NUMERICAL SMEARED FRACTURE ANALYSIS: NONLOCAL MICROCRACK INTERACTION APPROACH

A recently proposed new nonlocal concept based on microcrack interactions is discussed, its implementation in a smeared cracking finite element code for concrete is presented, numerical studies are reported, and comparisons with experimental results are made. The nonlocality is not merely a mathematical device to prevent excessive spurious localization into a zone of zero volume but is a necessary physical consequence of microcrack interactions. Since the constitutive law itself is strictly local, the new nonlocal concept can be combined with any type of constitutive law for strain-softening nonlocal damage, which is here chosen to be the microplane model. A simple method is formulated to approximately identify the material parameters in the model from the basic characteristics of concrete such as the tensile strength, fracture energy and maximum aggregate size. The results of finite element analysis are shown to be mesh insensitive, and good convergence is obtained. Cracking damage is found to localize into a volume whose size and shape depend on the macroscopic concrete properties as well as the current stress–strain state. Although the damage is considered to be tensile on the microlevel, due solely to mode I microcracks, the new nonlocal model can describe well not only mode I fracture tests but also complex shear-dominated and mixed-mode types of failure such a diagonal shear, and can do so for the same values of material parameters (which was not the case for previous nonlocal models). Most importantly, the new nonlocal model can correctly capture the size effect of quasibrittle fracture, in approximate agreement with Bažant's size effect law.     

Scaling of energy dissipation in crushing and fragmentation: a fractal and statistical analysis based on particle size distribution

An extensive experimental investigation on concrete specimens under crushing and fragmentation over a large scale range (1:10) – exploring even very small specimen dimensions (1 cm) – was carried out to evaluate the influence of fragment size distribution on energy density dissipation and related size effect. To obtain a statistically significant fragment production as well as the total energy dissipated in a given specimen, the experimental procedure was unusually carried out up to a strain of approximately –95%, practically corresponding to the initial fragment compaction between the loading platens. The experimental fragment analysis suggests a fractal law for the distribution in particle size; this simply means that fragments derived from a given specimen appear geometrically self-similar at each observation scale. In addition, clear size effects on dissipated energy density are experimentally observed. Fractal concepts permit to quantify the correlation between fragment size distribution and size effect on dissipated energy density, the latter being governed by the total surface area of produced fragments. The experimental results agree with the proposed multi-scale interpretation satisfactorily.     

Cohesive Crack with Rate-Dependent Opening and Viscoelasticity: I. Mathematical Model and Scaling

The time dependence of fracture has two sources: (1) the viscoelasticity of material behavior in the bulk of the structure, and (2) the rate process of the breakage of bonds in the fracture process zone which causes the softening law for the crack opening to be rate-dependent. The objective of this study is to clarify the differences between these two influences and their role in the size effect on the nominal strength of stucture. Previously developed theories of time-dependent cohesive crack growth in a viscoelastic material with or without aging are extended to a general compliance formulation of the cohesive crack model applicable to structures such as concrete structures, in which the fracture process zone (cohesive zone) is large, i.e., cannot be neglected in comparison to the structure dimensions. To deal with a large process zone interacting with the structure boundaries, a boundary integral formulation of the cohesive crack model in terms of the compliance functions for loads applied anywhere on the crack surfaces is introduced. Since an unopened cohesive crack (crack of zero width) transmits stresses and is equivalent to no crack at all, it is assumed that at the outset there exists such a crack, extending along the entire future crack path (which must be known). Thus it is unnecessary to deal mathematically with a moving crack tip, which keeps the formulation simple because the compliance functions for the surface points of such an imagined preexisting unopened crack do not change as the actual front of the opened part of the cohesive crack advances. First the compliance formulation of the cohesive crack model is generalized for aging viscoelastic material behavior, using the elastic-viscoelastic analog (correspondence principle). The formulation is then enriched by a rate-dependent softening law based on the activation energy theory for the rate process of bond ruptures on the atomic level, which was recently proposed and validated for concrete but is also applicable to polymers, rocks and ceramics, and can be applied to ice if the nonlinear creep of ice is approximated by linear viscoelasticity. Some implications for the characteristic length, scaling and size effect are also discussed. The problems of numerical algorithm, size effect, roles of the different sources of time dependence and rate effect, and experimental verification are left for a subsequent companion paper. This revised version was published online in July 2006 with corrections to the Cover Date.     

Size effect on compression strength of fiber composites failing by kink band propagation

The effect of structure size on the nominal strength of unidirectional fiber-polymer composites, failing by propagation of a kink band with fiber microbuckling, is analyzed experimentally and theoretically. Tests of novel geometrically similar carbon–PEEK specimens, with notches slanted so as to lead to a pure kink band (not accompanied by shear or splitting cracks), are conducted. They confirm the possibility of stable growth of long kind bands before the peak load, and reveal the existence of a strong (deterministic, non-statistical) size effect. The bi-logarithmic plot of the nominal strength (load divided by size and thickness) versus the characteristic size agrees with the approximate size effect law proposed for quasibrittle failures in 1983 by Bažant. The plot exhibits a gradual transition from a horizontal asymptote, representing the case of no size effect (characteristic of plasticity or strength criteria), to an asymptote of slope -1/2 (characteristic of linear elastic fracture mechanics, LEFM). A new derivation of this law by approximate (asymptotically correct) J-integral analysis of the energy release, as well as by the recently proposed nonlocal fracture mechanics, is given. The size effect law is further generalized to notch-free specimens attaining the maximum load after a stable growth of a kink band transmitting a uniform residual stress, and the generalized law is verified by Soutis, Curtis and Fleck's recent compression tests of specimens with holes of different diameters. The nominal strength of specimens failing at the initiation of a kink band from a smooth surface is predicted to also exhibit a (deterministic) size effect if there is a nonzero stress gradient at the surface. A different size effect law is derived for this case by analyzing the stress redistribution. The size effect law for notched specimens permits the fracture energy of the kink band and the length of the fracture process zone at the front of the band to be identified solely from the measurements of maximum loads. The results indicate that the current design practice, which relies on the strength criteria or plasticity and thus inevitably misses the size effect, is acceptable only for small structural parts and, in the interest of safety, should be revised in the case of large structural parts. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scaling of quasibrittle fracture: hypotheses of invasive and lacunar fractality, their critique and Weibull connection

Considerable progress has been achieved in fractal characterization of the properties of crack surfaces in quasibrittle materials such as concrete, rock, ice, ceramics and composites. Recently, fractality of cracks or microcracks was proposed as the explanation of the observed size effect on the nominal strength of structures. This explanation, though, has rested merely on intuitive analogy and geometric reasoning, and did not take into account the mechanics of crack propagation. In this paper, the energy-based asymptotic analysis of scaling presented in the preceding companion paper in this issue [1] is extended to the effect of fractality on scaling. First, attention is focused on the propagation of fractal crack curves (invasive fractals). The modifications of the scaling law caused by crack fractality are derived, both for quasibrittle failures after large stable crack growth and for failures at the initiation of a fractal crack in the boundary layer near the surface. Second, attention is focused on discrete fractal distribution of microcracks (lacunar fractals), which is shown to lead to an analogy with Weibull's statistical theory of size effect due to material strength randomness. The predictions ensuing from the fractal hypothesis, either invasive or lacunar, disagree with the experimentally confirmed asymptotic characteristics of the size effect in quasibrittle structures. It is also pointed out that considering the crack curve as a self-similar fractal conflicts with kinematics. This can be remedied by considering the crack to be an affine fractal. It is concluded that the fractal characteristics of either the fracture surface or the microcracking at the fracture front cannot have a significant influence on the law of scaling of failure loads, although they can affect the fracture characteristics. Walter P. Murphy, Professor| of This revised version was published online in July 2006 with corrections to the Cover Date.     

Fracture mechanic modeling of fiber reinforced polymer shear-strengthened reinforced concrete beam

A numerical method is developed to model shear-strengthening of reinforced concrete beam by using fiber reinforced polymer (FRP) composites. Tensile crack is simulated by a non-linear spring element with softening behavior ahead of the crack tip to model the cohesive zone in concrete. A truss element is used, parallel to the spring element, to simulate the energy dissipation rate by the FRP. The strain energy release rate is calculated directly by using a virtual crack closure technique. It is observed that the length of the fracture process zone (FPZ) increases with the application of FRP shear-strengthening. The present model shows that the main diagonal crack is formed at the support in the control beam while it appears through the shear span in the shear-strengthened beam. Another important observation is that the load capacity increases with the number of CFRP sheets in the shear span.     

Influence of Stress Singularities on Scaling of Fracture of Metal-Composite Hybrid Structures

It has been recently shown that the nominal structural strength of metal-composite structures depends on the structure size, and such dependence is strongly influenced by the stress singularities. Nevertheless, previous studies only focused on structures that exhibit very strong stress singularities, which are close to the crack-like stress singularity. In the actual engineering designs, due to the mismatch of material properties and complex structural geometries, many metalcomposite structures may contain stress singularities that are much weaker than the crack-like stress singularity. This paper presents a numerical study on the size dependence of scaling of fracture of metal-composite hybrid structures for a wide range of stress singularities. The numerical examples include a series of metalcomposite hybrid beams with a V-notch under three-point bending with different notch angles, which lead to various magnitudes of stress singularities. By assuming that the bimaterial interface is weaker than both metal and composite, we use a mixed-mode cohesive element model to simulate the fracture behavior of these hybrid beams. It is shown that the resulting size effect curves strongly depend on the magnitude of stress singularities. The simulation results agree well with a recently developed energetic-statistical scaling model.     

Fracture characterization of sandwich structures interfaces under mode I loading

The accurate prediction of failure of sandwich structures using cohesive mixed-mode damage models depends on the accurate characterization of the cohesive laws under pure mode loading. In this work, a numerical and experimental study on the asymmetric double cantilever beam (DCB) sandwich specimen is presented with the objective to characterize the debonding fracture between the face sheet and the core under pure mode I. A data reduction method based on beam theory was formulated in such a way to incorporate the complex damaging phenomena of the debonding due to the material and geometric asymmetry of the specimen, via the consideration of an equivalent crack length (a_e). Experimental DCB tests were performed and the proposed methodology was followed to obtain the debonding fracture energy (G_Ic). The experimental tests were numerically simulated and a cohesive damage model was employed to reproduce crack propagation. An inverse method was followed to obtain the local cohesive strength (σ_u,I) based on the fitting of the numerical and experimental load–displacement curves. With the value of fracture energy and cohesive strength defined, the cohesive law for interface mode I fracture is characterized. Good agreement between the numerical and the experimental R-curves validates the accuracy of the proposed data reduction procedure.     

定向钢纤维水泥基复合材料断裂理论分析及试验

基于非线性铰模型研究了定向钢纤维水泥基复合材料的裂缝断裂全过程理论分析方法,结合不同尺寸试件的三点弯曲梁断裂试验对本文方法进行了验证。进而利用该方法预测了大尺寸三点弯曲梁试件的裂缝断裂全过程,并研究了试件尺寸对名义强度的影响。通过理论分析与试验结果对比,表明本文方法可较好地预测定向钢纤维水泥基复合材料的裂缝断裂全过程;此外,定向钢纤维水泥基复合材料的名义强度存在一定的尺寸效应,但尺寸效应表现不明显。     

Asymptotic stress intensity factor density profiles for smeared-tip method for cohesive fracture

The paper presents a computational approach and numerical data which facilitate the use of the smeared-tip method for cohesive fracture in large enough structures. In the recently developed K-version of the smeared tip method, the large-size asymptotic profile of the stress intensity factor density along a cohesive crack is considered as a material characteristic, which is uniquely related to the softening stress-displacement law of the cohesive crack. After reviewing the K-version, an accurate and efficient numerical algorithm for the computation of this asymptotic profile is presented. The algorithm is based on solving a singular Abel's integral equation. The profiles corresponding to various typical softening stress-displacement laws of the cohesive crack model are computed, tabulated and plotted. The profiles for a certain range of other typical softening laws can be approximately obtained by interpolation from the tables. Knowing the profile, one can obtain with the smeared-tip method an analytical expression for the large-size solution to fracture problems, including the first two asymptotic terms of the size effect law. Consequently, numerical solutions of the integral equations of the cohesive crack model as well as finite element simulations of the cohesive crack are made superfluous. However, when the fracture process zone is attached to a notch or to the body surface and the cohesive zone ends with a stress jump, the solution is expected to be accurate only for large-enough structures.     

高混凝土坝温控防裂研究进展

该文提出了一种龄期相关的混凝土尺寸效应断裂模型。基于现有模型建立可用于确定试件尺寸和缝高比变化时混凝土断裂破坏的尺寸效应模型演化形式;结合模型参数的时变规律,提出一种考虑龄期影响的尺寸效应断裂模型;采用文献中试件龄期、尺寸和缝高比变化的混凝土断裂试验结果验证模型的适用性。研究发现：为保证模型对于特定龄期混凝土断裂破坏预测的精度,建议模型所用材料常数至少由3组且最大与最小等效裂缝长度之比不小于4的混凝土试件断裂试验结果确定。指数函数形式可较好地描述混凝土材料常数的时变特性。龄期相关的尺寸效应模型可准确预测试件龄期、尺寸和缝高比变化时混凝土构件的断裂破坏。

     

基于渐进损伤模型的复合材料斜接接头的拉伸强度

本文首先以斜接角度、搭接长度以及搭接厚度为参数分别建立了复合材料单边斜接接头和双边斜接接头在拉伸载荷下的参数化有限元模型,采用abaqus软件中UMAT子程序功能编写了材料损伤本构模型,并利用cohesive单元模拟胶接界面损伤。通过渐进损伤分析,模拟出斜接接头的三种破坏模式,最终得到了各参数变化对斜接接头拉伸强度的影响,其中母板最终破坏模式对应最大拉伸强度,并对单边斜接接头和双边斜接接头结果进行了对比分析,得出双边斜接接头强度大于单边斜接接头强度的结论。     

基于面-内胞模型的三维四向编织复合材料渐进损伤数值模拟

为了准确预测三维四向编织复合材料的纵向拉伸力学性能,对编织复合材料的面胞和内胞细观实体模型进行参数化建模,面胞模型考虑了纱线空间轨迹的偏移和横截面的挤压变形.用体素网格离散模型并施加合适的边界条件,将各组分材料的损伤模型编入到有限元分析软件ABAQUS用户定义材料子程序UMAT中.分别对内编织角为30°和45°的三维四...     

Influence of Features of Interphase Boundaries on Mechanical Properties and Fracture Pattern in Metal--Ceramic Composites

The results of a theoretical study on the influence of strength of interphase boundaries in metal-ceramic composite on macroscopical characteristics of composite response such as strength, deformation capacity, fracture energy and fracture pattern are presented. The study was conducted by means of computer-aided simulation by means of movable cellular automaton method taking account of a developed ＂mesoscopical＂ structural model of particle-reinforced composite. The strength of interphase boundaries is found to be a key structural factor determining not only the strength properties of metal-ceramic composite, but also the pattern and rate of fracture. The principles for achievement of the high-strength values of particle/binder interfaces in the metal-ceramic composition due to the formation of the wide transition zones （areas of variable chemical composition） at the interphase boundaries are discussed. Simulation results confirm that such transition zones provide a change in fracture mechanism and make the achievement of a high-strength and a high deformation capacity of metal-ceramic composite possible.     

缠绕线型对缠绕复合材料圆管轴向拉伸失效的影响

采用细观刚度模型的有限元分析（FEA）与改进的逐渐累积损伤方法相结合,建立了缠绕复合材料圆管轴向拉伸失效的分析方法与流程,以揭示缠绕线型对缠绕复合材料损伤失效的影响。对沿圆周方向分布有1个、3个和5个单胞的3种不同线型的缠绕复合材料圆管试件进行轴向拉伸破坏实验,获得其失效形式、平均拉伸强度及其随缠绕线型的变化规律。研究表明：缠绕复合材料圆管轴向拉伸失效主要以丧失承载能力的功能失效为主,缠绕线型对其拉伸强度有一定的影响;数值分析结果表明,轴向拉伸过程中,主要损伤为基体开裂与基纤剪切,纤维交叉容易引起损伤起始与扩展。     

3D C/SiC复合材料拉伸性能的声发射研究

采用声发射平均频率和相对能量以及幅值识别了3D C/SiC复合材料的拉伸损伤模式, 探讨了拉伸加卸载过程中材料的费利西蒂(Felicity)效应。通过分析具有不同拉伸性能试样的损伤过程, 研究了不同损伤模式的时间分布特征对材料拉伸性能的影响关系。分析结果表明, 3D C/SiC复合材料中基本不存在凯瑟(Kaiser)效应, Felicity比随着应力水平的升高而降低, 相对应力水平高于65%时出现突降。3D C/SiC复合材料高性能的决定性因素不是声发射波击总数, 而是高幅高能量信号发生的时间和次数。在加载前期(应变<0.15%)损伤较少是材料高强度的必要条件, 纤维簇断裂在加载中后期的分散分布有利于提高拉伸强度。      

A study on the influence of cohesive zone interface element strength parameters on mixed mode behaviour

This paper presents a detailed study of the influence of maximum interfacial stress on interface element analyses for composites delamination. The development of the non-linear cohesive zone ahead of a crack tip is analysed with respect to length, stress distribution and mode ratio. The energy absorbed by interface elements is compared with the crack tip strain energy release rate from fracture mechanics analyses. These studies are performed initially on standard fracture toughness specimens, where mode-ratio is fixed by the applied displacement constraints. Results show close agreement with linear elastic fracture mechanics solutions. A simple ply drop specimen is then modelled, where the mode ratio is not constrained by the boundary conditions, and results are compared with the Virtual Crack Closure Technique. In this case maximum interfacial stress has a far greater influence on the numerical results, due to its significant influence on cohesive zone length, mode ratio and energy absorbed.     

混凝土结构耐久性设计方法与寿命预测研究进展

为量化钢筋锈蚀与余震对钢筋混凝土结构抗震性能的影响,选取两栋按我国现行规范设计的中国东南沿海地区钢筋混凝土框架结构为研究对象,考虑未锈蚀和由低到高三种不同锈蚀率(5%、10%和15%)的四种工况,采用真实主余震序列作为输入,选取Park-Ang损伤指数作为结构损伤指标,开展了主余震序列作用下的未锈蚀与锈蚀钢筋混凝土框架结构的地震损伤评估与易损性分析。计算结果表明：锈蚀率的提高加剧了主余震序列作用下的结构累积损伤,其增长率最大可超过50%。由钢筋锈蚀单一因素引起的结构损伤在主余震累积损伤中的占比最高可超过30%。此外,钢筋锈蚀因素会导致结构的主余震易损性曲线发生显著提升。当锈蚀率较大时,钢筋锈蚀对结构易损性的影响与余震对结构易损性的影响相接近。钢筋锈蚀和余震两个因素的耦合作用会使结构的易损性水平发生更为显著的提升。因此,十分有必要在既有钢筋混凝土结构抗主余震性能评估中考虑钢筋锈蚀因素的影响。     

Structural geometry effect on the size-scaling of strength

The sensitivity of the empirical exponent of Bazant's size-effect scaling law on structural geometry is clarified through numerical experiments. For large centre- cracked tension panels, made of a linearly softening material, the best-fitting exponent is 0.90, whereas for large edge-cracked panels it is 0.75. For edge-cracked panels, the value of the exponent increases as a function of increasing crack-length-to-width-ratio. The results indicate that with structures of brittleness numbers below unity, reliable predictions of strength require the size-effect scaling law to be fitted for any particular structural geometry.     

纤维增强复合材料层合板缺口尺寸及形状效应数值模拟

通过考虑基体裂纹、纤维断裂、层内劈裂和层间脱层等破坏形式,建立三维有限元模型研究含中心圆孔和中心裂缝的准各向同性复合材料层合板([45/0/-45/90]_(2S))在拉伸载荷下的缺口尺寸效应及缺口形状效应。模拟结果显示:随着缺口尺寸的增大,层合板的破坏强度逐渐降低,然而,在本文研究范围内含中心裂缝的层合板破坏强度始终高于对应的含中心圆孔的层合板破坏强度。进一步分析有限元模拟结果表明,含中心裂缝的层合板亚临界损伤发生得更早,并且亚临界损伤范围更大,亚临界损伤会大大缓解缺口尖端的应力集中,从而使含中心裂缝层合板表现出更高的破坏强度。