An approximate description of the creep rupture of structures

The economic design of high temperature structures requires an accurate estimation of the creep rupture life. Earlier work by the authors has shown that it is possible to bound the life of a structure subject to fixed loading. The bounds, however, are well separated and it is important to establish where the actual lives lie relative to the two bounds. In this paper, detailed finite element calculations and experimental work on plate structures are reported. These results, together with the concept of local kinematic determinacy, lead to a correction factor on the upper bound life prediction. This enables a good measure of the load-carrying capacity of any ductile structure to be obtained from knowledge of the limit load, the elastic stress concentration factor and material stress rupture data.     

Estimates of the creep rupture lives of structures subjected to cyclic loading

Constitutive relationships are discussed for materials which undergo creep rupture due to cyclic loading. Relationships are proposed which describe the strain rates in terms of the current stress and a single state variable. An approximate method is derived which enables a lower bound on the rupture life to be obtained for kinematically determinate structures subjected to cyclic load and isothermal conditions. The bound on the rupture life is expressed in terms of the energy dissipation rates within the structure corresponding to stationary-state creep. The effect of multi-axial stress creep-rupture upon the structural performance is examined and bounds are derived for materials which obey maximum tension and octahedral shear stress criteria. For both multi-axial stress rupture laws and structures subjected to cyclic and reverse load conditions formulae are derived which express the lower bound rupture life in terms of the behaviour of a steady-load uni-axial creep rupture test. Results of experiments which have been carried out on copper and aluminium beams are presented for cyclic and reverse load conditions. For both rupture laws the experimental rupture times are closely predicted by the representative rupture stresses and uni-axial data.     

The sensitivity of the creep rupture of a pressurized cylinder to variations in the multiaxial rupture surface

The sensitivity of creep rupture life to variations in the multiaxial creep rupture surface is investigated for a long, thick-walled, internally pressurized circular cylinder. The cylinder is initially undamaged and accumulates damage at a rate dependent on both maximum principal stress and equivalent stress. It is shown that failure can initiate at the inner or outer radius, or at an intermediate radius, depending on the parameters in the creep and damage laws, and that the ratio of rupture time to initial failure time depends strongly on these parameters. The results are compared with estimates based on the mean diameter formula and in almost all cases a longer rupture life is predicted.     

Plastic collapse and energy absorption of circular filled tubes under quasi-static loads by computational analysis

This study presents the finite element analysis of plastic collapse and energy absorption of polyurethane-filled aluminium circular tubes under quasi-static transverse loading. Increasing focuses were given to impact damage of structures where energy absorbed during impact could be controlled to avoid total structure collapse of energy absorbers and devices designed to dissipate energy. ABAQUS finite element analysis application was utilized for modelling and simulating the polyurethane-filled aluminium tubes, different set of diameter-to-thickness ratios and span lengths, subjected to transverse three-point-bending load. Different sets of polyurethane-filled aluminium tubes subjected to the transverse loading were modelled and simulated. The failure modes and mechanisms of filled tubes and its capabilities as energy absorbers to further improve and strengthening of empty tube were also identified. The results showed that plastic deformation response was affected by the geometric constraints and parameters of the specimens. The diameter-to-thickness ratio and span lengths had shown to play crucial role in optimizing the PU-filled tube as energy absorber.     

Estimating the creep life of structures subjected to arbitrary cyclic loading

For general cyclic loading it is shown that the creep life of a structure based on initial failure may be bounded from above by solving an extremum problem. This result is developed to obtain a design method based on shakedown analysis in a manner similar to earlier work on steady loading which produced a design method based on limit analysis. The proposed design method is shown to provide conservative life predictions when compared to theoretical solutions for some simple structures.     

An experimental and theoretical investigation into the creep properties of a simple structure of 316 stainless steel

The paper describes a set of creep experiments conducted on 316 austenitic stainless steel in a coupled pair of uniaxial creep testing machines which simulate the performance of a two bar structure subjected to constant mechanical and cyclic thermal loading in the temperature range of 550–600°C. The experimental results are compared with theoretical predictions using a non-interactive viscous creep/plasticity model and a model which includes recovery effects. In addition, an upper bound solution based upon the “rapid cycle” creep solution is calculated. The comparison shows that the recovery model is in close agreement with experiment and that the rapid cycle solution can provide a simple conservative estimate of the average creep rate.Several of the tests specimens exhibited strain instabilities during the initial cycles of temperature when sudden increases in inelastic strain of up to 0.2% occurred. As the material had not shown such effects in standard isothermal constant stress tests, the effects of simultaneous variation of stress and temperature which occurred in the two bar tests seems to have contributed to the occurrence of these strain instabilities.     

Upper bounds on the creep rupture life of structures subjected to variable load and temperature

Upper bounds on the rupture life and time to initial rupture of a body obeying the Katchanov creep rupture equations are derived for cyclic load and temperature. The bounds are derived from the creep rupture equation without reference to the deformation properties. The relationship to previously derived bounds of this type are discussed, and the circumstances when the bounds can be both very good and very poor are demonstrated through simple examples.     

Post-failure behaviour of impulsively loaded circular plates

The dynamic plastic response of a simply supported circular plate is analysed. Emphasis is given to the plate behaviour after it has broken free from the supports due to a local material failure. The theoretical rigid plastic analysis predicts various features of the response such as the time to failure, residual kinetic energy and the critical velocity at failure. The residual kinetic energy of the plate could be significant enough to cause secondary impact damage. It is shown that the shape of the plate changes after breaking free from the supports, which is important for forensic investigations. The solution for various cases were proven to be exact in the context of the upper and lower bounds theorems of the theory of plasticity.     

Limit loads for the plastic bending in plane strain of cantilevers containing rectangular holes under end shear

Slip-line field solutions and upper and lower bounds are given for the plane strain plastic yielding of a rectangular section cantilever containing a rectangular hole subjected to bending with shear, the hole taking varying positions along the longitudinal axis of the cantilever. Using mild steel specimens and an etching technique, both the loads and the modes of deformation at plastic collapse are shown to well authenticate the theoretical results.     

含裂纹结构的极限载荷分析

将塑性极限分析应用于含裂纹结构极限承载能力的确定中 ,结合含裂纹结构达到的塑性极限条件和裂纹失稳扩展条件 ,判断结构是否达到极限状态 ,进而求出含裂纹结构的极限载荷 ,本文给出了这一计算过程的有限元普遍格式 ,并编制了相应的有限元程序 ,计算和分析了若干典型含裂纹平板的极限载荷 ,所得结论对研究含裂纹结构的失效模式和剩余强度确定具有理论和工程参考价值     

Accuracy of bounds of plastic deformation for dynamically loaded plates and shells

Both upper and lower bounds on final displacements of dynamically loaded, rigid-plastic structures can be easily calculated. These bounds are obtained from an assumed, statically admissible stress field and a kinematically admissible velocity field, respectively. The range between these bounds is a function of the difference between stresses in these assumed fields and the actual stress distribution in the structure. This paper identifies the manner in which structural characteristics and the load distribution influence accuracy of the bounds. Generally, the range between the bounds is small for one-dimensional deformations in response to uniformly distributed loads and larger for two-dimensional deformations and more concentrated loads.     

Limit analysis of frames involving unilateral supports with frictional contact

We consider the classical limit analysis problem of frame structures made up of rigid perfectly plastic members and involving some supports in unilateral frictional contact with the ground. A direct formulation as a mixed complementarity problem (MCP) is used. For the Coulomb case, which forms the focus of this paper, the corresponding MCP may admit multiple upper bound collapse load solutions. In order to identify the least upper bound solution, we propose two algorithms. The first one attempts to enumerate the possible multiple solutions, or at least map the solution space if the solutions are connected. The second scheme tries to find the least upper bound by directly formulating and solving a single nonconvex optimization problem, known in the literature as a mathematical program with equilibrium constraints (MPEC). Two simple examples are provided to illustrate application of these approaches. They also serve to highlight some key features of such structures.     

Shakedown of elastic-plastic solids with frictionless unilateral contact boundary conditions

Elastic perfectly plastic solids (or structures) in frictionless unilateral contact with a rigid obstacle and subjected to quasi-statically variable loads within a given domain are considered. In the hypothesis that the structure undergoes small displacements and complies with a d-stability requisite herein introduced, a Melantype shakedown theorem is presented. This theorem is conceptually similar to the classical one; namely, it requires that the unilateral-contact elastic stress response to the loads and to some initial plastic strains be plastically admissible everywhere in the body and for all load conditions. A method for evaluating the shakedown load boundary is also discussed. It is shown that, by virtue of the unilateral contact constraint, all the ratchetting collapse modes pertaining to the associated no-contact shakedown problem and characterized by ratchet normal displacements against the rigid obstacle are ruled out. A simple numerical example is presented.     

A model for the minimum cost configuration problem in flexible manufacturing systems

This paper presents a mathematical programming model to help select equipment for a flexible manufacturing system, i.e., the selection of the types and numbers of CNC machines, washing stations, load/unload stations, transportation vehicles, and pallets. The objective is to minimize equipment costs and work-in-process inventory cost, while fulfilling production requirements for an average period. Queueing aspects and part flow interactions are considered with the help of a Jacksonian-type closed queueing network model in order to evaluate the system's performance. Since the related decision problem of our model can be shown to be NP-complete, the proposed solution procedure is based on implicit enumeration. Four bounds are provided, two lower and two upper bounds. A tight lower bound is obtained by linearizing the model through the application of asymptotic bound analysis. Furthermore, asymptotic bound analysis allows the calculation of a lower bound for the number of pallets in the system. The first upper bound is given by the best feasible solution and the second is based on the anti-starshaped form of the throughput function.     

Enhancement of J estimation for typical nuclear pipes with a circumferential surface crack under tensile load

This paper is to report enhancement of engineering J estimation for semi-elliptical surface cracks under tensile load. Firstly, limitation of the sole solution suggested by Zahoor is shown for reliable structural integrity assessment of thin-walled nuclear pipes. An improved solution is then developed based on extensive 3D FE analyses employing deformation plasticity theory for typical nuclear piping materials. It takes over the structure of the existing solution but provides new tabulated plastic influence functions to cover a wide range of pipe geometry and crack shape. Furthermore, to facilitate easy prediction of the plastic influence function, an alternative simple equation is also developed by using a statistical response surface method. The proposed H ₁ values can be used for elastic-plastic fracture analyses of thin-walled pipes with a circumferential surface crack subjected to tensile loading.     

Tribology of human and artificial joints.

Studies of human joint lubrication mechanisms have led to the conclusion that under normal healthy conditions they are fluid film lubricated. The main features responsible for allowing this mechanism to operate are the dynamic nature of the loading and the compliance of the bearing surfaces (articular cartilage). In contrast, artificial joints, being made of much more rigid materials, have been demonstrated to be lubricated by a mixed regime, where some load is carried by the fluid film and some by solid to solid contact. Since some surface contact takes place then wear remains a problem and friction is much higher than in human joints. The use of compliant surface bearings for artificial joints has been explored and shown to be of great advantage, reproducing the effects of natural joints. However, elastomeric materials are known to degrade in aqueous solutions so this aspect has been examined to ensure a reasonable life in the human body. Joints of the lower limb--hip, knee, and ankle--have similar load and motion patterns and behave in a similar way in terms of lubrication. Joints of the hand are not in any way similar in their behaviour and so a typical upper limb joint, the finger, has been studied to see if improvements can be made to the design of replacement artificial joints. Novel suggestions like plastic on plastic joints have been shown to be an alternative which is worthy of further consideration.     

Diagnostics of Creep of Heat-Resistant Steels on the Basis of Measurements of the Ultrasonic Wave Velocity in Nondestructive Testing of Energy Equipment: I. Probes and Tools for Measuring the Velocity of Ultrasound

The designs of probes for measuring the time of propagation of bulk and surface ultrasonic waves and examples of their use for diagnostics of the process of metal creep are described. The results of measurements of the surface wave velocity in the elastic and plastic domains are given. It is shown that in the elastic domain (up to the yield limit of the metal) change in the surface wave velocity is not greater than 0.02%. In the plastic domain, a decrease in the surface wave velocity is observed and the magnitude of the decrease depends linearly on the loading rate.     

高温金属结构缺陷免予蠕变失效评定的条件

在有限蠕变变形前提下，定义了两个基于结构参考应力的状态参量：特征温度和特征服役寿命；从服役设备合乎使用的角度出发，在上述两个参量的基础上建立了高温缺陷免予蠕变失效评定的准则，即当工作温度或服役时间小于相应的特征温度和特征服役寿命时不需要进行蠕变分析，可以按照常温缺陷评定方法讲行评定：最后给出了一个工程应用案例。     

压弯组合应力下高强钢焊接板表面裂纹疲劳寿命计算

潜艇上浮下潜运动使得其耐压壳承受交变的外压载荷。潜艇耐压壳的疲劳热点为锥一柱过渡结构连接焊缝焊趾处，该处所受的应力特征为压弯组合应力。压弯组合应力下表面裂纹应力强度因子及其疲劳寿命的计算尚无报道。弄清楚压弯组合应力作用下带表面裂纹焊接板试件的疲劳特性对潜艇等结构的疲劳研究是必要的。文中提出用成一定角度的对接焊板试件和轴向加载获得压弯组合应力来模拟潜艇耐压壳锥一柱焊接结合区的应力特征的实验方法。用980高强钢作试件，研究焊趾处预制表面裂缝，并在压弯组合应力为特征的疲劳载荷作用下表面裂纹的疲劳行为。给出高强钢焊趾表面裂纹在压弯组合应力下应力强度因子及其疲劳寿命计算式。该结果可供海洋平台、压力容器及管道的某些受力特征为压弯组合应力的重要结构的疲劳设计时参考。     

The role of surface profilometry in failure diagnosis

Many machine failures are initiated at surfaces, often where two components interact, and before any realistic modification or remedial action can be pursued it is necessary to establish what initiated failure. Wear, plastic deformation, corrosion and adhesion/pick-up/transfer may be present in isolation or together and their positive identification can make large contributions to failure diagnosis. In such studies the role of surface topography is frequently significant, particularly where component size or the presence of ionizing radiation means that only surface replicas can be examined.This paper describes the use of profilometry as an aid to failure diagnosis in a number of applications including the following: a flow control valve where plastic deformation enabled the cause of malfunction to be positively identified; a static seal failure which was attributed to plastic deformation; positive identification of indentation arising under centrifugal loading; wear assessments to predict component life; the prediction of rolling element bearing life or reliability based on quantitative assessments of wear and oxide.