On the calibration of cohesive parameters for refractories from notch opening displacements in wedge splitting tests

Cohesive elements are commonly used to describe crack propagation in heterogeneous materials with toughening mechanisms. This work aims to provide a guideline on how these fracture parameters can be calibrated using notch opening displacements (NODs) measured via digital image correlation and force data from wedge splitting tests (WSTs). Weighted finite element model updating was applied to calibrate material and boundary condition parameters in the same framework. The influence of each parameter on force and NOD data are given together with uncertainties for the calibrated parameters. Numerical results were in very good agreement in terms of splitting force, NOD, displacement and gray level residual fields. It is shown that images obtained during WSTs focusing on the crack path (i.e., hiding the loading region) can be used to drive numerical simulations and obtain cohesive parameters.     

Cohesive properties of refractory castable at 600 °C: Effect of sintering and testing temperature

This paper aims to evaluate cohesive properties for an alumina refractory with mullite-zirconia aggregates from wedge splitting tests (WST), and to assess their sensitivity to sintering and testing temperature. Five experiments were analyzed of which four were performed at 600^°C. The sought parameters were determined via weighted finite element model updating. The cohesive strength and the fracture energy were successfully calibrated and resulted in simulated data close to their experimental counterparts (i.e., between 4 and 11 times the measurement uncertainty). Increasing the sintering temperature from 1400^°C to 1450^°C enhanced the cohesion between the mullite-zirconia aggregates and the alumina matrix (20 % increase of the fracture energy and of the fracture process zone length). When the WSTs were performed at 600^°C, the cohesive strength was 10 % smaller while the fracture energy was 70 % higher than that at room temperature.     

Modelling Damage and Failure in Adhesive Joints Using A Combined XFEM-Cohesive Element Methodology

In recent years, cohesive elements based on the cohesive zone model (CZM) have been increasingly used within finite element analyses of adhesively bonded joints to predict failure. The cohesive element approach has advantages over fracture mechanics methods in that an initial crack does not have to be incorporated within the model. It is also capable of modelling crack propagation and representing material damage in a process zone ahead of the crack tip. However, the cohesive element approach requires the placement of special elements along the crack path and is, hence, less suited to situations where the exact crack path is not known a priori. The extended finite element method (XFEM) can be used to represent cracking within a finite element and hence removes the requirement to define crack paths or have an initial crack in the structure. In this article, a hybrid XFEM-cohesive element approach is used to model cracking in the fillet area using XFEM where the crack path is not known and then using cohesive elements to model crack and damage progression along the interface. The approach is applied to the case of an aluminium–epoxy single lap joint and is shown to be highly effective.     

A laser irradiation disc test for fracture testing of refractory fine ceramics

The critical stress intensity factor, tensile strength and crack stability were analysed for a zirconia refractory by parameter identification based on a laser irradiation test and a finite element simulation. Furthermore, the results for the specific fracture energy were determined for different assumed cohesive behaviours. The tests were carried out on notched discs that were irradiated at their centres. During the tests, temperatures are recorded by a thermo vision camera and the crack propagation by an acoustic emission recorder. Acoustic emission allowed for the determination of the onset of crack initiation (time t₁) and unstable crack propagation (time t₂). A finite element model representing the geometry of the sample was built to determine the fracture mechanical parameters from t₁ and t₂. This method is believed to be favourable for rather brittle refractory ceramics, whereas for less brittle materials, a wedge splitting procedure according to Tschegg is considered more favourable.     

Finite element analysis of failure mechanisms in HDPE/CaCo3 particulate composite

Abstract

A finite element analysis of crack propagation in an HDPE/CaCo₃ composite was carried out using a combination of the extended finite element method (XFEM) and the cohesive zone method (CZM). A unit cell of an entire composite consisting of one particle was chosen as the study zone. The interphase was assumed as a cohesive surface between the matrix and the particle. Variable parameters were the interface adhesion, position of initial crack, volume fraction, and size of the particle. The results showed that, the energy release rate increases when increasing the particle size. Increasing the volume fraction from 5 to 10% has positive effects in decreasing the strain energy release rate; however, the effects of 10 and 15% of volume fraction on the energy release rate are almost the same. Increasing the values of interfacial adhesion strength increases the strength of composite.     

Fracture characteristics of concrete at early ages

The purpose of this study is to experimentally investigate, at early ages, the fracture characteristics of concrete such as critical crack tip opening displacement, critical stress intensity factor, fracture energy, and bilinear softening curve based on the concepts of the effective-elastic crack model and the cohesive crack model.A wedge-splitting test for Mode I was performed on cubical specimens with an initial notch at the edge. By taking various strengths and ages, load-crack mouth opening displacement (CMOD) curves were obtained and these curves were evaluated by linear elastic fracture mechanics and finite element analysis.The results from the test and analysis indicate that critical crack tip opening displacement decreases and critical stress intensity factor and fracture energy increase with concrete ages from Day 1 to Day 28. By numerical analysis, four parameters of bilinear softening curves from Day 1 to Day 28 were obtained. In addition, it was observed that the parameters f_t and f₁ increase and the parameters w₁ and w_c decrease with increasing age. The obtained fracture parameters and bilinear softening curves at early ages may be used as a fracture criterion and an input data for finite element analysis of concrete at early ages.     

Cohesive Zone Model Characterization of the Adhesive Hysol EA-9394

Abstract

The cohesive zone model approach is attractive for the analysis of failure of adhesively bonded structures. While the numerical implementation of cohesive elements has been well established, there remains a lack of cohesive material data. The present paper contributes to efforts to fill this void. An investigation of crack growth in the widely used structural adhesive Hysol EA-9394 is presented, and the adhesive is characterized by a cohesive zone law. Crack growth experiments were performed on specimens consisting of aluminum adherends bonded by use of the adhesive. Measurements of the surface topography leading reconstruction of fracture processes indicate that plastic deformation is absent during fracture. Thus, the cohesive zone law can directly be determined from the energy release rate and the material separation measured at the initial crack tip. The cohesive zone law is then applied in finite element model to predict crack growth. The predicted strain fields during crack growth are well matched to those obtained by digital image correlation measurements. An independent set of crack growth experiments was performed, and finite element models based on the cohesive law were used to predict the outcome of these experiments. Again good agreement between simulation and experiment was obtained. The results give confidence that the cohesive zone model parameters are transferable to the analysis of structures bonded with the adhesive Hysol EA-9394 in general. A comparison of the cohesive zone law for Hysol EA-9394 demonstrates that this adhesive possesses high strength and moderate toughness. Limits to the transferability regime are discussed.     

Microstructural toughening mechanisms in nanostructured Al2O3/GdAlO3 eutectic composite studied using in situ microscale fracture experiments

This work uses in situ transmission electron microscopy (TEM) based micromechanical testing to isolate and quantify the microstructural toughening mechanisms active in nanostructured Al₂O₃/GdAlO₃ eutectic samples. The effect of fracture direction across orthogonal sections of the rod-like eutectic was used to reveal the influence of different fracture paths and mechanisms on toughening. The average fracture toughnesses of the rod-like structures in the longitudinal cross-section and transverse cross-section are 2.4 MPa·m^1/2 and 2.7 MPa·m^1/2, respectively. Multiple samples tested in the longitudinal cross-section show significant R-curve toughening response, and obtain values greatly exceeding the initial values upon crack extension. It is concluded that nanoscale crack bridging induces deflection of the crack path, which leads extrinsic energy dissipation as the crack opens. Micropillar compressions are also performed to investigate the composite’s strength. Sample orientation strongly affects the deformation mode and interfacial sliding occurs when the maximal shear stress is parallel to the interface.     

A discrete crack approach to normal/shear cracking of concrete

This paper presents a numerical procedure for mixed mode fracture of quasi-brittle materials. The numerical procedure is based on the cohesive crack approach and extends it to mixed mode fracture. The crack path is obtained, and the mixed mode fracture model is incorporated into the crack path. The crack model is based on the formulation of the classical plasticity. The model is incorporated into a commercial finite element code by an user subroutine and is contrasted with experimental results. The numerical results agree quite well with two experimental sets of mixed mode fracture of concrete beams; one from Arrea and Ingraffea, the other from a nonproportional loading by the authors. Two other sets of experimental fracture results were modeled based on double-edge notched testing. The numerical procedure, mainly based on standard properties of the material measured by standard methods, predicts the experimental records of the load versus displacement at several control points of the specimens for three homothetic sizes of specimen.     

陶瓷叠层结构增韧设计的数值模拟及实验研究

本研究尝度将微机作为辅助手段引入仿生陶瓷复合材料的增韧设计。基于多层梁模型,采用有限元数值模拟方法模拟了仿生陶瓷叠层结构的断裂行为和裂纹逐次从硬层基片向弱界面层基片向弱界面层的拐折和扩展。后处理程序显示了三点弯曲试件的裂纹扩展路径,相应的载荷－位移曲线和增韧效应（断裂功大幅度提高）,还进一步分析了叠层陶瓷的韧性和强度受试件几何参数（硬软层层厚比,层数）和材料性能参数（断裂应变,Ｙｏｕｎｇ氏模量比等     

Cohesive zone modelling of crack growth in polymers Part 2 –Numerical simulation of crack growth

Abstract

Cohesive zone models, which incorporate some form of cohesive law as the fracture criterion within the localised damage zone, are increasingly being used in the fracture assessment of tough engineering materials. However, the exact characterisation of the material within the damage zone is crucial as it has a fundamental bearing on the computed crack growth rates. A procedure is presented for implementing a cohesive zone model using the finite volume method by incorporating experimentally measured traction curves as the local fracture criterion. Experimental load–time and crack growth data in tough polyethylene for a three point bend geometry are compared with numerical predictions. Reasonable agreement is achieved between experiment and model predictions when a single fixed rate traction–separation curve is used for all cells along the prescribed crack path. Predictions are improved by incorporating a scheme for switching between a family of rate dependent curves in place of a single fixed rate curve. Results also indicate the necessity of incorporating the effect of difference in constraint along the crack path into the choice of the local traction–separation law.     

Comparison of cohesive zone elements and smoothed particle hydrodynamics for failure prediction of single lap adhesive joints

This research investigates the use of a meshless smoothed particle hydrodynamics (SPH) method for the prediction of failure in an adhesively bonded single lap joint. A number of issues concerning the SPH based finite element modelling of single lap joints are discussed. The predicted stresses of the SPH finite element model are compared with the results of a cohesive zone based finite element model. Crack initiation and crack propagation in the adhesive layer are also studied. The results show that the peel stresses predicted by the SPH finite element model are higher and the shear stresses are lower than those predicted by the cohesive zone finite element model. The crack initiation and propagation response of the two models is similar, however, the SPH finite element model predicted a lower failure load than the cohesive zone finite element model. It is concluded that the current implementation of SPH method is a promising method for modelling cohesive failure in bonded joins but requires further development to allow for interfacial crack growth and better stress prediction under tensile loading to compete with existing methods.     

Analysis of a castable refractory using the wedge splitting test and cohesive zone model

A cohesive zone approach is applied to the wedge splitting test (WST) using the finite element code Abaqus to obtain the tensile strength, the fracture energy and insight about the crack wake region. A finite element model updating (FEMU) method, with a cost function based on the measured load (FEMU-F), is used to calibrate the sought parameters. Digital image correlation (DIC) provided the kinematic boundary conditions, and the images were also used to define the geometry for the finite element analysis. Besides the fracture energy analysis and the experimental load, gray level images and displacement fields are analyzed in order to validate the results. The cohesive region is active in the whole analyzed test as confirmed by estimates using the cohesive length.     

Mode-l Fracture Behaviour of Adhesive Joints. Part I. Relationship Between Fracture Energy and Bond Thickness

The fracture properties of adhesive joints of aluminium were investigated using a rubber-modified tough epoxy resin system (G_IC = 2.76 kJ/m²) as adhesive material. Compact tension (CT) adhesive joints were manufactured for a wide range of bond thickness t (from 0.05mm to 10mm) and fracture tests conducted under static load. Scanning electron microscopy (SEM) was used to examine the fracture surface morphology. A large deformation elastic- plastic finite element model was developed to evaluate the J-integral value for different bond thickness. The fracture energy, J_c , was found to be highly dependent on the bond thickness and was lower than that of the bulk adhesive. As the bond thickness was increased J_c also increased, though not monotonically, towards the fracture energy of the bulk adhesive. This result was caused by the complicated interactions between the stress and strain fields, plastic deformation of the adhesive around the crack tip, constraint from the adherends and the failure path. It was shown that values of J_c as a function of bond thickness correlated well with the variation of plastic zone height. Scanning electron micrographs from the fracture surfaces of the CT adhesive joints illustrated that the failure path was mainly cohesive through the centre-plane of the adhesive layer. Brittle fracture mechanisms were observed for thin bonds (0.04mm < t< 0.5 mm) but tough fracture mechanisms were identified for thick bonds (t > 1 mm).     

Bioinspired nacre-like 2024Al/B4C composites with high damage tolerance

The bio-inspired 2024Al/B₄C composites with a laminate-reticular hierarchical architecture were constructed by squeeze casting of 2024Al into loose freeze-cast ceramic scaffolds. This pressurized infiltration process provided a clean and well-bonded interface without physical gaps. By regulating the initial suspension concentration (20, 25, 30 and 35 vol%), the effects of different ceramic content on the microstructure, damage-tolerance behavior and toughening mechanisms of the composites parallel and perpendicular to the ice-growth direction were investigated. The strength and toughness in the longitudinal direction were greater than that in the transverse direction. The 2024Al/20 vol% B₄C composite in the longitudinal direction yielded the highest flexural strength of 658 MPa, crack-initiation toughness (K_Ic) of 18.4 MPa m^1/2 and crack-growth toughness (K_Jc) of 27.5 MPa m^1/2. The unique damage-tolerant properties were attributed to multiple toughening mechanisms, including crack deflection, branching and blunting, ductile-ligament bridging and multiple-crack propagation, as evidenced by the stable crack growth and rising R-curve behavior during fracture. The significantly decreased damage tolerance in the transverse direction was mainly due to inadequate toughening tools. On the other hand, both the flexural strength and fracture toughness reduced remarkably as the ceramic content increased. The 2024Al/35 vol% B₄C composite fractured in a single-crack mode and the crack growth path was almost straight, showing a relatively low ?exural strength (502 MPa) and crack-initiation toughness (9.1 MPa m^1/2). The toughening mechanism was discussed in terms of the relationship between structural characteristics and cracking mode.     

Effects of Internal Stresses Due to a Dispersed Phase on the Fracture Toughness of Glass

The effects of thermal contraction mismatch on the toughening of glass by a dispersed phase were measured in a model system. Three toughening mechanisms were observed: prestressing of the dispersed phase, deflection of the crack by the stress field of the particle, and crack bowing between particles; deflection provided the greatest toughening. Toughening was increased by increasing particle size, decreasing particle spacing along the crack front, and increased particle spacing along the crack path.     

Predicting environmental degradation of adhesive joints using a cohesive zone finite element model based on accelerated fracture tests

A framework was developed to predict the fracture toughness of degraded adhesive joints by incorporating a cohesive zone finite element (FE) model with fracture data of accelerated aging tests. The developed framework addresses two major issues in the fracture toughness prediction of degraded joints by significant reduction of exposure time using open-faced technique and by the ability to incorporate the spatial variation of degradation with the aid of a 3D FE model. A cohesive zone model with triangular traction-separation law was adapted to model the adhesive layer. The degraded cohesive parameters were determined using the relationship between the fracture toughness, from open-faced DCB (ODCB) specimens, and an exposure index (EI), the time integration of the water concentration. Degraded fracture toughness predictions were done by calculating the EI values and thereby the degraded cohesive parameters across the width of the closed joints. The framework was validated by comparing the FE predictions against the fracture experiment results of degraded closed DCB (CDCB) joints. Good agreement was observed between the FE predictions and the experimental fracture toughness values, when both ODCB and CDBC were aged in the same temperature and humidity conditions. It was also shown that at a given temperature, predictions can be made with reasonable accuracy by extending the knowledge of degradation behavior from one humidity level to another.     

Toughening epoxies with halloysite nanotubes

An experimental attempt was made to characterize the fracture behaviour of epoxies modified by halloysite nanotubes and to investigate toughening mechanisms with nanoparticles other than carbon nanotubes (CNTs) and montmorillonite particles (MMTs). Halloysite-epoxy nanocomposites were prepared by mixing epoxy resin with halloysite particles (5 wt% and 10 wt%, respectively). It was found that halloysite nanoparticles, mainly nanotubes, are effective additives in increasing the fracture toughness of epoxy resins without sacrificing other properties such as strength, modulus and glass transition temperature. Indeed, there were also noticeable enhancements in strength and modulus for halloysite-epoxy nanocomposites because of the reinforcing effect of the halloysite nanotubes due to their large aspect ratios. Fracture toughness of the halloysite particle modified epoxies was markedly increased with the greatest improvement up to 50% in K_IC and 127% in G_IC. Increases in fracture toughness are mainly due to mechanisms such as crack bridging, crack deflection and plastic deformation of the epoxy around the halloysite particle clusters. Halloysite particle clusters can interact with cracks at the crack front, resisting the advance of the crack and resulting in an increase in fracture toughness.     

Bimodal microstructure toughens plasma sprayed Al2O3-8YSZ-CNT coatings

Current work pursues generating controlled bimodal microstructure by plasma spraying of micrometer-sized Al₂O₃ and nanostructured spray-dried agglomerate with reinforcement of 20 wt% of 8 mol % yttria stabilized zirconia (8YSZ) and 4 wt% carbon nanotube (CNT) as potential thermal barrier coating (TBC) on the Inconel 718 substrate. Composite coatings exhibit bimodal microstructure of: (i) fully melted and resolidified microstructured region (MR), and (ii) partially melted and solid state sintered nanostructured regions (NR). Reinforcement with 8YSZ has led to an increase in hardness from ∼12.8 GPa (for μ-Al₂O₃) to ∼13.9 GPa in MR of reinforced Al₂O₃-YSZ composite. Further, with the addition of CNT in Al₂O₃-8YSZ reinforced composite, hardness of MR has remained similar ∼13.9 GPa (8YSZ reinforced) and ∼13.5 GPa (8YSZ-CNT reinforced), which is attributed to acquiescent nature and non-metallurgical bonding of CNT with MR. Indentation fracture toughness increased from 3.4 MPam^0.5 (for μ-Al₂O₃) to a maximum of 5.4 MPam^0.5 (8YSZ- CNT reinforced) showing ∼57.7% improvement, which is due to crack termination at NR, retention of t-ZrO₂ (∼3.3 vol%) crack bridging, and CNT pull-out toughening mechanisms. Modified fractal models affirmed that the introduction of bimodal microstructure (NR) i.e., nanometer-sized- Al₂O₃, nanostructured 8YSZ and CNTs in the μ-Al₂O₃ (MR) contributes ∼44.6% and ∼72% towards fracture toughness enhancement for A8Y and A8YC coatings. An enhanced contribution of nanostructured phases in toughening microstructured Al₂O₃ matrix (in plasma sprayed A8YC coating) is established via modified fractal model affirming crack deflection and termination for potential TBC applications.     

定向钢纤维增强水泥基复合材料断裂特性模拟分析

利用钢纤维随机生成算法建立了钢纤维增强水泥基复合材料有限元模型,基于粘聚裂纹模型模拟了定向钢纤维水泥砂浆三点弯曲断裂全过程.将数值模拟得到的荷载-绕度曲线与已有试验结果进行对比,验证了数值模型的可靠性.研究了砂浆基体不同粘聚律对定向钢纤维水泥砂浆断裂全过程的影响.计算分析了不同尺寸试件模型的断裂全过程,研究了试件尺寸对定向钢纤维水泥砂浆断裂特性的影响.结果表明:本文建立的定向钢纤维水泥砂浆有限元模型的数值结果与试验结果对比较好,粘聚律的变化对断裂全曲线影响较小;随着试件尺寸的增大,定向钢纤维水泥砂浆的名义强度存在一定的尺寸效应,本文建立的细观模型可有效研究钢纤维增强水泥基复合材料的细观断裂机理.