ELIMIMATION OF RANDOM DEFACTS IN AEROSPACE MATERIALS

In the pastfew years,severalnew melting processeshavebeenindustrialised forthe produc tion ofsuperalloys,titanium alloysand high qualitysteelsfor useintheaero engineindustry.Theseincludeelectron beam , plasma,inductionskull,andthe”triple melt”process( VIM + ESR+ VAR) . These developments have allbeen instituted in responsetothe major per ceived problem oftheindustry ;that oftheincidence of random defectsin the alloys whichcause problemsinregardto predictablelifing ofthefinished partinservice. Thedirectconse quenceofthe uncertaintyislossof revenue due to premature retirement of parts which mayhavecompleted on a fraction oftheir actualservicelife; a conservatism on the partof design parameters whichleadsto uneccesary weightin thepart;and ariskofeitherservicefailuresor partrecalls whichinterruptengine performance. Thebenefitsoftheprocesschangesinrespectoftheproducts’absolute propertiesand alsoonthereproducibility and inspectability ofthose properties have been substantial. Itisclearthattheprocesses offer the industry a solution to the present dilem ma of how to treatthe ”rare”defectsfrom the pointof view of fracture mechanicslifing methodology. The use ofprocesscontrols which guarantee”zero defect”productisdevelopingintoacriticaltoolfortheextension oftherangeof a given alloy’s use. Itislikelyto permit very substantial gainsinboth componentlife and intheallowablestressin rotating parts withoutthe needtointroduce new materials carrying new problems of user confidence, production reliability and data base. Weconcludethatthenew processesareatastageof development wherethey arereadyforwideindustry usein production. They will not add significantly tothecomponentcost andthey willgive a renwed lifespan to the more familiar materials and methodsof aero engineconstruction.

Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials

This paper discusses a statistical second-order two-scale（SSOTS） analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.

Resonance analysis of a high-speed railway bridge using a stochastic finite element method

There is always some randomness in the material properties of a structure due to several circumstances and ignoring it increases the threat of inadequate structural safety reserves.A numerical approach is used in this study to consider the spatial variability of structural parameters.Statistical moments of the train and bridge responses were computed using the point estimation method(PEM),and the material characteristics of the bridge were set as random fields following Gaussian random distribution,which were discretized using Karhunen-Loève expansion(KLE).The following steps were carried out and the results are discussed herein.First,using the stochastic finite element method(SFEM),the mean value and standard deviation of dynamic responses of the train-bridge system(TBS)were examined.The effectiveness and accuracy of the computation were then confirmed by comparing the results to the Monte-Carlo simulation(MCS).Next,the influence of the train running speed,bridge vibration frequency,and span of the bridge on dynamic coefficient and dynamic response characteristics of resonance were discussed by using the SFEM.Finally,the lowest limit value of the vibration frequency of the simple supported bridges(SSB)with spans of 24 m,32 m,and 40 m are presented.

Statistical Analyses of the Strengths of Particulate Reinforced Metal Matrix Composites(PRMMCs)Subjected to Multiple Tensile and Shear Stresses

For design and application of particulate reinforced metal matrix composites(PRMMCs),it is essential to predict the material strengths and understand how do they relate to constituents and microstructural features.To this end,a computational approach consists of the direct methods,homogenization,and statistical analyses is introduced in our previous studies.Since failure of PRMMC materials are often caused by time-varied combinations of tensile and shear stresses,the established approach is extended in the present work to take into account of these situations.In this paper,ultimate strengths and endurance limits of an exemplary PRMMC material,WC-Co,are predicted under three independently varied tensile and shear stresses.In order to cover the entire load space with least amount of weight factors,a new method for generating optimally distributed weight factors in an n dimensional space is formulated.Employing weight factors determined by this algorithm,direct method calculations were performed on many statistically equivalent representative volume elements(SERVE)samples.Through analyzing statistical characteristics associated with results the study suggests a simplified approach to estimate the material strength under superposed stresses without solving the difficult high dimensional shakedown problem.

A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for Random Composite Materials

The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random coefficients.However,many random composite materials in scientific and engineering computing do not satisfy the stationary assumption.To overcome the difficulty,we propose a normalizing field flow induced two-stage stochastic homogenization method to efficiently solve the random elliptic problem with non-stationary coefficients.By applying the two-stage stochastic homogenization method,the original elliptic equation with random and fast oscillatory coefficients is approximated as an equivalent elliptic equation,where the equivalent coefficients are obtained by solving a set of cell problems.Without the stationary assumption,the number of cell problems is large and the corresponding computational cost is high.To improve the efficiency,we apply the normalizing field flow model to learn a reference Gaussian field for the random equivalent coefficients based on a small amount of data,which is obtained by solving the cell problems with the finite element method.Numerical results demonstrate that the newly proposed method is efficient and accurate in tackling high dimensional partial differential equations in composite materials with complex random microstructures.