number of computational simulations, a general methodology for assessing instrumented indentation response of plastically graded materials is formulated so that quantitative interpretations of depth-sensing indentation experiments could be performed. The specific case of linear variation in yield strength with depth below the indented surface is explored in detail. Universal dimensionless functions are extracted from FEM simulations so as to predict the indentation load versus depth of penetration curves for a wide variety of plastically graded engineering metals and alloys for interpretation of, and comparisons with, experimental results. Furthermore, the effect of plasticity gradient on the residual indentation pile-up profile is systematically studied. The computations reveal that pile-up of the graded alloy around the indenter, for indentation with increasing yield strength beneath the surface, is noticeably higher than that for the two homogeneous reference materials that constitute the bounding conditions for the graded material. Pile-up is also found to be an increasing function of yield strength gradient and a decreasing function of frictional coefficient. The stress and plastic strain distributions under the indenter tip with and without plasticity gradient are also examined to rationalize the predicted trends. In Part II of this paper, we compare the predictions of depth-sensing indentation and pile-up response with experiments on a specially made, graded model Ni-W alloy with controlled gradients in nanocrystalline grain size.     

Size effect in the initiation of plasticity for ceramics in nanoindentation

The indentation size effect has been observed for many years and is usually associated with increasing hardness as the depth of indentation is reduced for pyramidal indenters. The indentation size effect for spherical indenters has recently been associated with an increase in the yield stress of metals proportional to the inverse cube root of indenter radius [Spary, I.J., Bushby, A.J., Jennett, N.M., 2006. On the indentation size effect in spherical indentation. Philos. Mag. 86 (33), 5581-5593]. Here we investigate ceramic materials where the yield point is high enough to be easily distinguished in nanoindentation tests. A robust method for determining the yield point from a nanoindentation test with spherical indenters is presented. The results for a range of ceramics confirm that the increase in yield pressure is directly proportional to the inverse cube root of indenter radius. Furthermore, the yield pressure is also shown to be proportional to the inverse square root of the contact radius. Revisiting data in the literature shows that this inverse square root relationship is also true for pyramidal indenters. This implies that the indentation size effect is driven by the contact area rather than by the depth of indentation or by the indenter radius.     

爆炸法消除焊接接头残余应力的数值模拟

利用非线性动力有限元法对爆炸处理消除焊接接头残余应力的全过程进行了数值模拟。首先，采用温度场与位移场的间接耦合方法计算了钢板对接焊的焊后冷却及残余应力的生成过程，求得焊接接头处由高温冷却到室温由于变形受到阻碍而产生的不均匀的残余塑性变形和应力。然后，在焊缝区引入移动的爆炸载荷，计算了爆炸波作用下该钢板焊接接头附近应力的变化。计算结果表明，爆炸处理可引起板内应力的重新分布，从而有效地释放超过塑性极限的残余应力。利用炸药爆炸消除大型焊接结构残余应力是一种经济有效的方法，本文的数值模拟为研究炸药爆炸消除焊接结构残余应力的机理提供了有力的工具。     

Influence of penetration depth and mechanical properties on contact radius determination for spherical indentation

Knowledge of the relationship between the penetration depth and the contact radius is required in order to determine the mechanical properties of a material starting from an instrumented indentation test. The aim of this work is to propose a new penetration depth–contact radius relationship valid for most metals which are deformed plastically by parabolic and spherical indenters. Numerical simulation results of the indentation of an elastic–plastic half-space by a frictionless rigid paraboloïd of revolution show that the contact radius–indentation depth relationship can be represented by a power law, which depends on the reduced Young’s modulus of the contact, on the strain hardening exponent and on the yield stress of the indented material. In order to use the proposed formulation for experimental spherical indentations, adaptation of the model is performed in the case of a rigid spherical indenter. Compared to the previous formulations, the model proposed in the present study for spherical indentation has the advantage of being accurate in the plastic regime for a large range of contact radii and for materials of well-developed yield stress. Lastly, a simple criterion, depending on the material mechanical properties, is proposed in order to know when piling-up appears for the spherical indentation.     

Determination of mechanical properties by instrumented indentation

The paper reviews the current state of the depth-sensing indentation (sometimes called nanoindentation), where the information on material behaviour and properties is obtained from the indenter load and depth, measured continuously during loading and unloading. It is shown how the contact parameters and principal characteristics are determined using pointed or spherical indenters. Indentation tests can be used for the measurement of hardness and elastic modulus, and also of the yield stress and for the construction of stress–strain diagrams, for the determination of the work of indentation and its components. Most devices use monotonic loading and unloading, but some also enable measurement under a small harmonic signal added to the basic monotonously increasing load. This makes possible continuous measurement of contact stiffness and the study of dynamic properties and the determination of properties of coatings. One section is devoted to the measurement on viscoelastic-plastic materials, where the delayed deforming must be considered during the measurement as well as in data evaluation. Instrumented indentation can also be used for the study of creep under high temperatures. The paper also discusses the errors arising in depth-sensing measurements and informs briefly about some other possibilities of the method.     

Analysis of repeated impacts on a steel rod with visco-plastic material behavior

In machine dynamics impacts are usually common phenomena, resulting from collisions of moving bodies. Even low velocity impacts might produce high stresses in the contact region, which result in inelastic deformation. Thereby, visco-plastic materials, such as steel, show a significant increase of the yield stress with the strain rate. In machine dynamics repeated collisions occur, resulting in repeated impacts on a previously deformed contact area. Then, inelastic deformation and the resulting residual stresses produced by previous impacts have an influence on the behavior of the following impacts. Thus, the impact behavior varies with the number of impacts. This paper presents a numerical and experimental evaluation of repeated impacts with identical impact velocity up to 3 m/s, whereby the deformation history of the contact area, due to previous impacts, is included. The approach is applied to longitudinal impacts of an elastic steel sphere on a steel rod with distinct visco-plastic material behavior which is identified by Split Hopkinson Pressure Bar tests. A Finite Element analysis and experimental verification using two Laser-Doppler-Vibrometers are performed. It is shown that for an accurate impact simulation the FE model must include the visco-plastic material behavior of the steel. Further it is found that the maximal contact force, the rebound velocity and the coefficient of restitution increase with the number of impacts, while the contact duration decreases with the number of impacts. After several impacts these quantities show saturation to a constant value, indicating no significant additional inelastic deformation in the later impacts. Further, the residual stress distribution, the maximal von Mises stress distribution and the local deformation at the contact point are evaluated and a characteristic force-deformation diagram is obtained. Finally, an analysis is performed to describe the relation between maximal force and remaining crater at the contact point.     

发动机缸体铸铁件消应热处理工艺的评价

发动机缸体铸铁件生产过程中产生的铸造残余应力需要采取合适的热处理工艺消除，缸体热处理前后的残余应力变化情况可用于评价热处理工艺的有效性．文中首次采用压痕应变法与深孔法相结合，分别测量发动机缸体表面与内部残余应力分布规律，综合评价了发动机缸体铸铁件热处理前后的残余应力水平．两种不同型号缸体热处理前后残余应力测量结果表明，目前的热处理工艺并不能有效降低残余应力峰值，该热处理工艺需要进一步优化调整或考虑取消现有的热处理工艺方案．     

基于压力隧洞模型的复合材料横向热残余应力分析

考虑碳纤维横向刚度情况下,将复合材料横向热残余应力问题简化为压力隧洞模型.利用该模型推导出复合材料固化成型过程中形成的横向热残余应力,其中分析得出了单纤维与树脂的接触压力以及该压力传递到纤维和树脂后的分布情况.结果表明接触压力传递到纤维内部后成一固定值,传递到树脂后以正比于r.函数衰减.在其基础上提出场叠加方法,得出纤维之间相互耦合的接触压力与残余应力场.通过有限元模拟,理论模型和数值模拟基本一致.