Homogenization of some variational problems connected to the theory of lubrication

An important problem in the theory of lubrication is to model and analyze the effects of surface roughness on the hydrodynamic performance. An efficient method to do this is homogenization. In this paper we prove a general homogenization result which allows us to consider unstationary variational problems, related to Reynolds type equations, where the lubricant may be Newtonian or non-Newtonian. Recently, the idea of finding upper and lower bounds on the effective behavior, obtained by homogenization, was applied for the first time in tribology. The homogenization result in this work may therefore also serve as a rigorous starting point for developing these successful results to unstationary problems.     

Prediction of fragment size and ejection distance of masonry wall under blast load using homogenized masonry material properties

The fragment hazard resulting from a nearby explosion is a major concern in the design of structures which may be subjected to blast loads. This paper presents a predictive method based on the theories of continuum damage mechanics and mechanics of micro-crack development, and numerical simulation to determine the probabilistic fragment size distribution and the launch distances. Theoretical derivations are presented to calculate fragment distribution. The fragmentation process is modeled according to the crack initiation and propagation, which depend on the material damage levels and are estimated using continuum damage mechanics theory. The proposed method involves two steps. First a finite element model is developed to estimate the material damage, fragment distribution and the ejection velocity. Then a simple algorithm is used to predict the fragment trajectory and the launch distance based on the fragment size and the ejection velocity. A masonry wall is used as an example in this study. The wall is modeled with both the distinctive consideration of the brick and mortar material properties and the homogenized masonry material properties. The reliability and efficiency of using the homogenized masonry material model in predicting the masonry wall damage and fragmentation are proven. The program AUTODYN is used in this study to conduct the numerical simulations with the proposed models linked to it as user subroutines. The numerical results indicate that the masonry fragments approximately follow the Weibull distribution, which is consistent with some empirical fragment distributions. The proposed method avoids using erosion technique, which inevitably results in a loss of fragment mass, and avoids discretizing the structure into particles or predefining the failure planes, which may lead to unrealistic prediction of damage propagation and evolution and therefore inaccurate fragmentation process and fragment size distributions.     

Experiments and mesoscopic modelling of dynamic testing of concrete

Due to their large aggregates size and their heterogeneous microstructure, concretes are difficult materials to test at high strain-rates. Direct tensile tests, spalling tests and edge-on impact experiments have been especially developed and performed on a standard concrete (max grain size of 8 mm). The influence of free water on the high strain rate behaviour has been carefully evaluated. Numerical simulations of dynamic testing have been also performed using a mesoscopic approach in which the matrix and the aggregates are differentiated. Numerical and analytical homogenization methods have been employed to define a model-concrete which fits experimental data of simple and œdometric compression tests. Then, the numerical simulations with several random distributions of aggregates were conducted to validate the processing methods applied to the experimental data of the dynamic tests. Moreover an anisotropic damage model coupled to the mesoscopic approach has been used to simulate the dynamic behaviour of concrete under impact. It allows predicting the increase of strength and cracking density with strain-rate and the free water influence on the dynamic behaviour of concrete.     

Overall behavior and microstructural deformation of R-CNT/polymer composites

Carbon nanotubes (CNTs) are an excellent candidate for the reinforcement of composite materials owing to their distinctive mechanical and electrical properties. Reticulate carbon nanotubes (R-CNTs) with a 2D or 3D configuration have been manufactured in which nonwoven connected CNTs are homogeneously distributed and connected with each other. A composite reinforced by R-CNTs can be fabricated by infiltrating a polymer into the R-CNT structure, which overcomes the inherent disadvantages of the lack of weaving of the CNTs and the low strength of the interface between CNTs and the polymer. In this paper, a 2D plane strain model of a R-CNT composite is presented to investigate its micro-deformation and effective stiffness. Using the two-scale expansion method, the effective stiffness coefficients and Young’s modulus are determined. The influences of microstructural parameters on the micro-deformation and effective stiffness of the R-CNT composite are studied to aid the design of new composites with optimal properties. It is shown that R-CNT composites have a strong microstructure-dependence and better effective mechanical properties than other CNT composites.     

Microstructure–strength models for heat treatment of Al–Si–Mg casting alloys I: microstructure evolution and precipitation kinetics

A comprehensive microstructure–strength mathematical model for the heat treatment of Al–Si–Mg casting alloys is presented. As part of the model development, the evolution of microstructure and mechanical properties during heat treatment of an industrially cast A356 aluminium alloy was studied in an extensive experimental investigation. For the solution treatment process, the changes in dendritic composition and eutectic morphology in the temperature range 773–833 K (500–560°C) were quantified using microprobe and image analysis techniques. For natural and artificial ageing, the kinetics of precipitation/clustering was determined using an isothermal calorimetry technique in conjunction with hardness and mechanical property measurements. Two other Al–Si–Mg model alloy compositions were used to study the effects of alloy chemistry on microstructure response during heat treatment. The overall aim of the experimental work presented here is to facilitate the development of a comprehensive microstructure–strength model for the heat treatment of Al–Si–Mg casting alloys that will be presented in part II of this paper.

On présente un modèle mathématique détaillé de la microstructure-résistance du traitement thermique des alliages de moulage d'Al–Si–Mg. Faisant partie du développement du modèle, on a étudié l'évolution de la microstructure et des propriétés mécaniques lors du traitement thermique d'un alliage d'aluminium A356 moulé industriellement lors d'un examen expérimental de grande envergure. Pour le traitement de mise en solution, on a quantifié les changements de la composition dendritique et la morphologie de l'eutectique dans la gamme de température de 773 à 833 K (500 à 560 °C) en utilisant les techniques de la microsonde et de l'analyse d'image. Pour le vieillissement naturel et artificiel, on a déterminé la cinétique de précipitation/agrégation en utilisant une technique de calorimétrie isotherme en conjonction avec les mesures de dureté et de propriétés mécaniques. On a utilisé deux autres compositions de l'alliage modèle d'Al–Si–Mg pour étudier les effets de la chimie de l'alliage sur la réponse de la microstructure lors du traitement thermique. Le but global du travail expérimental présenté ici est de faciliter le développement d'un modèle détaillé de microstructure-résistance du traitement thermique des alliages de moulage d'Al–Si–Mg qui sera présenté dans la seconde partie de cet article.     

7050铝合金铸锭的热处理

对铸造7050铝合金进行均匀化热处理,并对处理后的试样硬度和微观组织进行分析,找出7050铝合金均匀化的最优化生产工艺。结果表明,均匀化处理工艺为480℃×24h;在该热处理工艺下,均匀化处理组织情况较好,过烧较少且硬度较高,晶界处仍含有以Cu为主的未溶第二相,但其形态由初始的块状变为断续的颗粒状。     

基于均匀化混沌系统生成S盒的算法研究

该文给出了一个新的二次多项式混沌系统,并利用系统与Tent映射拓扑共轭的性质,给出了系统的概率密度函数,基于概率密度的形式,进一步设计了一个变换函数,实现了系统的均匀化。针对均匀化前后的混沌系统构造了S盒生成算法,对该算法产生的300个S盒进行差分概率(DP)和线性概率(LP)的统计分析,结果表明均匀化后混沌系统产生的S盒的DP和LP略优于均匀化前的值。     

Micromechanical modeling of dual phase steels

Dual phase (DP) steels having a microstructure consisting of a Ferrite matrix, in which particles of Martensite are dispersed, have received a great deal of attention due to their useful combination of high strength, high work hardening rate and ductility, all of which are favorable properties for forming processes. Experimental investigation into the effect of the harder phase volume fraction, morphology and phase distribution on mechanical properties of the dual phase steels is well established and comprehensive in the literature. In the present work, a micromechanical model is developed to capture the mechanical behavior of such materials, adopting the constitutive behavior of the constituents from the literature. Analytical approaches have been used in the past to model the DP steel material behavior, but theoretical treatments are based on the assumption of uniform deformation throughout the constituents, neglecting the local strain gradients. This assumption contradicts experimental observations, reduces the understanding of the mechanics and mechanism of deformation of such materials. Based on the micromechanical modeling of cells, several idealizations are investigated out of which the axisymmetric model is shown to display intrinsic ability to capture the expected material behavior in terms of the trend of the stress–strain curves with increasing volume fraction of the second phase and in terms of the deformation fields of the constituents.