混凝土拉伸断裂的细观数值分析

根据混凝土试件拉伸和三点弯曲的物理模型,用梁-颗粒模型BPM 2D(B eam-Particle M ode l)模拟了混凝土拉伸和三点弯曲试件微裂纹的萌生、扩展直至试件宏观破坏的全过程。在梁-颗粒模型中用三种类型梁单元形成混凝土细观数值模型,每种类型梁单元的力学性质均按韦伯(W e ibu ll)分布随机赋值以模拟混凝土细观结构的非均匀性。数值模拟结果给出了混凝土拉伸应力-应变曲线和三点弯曲载荷-位移曲线,以及混凝土试件破坏过程最大应力分布图和裂纹扩展图。数值模拟结果显示混凝土破坏过程实际上就是微裂纹萌生、扩展、贯通,直到宏观裂纹产生导致混凝土失稳断裂的过程。通过对数值模拟结果的分析,揭示出混凝土在拉伸条件下裂纹尖端的拉应力集中是裂纹扩展的动力,混凝土组成材料力学性质的非均匀性是造成裂纹扩展路径曲折的重要原因。     

Numerical simulation of the failure process of unreinforced masonry walls due to concentrated static and dynamic loading

Finite element analyses of brick masonry subjected to in-plane concentrated static and dynamic loads are carried out to study crack initiation and propagation during the failure process of unreinforced masonry walls. The numerical model is firstly validated by the experimental tests by using the same materials parameters and loading conditions. Then, the static and dynamic concentrated loads are applied to the mortar joints and brick, respectively, and numerical simulations are used to compare the fracture characteristics for these loads. In addition, a comparison of fracture mechanisms for the concentrated loads on the mortar joint and brick is also given. Finally, the effect of dynamic pressure (P_max) on the failure mechanism of brick masonry is considered.     

Numerical simulation of flows over 2D and 3D backward-facing inclined steps

The work deals with the numerical solution of incompressible turbulent flow in a channel with a backward-facing step having various inclination angles. Also, the inclination of upper wall is considered. The mathematical model is based on the Reynolds averaged Navier–Stokes equations. The governing equations are closed by the explicit algebraic Reynolds stress (EARSM) model according to Wallin and Johansson or by linear eddy viscosity models (SST, TNT k–ω). The numerical solution is carried out by the implicit finite-volume method based on the artificial compressibility and by the finite-element method amd both approaches compared. The numerical simulations use as reference the experimental data by Makiola and Driver and Seegmiller in large aspect ratio channels. In these cases, the results are obtained by 2D and 3D simulations. Further narrow channel PIV experimental data are used as reference for 3D simulations.     

The effects of micro-defects and crack on the mechanical properties of metal fiber sintered sheets

The effects of three types of defect (i.e., two micro defects—broken fibers and separation of fiber joints and one macro defect—crack) on the mechanical properties of porous metal fiber sintered sheets (MFSSs) are investigated by a combination of numerical simulation, analytical modeling, and experimental test. All simulations are based upon the previously developed micromechanics random beam model (Jin et al., 2013). Broken fibers are realized by removing cell edges (i.e., fibers between two joints) in an otherwise perfect model. Their induced decreases in the elastic moduli and strengths are found to be much lower than those of two dimensional (2D) foams and Kagome grids. For the defect in the form of separation of fiber joints, both analytical and numerical models are developed. The predicted linear decreases in the moduli and strengths (except for the compressive strength) with increasing number of separated fiber joints indicate that MFSSs be insensitive to the defect of joint separation. To explore the effect of crack, fracture toughness of MFSSs is measured and is found to be significantly higher than that of metal foams of the same relative density (i.e., volume fraction of the constituent solid material). The underlying ductile mechanism of MFSSs is further investigated by numerical simulations, showing that plastic deformation spreads all over the fibers in ligament rather than concentrates around crack tip. This study shows that MFSSs are superior in view of their resistance to the considered micro-defects and crack.     

Nonlinear viscoelastic multi-scale repetitive unit cell model of 3D woven composites with damage evolution

Three-dimensional (3D) textile composites have great potential applications to aircrafts and high speed vehicles because of the high strength/weight ratios and the capabilities of manufacturing complex, net-shape preforms. This paper reports the nonlinear viscoelastic responses and damage mechanisms of one kind of 3D textile composites, named as 3D orthogonal woven composite (3DOWC) under quasi-static tensile loading based on a micro/meso-scale repetitive unit cells (RUCs) model. In the RUCs model, the resin is described with a nonlinear viscoelastic material and the fibers/tows with an elastic material. The damage initiation and propagation in resin are simulated by the post-damage constitutive models with maximum principal theory failure criteria. The fibers/tows impregnated with resin are defined by elastic transverse-isotropic material model with ultimate strengths failure of ‘expanded smeared crack’ both along and perpendicular to fibers/tows axis direction. The engineering parameters and ultimate strengths of homogenized fibers/tows filled with matrix in meso-RUCs model are transferred from the numerical analysis of the micro-RUCs. The results are compared with experimental and theoretical values of RUC deformation and damage initiation and propagation under monotonic axial loading. The methodology of establishing the nonlinear visco-elastic multi-scale model of 3D textile composites without introducing the real fabric architecture in finite element analyses is explained. With the multi-scale RUCs model, the mechanical behaviors of other kinds of 3D textile composites can also be predicted.     

FINITE ELEMENT MODELLING OF COMPLEX 3D STATIC AND DYNAMIC CRACK PROPAGATION BY EMBEDDING COHESIVE ELEMENTS IN ABAQUS

<正>This study proposes an algorithm of embedding cohesive elements in Abaqus and develops the computer code to model 3D complex crack propagation in quasi-brittle materials in a relatively easy and efficient manner.The cohesive elements with softening traction-separation relations and damage initiation and evolution laws are embedded between solid elements in regions of interest in the initial mesh to model potential cracks.The initial mesh can consist of tetrahedrons,wedges,bricks or a mixture of these elements.Neither remeshing nor objective crack propagation criteria are needed.Four examples of concrete specimens,including a wedge-splitting test,a notched beam under torsion,a pull-out test of an anchored cylinder and a notched beam under impact,were modelled and analysed.The simulated crack propagation processes and load-displacement curves agreed well with test results or other numerical simulations for all the examples using initial meshes with reasonable densities.Making use of Abaqus's rich pre/post-processing functionalities and powerful standard/explicit solvers,the developed method offers a practical tool for engineering analysts to model complex 3D fracture problems.     

Multiscale behavior of crack initiation and growth in piezoelectric ceramics

The multiscale nature of cracking in ferroelectric ceramics is explored in relation to the crack growth enhancement and retardation behavior when the direction of applied electric field is reversed with reference to that of poling. An a priori knowledge of the prevailing fracture behavior is invoked for the energy dissipated in exchange of the macro- and micro-crack surface. To avoid the formalism of developing a two-scale level model, a single dominant crack is considered where the effect of microcracking could be reflected by stable crack growth prior to macro-crack instability. This is accounted for via a length ratio parameter λ. Micro- and macro-crack damage region would necessarily overlap in the simplified approach of applying equilibrium mechanics solutions to different scale ranges that are connected only on the average over space and time. The strain energy density theory is applied to determine the crack growth segments for conditions of positive, negative and zero electric field. The largest and smallest crack segments were found to correspond, respectively, to the positive and negative field. All of the three piezoceramics PZT-4, PZT-5H and P-7 followed such a trend. This removes the present-day controversy arising from the use of the energy release rate concept that yields results independent of the sign of the electric field. Interaction of non-similar crack growth with the direction of electric field is also discussed in relation to Mode II cracking. The crack initiation angle plays a dominant role when the growth segment is sufficiently small. Otherwise, a more complex situation prevails where consideration should also be given to the growth segment length. Failure stresses of Modes I and II cracking are also obtained and they are found to depend not only on the electric field density but also on crack length and the extent of slow crack growth damage. These findings suggest a series of new experiments.     

Particle-based numerical modeling of AE statistics in disordered materials

We present some numerical simulations of AE due to damage propagation in disordered materials under compression and bending. To this purpose, the AE cumulative number, the time frequency analysis and the statistical properties of AE time series will be numerically simulated adopting the so-called “particle method strategy” (Cundall in Proceedings ISRM Symp., Nancy, France, vol. 2, pp. 129–136, 1971). The method provides the velocity of particles in a set simulating the behavior of a granular system and, therefore, is suitable to model the compressive wave propagation and acoustic emission (corresponding to cracking) in a solid body. The numerical simulations (Abe et al. in Pure Appl. Geophys. 161:2265–2277, 2004) correctly describe the compression test in terms of mean stress-strain response and crack pattern (Invernizzi et al. in Proceedings of the SEM annual conference, Society for Experimental Mechanics Inc., USA, SEM Annual Conference, Indianapolis, Indiana, USA, June 7–10, 2010). The size effects on the peak compressive strength and on the AE count are correctly reproduced. In addition, the amplitude distribution (b-value) and temporal evolution of AE events due to cracking, crucial for the evaluation of damage and remaining lifetime, were simulated and result in agreement with the experimental evidences.     

Fatigue crack growth of cable steel wires in a suspension bridge: Multiscaling and mesoscopic fracture mechanics

Intrinsically, fatigue failure problem is a typical multiscale problem because a fatigue failure process deals with the fatigue crack growth from microscale to macroscale that passes two different scales. Both the microscopic and macroscopic effects in geometry and material property would affect the fatigue behaviors of structural components. Classical continuum mechanics has inability to treat such a multiscale problem since it excludes the scale effect from the beginning by introducing the continuity and homogeneity assumptions which blot out the discontinuity and inhomogeneity of materials at the microscopic scale. The main obstacle here is the link between the microscopic and macroscopic scale. It has to divide a continuous fatigue process into two parts which are analyzed respectively by different approaches. The first is so called as the fatigue crack initiation period and the second as the fatigue crack propagation period. Now the problem can be solved by application of the mesoscopic fracture mechanics theories developed in the recent years which focus on the link between different scales such as nano-, micro- and macro-scale.On the physical background of the problem, a restraining stress zone that can describe the material damaging process from micro to macro is then introduced and a macro/micro dual scale edge crack model is thus established. The expression of the macro/micro dual scale strain energy density factor is obtained which serves as a governing quantity for the fatigue crack growth. A multiscaling formulation for the fatigue crack growth is systematically developed. This is a main contribution to the fundamental theories for fatigue problem in this work. There prevail three basic parameters μ^∗, σ^∗ and d^∗ in the proposed approach. They can take both the microscopic and macroscopic factors in geometry and material property into account. Note that μ^∗, σ^∗ and d^∗ stand respectively for the ratio of microscopic to macroscopic shear modulus, the ratio of restraining stress to applied stress and the ratio of microvoid size ahead of crack tip to the characteristic length of material microstructure.To illustrate the proposed multiscale approach, Hangzhou Jiangdong Bridge is selected to perform the numerical computations. The bridge locates at Hangzhou, the capital of Zhejiang Province of China. It is a self-anchored suspension bridge on the Qiantang River. The cables are made of 109 parallel steel wires in the diameter of 7 mm. Cable forces are calculated by finite element method in the service period with and without traffic load. Two parameters α and β are introduced to account for the additional tightening and loosening effects of cables in two different ways. The fatigue crack growth rate coefficient C₀ is determined from the fatigue experimental result. It can be concluded from numerical results that the size of initial microscopic defects is a dominant factor for the fatigue life of steel wires. In general, the tightening effect of cables would decrease the fatigue life while the loosening effect would impede the fatigue crack growth. However, the result can be reversed in some particular conditions. Moreover, the different evolution modes of three basic parameters μ^∗, σ^∗ and d^∗ actually have the different influences on the fatigue crack growth behavior of steel wires. Finally the methodology developed in this work can apply to all cracking-induced failure problems of polycrystal materials, not only fatigue, but also creep rupture and cracking under both static and dynamic load and so on.     

An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression

This study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC^2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.     

A 3-D ellipsoidal flaw model for brittle fracture in compression

Engineering materials are rarely free of flaws. Mode I cracking from pre-existing flaws is the major cause of the brittle fracture in compression of materials such as concrete and rock. A 3-D ellipsoidal flaw model is used to show the significant influence of flaw geometry on crack initiation in uniform uniaxial, biaxial and triaxial compression. The model shows that the governing criterion for crack initiation may change from energy to stress with increasing crack size, and that for voids of similar size a spherical void is the most critical shape for crack initiation. The model thus provides a basis for a better understanding of both the phenomenon and the mechanism of brittle fracture in compression.     

准静态压力作用下岩体爆破成缝方向与机理的研究

本文在讨论了现有的爆破成缝理论以后,首先将岩体在爆生气体作用下的成缝过程分为开裂、扩展和止裂三个阶段,建立了这三个阶段的力学模型。然后,着重分析了爆破成缝方向和机理,提出了相应的断裂判据。最后,结合在大理石试块上进行的爆破成缝试验,通过计算分析,验证了本文提出的成缝机理。     

Fissuration polymodale dans les matériaux viscoélastiques orthotropes

This Note deals with an algorithmic approach about the crack initiation and the crack growth in a viscoelastic media for mixed mode configurations. This numerical model couples a finite element resolution of viscoelastic behavior and the Mθ integral calculus allowing a mixed mode separation in terms of stress intensity factors and energy release rate. The numerical application uses a 2MCG specimen allowing, in the same time, different mixed mode ratios and a crack growth stability. The finite element algorithm allows us to model the crack tip advance by taking into account the crack lip uncohesion in the process zone. It size is defined by taking into account stress field in the crack tip vicinity. To cite this article: R. Moutou Pitti, F. Dubois, C. R. Mecanique 337 (2009).     

巴西圆盘泥岩试件裂纹扩展及应变演化实验研究

为了研究准静态加载条件下岩石试件巴西劈裂裂纹扩展规律,采用MTS试验机进行准静态加载,同时用高速摄像机记录裂纹扩展过程。采用白光数字散斑处理软件对摄像机记录的照片进行处理,得到试件裂纹扩展过程中应变场的演化情况。通过实验和分析可以看出,由于端部效应及加载方式的原因,因此裂纹起裂点在底部加载部位;泥岩试件表面裂纹的平均扩展速度为252m/s;岩石的非均质性即内部微缺陷、微裂纹使得泥岩试样的开裂并不是沿着中心直径方向,而是偏离一定的角度,初始偏离角度约为17°。裂纹扩展过程可以划分为三个阶段:泥岩试件宏观变形阶段(宏观无裂纹)、宏观裂纹稳定扩展阶段、宏观裂纹动态张裂阶段。同时,在裂纹扩展过程中,表面第一主应变场、水平位移场等变化明显,在开裂部位第一主应变最大。通过对圆盘泥岩试件裂纹扩展实验研究,可为研究岩石破裂及其演化规律提供依据。     

Experimental and numerical investigation of fracture in a cast aluminium alloy

This paper describes an experimental and numerical investigation on the fracture behaviour of a cast AlSi9MgMn aluminium alloy. In the experiments, a modified Arcan test set-up was used to study mixed-mode fracture. During testing, the tension load and the displacement of the actuator of the test machine were recorded, simultaneously as a high-resolution digital camera was used to record a speckle-patterned surface of the specimen. The recorded images were post-processed using an in-house digital image correlation (DIC) software to obtain information of the displacement and strain fields in the specimen during the test. In addition, some newly implemented features in the DIC software allowed us to detect and follow the crack propagation in the material. The numerical calculations were carried out with a user-defined material model implemented in an explicit finite element code. In the model, the material behaviour is described by the classical J₂ flow theory, while fracture was modelled by the Cockcroft–Latham criterion, assuming the fracture parameter to follow a modified weakest-link Weibull distribution. With the proposed probabilistic fracture modelling approach, the fracture parameter can be introduced as a random variable in the finite element simulations. Crack propagation was modelled by element erosion, and a non-local damage formulation was used to reduce mesh-size sensitivity. To reveal the effect of mesh density and meshing technique on the force–displacement curves and the crack propagation, several different meshes were used in the numerical simulations of the modified Arcan tests. The numerical results were finally compared to the experimental data and the agreement between the measured and predicted response was evaluated.     

Analytical model for delamination growth during small mass impact on plates

An analytical model is presented for delamination initiation and growth and the resulting response during small mass impact on orthotropic laminated composite plates, which typically is caused by runway debris and other small objects. The solution is obtained by a fast stepwise numerical solution of a single integral equation. Delamination size, load and deflection history are predicted by extension of an earlier elastic impact model by the author. Good agreement is demonstrated in comparisons with finite element simulations and experiments.     

基于单元破裂的岩石裂纹扩展模拟方法

传统离散元方法在处理破裂问题时, 采用界面上的准则进行判断, 裂纹只能沿着单元边界扩展. 当物理问题存在宏观或微观裂隙时, 在界面上应用准则具有其合理性; 而裂纹沿着单元边界扩展, 使得裂纹路径受网格影响较大, 扩展方向受到限制. 针对上述情况, 可以基于单元破裂的方式, 构建连续- 非连续单元法, 并应用于岩石裂纹扩展问题的模拟. 该方法在连续计算时, 将单元离散为具有物理意义的弹簧系统, 在局部坐标系下由弹簧特征长度、面积求解单元变形和应力, 通过更新局部坐标系和弹簧特征量, 可进一步计算块体大位移、大转动, 连续问题计算结果与有限元一致, 同时提高了计算效率. 在此基础上, 引入最大拉应力与莫尔—库伦的复合准则, 判断单元破裂状态和破裂方向, 并采用局部块体切割的方式, 在单元内形成初始裂纹. 裂纹两侧相应增加新的计算节点, 同时引入内聚力模型描述裂纹两侧的法向、切向作用与张开度及滑移变形之间的关系. 按此方式, 裂纹尖端处的扩展路径可穿过单元内部和单元边界, 在扩展方向的选取上更为准确. 最后, 通过三点弯曲梁、单切口平板拉伸、双切口试样等典型数值试验, 模拟裂纹在拉伸、压剪等各种应力状态下的扩展问题, 并对岩石单轴压缩试验的破坏过程进行模拟, 分析裂纹形成与应力—应变曲线各阶段之间的对应关系. 结果表明: 连续—非连续单元法通过单元内部破裂的方式, 可以显示模拟裂纹萌生、扩展、贯通直至形成宏观裂缝的过程.      

Modeling and simulation of large-scale ductile fracture in plates and shells

The work is concerned with the modeling and simulation of large scale ductile fracture in plate and shell structures. A meshfree method – the reproducing kernel particle method (RKPM) – is used in numerical computations in order to enact dynamic crack propagation without remeshing. There are several novelties in the present approach. First, we have developed a crack surface approximation and particle split algorithm for three-dimensional through-thickness cracks. Second, to represent evolving crack surface in 3D shell structures, a 3D parametric visibility condition algorithm is proposed, which re-constructs the local connectivity map for particles near the crack tip or crack surfaces, so that the meshfree interpolation field can represent physical material separation in the computational domain. Third, the constitutive update formulas in explicit time integration by different versions of Gurson models and the rate-dependent Johnson–Cook model are implemented for 3D computations. Finally, the performance of different Gurson-type models are investigated and compared with the experimental data of large scale in-plate tear process. Numerical simulations of crack propagation in stiffened plates and shells demonstrate that the proposed method provides an effective means to simulate ductile fracture in large scale plate/shell structures with engineering accuracy.