脆性断裂统计理论

本文试图用统计方法,将金属脆性断裂的微观过程与宏观过程结合起来,把断裂理论建立于微裂纹发展动力学的统计基础上。脆性断裂实质上是在小的范性变形过程中微裂纹成核长大的非平衡统计过程和单个主裂纹的传播过程。本文导出了描述这种非平衡统计过程的微分积分方程,并从位错机理出发研究了微裂纹动力学,从而解出了微裂纹的分布函数,求出了金属试样的断裂几率,进而导出了延伸率、断裂强度、范性功、裂纹扩展力、断裂韧性、临界裂纹长度、范性-脆性转变温度以及它们的统计偏差与其它有关物理量之间的函数关系。 关键词：     

金属穿晶脆性断裂统计理论

讨论了金属穿晶脆性断裂统计理论.根据穿晶裂纹和晶界作用的界面能模型及断裂非平衡统计理论框架,推导出了裂纹扩展速率、断裂强度、断裂韧性、脆性—韧性转变温度及其统计分布函数随晶粒尺度和界面能变化的公式. 关键词：     

微裂纹演化的随机模型

本文用非平衡统计的概念和方法探讨了各种断裂过程中的共同问题——微裂纹或微空洞的演化。文中从描述微裂纹演化过程的多元主方程出发,导出了微裂纹演化动力学方程,指出了微观机理与宏观过程相结合的途径,讨论了微裂纹分布函数应有的性质。 关键词：     

射线引起DNA双链断裂的统计分布

辐射过程引起的生物细胞的DNA双链断裂是一种很重要的细胞损伤过程.射线在细胞中能量沉积比较大时,DNA双链断裂的碎片分布会偏离随机断裂模型给出的结果,为此发展了新的模型分析方法-统计碎裂模型.根据统计物理学的原理和方法，放射性射线照射细胞后，将射线的能量传递给细胞中的DNA分子，当沉积的能量比较大时，体系会经过一个弛豫过程，DNA碎片大小l按照统计规律分布.体系熵值取极大的分布是最可几的分布，从而得到了辐射导致DNA双链断裂后碎裂片段随其大小l的分布函数exp(αl+βl²)，它对应于 两种成分，一种成分随碎裂片段的大小l的增大而迅速减小，这对应于分布函数中的exp(βl ²)项，对于质量比较小的碎裂片段，这种成分是主要贡献；另外一种成分随碎 裂片段的大小l的增大而缓慢减小，这对应于分布函数中的exp(αl)项，对于质量比较大的 碎裂片段，这种成分是主要贡献.根据实验所测的碎裂片段分布，通过数值解法解积分方程 ，将热力学参数α，β解出，与实验结果进行比较，实验的结果支持了DNA双链断裂后碎裂 片段分布的统计碎裂模型. 关键词： 熵 统计碎裂模型 DNA双链断裂     

金属的断裂韧性

本文根据微裂纹的随机演化及其长大需要堆积位错群进一步滑移以将领首位错挤入微裂纹中的机理,导出了微裂纹扩展力和断裂韧性及其统计分布函数,讨论了影响因素。 关键词：     

组成论介绍(下):广泛的应用

1　概念的应用1.1　广义集合与分布函数概念的应用广义集合概念使“客观事物”概念清楚了一层 .广义集合连同分布函数概念又超脱过细的学科分类 ,它们具有“相对普适性”、“相对确切性”和“形式的相对具体性”[7] .这使它们比“客观事物”概念更容易进入各个自然 (社会 )科学领域 .概率分布是概率论中的重要概念 ,也是新定义的分布函数的特例 .分布函数是统计物理学中的重要概念 ,也是新定义的分布函数的特例 .所以分布函数早就在这些领域广泛应用了 .把一般事物整理为广义集合 ,这为发现分布函数理清了思路 .发现一个函数就是找到一种客…     

悬浮颗粒散射脉冲信号群的统计分形特性

将PCI-9812高速数据采集卡与激光尘埃粒子计数光电传感器结合,对空气中悬浮颗粒群产生的散射脉冲信号数随幅度的统计分布p(l)进行高分辨率的测定.实验数据表明,在大样本条件下,脉冲信号集合整体及不同脉宽信号子集的p(l)函数在幅度定义域(V0,VM)内均以很高的精度满足对数正态分布形式,即该随机脉冲信号群具有统计分形(自相似)特征.进一步理论研究表明,p(l)函数具有非线性缩放不变性;且当统计参数满足(lnl-lnl)2lnl时,该函数与幂函数l-(1-ε)表现出几何相似性,其中ε1.     

PBX炸药含各向异性损伤的黏弹性统计微裂纹本构模型初步研究

建立含损伤本构模型是研究炸药动态力学响应规律的基础。基于PBX炸药材料的宏观黏弹性特征和细观上微裂纹面的方向性,建立了含各向异性损伤的黏弹性统计微裂纹(Aniso-Visco SCRAM)本构模型,简化后得到单轴应力加载下的本构方程。利用数值计算程序,以PBX9501为例,分析了微裂纹扩展的各向异性、PBX炸药破坏强度及临界应变的拉压异性和应变率相关性,考察了微裂纹数密度、初始微裂纹尺寸、微裂纹面摩擦系数及断裂表面能4个主要参数的敏感性及影响规律。结果表明,它们对微裂纹的扩展演化有较大影响,进而导致材料表现出不同的力学响应。     

陶瓷材料中圆形夹杂的本征应变导致的微开裂

由夹杂转变引起的微开裂与陶瓷材料的断裂和增韧机制密切相关。本文采用位错连续分布的方法,导出圆形夹杂发生本征应变时在母体材料中形成的微裂纹的位错密度函数、张开位移及应力强度因子的解析表达式,并据本文得到的结果进行了分析和讨论。 关键词：     

一类相空间中的准几率分布函数系

定义了一类相空间中的准几率分布函数系，这个准几率分布函数系直接建立在具有更加广泛意义的量子相空间Schr?dinger方程解的基础之上，其中定义_α=αp-i?q和_α=(1-α)q+i?p.发现了两个有趣的关系.(1)建立的量子相空间Schr?dinger方程的解实际上是对函数φ(λ)exp［i(1-α)qp］做窗口Fourier变换.(2)这个窗口函数g(λ)起着选择窗口形式的作用，而且不同的窗口对应着不同的分布函数.当g(λ)是一个代表Gauss窗的Gauss函数的时候，准几率分布函数就是一个类似于Husimi的分布函数f^HL_α(q,p)；当g(λ)是一个表示椭圆的复函数时，准几率分布函数就是一个椭圆分布函数f^E_α(q,p)；再在g(λ)为复函数的基础上附加α=0，就可得到标准序分布函数f^S(q,p)、反标准序分布函数f^AS(q,p)和Wigner分布函数f^W(q,p)，此时g(λ)表示高度为1/12π?而长度为λ的矩形窗. 关键词： 窗口Fourier变换 相空间 Wigner分布函数     

脆性断裂的统计理论

本文试图从位错理论出发来探索晶体脆性断裂的统计理论。脆性断裂过程,实质上是微裂缝在极小的范性形变过程中形成长大和传播的随机过程。本文导出了描述这种随机过程的微分方程,利用微裂缝形成长大的位错机理,解出了微裂缝大小的统计分布函数。文中给出了范性形变、加工硬化和活动位错源数目与微裂缝数目和大小之间的函数关系。过去研究脆性断裂时,范性变形只是含糊地包括在有效表面能之内,而加工硬化和活动位错源数目则一向被略去。从微裂缝大小的统计分布函数和微裂缝的传播条件,导出了强度的统计分布函数,从而求得了脆性断裂判别式、脆性断裂强度及脆性-范性转变温度。     

Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of micro-crack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field.     

A framework for statistical modelling of plastic yielding initiated cleavage fracture of structural steels

The well established consensus that cleavage fracture is preceded by plastic deformation in structural steels implies that plastic yielding is the threshold stress state for a volume element to incur cleavage fracture. An accurate compliance with this consensus underlies the normalisation of cumulative cleavage fracture probability and the justification of constraint effect on cleavage fracture. These understandings lead to the proposal of a framework for statistical modelling of cleavage fracture in structural steels. The framework takes the spatial microcrack distribution into account to formulate the cumulative failure probability model that allows for a pertinent physical interpretation of Weibull statistics, and derives the fracture probability of an elemental volume in conformity with the yielding condition from a set of commonly adopted microcrack size or strength distributions. Alternative approaches to calibrating model parameters are suggested based on frequency analysis of brittle particles as cleavage initiators and on statistical analysis of cleavage fracture stress. The strict adherence to plastic yielding as a prerequisite to cleavage fracture also reveals the probabilistic nature of notch brittleness and ductile-to-brittle transition behaviour.     

Fatigue life of metal treated by magnetic field

This paper investigates theoretically the influence of magnetization on fatigue life by using non-equilibrium statistical theory of fatigue fracture for metals. The fatigue microcrack growth rate is obtained from the dynamic equation of microcrack growth, where the influence of magnetization is described by an additional term in the potential energy of microcrack. The statistical value of fatigue life of metal under magnetic field is derived, which is expressed in terms of magnetic field and macrophysical as well as microphysical quantities. The fatigue life of AISI 4140 steel in static magnetic field from this theory is basically consistent with the experimental data.     

An experimental test of the critical behaviour of fracture precursors

The statistical properties and the localization of fracture precursors on heteregeneous materials is studied by recording their acoustic emission as a function of the applied load. It's found that the microcrack cluster together as the load increases and the instantaneous acoustic energy has an invariant power law distribution. The integrated acoustic energy presents a critical divergency close to the failure load for the sample. These result support the idea that fracture can be viewed as a critical phenomenon. Finally a measure of the concentration of microcraks, which allows us to predict the failure load, is introduced. These properties are studied also when a periodic load is applied to the sample. It's found that the Kaiser effect is not strictly satisfied in heteregeneous materials. Received: 23 January 1998 / Revised: 20 April 1998 / Accepted: 17 June 1998     

A macro-micro connected failure evolution equation for brittle metals

A macro-micro connected statistical failure evolution equation for brittle metals is derived. The coefficients of this equation, the microcrack growth rate and the microcrack nucleation rate, come from a micromechanism. The macro mechanical quantities and their statistical distribution functions can be calculated from the solution of this equation.     

Influence of grain boundary sliding on fracture toughness of nanocrystalline ceramics

A theoretical model is proposed describing a new physical microscopic mechanism of increased fracture toughness of nanocrystalline ceramics. According to this model, when a ceramic with a microcrack is deformed, intensive grain boundary sliding occurs near the crack tip under certain conditions. This sliding is accompanied by the formation of an array of disclination dipoles (rotational defects) producing elastic stresses. These stresses partially compensate the high local stresses concentrated near the microcrack tip and thereby hamper the microcrack growth. The proposed model is used to theoretically estimate the increase in the critical microcrack length (the length above which the catastrophic growth of microcracks occurs) caused by the formation of disclination dipoles during grain boundary sliding in nanoceramics. The increase in the critical microcrack length is a quantitative characteristic of the increased fracture toughness of nanoceramics.     

Influence of structural interfaces on the statistics of corrosion microcracks

The amplitude distributions of acoustic emission signals generated during the formation of corrosion microcracks in loaded welded joints connecting two corrosion-resistant steel tubes are studied. For acoustic emission signal amplitudes of less than 0.6 mV and a microcrack concentration of ～10 mm^?3, the distribution density of the signal amplitudes is described by a gamma function. For acoustic emission signal amplitudes exceeding 1.0 mV and a microcrack concentration of greater than or equal to 10² mm^?3, the distribution density of the amplitudes exhibits two maxima, whose shape is described by a Gaussian function. The mean amplitudes of acoustic emission signals differ by a factor of 3. The change in the amplitude distribution of acoustic emission signals is explained by the effect exerted by the weld-metal interface on the microcrack formation.