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

This study proposes an algorithm of embedding cohesive elements in Abaqus and develops the computer code to model 3D complex cragk 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 wedgesplitting 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.

Fracture propagation and evolution law of indirect fracturing in the roof of broken soft coal seams

Indirect fracturing in the roof of broken soft coal seams has been demonstrated to be a feasible technology.In this work,the No.5 coal seam in the Hancheng block was taken as the research object.Based on the findings of true triaxial hydraulic fracturing experiments and field pilot under this technology and the cohesive element method,a 3D numerical model of indirect fracturing in the roof of broken soft coal seams was established,the fracture morphology propagation and evolution law under different conditions was investigated,and analysis of main controlling factors of fracture parameters was conducted with the combination weight method,which was based on grey incidence,analytic hierarchy process and entropy weight method.The results show that“士”-shaped fractures,T-shaped fractures,cross fractures,H-shaped fractures,and“干”-shaped fractures dominated by horizontal fractures were formed.Different parameter combinations can form different fracture morphologies.When the coal seam permeability is lower and the minimum horizontal principal stress difference between layers and fracturing fluid injection rate are both larger,it tends to form“士”-shaped fractures.When the coal seam permeability and minimum horizontal principal stress between layers and perforation position are moderate,cross fractures are easily generated.Different fracture parameters have different main controlling factors.Engineering factors of perforation location,fracturing fluid injection rate and viscosity are the dominant factors of hydraulic fracture shape parameters.This study can provide a reference for the design of indirect fracturing in the roof of broken soft coal seams.

基于内聚力单元法的船舶与重叠冰碰撞数值模拟研究

The gradual increase in shipping and drilling activities in the Arctic regions has resulted in the increased importance of studying the structural safety of polar ships in various ice conditions.Rafted ice refers to a type of accumulated and overlapped sea ice;it is driven by external forces,such as wind and waves,and may exert high loads on ships and threaten their structural safety.Therefore,the properties of rafted ice and the construction of numerical models should be studied before exploring the interaction and collision between ships and rafted ice.Based on the nonlinear finite-element method,this paper introduces the cohesive element model for the simulation of rafted ice.The interaction between ships and rafted ice is studied,and the ice force of the hull is obtained.Numerical simulation results are compared with model test findings,and the effectiveness of the cohesive element method in the construction of the model of rafted ice materials is verified.On this basis,a multilayer rafted ice model is constructed,and its interaction with the ship is studied.The research unveils that rafted ice parts impede crack generation and slow down crack propagation to a certain extent.

Separation work analysis of cohesive law and consistently coupled cohesive law

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model （CZM） and the cohesive element method. The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models. Based on the proposed consistently coupled rule/principle, the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive law by analyzing the surface separation work. It is shown that the Xu-Needleman law is only valid in the mixed mode fracture when the normal separation work equals the tangential separation work. Based on the consistently coupled principle and the modification of the Xu-Needleman law, a consistently coupled cohesive （CCC） law is given. It is shown that the proposed CCC law has already overcome the non-consistency defect of the Xu-Needleman law with great promise in mixed mode analyses.

Numerical simulation of plate rigid restraint cracking tests based on cohesive element model

Cohesive element is developed from the Dugdal-Barenblatt model in the field of fracture mechanics. The mechanical constitutive relation of cohesive element can be artificially assumed depending on the specific applications. It has been successfully applied in the study of crystal plasticity/brittle fracture process and decohesion between delaminations. In this paper, tensile experiments of large steel plate with different length of pre-existing cracks are conducted. Based on commercial software ABAQUS, cohesive element is adopted to simulate the tensile tests, and appropriate parameter values are obtained by fitting displacement-force curves. Using these parameters, a numerical method is presented by applying cohesive element to thermo-elastic-plastic finite element method （TEP-FEM） to simulate plate rigid restraint cracking （PRRC） tests. By changing constitutive relation of cohesive element, dimensions of the model and welding conditions, the influence of welding restraint intensity and welding conditions on the crack propagation are discussed, respectively. Three types of welding cold cracking are simulated. Significant influence of welding cold cracking on resistant stress in welding line is captured by this numerical method.

Relations of Microstructural Attributes and Strength-Ductility of Zirconium Alloys with Hydrides

As the first safety barrier of nuclear reactors,zirconium alloy cladding tubes have attracted extensive attention because of its good mechanical properties.The strength and ductility of zirconium alloy are of great significance to the service process of cladding tubes,while brittle hydrides precipitate and thus deteriorate the overall performance.Based on the cohesive finite element method,the effects of cohesive strength,interfacial characteristics,and hydrides geometric characteristics on the strength and ductility of two-phase material(zirconium alloy with hydrides)are numerically simulated.The results show that the fracture behavior is significantly affected by the cohesive strength and that the overall strength and ductility are sensitive to the cohesive strength of the zirconium alloy.Furthermore,the interface is revealed to have prominent effects on the overall fracture behavior.When the cohesive strength and fracture energy of the interface are higher than those of the hydride phase,fracture initiates in the hydrides,which is consistent with the experimental phenomena.In addition,it is found that the number density and arrangement of hydrides play important roles in the overall strength and ductility.Our simulation provides theoretical support for the performance analysis of hydrogenated zirconium alloys during nuclear reactor operation.

Influence of inter-grain cementation stiffness on the effective elastic properties of porous Bentheim sandstone

Effective elastic properties of porous media are known to be significantly influenced by porosity.In this paper,we investigated the influence of another critical factor,the inter-grain cementation stiffness,on the effective elastic properties of a granular porous rock(Bentheim sandstone)using an advanced numerical workflow with realistic rock microstructure and a theoretical model.First,the disparity between the experimentally tested elastic properties of Bentheim sandstone and the effective elastic properties predicted by empirical equations was analysed.Then,a micro-computed tomography(CT)-scan based approach was implemented with digital imaging software AVIZO to construct the 3D(three-dimensional)realistic microstructure of Bentheim sandstone.The microstructural model was imported to a mechanics solver based on the 3D finite element model with inter-grain boundaries modelled by cohesive elements.Loading simulations were run to test the effective elastic properties for different shear and normal intergrain cementation stiffness.Finally,a relation between the macroscale Young’s modulus and inter-grain cementation stiffness was derived with a theoretical model which can also account for porosity explicitly.Both the numerical and theoretical results indicate the influence of the inter-grain cementation stiffness,on the effective elastic properties is significant for porous sandstone.The calibrated normal and shear stiffnesses at the inter-grain boundaries are 1.2×10^(5) and 4×10^(4) GPa/m,respectively.

Computational Modeling of Intergranular Crack Propagation in an Intermetallic Compound Layer

A micromechanical model is presented to study the initiation and propagation of microcracks of intermetallic compounds(IMCs)in solder joints.The effects of the grain aggregate morphology,the grain boundary defects and the sensitivity of the various cohesive zone parameters in predicting the overall mechanical response are investigated.The overall strength is predominantly determined by the weak grain interfaces;both the grain aggregate morphology and the weak grain interfaces control the crack configuration;the different normal and tangential strengths of grain interfaces result in different intergranular cracking behaviors and play a critical role in determining the macroscopic mechanical response of the system.

Features of fracture height propagation in cross-layer fracturing of shale oil reservoirs

Triaxial fracturing modeling experiments were carried out on whole diameter shale cores from different layers of Shahejie Formation in the Dongpu sag,Bohai Bay Basin to find out the vertical propagation shapes of hydraulic fractures in different reservoirs.A numerical simulation method of inserting global cohesive elements was adopted to build a pseudo-three-dimension fracture propagation model for multiple shale oil reservoirs considering interface strength,perforation location,and pump rate to research the features of hydraulic fracture(HF)penetrating through layers.The hydraulic fracture propagates in a cross pattern in tight sandstone layers,in a straight line in sandstone layers with natural fractures,forms ladder fracture in shale layers with beddings.The hydraulic fracture propagates in a stripe shape vertically in both sandstone and shale layers,but it spreads in the plane in shale layers after connecting beddings.Restricted by beddings,the hydraulic fractures in shale layers are smaller in height than those in sandstone layers.When a sandstone layer and a shale layer are fractured at the same time,the fracture extends the most in height after the two layers are connected.Perforating at positions where the sandstone-shale interface is higher in strength and increasing the pumping rate can enhance the fracture height,thus achieving the goal of increasing the production by cross-layer fracturing in multiple shale oil layers.

Investigation of the Mechanical Behavior of a Thin Composite Stiffened Skin with a Combined Joint

Many joint models available to predict secondary bending moments in the structure have a stiffness mismatch, while this type of structure widely used in aircraft. To determine how to represent a structure with a stiffness mismatch in a combined joint （bonded/riveted）, a non-linear finite element analysis was performed. The detailed validation of this analysis identified the composite stiffened skin as the most suitable model in three dimensions. The use of this model for validating the secondary bending moment to calculate the behavior of the stiffener edge is straightforward and reliable. Experiments were performed to determine the distribution of the load in a combined joint under a tensile load that creates a secondary bending moment in a structure with a stiffness mismatch. The influence of related joint design considerations on the load transferred by the joint were examined through a finite element parameter analysis. The results are compared to determine best approach to predict the mechanical behavior at the edge of the stiffener. A close agreement between the finite element analysis and experimental results was obtained. Test observations using a C-scan compared well with the predictions of the onset of crack growth.

Numerical Simulation of Particle/Matrix Interface Failure in Composite Propellant

Interface debonding between particle and matrix in composite propellant influences its macroscopic mechanical properties greatly. For this, the laws of interface cohesive damage and failure were analyzed. Then, its microscopic computational model was established. The interface mechanical response was modeled by the bilinear cohesive zone model. The effects of interface properties and particle sizes on the macroscopic mechanical behavior were investigated. Numerical simulation of debonding damage evolution of composite propellant under finite deformation was carried out. The debonding damage nucleation, propagation mechanism and non-uniform distribution of microscopic stress-strain fields were discussed. The results show that the finite element simulation method based on microstructure model can effectively predict the trend of macroscopic mechanical behavior and particle/matrix debonding evolution process. It can be used for damage simulation and failure assessment of composite propellants.

Experimental and Numerical Investigation on the Tensile Fracture of Compacted Clay

This paper performed flexural test and numerical simulation of clay-beams with different water contents to study the tensile fracture of clay soil and the relevant mechanisms.The crack initiation and propagation process and the accompanied strain localization behaviors were all clearly observed and analyzed.The exponential cohesive zone model was proposed to simulate the crack interface behavior of the cohesive-frictional materials.The experimental results show that the bending capacity of clay-beams decrease with the water content,while those of the crack mouth opening displacement,crack-tip strain and the strain localization range increase.The numerical predictions successfully reproduce the evolving tensile cracks and the strain localization phenomenon of the clay beams with different fracture ductility,which demonstrates the validity of the proposed cohesive zone model in modelling clay fractures.

Mechanical Properties of Boron Carbide/Reducedgraphene-oxide Composites Ceramics

Reduced graphene oxide(rGO)enhanced B_(4)C ceramics was prepared by SPS sintering,the enhancement effect of rGO on the microstructure and mechanical properties of composites was studied through experiments and numerical simulation.The results show that the composite with 2wt%rGO has the best comprehensive mechanical properties.Compared with pure boron carbide,vickers hardness and bending strength are increased by 4.8%and 21.96%,respectively.The fracture toughness is improved by 25.71%.The microstructure observation shows that the improvement of mechanical properties is mainly attributed to the pullout and bridge mechanism of rGO and the crack deflection.Based on the cohesive force finite element method,the dynamic crack growth process of composites was simulated.The energy dissipation of B_(4)C/rGO multiphase ceramics during crack propagation was calculated and compared with that of pure boron carbide ceramics.The results show that the fracture energy dissipation can be effectively increased by adding graphene.

Cohesive zone model-based analyses of localized leakage of segmentally lined tunnels

This paper presents a novel approach for simulating the localized leakage behavior of segmentally lined tunnels based on a cohesive zone model.The proposed approach not only simulates localized leakage at the lining segment,but also captures the hydromechanically coupled seepage behavior at the segmental joints.It is first verified via a tunnel drainage experiment,which reveals its merits over the existing local hydraulic conductivity method.Subsequently,a parametric study is conducted to investigate the effects of the aperture size,stratum permeability,and spatial distribution of drainage holes on the leakage behavior,stratum seepage field,and leakage-induced mechanical response of the tunnel lining.The proposed approach yields more accurate results than the classical local hydraulic conductivity method.Moreover,it is both computationally efficient and stable.Localized leakage leads to reduced local ground pressure,which further induces outward deformation near the leakage point and slight inward deformation at its diametrically opposite side.A localized stress arch spanning across the leakage point is observed,which manifests as the rotation of the principal stresses in the adjacent area.The seepage field depends on both the number and location of the leakage zones.Pseudostatic seepage zones,in which the seepage rate is significantly lower than that of the adjacent area,appear when multiple seepage zones are considered.Finally,the importance of employing the hydromechanical coupled mechanism at the segment joints is highlighted by cases of shallowly buried tunnels subjected to surface loading and pressure tunnels while considering internal water pressure.

不同尺寸橡胶/帘线H型拉拔试验界面参数的归一化处理评价方法

H型拉拔试验被广泛应用于橡胶/帘线复合材料界面粘结强度的估算.然而,目前的国际标准只要求在橡胶/帘线H型拉拔试验中记录拔出力的大小,并强调从不同尺寸的样品中获得的结果不具有可比性.在本文中,我们研究了不同尺寸橡胶/帘线试验样品的H拔出结果的可比性,并提出了一种归一化的评价方法来处理这些结果.分别对尺寸为5 mm、6.4 mm、10 mm的试验样品进行橡胶/帘线H拉拔试验(尺寸为7.5 mm、8.5 mm的试件结果作为支撑性试验).在试验结果的基础上,采用有限元法内聚单元模型对界面粘结强度进行了分析,所得出的内聚力参数比国际标准中所规定的拔出力更能准确地反映界面粘结性能.因此,采用内聚单元法能够更合理地比较不同橡胶/帘线试样的界面粘结强度.我们首先基于6.4 mm尺寸样品的试验结果建立有限元模型,并确定满足条件的内聚单元参数,然后将其应用于其他尺寸的样品模型.尽管试验样品的尺寸大小在变化,但在保持内聚单元参数不变的前提下,模拟结果与试验结果仍然保持良好的一致性,这表明内聚参数不受样本尺寸的影响.在此基础上,我们提出了一种归一化方法,使不同尺寸样品的橡胶/帘线H拉拔试验的结果具有了可比性.本文提出的归一化方法是对现有国际、国内标准实验方法的扩展.

The effects of mismatch fracture properties in encapsulation-based self-healing concrete using cohesive-zone model

Finite element analysis is developed to simulate the breakage of capsule in capsule-based self-healing concrete.A 2D circular capsule with different core-shell thickness ratios embedded in the mortar matrix is analyzed numerically along with their interfacial transition zone.Zero-thickness cohesive elements are pre-inserted into solid elements to represent potential cracks.This study focuses on the effects of mismatch fracture properties,namely fracture strength and energy,between capsule and mortar matrix into the breakage likelihood of the capsule.The extensive simulations of 2D specimens under uniaxial tension were carried out to investigate the key features on the fracture patterns of the capsule and produce the fracture maps as the results.The developed fracture maps of capsules present a simple but valuable tool to assist the experimentalists in designing appropriate capsule materials for self-healing concrete.

Fracture behavior and self-sharpening mechanisms of polycrystalline cubic boron nitride in grinding based on cohesive element method

Unlike monocrystalline cubic boron nitride(CBN), polycrystalline CBN(PCBN) shows not only higher fracture resistance induced by tool-workpiece interaction but also better selfsharpening capability;therefore, efforts have been devoted to the study of PCBN applications in manufacturing engineering. Most of the studies, however, remain qualitative due to difficulties in experimental observations and theoretical modeling and provide limited in-depth understanding of the self-sharpening behavior/mechanism. To fill this research gap, the present study investigates the self-sharpening process of PCBN abrasives in grinding and analyzes the macro-scale fracture behavior and highly localized micro-scale crack propagation in detail. The widely employed finite element(FE) method, together with the classic Voronoi diagram and cohesive element technique,is used considering the pronounced success of FE applications in polycrystalline material modeling.Grinding trials with careful observation of the PCBN abrasive morphologies are performed to validate the proposed method. The self-sharpening details, including fracture morphology, grinding force, strain energy, and damage dissipation energy, are studied. The effects of maximum grain cut depths(MGCDs) and grinding speeds on the PCBN fracture behavior are discussed, and their optimum ranges for preferable PCBN self-sharpening performance are suggested.

A random medium model for simulation of concrete failure

A random medium model is developed to describe damage and failure of concrete.In the first place,to simulate the evolving cracks in a mesoscale,the concrete is randomly discretized as irregular finite elements.Moreover,the cohesive elements are inserted into the adjacency of finite elements as the possible cracking paths.The spatial variation of the material properties is considered using a 2-D random field,and the stochastic harmonic function method is adopted to simulate the sample of the fracture energy random field in the analysis.Then,the simulations of concrete specimens are given to describe the different failure modes of concrete under tension.Finally,based on the simulating results,the probability density distributions of the stress-strain curves are solved by the probability density evolution methods.Thus,the accuracy and efficiency of the proposed model are verified in both the sample level and collection level.

Interaction between matrix crack and circular capsule under uniaxial tension in encapsulation-based self-healing concrete

This paper investigates the fracture process of a capsule when subjected to uniaxial tension in encapsulation-based self-healing concrete.A circular capsule embedded in the mortar matrix is considered along with different ratios of core-shell thickness.To represent potential cracks,zero thickness cohesive elements are pre-inserted throughout element boundaries.The effects of fracture strength around the interfacial transition zone of the capsule are analyzed.The crack nucleation,propagation,and fracture mode of capsule are also discussed.The numerical results indicate that increasing the strength of the interfacial transition zone around the capsule can increase the load-carrying capacity of self-healing concrete.Moreover,given a similar fracture strength around the interface of the capsule,the fracture probability of capsule in encapsulation-based self-healing concrete is strongly dependent on the core-shell thickness ratio..

Computational modeling of fracture in capsule-based self-healing concrete: A 3D study

We present a three-dimensional(3D)numerical model to investigate complex fracture behavior using cohesive elements.An efficient packing algorithm is employed to create the mesoscale model of heterogeneous capsulebased self-healing concrete.Spherical aggregates are used and directly generated from specified size distributions with different volume fractions.Spherical capsules are also used and created based on a particular diameter,and wall thickness.Bilinear traction-separation laws of cohesive elements along the boundaries of the mortar matrix,aggregates,capsules,and their interfaces are pre-inserted to simulate crack initiation and propagation.These pre-inserted cohesive elements are also applied into the initial meshes of solid elements to account for fracture in the mortar matrix.Different realizations are carried out and statistically analyzed.The proposed model provides an effective tool for predicting the complex fracture response of capsule-based self-healing concrete at the meso-scale.