A theory of smeared continuum damage mechanics

This paper considers smeared continuum damage mechanics based on the equivalent elliptical crack representation of a local damage. This approach provides a means of utilizing the crack energies derived in fracture mechanics, and of identifying the local damage state from local stress and strain information. The strain energy equivalence principle is used to derive the effective continuum elastic properties of a damaged solid in terms of the undamaged elastic properties and a scalar damage variable. The scalar damage variable is used to develop a consistent damage evolution equation. The combination of representing local damage as an equivalent elliptical crack, the determination of effective elastic properties using a strain energy equivalence principle, and a consistent damage evolution equation yields a simple, yet powerful local approach for continuum damage analysis     

Stress concentration analyses of bi-material bonded joints without in-plane stress singularities

The problem of stress concentration in bi-material bonded joint is investigated under the condition of without stress singularities. Disappearance conditions of stress singularity near interface corners and edges are determined based on analyses of eigenvalue equations. Straight-side and curved interface of materials are designed for the bi-material models to avoid singular stress fields around the interface corner and edge. Assuming that one stress component or combined stresses are responsible for failure at or near the interface, the stress concentration becomes critical for the design of bi-material joints with higher interfacial strength. Numerical results show that the stress state near the interface depends strongly on both the interface geometry and the combination of materials, and stress concentration may always occurs at or near the interface. Emphasis is placed on the necessity for geometric optimization of an interface in order to design singularity-free junction with higher interfacial strength.     

Effect of temperature on stresses and delamination failure of z-pinned joints

Although z-pins have been shown effective in preventing delaminations in adhesively bonded and co-cured joints, their applicability depends on a reliable assessment of the strength of a z-pin-composite assembly. In particular, high residual thermal stresses that have been found in experiments dictate the necessity in a local stress analysis. Elevated temperature applied to the joint during its lifetime may also affect its effectiveness in preventing delaminations. The present paper illustrates an approach to determining local residual stresses confirming the observations regarding a possible delamination and cracking in the composite structure due to high post-processing transverse stresses. The analysis of the effect of elevated temperature applied at one of the surfaces on the response of a z-pinned joint is conducted using the concept of a double cantilever beam with an “insulated” crack. In addition, it is illustrated that an elevated temperature may actually benefit the integrity of the joint if it causes an increase in the z-pin-composite interfacial strength.     

Calibration and evaluation of seven fracture models

Over the past 5 years, there has been increasing interest of the automotive, aerospace, aluminum, and steel industries in numerical simulation of the fracture process of typical structural materials. Accordingly, there is a pressure on the developers of leading commercial codes, such as ABAQUS, LS-DYNA, and PAM-CRASH to implement reliable fracture criteria into those codes. Even though there are several options to address fracture in these and other commercial codes, no guidelines are given for the users as to which fracture criterion is suitable for a particular application and how to calibrate a given material for fracture. The objective of the present paper is to address the above issues and present a thorough comparative study of seven fracture criteria that are included in libraries of material models of non-linear finite element codes. A set of 15 tests recently conducted by the authors on 2024-T351 aluminum alloy is taken as a reference for the present study. The plane stress prevails in all these tests. These experiments are compared with the constant equivalent strain criterion, the Xue–Wierzbicki (X–W) fracture criterion, the Wilkins (W), the Johnson–Cook (J–C) and the CrachFEM fracture models. Additionally, the maximum shear (MS) stress model, and the fracture forming limit diagram (FFLD) are included in the present evaluation. All criteria are formulated in the general 3-D case for the power law hardening materials and then are specified for the plane stress condition. The advantage of working with plane stress is that there is one-to-one mapping from the stress to the strain space. Therefore, the fracture criteria formulated in the stress space can be compared with those expressed in the strain space and vice versa. Fracture loci for all seven cases were constructed in the space of the equivalent fracture strain and the stress triaxiality. Interesting observations were made regarding the range of applicability and expected errors of some of the most common fracture criteria. Besides evaluating the applicability of several fracture criteria, a detailed calibration procedure for each criterion is presented in the present paper. It was found rather unexpectedly that the MS stress fracture model closely follows the trend of all tests except the round bar tensile tests. The X–W criterion and the CrachFEM models predict correctly fracture in all types of experiments. The W criterion is working well in certain ranges of the stress triaxiality.     

微电子封装中焊点疲劳模型的现状和发展

在电子元件的设计和电子封装的可靠性评估中焊点的热-机械可靠性是一个关键的因素.已经有许多疲劳模型提出和发展用于分析焊点在热-机械疲劳载荷下的可靠性问题.对这些模型进行了回顾,并对它们的应用和局限性作出了评价.     

Analysis and tests of boned insulted rail joints subjected to vertical wheel loads

In traditional railroad tracks, joint bars are being used to connect the ends of adjoining rails. Because the vertical bending stiffness of two bars is generally much lower than of the rails, the passing wheels generate larger deflections in the joint region. This in turn leads to larger wheel forces caused by the dynamics of the passing vehicles and to accelerated track deterioration. In recent decades these expansion joints are being eliminated by the introduction of the continuously welded rails (CWRs). However, the retention of the automatic block signaling system created the need for electrically insulated joints is that the bending stiffness of the insulated joints bars is even smaller than of the non-insulated bars that are being eliminated. There are very few published analyses of joints in track; especilly of insulated joints. The purpose of this paper is to contribute to a better understanding of the mechanics of rail joints. At first an analysis is presented for the joint tests to be conducted. Then a test program is described that utilizes actual bonded joints. The obtained test results are then compared with the corresponding analytical results. The agreement is good. This confirms the validity of the assumed joint model and of the presented analysis. The paper concludes by analyzing the effect of a rail joints in a CWR track caused by a vertical wheel load.     

Effects of substrate materials on fracture toughness measurement in adhesive joints

To understand the effects of substrate materials on the fracture behavior of adhesive joints, experimental studies and finite element analyses have both been conducted for double-cantilever-beams (DCB) with aluminum and steel substrates at different bond thickness (h). Numerical results show that the region dominated by the crack singularity is much smaller than by the bond thickness. Very small plastic deformation may hence violate the requirements for small-scale yielding where the crack-tip field can be characterized uniquely by the stress intensity factor. Both critical strain energy release rate and J-integral for the joints with steel substrate are lower than those for the joints with aluminum substrate. Compared to the critical strain energy release rate, the critical J-integral is less sensitive to the substrate material if small plastic deformation occurs before cohesive failure takes place through the adhesive layer. For the joints with aluminum substrate, the fracture toughness initially increases and then decreases with bond thickness. Elastic–plastic crack-tip analysis indicates that at the same level of loading, a higher opening stress is observed in the joint with a smaller bond thickness. A self-similar stress field can be obtained by the normalised loading parameter, J/hσ₀.     

机械螺栓法兰连接的有限元力学模型比较研究

机械螺栓-法兰连接结构中存在着复杂的接触、摩擦和预紧等非线性因素.螺栓-法兰连接结构的有限元力学模型应当充分包含这些因素.首先介绍了连接结构接触分析的有限元法理论,然后比较研究了二维轴对称力学模型和三维实体模型在螺栓一法兰连接结构建模中的差剐,之后研究了温度载荷法、过盈配合法和等效外载法等三种不同的螺栓预紧力建模方法.计算结果表明:二维模型在处理螺栓-_法兰连接结构上计算耗费小,但计算精度较三维模型差别较大,结果粗糙;三种预紧力模拟方法都能模拟螺栓预紧载荷,但在适用范围、等效方法和计算精度等方面有区别.     

A fracture mechanics life prediction methodology applied to dovetail fretting

This work evaluates a fracture mechanics based crack growth life prediction methodology for dovetail fretting fatigue laboratory experiments. The Ti–6Al–4V specimens were configured with angles of 35°, 45° and 55°. Experiments were conducted with constant amplitude loading at R of 0.1 and 0.5 with lives ranging from 100,000 to 10 million cycles. The approach included the contact loads and bulk stress calculated from the finite element method as inputs to the stress and life analysis. Contact stresses were calculated using the contact stress analysis software CAPRI. These stresses were input into a stress intensity factor calculation at the edge of contact. Crack propagation life was calculated from an assumed initial crack size. Analysis showed that propagation consumes a majority of the total life and is insensitive to a large range of initial crack sizes.     

Comparison between Gurson and Lemaitre damage models in wiping die bending processes

This paper is devoted to a finite element prediction of material damage distribution within the workpiece during wiping die bending processes. The damage mechanics approach has been used in this investigation in order to describe the progressive damage evolution within the sheet. A comparative study between the results obtained by the simulations using the Lemaitre and Gurson damage models is presented and discussed. The elastoplastic constitutive laws are integrated by means of an incremental formulation which has been implemented in the finite element code ABAQUS. The punch load, influenced by the friction coefficient, is investigated for different cases of die radius. The springback angle, which depends on the elastic properties of the material, is computed for all cases. Both models give similar results in the modelling of bending operations. The Gurson one is shown to have more flexibility for applications.     

Frictional resistance of new and explanted artificial hip joints

The frictional resistance of 54 explanted Charnley joints and 32 new joints (various types) has been measured in a hip function simulator in dry and lubricated environments.

The friction factors (torque/(normal load × radius) ) for new prostheses were remarkably similar no matter what material or head size was used provided the acetabular component was made of ultra high molecular weight polyethylene (UHMWPE).

Charnley joints, implanted for up to 17 years, were removed from the patients at revision operations and showed that most had a friction factor similar to that of new joints. However, 30% had a friction factor greater than 0.16 when dry and 39% showed friction factors in excess of 0.07 when lubricated (cf 0.1 and 0.04 respectively when new).

All the joints operated under a mixed lubrication regimen.

When the acetabular component was made from UHMWPE, the friction factors were hardly affected by the material of the femoral component. 30% of explanted joints had friction almost twice as great as new joints, but loosening of the prostheses also occurred in some joints whose friction remained low.     

Experimental and mechanical model for predicting the behaviour of minor axis beam-to-column semi-rigid joints

This paper describes a series of experimental tests followed by finite element simulations produced to enable the prediction of moment resistance and rotation capacity of minor axis beam-to-column semi-rigid connections. These investigations motivated the development of a mechanical model to assess the connection's structural response. The mechanical model is based on the component method of design, in accordance with the Eurocode 3 specification. This philosophy implies that each joint component is represented by a spring possessing a non-linear force versus displacement (F-Δ) curve. The model was subsequently calibrated against experimental and finite element results previously performed.     

车床应力断料辅具的设计及动态特性研究

介绍了一种能够应用于车床的应力断料辅具的结构及工作原理,通过pro/e三维实体建模,并在ADAMS软件中进行动力学仿真获得了关键部件的动态性能参数,证明了机构设计的合理性.     

A variationally based nonlocal damage model to predict diffuse microcracking evolution

We explore a variationally based nonlocal damage model, based on a combination of a nonlocal variable and a local damage variable. The model is physically motivated by the concept of “nonlocal” effective stress. The energy functional which depends on the displacement and the damage fields is given for a one-dimensional bar problem. The higher-order boundary conditions at the boundary of the elasto-damaged zone are rigorously derived. We show that the gradient damage models can be obtained as particular cases of such a formulation (as an asymptotic case). Some new analytical solutions will be presented for a simplified formulation where the stress–strain damage law is only expressed in a local way. These Continuum Damage Mechanics models are well suited for the tension behaviour of quasi-brittle materials, such as rock or concrete materials. It is theoretically shown that the damage zone evolves with the load level. This dependence of the localization zone to the loading parameter is a basic feature, which is generally well accepted, from an experimental point of view. The computation of the nonlocal inelastic problem is based on a numerical solution obtained from a nonlinear boundary value problem. The numerical treatment of the nonlinear nonlocal damage problem is investigated, with some specific attention devoted to the damageable interface tracking. A bending cantilever beam is also studied from the new variationally based nonlocal damage model. Wood’s paradox is solved with such a nonlocal damage formulation. Finally, an anisotropic nonlocal tensorial damage model with unilateral effect is also introduced from variational arguments, and numerically characterized in simple loading situations.     

Squeeze films between a rigid cylinder and an elastic layer bonded to a rigid foundation

A numerical solution to the elastohydrodynamic lubrication problem of a rigid cylinder and an elastic layer firmly bonded to a rigid substrate in normal approach and separated by a fluid of constant viscosity is presented. The rate of change of the deformation with time was neglected in the present investigation. The governing equations were solved via an iterative method in order to compute the pressure distribution and the corresponding film profile.Influences of the layer thickness, the layer compressibility and the central squeeze-film velocity on the results were investigated. In the case of the Hertzian contact, the present method was validated against the results reported in Herrebrugh [Elastohydrodynamic squeeze films between two cylinders in normal approach, Trans ASME, J Lubric Technol Ser F 1970; 92:292–302] where the results showed a very good agreement.     

Comparison between Lemaitre and Gurson damage models in crack growth simulation during blanking process

In this paper, the numerical results obtained by a finite element analysis in the case of sheet metal blanking process are compared with the experimental ones to verify the validity of Gurson and Lemaitre damage models in describing the initiation and propagation of cracks during the process evolution. The concept of continuum damage mechanics has been retained to describe the progressive damage accumulation into the sheet metal leading to the final rupture. During the analysis, the crack propagation is simulated by the propagation of a completely damaged area. The comparative study of the results obtained by simulations using different damage models and experimental ones, showed that Gurson damage model is not able to predict the fracture propagation path in a realistic way. Only Lemaître damage model gives good results.     

Mechanical behavior and numerical estimation of fracture resistance of a SCS6 fiber reinforced reaction bonded S13N4 continuous fiber ceramic composite

Continuous fiber ceramic composites (CFCCs) have advantages over monolithic ceramics: Silicon Nitride composites are not well used for application because of their low fracture toughness and fracture strength, but CFCCs exhibit increased toughness for damage tolerance, and relatively high stiffness in spite of low specific weight. Thus it is important to characterize the fracture resistance and properties of new CFCCs materials. Tensile and flexural tests were carried out for mechanical properties and the fracture resistance behavior of a SCS6 fiber reinforced Si₃N₄ matrix CFCC was evaluated. The results indicated that CFCC composite exhibit a rising R curve behavior in flexural test. The fracture toughness was about 4.8 MPa m^1/2 , which resulted in a higher value of the fracture toughness because of fiber bridging. Mechanical properties as like the elastic modulus, proportional limit and the ultimate strength in a flexural test are greater than those in a tensile test. Also a numerical modeling of failure process was accomplished for a flexural test. This numerical results provided a good simulation of the cumulative fracture process of the fiber and matrix in CFCCs.     

Isolation and analysis of articular joints wear debris generated in vitro

The total replacement of damaged or diseased synovial joints represents one of the greatest advances in orthopaedic surgery of the 20th century. Whereas replacements are available for the shoulder, ankle, elbow, and knee, hip accounts particularly for the most surgical interventions. In France, 100,000 hip joints per year are replaced and all the implants consist of a sliding pair represented by a hard counter face, either metal or ceramic, and commonly a softer polymer. Ultra high molecular weight polyethylene (UHMWPE) was first used in joint replacement in the early 1960s. Since that time, it had been the dominant polymer for bearing surfaces in orthopaedic surgery. However, generation of UHMPWE wear debris from bearing surfaces in patients is the major problem for long term implants. Both volume and morphology of the wear particles determine the response of the body to debris, and subsequent effects on secure fixing.This paper presents a review of the type of particles most frequently found in biopsies of tissues from explanted prostheses. Indeed, the size and the amount of these debris are very important factors for a better understanding of wear and corrosion wear processes in artificial joints. Real wear particles are also described in this paper.     

Accuracy and strength of a joint loaded by suddenly applied torque

The influence of the required quality (fit and degree of accuracy) of prismatic joints to achieve guaranteed clearance was a speciality of experienced designers. The problem becomes quite complicated owing to stresses arising in the joint elements during torque transmission under dynamic loading.In this paper a widely used prismatic joint with a hexagonal cross-section is considered. A dynamic loading, generated by a spring mechanism is applied. D'Alambert's principle was employed in solving the kinesthetic problem.The paper presents equations for the dynamic coefficient, the angle of clearance, _i and the maximum tangential stress. It is pointed out that torque-loaded elements cannot be produced from rolled stock, obtained from drawings.The presented graphs permit selection of the steel grade in accordance with the fit and the degree of accuracy of the joint and with the permissible torsional stress.The proposed procedures may be used for computer-aided design of torque-transmitting prismatic splines, key joints and torsion mechanisms.Nomenclature d ₁ diameter of hole (see Fig. 1) - d _max D _n + es maximum limit of shaft size - d _min D _n + is minimum limit of shaft size - D _max D _n + ES maximum limit of hole size - D _min D _n + EI minimum limit of hole size - D _n nominal size of the hole and of shaft - ES, es upper deviation of hole and shaft - EI, ei lower deviation of hole and shaft - F area of hexagon - G modulus of transverse elasticity - (see Fig. 1) - I _p polar moment of intertia - polar moment of inertia of hexagon - polar moment of inertia of circle - K dynamic coefficient - l length of shaft - m number of polygon sides - M _d torque under dynamic loading - M _s torque under static loading - S _i clearance - S _max = ES-ei maximum clearance of joint - S _min = EI-es minimum clearance of joint - T tolerance - W section modulus of torsion - W _c circle section modulus of torsion - W _h hexagon section modulus of torsion - (see Fig. 1) - maximum tangential stress under dynamic loading - maximum tangential stress under static loading - _d twist angle under dynamic loading - _i angular displacement - _s twist angle under static loading     

Elastodynamic response of a crack perpendicular to the graded interfacial zone in bonded dissimilar materials under antiplane shear impact

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of antiplane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.