热激活断裂统计理论

本文研究了原子键机理与宏观特性相结合的热激活断裂非平衡统计理论,统一导出了微裂纹分布函数、断裂几率、可靠性、断裂寿命分布函数和平均断裂寿命。     

脆性断裂的微观机理和非平衡统计特性

Ⅰ.引言如何才能将断裂的微观机理与宏观特性结合起来,把断裂理论建立于微裂纹演化的微观动力学基础上,从而统一导出所有重要的宏观力学量并以某些更基本的物理量表示之?这是人们为实现材料的强度和韧性设计必需解决的一个重要理论课题。就脆性断裂来说,尽管现有几个主要代表性的理论如断裂力学理论、位错理论和统计理论都各取得一定成就,但就其理论框架来说,由于明显的局限性,却难以发展成可供指导设计的理论。因此,人们在探索微观与宏观相结合的断裂理论。最近的工作表明:从微裂纹演      

损伤和断裂的统一

本文讨论了连续损伤力学基础的缺陷,从微裂纹随机演化出发给损伤概念作出新的普适的统计定义,导出了损伤断裂几率的动力学方程,使损伤、断裂、统计、微观机理及宏观特性五者有机地相结合,从而有可能形成一个统一的损伤断裂微观统计理论。     

单轴拉伸条件下脆性岩石微裂纹损伤模型研究

利用断裂力学、损伤力学和均匀化原理,对脆性岩石单轴拉伸条件下的力学特性进行分析,建立了脆性岩石的微裂纹损伤本构模型.首先对岩石内部微裂纹的统计分布规律进行分析,给出了理论分析过程中微裂纹分布的假设条件,在此基础上,参考已有研究成果,得到含细长微裂纹脆性岩石有效弹性参数的计算公式.然后,对岩石内部单一微裂纹进行断裂力学和损伤力学分析,得到了扩展裂纹尖端的应力强度因子计算公式,在一定微裂纹断裂扩展准则和断裂扩展速率的假设基础上,利用积分原理,得到了岩石整体的损伤变量和损伤演化方程,由此建立单轴拉伸条件下脆性岩石的微裂纹损伤本构模型.最后,通过一花岗岩的单轴拉伸试验结果对微裂纹损伤本构模型进行了验证.     

陶瓷材料动态压缩损伤本构模型

运用细观损伤力学理论,从动态压缩载荷下陶瓷材料内翼型裂纹的产生和扩展的损伤机理出发,建立了陶瓷材料的弹脆性动态损伤本构模型,给出相应的损伤演化方程.假设裂纹成核满足Weibull分布,讨论了成核分布参数、原始缺陷尺寸对材料动态断裂应力、断裂应变的影响,并用动态损伤演化模型计算了冲击载荷下AD90陶瓷的动态应力应变曲线,计算结果和实验结果符合很好.     

基于微-细观机理的混凝土疲劳损伤本构模型

该文致力于混凝土疲劳损伤发展机理的微细观解释. 以速率过程理论为基础,通过考虑裂纹断裂过程区中的水分子动力作用,在细观尺度上建立了具有物理机理的疲劳损伤能量耗散表达式. 结合细观随机断裂模型,以宏观损伤力学为框架,建立了疲劳损伤演化方程. 通过数值模拟,计算了单轴受拉时的疲劳损伤演化以及不同加载幅度下的疲劳寿命. 与相关试验结果的对比显示出该文模型能够很好地表现混凝土材料的疲劳损伤演化过程.      

THE FATIGUE CONSTITUTIVE MODEL OF CONCRETE BASED ON MICRO-MESO MECHANICS

该文致力于混凝土疲劳损伤发展机理的微细观解释. 以速率过程理论为基础,通过考虑裂纹断裂过程区中的水分子动力作用,在细观尺度上建立了具有物理机理的疲劳损伤能量耗散表达式. 结合细观随机断裂模型,以宏观损伤力学为框架,建立了疲劳损伤演化方程. 通过数值模拟,计算了单轴受拉时的疲劳损伤演化以及不同加载幅度下的疲劳寿命. 与相关试验结果的对比显示出该文模型能够很好地表现混凝土材料的疲劳损伤演化过程.     

基于近场动力学理论的准脆性材料的本构力函数的构建

近场动力学理论(PD)是基于非局部思想的连续介质力学新理论,用于研究材料破坏问题。根据准脆性材料破坏的线性和非线性的力学行为,在初始微观弹脆性材料(PMB)的本构力函数中引入了键的损伤模型,将键的断裂过程分成了线性的弹性变形阶段和非线性的损伤变形阶段,以此构建了准脆性材料的本构力函数的基本形式。以典型的准脆性材料为例构建了其本构力函数,通过在压缩载荷下对含预制不同角度单裂纹缺陷的类岩材料的裂纹扩展进行PD数值模拟仿真,裂纹起裂位置和扩展方向与试样试验结果在一定程度上保持了一致,证明了该基于近场动力学理论的典型准脆性材料的本构力函数可用于该类材料的破坏分析。     

考虑微裂纹相互作用的的岩石微观力学弹塑性损伤模型研究

本文建立基于微裂纹扩展的岩石弹塑性损伤微观力学模型。用自洽方法考虑裂隙间相互影响,压缩载荷下微裂纹尖端翼裂纹稳定扩展表征岩石的微观损伤,基于应变能密度准则用Newton迭代法求复合型断裂的翼裂纹扩展长度,并采用微裂隙统计的二参数Weibull函数模型反映绝对体积应变对微裂纹分布数目影响,进而用翼裂纹扩展所表征的应力释放体积和微裂纹数目来表示含有微裂隙的岩石损伤演化变量;宏观塑性屈服函数采用Voyiadjis等的等效塑性应变的硬化函数,反映塑性内变量对硬化函数的影响;建立岩石的弹塑性损伤本构关系及其数值算法,并用回映隐式积分算法编制了弹塑性损伤模型的程序。从围压和微裂隙长度等因素分析弹塑性损伤模型的岩石的损伤和宏观塑性特性。     

含初始裂纹巴西圆盘劈裂问题的非局部近 场动力学建模

巴西圆盘劈裂是弹性力学及岩石力学与工程中的经典问题。在非局部键型近场动力 学理论的基础上,引入物质点对的转动自由度构建双参数微观弹脆性近场动力学本构力模型 以突破常规模型的应用范围限制,并考虑岩石混凝土类材料的宏观拉压异性和断裂特征。引 入动态松弛、粒子系统力边界条件和系统平衡弛豫等算法,实现了含不同倾角中心裂纹巴西 圆盘受压劈裂破坏全过程的近场动力学数值模拟,裂纹扩展路径及破坏形式均与试验结果高 度吻合,为裂纹扩展和断裂破坏问题的数值模拟提供了新的选择。     

Nonequilibrium statistical foundation of fatigue fracture

The physical foundation of statistical law of fatigue fracture is discussed. The universal forms of the microcrack growth rate, fluctuation growth coefficient and distribution function and fatigue life distribution function have been given. The project is supported by the National Natural Science Foundation of China     

基于裂纹扩展脆性岩石动力压缩力学特性研究

动态压缩荷载作用下，脆性岩石内部动态细观裂纹扩展特性，对岩石宏观动态力学特性有着重要的影响。然而，对岩石内部动态细观裂纹扩展与宏观动态力学特性的关系研究较少。基于准静态裂纹扩展作用下的应力-应变本构模型、准静态与动态裂纹扩展断裂韧度关系、裂纹速率与应变率关系模型及应变率与动态断裂韧度关系，提出了一种基于细观力学的动态应力-应变本构模型。其中裂纹速率与应变率关系，是根据裂纹长度与应变关系的时间导数推出；应变率与动态断裂韧度关系，是根据推出的裂纹速率及应变率关系，与裂纹速率及断裂韧度关系相结合而得到。研究了应变率对应力-应变本构关系及动态压缩强度影响。并通过试验结果验证了模型的合理性。讨论了岩石初始损伤、围压、模型中参数m、ε₀和R对应力-应变关系、动态压缩强度和动态弹性模量的影响。研究结果可为动态压缩荷载作用下深部地下工程脆性围岩稳定性分析提供了一定的理论支持。     

随机分布共线微裂纹的强相互作用

微裂纹串接为宏观灾难性裂纹的过程取决于相邻微裂纹的强相互作用。微裂纹的分布规律影响材料的强度和韧性。本文研究简单的共线微裂纹构型，确定由于微裂纹长度和韧度尺寸的统计分布所产生的影响。研究结果预计了脆性材料的尺度效应，即对于相同密度的微裂纹分布，大尺寸构件的强度比小尺寸构件要低。计算还表明脆性体的强度随微裂纹分布函数标准方差的增加而减小。     

Progressive failure constitutive model of fracture plane in geomaterial based on strain strength distribution

Progressive failure constitutive model of fracture plane in geomaterial based on strain strength distribution is proposed. The basic assumption is that strain strength of geomaterial comply with a certain distribution law in space. Failure of tensile fracture plane and shear fracture plane in representative volume element (RVE) with iso-strain are discussed, and generalized failure constitutive model of fracture plane in RVE is established considering combined effect of tension and shear. Fracture plane consists of elastic microplanes and fractured microplanes. Elastic microplanes are intact parts of the fracture plane, and fractured microplanes are the rest parts of the fracture plane whose strain have ever exceeded their strain strength. Interaction mode on elastic microplanes maintains linear elasticity, while on fractured microplanes it turns into contact and complies with Coulomb’s friction law. Intact factor and fracture factor are defined to describe damage state of the fracture plane which can be easily expressed with cumulative integration of distribution density function of strain strength. Strong nonlinear macroscopic behavior such as yielding and strain softening can be naturally obtained through statistical microstructural damage of fracture plane due to distribution of strain strength. Elastic–brittle fracture model and ideal elastoplastic model are special cases of this model when upper and lower limit of distribution interval are equal.     

Fractal dimension evolution of microcrack net in disordered materials

Fractal geometry is used to evaluate the degree of disorder of crack size distribution in brittle damaging materials. The fractal dimension of the 2D microcrack net turns out to increase from one to two during the loading process and microcrack propagation. This means that the material becomes more disordered with the damage evolution. The longer cracks, in fact, propagate more rapidly than the shorter and, at the same time, the crack size distribution increases its statistical dispersion. Some numerical examples, related to different initial microcrack densities and size distributions, are illustrated with the computer simulation of the system evolution.     

A statistical model of microcracking of concrete under uniaxial compression

At increasing external load, numerous microcracks propagate in discrete and successive stages within a body of concrete material according to the hierarchy of their tensile fracture strengths. Each microcrack propagation is conditional upon the statistical encounter of its associated fracture criterion. This paper shows the development of a statistical model for the progressive microcrack growth process within a body of concrete material at monotonic uniaxial loading in compression to ultimate failure. This model is formulated by using the Weibull's statistical theory of the strength of materials. The body of heterogeneous concrete material is simulated as a continuum comprising a large population of microscopic “weakest-link” isoenergy elements, each of which contains a unit-volume of representative micro-structural material which is linearly elastic, homogeneous and isotropic. The statistical modelling is derived from the stochastic evaluation of the tensile micro-fracture probabilities of these isoenergy elements at increasing global uniaxial compressive strains.     

A new damage model for microcrack-weakened brittle solids

In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically increasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given. The project supported by National Natural Science Foundation of China