A Finite Element Analysis of a Tapered Flat Sheet Tensile Specimen

A uniaxial tension sheet metal coupon with a tapered instead of a straight gage section has been used for centering the location of diffuse neck and for measuring sheet stretchability in a non-uniform strain field. A finite element analysis of such a tensile coupon made of automotive steel sheet metals has been carried out to assess the effect of the tapered gage section geometry and material plastic strain hardening characteristics on the development of local plastic deformation pattern and local stress state, especially beyond the onset of diffuse necking but before localized necking. In particular, the finite element analysis was used in this study to evaluate the accuracy and reliability of an experimental data analysis method for estimating the post-necking effective plastic stress-strain curve based on the direct local surface axial plastic strain measurements for base metal, heat-affected zone, and weld metals of a dual-phase steel DP600. It is concluded that the estimated lower and upper bounds of the effective stress-strain curve at large strains are not satisfactory for low strain-hardening materials such as heat-affected zone and weld metals with the tapered tension coupons. A simple correction method utilizing only the additional local surface strain measurement in the transverse direction is proposed and it is shown to be effective in correcting the estimated effective stress-strain curve of dual-phase steel weld metals obtained for two tapered gage section geometries.     

Two Dimensions Residual Stresses Analysis Through Incremental Groove Machining Combined with Electronic Speckle Pattern Interferometry

In this study a new residual stress determination method in two directions simultaneously is presented. This method is based on stresses relaxation in a groove that is machined incrementally. The residual stresses relaxation occurs simultaneously from both the depth and the length of the groove. Thus, measuring the surface strain field generated by the relaxation enables to determine the stress gradient both along the depth and the length of the groove. To measure the surface strain in a direction perpendicular to the groove, a digital speckle pattern interferometer is used. This method is suitable when the residual stress field in the structure varies in the depth as well as along the surface of the part, like for example in a welded structure. The method is tested here on an aluminium plate in which a central band has been shot peened.     

混凝土一维应力层裂实验的全场DIC分析

基于74mm直径分离式Hopkinson杆(SHPB)实验平台进行了混凝土杆的一维应力层裂实验.采用超高速相机(采样频率:2 $\mu$s/frame)结合数字图像相关法(DIC),记录混凝土试件中的动态位移场实时变化情况,探讨了混凝土在拉伸断裂过程中的表面位移场及速度场演化规律.针对实验中出现的多重层裂现象,基于一维应力波传播理论,指出各个位置在发生层裂时,其最大拉应力均由透射压缩波与反射拉伸波叠加而成,各处层裂发生时均处于一维应力状态.并提出了根据层裂位置左右两点速度趋势变化判断层裂发生时刻的判据.该判据可以给出所有层裂的起裂时间,结合DIC分析直接给出了混凝土多重层裂应变.结果显示混凝土的拉伸强度具有明显的应变率效应,在30 s$^{-1}$的应变率下,其拉伸强度的动态增强因子(DIF)可以达到5.与传统的波叠加法和自由面速度回跳法相比,DIC全场分析法不受加载波形限制,可以精确给出每个层裂的位置和起裂时间,从而得到试件在高应变率加载下不同位置处的断裂应变、拉伸强度及相应应变率,提高了测量效率.      

A theory for stress-driven interfacial damage upon cationic-selective oxidation of alloys

Imagine a void at an interface, separating an outwardly growing oxide and a substitutional solid solution of two metallic elements A and B. Assume the metal interface oxidizes, but the void-free surface does not. Interdiffusion inside the metal, and misfit dislocation activities at the oxidizing interface, both generate a stress-free strain rate field. The compositional and material constraints in the presence of a non-oxidizing void give rise to a multi-axial tensile stress field, while a viscoplastic strain field arises to relax stress. The tensile stress at the interface enforces a concave curvature near the void tip through the continuity condition of the chemical potential. Atoms interflow along the void surface under the combined action of curvature, stress and composition gradients. They enter the metal/oxide interface and flow under the action of local stress, curvature and composition fields. The void grows. The stress at the interface relaxes, and the interface recedes partially and non-uniformly. Interfacial voiding upon cationic-selective oxidation is a long-standing topic in the world of thermal barrier coating and interconnect systems. This paper develops governing equations, within the alloy, for stress generation upon composition evolution and induced plastic strain. Governing equations at the interface and the void surface are next formulated to describe a moving boundary problem that accounts for the simultaneous void extension and interface recession. These governing equations are boundary conditions for the bulk formulation.     

Reduction of dimensions in random,elastic soil medium

The paper deals with an application of the plane strain analysis in a stochastic three-dimensional soil medium. In a framework of random elasticity theory, the geostatical state of stresses and the problem of a unit force acting in a statistically homogeneous half-space are considered. Only the modulus of elasticity is considered to be random and is modelled as a three-dimensional (3-D) homogeneous random field. As the result of imposed constrains due to the plane strain assumption the additional body and surface forces are induced. In order to determine them, additional equations must be introduced. The equations in a form of constrain relations are proposed in this paper. These equations are also valid for a case of uniformly distributed external loading.First, the two-dimensional (2-D) problem and its reduction to the uni-axial strain state, for the gravity forces and uniform, unlimited surface loading is considered. Then, it is generalised into a 2-D schematization of the 3-D state. Next, the problem of a unit force acting in a statistically homogeneous half-space is considered. For a 3-D state of stress and strain the resulting stresses are compared with those for a 2-D state. These stresses for the multidimensional state of strain and stress are presented as a sum of two components. The first one reflects plane strain state stresses and is given in a form of a 3-D random field. This term allows for incorporating a spatial, 3-D soil variability into a two-dimensional analysis. The second component can be treated as a correction term and it represents the longitudinal influence of a 3-D analysis.Some numerical results are presented in this paper. The proposed method can be regarded as a framework for further research aiming at application to a variety of geotechnical problems, for which the plane strain state is assumed.     

基于DIC技术的爆炸应力波过异质界面应变场演化规律实验研究

采用氯仿粘结聚碳酸酯（polycarbonate, PC）板和聚甲基丙烯酸甲酯（polymethylmethacrylate, PMMA）板模拟含异质界面模型;在PC介质中布置柱状炮孔并与界面呈一定角度,根据炮孔端部与界面相对位置,分别于柱状炮孔两个端部设置起爆点,起爆点远离界面端部时定义为孔口起爆,靠近界面端部时定义为孔底起爆;借助数字图像相关实验系统,研究爆炸应力波通过异质界面后PMMA介质应变场演化过程及炮孔底部区域拉、压应变变化规律。实验结果表明,异质界面改变了爆炸应力波过界面后的传播形态。孔口起爆时,异质界面受爆破荷载作用后易形成应力集中区,界面处产生开裂,横向拉伸波作用是造成异质界面开裂的主要原因。起爆方式对过界面后介质PMMA的横/纵向拉、压应变场作用贡献不同,主要体现在应变场强度、拉/压应变场位置分布2个方面。在炮孔底部区域,起爆方式对应变场时程特性的影响主要体现在作用时效长短和应变强度2个方面。孔口起爆时,横/纵向应变体现出短时效、高强度的变化特征。就应变强度而言,起爆方式对横向压应变的影响显著强于其对纵向拉应变的影响。对空间分布特性影响主要体现在衰减程度,起爆方式对纵向应变衰减程度影响较大。无论采用何种起爆方式,爆炸应变场在PC介质中衰减速度较快,进入PMMA介质后衰减速度显著降低。     

Finite-element analysis of creep and plasticity tensile-test specimens

Traditionally, mechanical properties as determined from sensile-test specimens are assumed to be truly uniaxial and are used directly in finite-element codes for design purposes. In this paper, the stress and strain distributions in two test geometries, an hourglass specimen and a cylindrical specimen, are critically examined by means of the nonlinear finite-element code CREEP-PLAST. Since some triaxiality of the stress state is inevitable in any region with a transition, it is difficult to have a truly uniaxial test specimen. The determination of the internal stress and strain distributions makes it possible to assess the accuracy of the mechanical properties as indicated by tests on a particular specimen. Furthermore, the data given here guide the choice between the hourglass and the cylindrical specimen for applications in creep, plasticity and fatigue. Extensometry techniques permit measurements to be made only on the surface of the specimen. Thus, trouble can be caused by the nonuniform strain state present in both geometries. With the finite-element analysis, the strain field within the specimens is correlated to that on the surface; extensometry correction factors are given for selected cases.     

High-order time integration applied to metal powder plasticity

The present article treats two objectives. In the first investigation attention is focused on the application of time-adaptive finite elements formulated on the basis of a high-order time integration procedure on a constitutive model for compressible finite strain viscoplasticity for metal powder. In this connection, it has to be emphasized that the integration procedure is not only applied to the evolution equations on Gauss-point level but on the total system of differential–algebraic equations resulting from the application of the vertical line method on the quasi-static finite element equations. The specific application emerges from the field of metal powder compaction. Particular studies are carried out using stiffly accurate, diagonally implicit Runge–Kutta methods in combination with the Multilevel-Newton algorithm for solving the DAE-system. In this respect, the effort vs. accuracy behavior is investigated which is also related to order reduction known in elastoplasticity. The second topic treats the local stress algorithm for taking into account the yield function based finite strain viscoplasticity model, where the classical Newton–Raphson method fails. This is the reason why most constitutive models of powder materials are implemented into explicit finite element codes. Thus, the proposed investigations compare different methods in view of a stable and efficient integration process in implicit finite element formulations.     

建筑织物膜材双轴剪切试验与分析

为了研究建筑织物膜材的剪切力学性能,提出一种新的剪切测试方法。采用中心区域宽度和四臂长度均为16cm的十字形试件,试件纱线的经纬向与加载方向呈45°角。根据膜材变形和应力关系,推导了剪应力和剪应变的计算方法。定义了使试件中心区域产生三个循环剪应力场的加载谱,循环产生正负交替的剪切应力。试验采用表面抛光的(Polyvinylidene Fluoride,聚偏氟乙烯)涂层膜材,测量x、y两个方向的应力和应变,通过计算得到剪切应力应变曲线,并对试验结果进行分析。结果表明,新的剪切测试方法能够反映建筑织物膜材剪切力学性能。最后通过有限元方法模拟材料受剪状态下的应力和应变,与试验得到的应力值和应变值相近。     

Blind-hole residual stress determination using optical interferometry

The in-plane method and the out-of-plane method are used to analyze blind-hole residual stress as measured by optical interferometry. The in-plane method, which constructs a relation between the in-plane displacement field and the residual stress released from blind-hole drilling, is applicable when the sensitivity vector of the interferometer used in the measuring system is parallel to the object surface. Three in-plane displacements obtained from one interference pattern are sufficient to determine the residual stress. The out-of-plane method, which establishes a new relation between the out-of-plane displacement field and the released residual stress, is suggested when the sensitivity vector is perpendicular to the object surface. Two relative out-of-plane displacements extracted from one interference pattern are sufficient to determine the residual stress. With the adoption of these two methods, interpolating calculation is not needed to determine the fringe order of each data point, since the selections of the required data points are flexible using these two methods. Two experiments, one for the in-plane method and the other for the out-of-plane method, were carried out to illustrate the applicability and usefulness of these two methods.     

瓷修复体界面断裂行为的模拟实验研究

本文利用云纹干涉法和云纹干涉－－有限元混合法，对瓷修复体的模拟双材料模型界面断裂问题进行了实验研究。用云纹干涉和数字错位云纹干涉法测量带边裂纹的双材料四点简支梁在剪切作用下界面表面的剪应变分布及界面两侧局部表面的位移场，实验表明，由于界面两两侧材料力学性质不同，表现出界面剪切断裂问题的非称性和裂尖附近复合型断裂的特点；用云纹干涉法和有限元法相结合的混合法对粘接界面角点应力奇异性进行研究，并对角点附近应力应变场作了分析，得到了应力奇异指数与边界楔角，载荷的关系，证明了用界面应力强度因子Kf来描述界面端部区域应力分布的公式，并得到了双材料界面端部区域的应力应变分布情况。本文的实验结果为进一步研究口腔金瓷修复体界面的优化设计提供了基础，同时也说明云纹干涉法对于双材料界面断裂行为的研究是有效的。     

Evaluation of residual stresses and strains using the Eigenstrain Reconstruction Method

The study of residual stress has long been an important research field in science and engineering, due to the fact that uncontrolled residual stresses are detrimental to the performance of products. Numerous research contributions have been devoted to the quantification of residual stress states for the purpose of designing engineering components and predicting their lifetime and failure in service. For the purposes of the present study these can be broadly classified into two main approaches, namely, the interpretation of experimental measurements and process modelling. In this paper, a novel approach to residual stress analysis is developed, called here the Eigenstrain Reconstruction Method (ERM). This is a semi-empirical approach that combines experimental characterisation, specifically, residual elastic strain measurement by diffraction, with subsequent analysis and interpretation based on the eigenstrain theory. Three essential components of the ERM, i.e. the residual strain measurement, the solution of the inverse problem of eigenstrain theory, and the Simple Triangle (SIMTRI) method, are described. The ERM allows an approximate reconstruction of the complete residual strain and stress state in the entire engineering component. This is a significant improvement compared to the experimentally obtained limited knowledge of stress components at a selected number of measurement points, or to the simple interpolation between these points.     

Stress concentration due to an array or hemispherical cavities at the surface of an elastic half-space

The paper investigates the perturbation in an otherwise uniform stress field in an elastic half-space due to a doubly-periodic array of small hemispherical holes at the free surface. The solution is obtained using three potential functions of double Fourier series form in Galerkin's strain potential solution, the coefficients of which are determined using the collocation method. The unperturbed field is taken to be one of uniform plane stress parallel to the free surface. Two special cases are studied—uniform tension and uniform shear stress. Numerical results for these cases can be generalized by superposition to give solutions for a general state of biaxial plane stress. It is found that, for both tension and shear, the maximum stress concentration occurs at the bottom of the holes. The stress concentration factor increases with the ratio of hole spacing to radius, approaching the known solution for a single hemispherical hole at large ratios.     

Determination of the effective elastic–plastic response of metal–ceramic composites

The mechanical response of metal–ceramic composites is analysed through a homogenization model accounting for the mechanical behaviour of the constituent materials. In order to achieve this purpose a nonlinear homogenization method based on the phase field approach has been suitably implemented into a numerical code. A prescribed homogenized strain state is applied to a unit volume element of a metal–ceramic composite with proportional loading in which all components of the strain tensor are proportional to one scalar parameter. The mechanical response of the material has been modeled by considering a von Mises plasticity model for the metal phase and a Drucker–Prager associative elastic–plastic material model for the ceramic phase. A two stages plasticity has been obtained in which inelastic strain develops in the metal phase followed by a fully plastic response. A comparison with a finite element model of the stress–strain response of an axisymmetric unit cell has been carried out with the purpose to validate the homogenization based modeling presented in the paper. Plastic parameters of a Drucker–Prager yield surface for the homogenized composite have been calculated at different materials compositions. Associative Drucker–Prager plasticity has been found to be accurate for high ceramic content.     

Correlation of notch bar, metal overturn and forming data involving effective plastic strain and stress triaxiality ratio

Starting with a macrodamage parameter that relates the effective plastic strain and exponential function of stress triaxiality, a simple expression is obtained that is reminiscent of those used by other in void growth prediction. Good correlations are obtained for data on notched circular bar and sheet metal forming in addition to the problem where the triaxial stress state reversed sign. The results are affected by the fabrication condition. What has been provided is a simple means of ranking the workability of metal products that undergo plastic deformation. Limits are established in accordance with the onset of macrocracking.     

低碳钢试件弹塑性边界的白光相关检测

金属试件的弹塑性边界检测对判断该试件是否失效有着重要意义,因此一直是研究人员较感兴趣的研究课题。利用激光和白光作为照明光源的方法都曾被提出以检测金属试件的弹塑性边界以及塑性变形。为避免激光测量的诸多缺点,本文提出一种用白光作为照明光源并结合数字图像处理来检测低碳钢试件弹塑性边界的方法。该方法将数字图像相关和低碳钢试件表面弹塑性变形前后对照明光强的反射特性结合起来以判断试件是否进入塑性屈服。文中通过对加载过程中低碳钢试件表面序列图像的处理,准确地判断了该试件是否进入塑性屈服,验证了该方法的可行性。     

爆炸加载下混凝土表面的裂纹扩展

为深入研究内爆加载下岩土类材料的破坏机理，提出了一种新的爆炸裂纹检测算法，采用数字图像相关方法测量表面位移场和应变场，建立了裂纹扩展和扩张模型，并通过混凝土内爆试验观测裂纹扩展过程，研究了裂纹长度扩展与宽度扩张规律。结果表明，裂纹长度扩展是应力波和爆生气体共同作用的结果，裂纹最大扩展速度为225.95 m/s，平均速度为122.27 m/s，裂纹总长159.92 mm，长度扩展止于1.75 ms；裂纹的张开由气体主导，最大宽度1.59 mm，作用时间长达4.5 ms；拉应变集中区先于裂纹出现，其形状决定了裂纹的走向和趋势，爆炸加载下断裂过程区长度为骨料粒径的8～9倍。     

大挠度橡胶圆板的数值解及对其Hencky解的修正

将橡胶圆板视为薄膜，根据薄膜的无矩特性，巧妙采用数学方法求得橡胶圆板的膨胀状态几何特性描述，进而通过应力应变求得挠度与载荷的关系。同时，基于Hencky方法求得了挠度与载荷关系的Hencky解。对两种方法所得到的结果进行比较分析，并对Hencky解所产生的偏差进行校正的方法作了探讨。     

一种从离散模拟到连续介质弹性模拟的过渡方法

提出了一种从离散分子动力学模拟(MD)到连续介质弹性有限元计算分析(FEA)的过渡方法, 简称MD-FEA方法. 首先通过MD计算获得晶体材料原子的移动位置, 然后根据晶体结构的周期性特征构造连续介质假设下的有限单元变形模型, 进一步结合材料的力学行为本构关系获得应变和应力场. 为了检验MD-FEA方法的有效性, 将该方法应用于详细分析Al-Ni软硬组合两相材料纳米柱体的拉伸变形问题和基底材料为Al球形压头材料为金刚石的纳米压痕问题. 采用MD-FEA方法获得了上述两种问题的应力?应变场, 并将计算结果分别与传统MD方法中通过变形梯度计算的原子应变以及原子的位力应力进行了比较, 详细讨论了用MD-FEA方法计算的应力?应变场与传统MD原子应变和位力应力的区别, 并对MD-FEA方法的有效性及其相较于传统MD方法所具有的优势进行了探讨. 结论显示, MD-FEA方法与传统MD方法在应力?应变变化平缓的区域得到的结果接近, 但在变化剧烈的区域以及材料的表/界面区域, MD-FEA方法能够得到更加精确的结果. 同时, MD-FEA方法避免了传统MD方法中, 需要人为选取截断半径以及加权函数所导致的误差. 另外, 当应变较大时, MD-FEA方法计算的小应变与传统MD方法计算的格林应变存在一定差异, 因此, MD-FEA方法更适合应变较小的情形.      

软化Mohr-Coulomb材料强度参数的测定方法

为了得到试件的粘聚力和内摩擦角随轴向塑性压应变变化的曲线提出本方法。试件的弹塑性本构关系遵循相关联的Mohr-Coulomb强度准则;对常规三轴试验,试件受力进入塑性状态后,处在棱椎状屈服面的棱上,加载过程遵循Koiter流动法则。按经典塑性力学理论,推导得到轴向塑性压应变与轴向应力与轴向应变的关系;在常规三轴试验机上获得不同围压下试件的全程应力-应变曲线,进而可得到各自围压下轴向塑性压应变随加载过程的变化曲线;把来自不同围压下对应同一轴向塑性压应变的应力分别代入屈服面方程,即可求得对应的粘聚力和内摩擦角。结果表明,Mohr-Coulomb材料的两个强度参数的变化由轴向塑性压应变确定。轴向塑性压应变可以作为塑性变形的状态参数,它和试件的受力过程可以唯一确定试件的变形过程。