结构破坏的尺度律

文中综述了结构破坏的尺度律和尺寸效应的研究进展,尤其将重点放在准脆性材料的分析上,因为它们的尺寸效应是重要和复杂的．在回顾了尺寸效应研究的悠远发展史以后。着重讨论了三种主要类型的尺寸效应,即由于强度随机性引起的统计尺寸效应、能量释放的尺寸效应和由于微裂纹或断裂的分形特性可能引起的尺寸效应．得出了这些理论应用的明确结论．之后讨论了如何运用已知的尺寸效应律来测量材料的断裂特性,并采用内聚裂纹模型（cohesivecrackmodel）、非局域化有限元模型和离散元模型等对尺寸效应进行模化．文中还进而分析了尺寸效应在压缩失效和车相关材料行为下的有关问题,并讨论了在断裂扩展区描述含微裂纹材料所需的损伤本构关系．最后也讨论了尺寸效应对准脆性材料的多种应用,这些材料包括,如混凝土、海冰、纤维复合材料、岩石和陶瓷等．本文包含了参考文献377篇     

用试验室尺寸的试样预测混凝土及岩石结构的准脆性断裂

0Introduction Thefracturepropertiesofconcreteandrockmaterials,suchasfracturetoughnessKICand strengthfthavebeenofgreatinterestsformanyyearsbecauseoftheirimportantroleincontrolling thestructuralintegrityofvariousengineeringstructures[1-27].Varioustestingtec…     

Numerical experiments on the rupture of brittle solids––variation of microstructure,loading and dimensions

The significance of microstructural parameters for the damage and rupture of brittle materials is investigated by a numerical model that accounts for separation of grain interfaces. The microcracking approach refers to a specified material structure; synthetic random sampling allows for fluctuations. Thus, damage progression is simulated and the strength of material specimens is estimated by employing fracture mechanics within a microstructure that exhibits statistical variability. The issues addressed regard failure behaviour, strength level and sensitivity to microstructural parameters. Also discussed is the effect of specimen dimensions in connection with rupture.     

Meso-scale modelling of the size effect on the fracture process zone of concrete

The size effect on the fracture process zone in notched and unnotched three point bending tests of concrete beams is analysed by a meso-scale approach. Concrete is modelled at the meso-scale as stiff aggregates embedded in a soft matrix separated by weak interfaces. The mechanical response of the three phases is modelled by a discrete lattice approach. The model parameters were chosen so that the global model response in the form of load-crack mouth opening displacement curves were in agreement with experimental results reported in the literature. The fracture process zone of concrete is determined numerically by evaluating the average of spatial distribution of dissipated energy densities of random meso-scale analyses. The influence of size and boundary conditions on the fracture process zone in concrete is investigated by comparing the results for beams of different sizes and boundary conditions.     

Size effect and asymptotic matching analysis of fracture of closed-cell polymeric foam

The effect of structure size on the nominal strength of closed-cell PVC foam (Divinycell H100) is investigated experimentally, theoretically and numerically. Two types of size effect are considered––Type I, characterizing failure of structures with large cracks or notches, and Type II, characterizing failure at crack initiation. Geometrically similar single edge-notched prismatic specimens of cross section widths 6.35, 43.9 and 305 mm, are tested under tension. The results are shown to agree with Bažant’s law for type I energetic (deterministic) size effect derived by asymptotic matching of a solution by equivalent linear elastic fracture mechanics for large sizes and plastic crack solution for small sizes (in the derivation, the statically indeterminate size-dependent lateral shift of the axial load resultant due to rotational end restrain is taken into account). Fitting this law, previously verified for many quasibrittle materials, to the test results furnishes the values of the fracture energy of the foam as well as the characteristic size of the fracture process zone of foam. The size effect method of measuring the fracture characteristics of foam is further supported by analysis of recent notched beam tests of Zenkert and Bäcklund. Furthermore, it is shown that compressed V-notched specimens exhibit no size effect. Subsequently, the size effect of Type II is studied using previous test data of Fleck, Olurin and co-workers for dissimilar long holed panels having different width and different diameter-width ratios. An asymptotic matching formula for this type of size effect (similar to a previously derived formula for kink band failure of fiber composites) is set up and is shown capable of matching the test data well. But its verification as a predictive tool cannot yet be claimed because of inaccurate asymptotic properties of the available energy release function. Finally, the size effect of Type I is analyzed using the eigenvalue method for the cohesive crack model and the numerical results are shown to agree again with both Bažant’s size effect law and the test results.     

Effect of Randomness of Interfacial Properties on Fracture Behavior of Concrete Under Uniaxial Tension

Interfacial transition zones(ITZs) between aggregates and mortar are the weakest parts in concrete. The random aggregate generation and packing algorithm was utilized to create a two-phase concrete model, and the zero-thickness cohesive elements with different normal distribution parameters were used to model the ITZs with random mechanical properties. A number of uniaxial tension-induced fracture simulations were carried out, and the effects of the random parameters on the fracture behavior of concrete were statistically analyzed. The results show that, different from the dissipated fracture energy, the peak load of concrete does not always obey a normal distribution, when the elastic stiffness, tensile strength, or fracture energy of ITZs is normally distributed. The tensile strength of the ITZs has a significant effect on the fracture behavior of concrete, and its large standard deviation leads to obvious diversity of the fracture path in both location and shape.     

Computations of size effects in granular bodies within micro-polar hypoplasticity during plane strain compression

The numerical investigations of size effects in granular bodies during a plane strain compression test are performed. To describe a mechanical behaviour of a cohesionless granular material during a monotonous deformation path in a plane strain compression test, a micro-polar hypoplastic constitutive model was used. It includes particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. In the paper, deterministic and statistical size effects in geometrically similar granular specimens are analysed. The deterministic calculations were carried out with a uniform distribution of the initial void ratio. To investigate a statistical size effect, in order to reduce the number of realizations without loosing the accuracy of the calculations, a Latin hypercube method was applied to generate Gaussian truncated random fields in a granular specimen. The results show that the statistical size effect is significantly stronger than the deterministic one. The shear resistance decreases and the rate of softening increases with increasing specimen size. The effect of the boundary roughness on shear localization is pronounced.     

基于一类非局部宏-微观损伤模型的混凝土典型试件力学行为模拟

混凝土是一类典型的准脆性材料, 其受力过程中的非线性分析与裂纹模拟依然是具有挑战性的问题. 经典的断裂力学与损伤力学分别从间断与连续的视角对裂纹拓扑进行了描述, 是早期人们研究固体破坏问题的有力工具. 21世纪以来, 相场理论和近场动力学在预测裂纹的萌生、扩展与非线性分析方面取得了重要的进展. 最近, 结合统一相场理论与近场动力学的基本思想, 发展了一类非局部宏-微观损伤模型. 该模型引入物质点偶的概念来刻画由于变形引起的微细观损伤, 对微细观损伤在作用域中进行加权平均得到定量描述物质不连续程度的拓扑损伤. 通过具有物理机制的能量退化函数, 将拓扑损伤嵌入到连续介质-损伤力学的框架中, 这使得该模型在进行非线性分析的同时可以自然地进行裂纹模拟, 而毋须预设初始裂纹与裂纹扩展路径. 本文考虑细观物理参数的空间变异性, 采用非局部宏-微观损伤模型进行混凝土试件受力全过程的精细化模拟. 通过一维建模标定模型细观参数, 并探讨了细观参数与混凝土材料细观物理-几何特性之间的内在关联, 在此基础上采用二维模型进行精细化分析. 进而, 考察了材料参数空间变异性对混凝土单轴受拉试件和带缺口三点弯曲试件力学行为的重要影响. 本文的研究工作为非局部宏-微观损伤模型细观参数的试验标定与复杂应力状态下混凝土等准脆性材料的非线性力学行为研究提供了有意义的参考.      

计及剪切影响的RC梁的非线性分析

为提高钢筋混凝土RC梁的计算效率和精度,提出了一种基于梁截面弯矩-曲率关系的宏观有限元方法,可用于各种跨高比RC梁的材料非线性分析。首先假定了混凝土和钢筋的非线性应力-应变关系,然后引入经过修正的Rodriguez截面模型,根据边界顶点把截面划分成若干梯形单元,利用quasi-Newton法求解由两个变量耦合而成的截面非线性平衡方程,由此建立RC截面的弯矩-曲率关系。在此基础上利用Timoshenko梁弯曲理论建立考虑横向剪切变形影响的RC梁的有限元分析模型。通过对试验梁的分析对比验证了所提出的分析方法的适用性。     

Statistical distribution and size effect of residual strength of quasibrittle materials after a period of constant load

In preceding studies, the type of cumulative probability distribution functions (cdf) of strength and of static lifetime of quasibrittle structures, including their tails, was mathematically derived from atomistic scale arguments based on nano-scale cracks propagating by many small, activation energy-controlled, random breaks of atomic bonds in the nanostructure. It was shown that a quasibrittle structure (of positive geometry) must be modeled by a finite (rather than infinite) weakest-link model, and that the cdf of structural strength as well as lifetime varies from nearly Gaussian to Weibullian as a function of structure size and shape. Excellent agreement with the observed distributions of structural strength and static lifetime was demonstrated. Based on the same theoretical framework, the present paper formulates the statistics of the residual structural strength, which is the strength after the structure has been subjected to sustained loading. A strength degradation equation is derived based on Evans' law for static crack growth during sustained loading. It is shown that the rate of strength degradation is not constant but continuously increasing. The cdf of residual strength of one RVE is shown to be closely approximated by a graft of Weibull and Gaussian (normal) distributions. In the left tail, the cdf is a three-parameter Weibull distribution consisting of the (n+1)th power of the residual strength, where n is the exponent of the Evans law and the threshold is a function of the applied load and load duration. The finiteness of the threshold, which is typically very small, is a new feature of quasibrittle residual strength statistics, contrasting with the previously established absence of a threshold for strength and lifetime. Its cause is that there is a non-zero probability that some specimens fail during the static preloading, and thus are excluded from the statistics of the overload. The predictions of the theory are validated by available test data on glass–epoxy composites and on borosilicate and soda-lime silicate glasses. The size effect on the cdf of residual strength is also determined. The size effect on the mean residual strength is found to be as strong as the size effect on the mean initial strength.     

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Engineering structures must be designed for an extremely low failure probability such as 10⁻⁶, which is beyond the means of direct verification by histogram testing. This is not a problem for brittle or ductile materials because the type of probability distribution of structural strength is fixed and known, making it possible to predict the tail probabilities from the mean and variance. It is a problem, though, for quasibrittle materials for which the type of strength distribution transitions from Gaussian to Weibullian as the structure size increases. These are heterogeneous materials with brittle constituents, characterized by material inhomogeneities that are not negligible compared to the structure size. Examples include concrete, fiber composites, coarse-grained or toughened ceramics, rocks, sea ice, rigid foams and bone, as well as many materials used in nano- and microscale devices.This study presents a unified theory of strength and lifetime for such materials, based on activation energy controlled random jumps of the nano-crack front, and on the nano-macro multiscale transition of tail probabilities. Part I of this study deals with the case of monotonic and sustained (or creep) loading, and Part II with fatigue (or cyclic) loading. On the scale of the representative volume element of material, the probability distribution of strength has a Gaussian core onto which a remote Weibull tail is grafted at failure probability of the order of 10⁻³. With increasing structure size, the Weibull tail penetrates into the Gaussian core. The probability distribution of static (creep) lifetime is related to the strength distribution by the power law for the static crack growth rate, for which a physical justification is given. The present theory yields a simple relation between the exponent of this law and the Weibull moduli for strength and lifetime. The benefit is that the lifetime distribution can be predicted from short-time tests of the mean size effect on strength and tests of the power law for the crack growth rate. The theory is shown to match closely numerous test data on strength and static lifetime of ceramics and concrete, and explains why their histograms deviate systematically from the straight line in Weibull scale.Although the present unified theory is built on several previous advances, new contributions are here made to address: (i) a crack in a disordered nano-structure (such as that of hydrated Portland cement), (ii) tail probability of a fiber bundle (or parallel coupling) model with softening elements, (iii) convergence of this model to the Gaussian distribution, (iv) the stress-life curve under constant load, and (v) a detailed random walk analysis of crack front jumps in an atomic lattice. The nonlocal behavior is captured in the present theory through the finiteness of the number of links in the weakest-link model, which explains why the mean size effect coincides with that of the previously formulated nonlocal Weibull theory. Brittle structures correspond to the large-size limit of the present theory. An important practical conclusion is that the safety factors for strength and tolerable minimum lifetime for large quasibrittle structures (e.g., concrete structures and composite airframes or ship hulls, as well as various micro-devices) should be calculated as a function of structure size and geometry.     

Size effect in quasibrittle failure: Analytical model and numerical simulations using cohesive zone model

The recent rewriting of the Ba?ant’s size effect law (Morel, 2008) which has suggested the existence of an additional asymptotic regime for intermediate structure sizes is now compared to numerical simulations of fracture of geometrically similar notched structures of different sizes extending over 2.4 decades. The quasibrittle fracture behavior is simulated through cohesive zone model (bilinear softening) using a constant set of cohesive parameters whatever the specimen size D is. The R-curves resulting from the load–displacement responses are estimated and appear as size-independent. On this basis, the different asymptotic regimes expected for the size effect on fracture properties at peak load such as the relative crack length, the resistance to crack growth and the nominal strength are shown in fair agreement with the size effect observed on the results obtained from numerical simulations.     

骨料堆积注浆再生混凝土的抗压强度及其影响因素

为提高再生粗骨料利用率及降低再生混凝土质量控制难度,本文采用骨料堆积注浆法制备早强型再生混凝土。利用Griffith断裂力学理论及"实际水料比与名义水料比"的差异,分析了骨料性能对混凝土强度的影响,并通过扫描电子显微镜(SEM)分析了再生混凝土界面过渡区(interfacial transition zone,ITZ)的特点。结果表明,骨料强度及吸水率均对再生混凝土强度具有影响,且骨料吸水作用对混凝土强度提高具有促进作用,再生混凝土的界面结合强度较高。     

Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension

A meso-scale analysis is performed to determine the fracture process zone of concrete subjected to uniaxial tension. The meso-structure of concrete is idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces. The mechanical response of the matrix, the inclusions and the interface between the matrix and the inclusions is modelled by a discrete lattice approach. The inelastic response of the lattice elements is described by a damage approach, which corresponds to a continuous reduction of the stiffness of the springs. The fracture process in uniaxial tension is approximated by an analysis of a two-dimensional cell with periodic boundary conditions. The spatial distribution of dissipated energy density at the meso-scale of concrete is determined. The size and shape of the deterministic FPZ is obtained as the average of random meso-scale analyses. Additionally, periodicity of the discretisation is prescribed to avoid influences of the boundaries of the periodic cell on fracture patterns. The results of these analyses are then used to calibrate an integral-type nonlocal model.     

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.     

一般大气环境下锈蚀钢筋混凝土梁的时变可靠度分析

根据一般大气环境下锈蚀钢筋混凝土梁中的钢筋截面损失时变模型和抗剪、抗弯承载力退化模型,建立了考虑其随机性的极限状态方程。基于概率守恒原理分析得到满足该极限状态方程的概率密度演化方程,并引入吸收边界条件,提出了梁时变可靠度的计算方法。以受对称集中荷载的锈蚀钢筋混凝土简支梁为例,展示了目标函数的概率密度演化过程,并讨论了配置不同直径箍筋和不同厚度保护层时的时变可靠度。结果表明,在保证梁具有足够初始抗剪强度和抗弯强度的前提下,适当增大保护层厚度和箍筋直径(具有相同配箍率)能延缓混凝土构件力学性能的退化。通过和100万次蒙特卡洛模拟结果的对比可知,选用本文方法能在以付出较小计算代价的前提下,获得计算精度良好的分析结果。     

Crack shielding and material deterioration in damaged materials: an antiplane shear fracture problem

Summary A simple damage evolution model is proposed for a quasibrittle material in the framework of continuum damage mechanics. The model is used to obtain a closed form solution for a mode-III stationary crack under small scale damage conditions. It is found that the crack tip stress intensity factor is reduced, i.e., the crack is shielded by the damage. However, this shielding effect is completely offset by the material deterioration caused by the damage. It also holds for steady state crack growth. When the most effective shielding is reached for the stationary crack, the zone dominated by the stress intensity factor shrinks to the crack tip. The results for the antiplane shear problem should shed some light on the in- plane fracture problem. Received 4 August 1997; accepted for publication 7 October 1997     

混凝土黏聚开裂模型若干进展

黏聚模型是用来描述混凝土断裂行为的基本模型, 首先介绍了混凝土的黏聚开裂模型的基本概念,总结了确定黏聚区的本构方程的各种方法,即直接单轴拉伸测试、J积分方法、R曲线法、柔度法和逆推法.然后介绍了黏聚模型在I型和复合型裂纹问题、疲劳断裂问题中的应用以及黏聚模型与混凝土尺寸效应的关系.最后对黏聚开裂模型与桥联模型、带状裂缝模型进行了比较和总结, 指出了该模型存在的问题, 并对其以后的发展方向提出了建议.      

Necessary and Sufficient Fracture Criteria for a Composite with a Brittle Matrix. Part 2. High-Strength Reinforcement

Experimental results on fracture of composite specimens with a brittle matrix are given. A modification is proposed for the shear model that describes deformation of a composite with failed matrix. A three-parameter sufficient criterion of quasibrittle strength of the composite is constructed, based on the equations of an orthotropic medium. Simple analytical expressions that relate the macrocrack length to the loading, structural, stiffness, and strength parameters of the composite medium are obtained. An approach for constructing multi-parameter criteria that take into account special features of deformation of the materials of the composite components is discussed.