Analysis of cohesive failure in adhesively bonded joints with the SSPH meshless method

Adhesives have become the method of choice for many structural joining applications. Therefore, there is a need for improved understanding of adhesive joint performance, especially their failure, under a variety of loading conditions. Various numerical methods have been proposed to predict the failure of adhesive bonded material systems. These methods generally use a cohesive zone model (CZM) to analyze crack initiation and failure loci. The CZM incorporates a traction–separation law which relates the jump in surface tractions with the jump in displacements of abutting nodes of the cohesive segment; the area under the curve relating these jumps equals the energy release rate which is determined from experimental data. Values of parameters in the CZM are usually obtained through the comparison of results of numerical simulations with the experimental data for pure mode I and mode II deformations. Here a numerical approach to simulate crack initiation and propagation has been developed by implementing CZM in the meshless method using the symmetric smoothed particle hydrodynamics (SSPH) basis functions, and using the design of experiments technique to find optimal values of CZM parameters for mode I failure. Unlike in the finite element method where a crack generally follows a path between element boundaries, in the meshless method a crack can follow the path dictated by the physics of the problem. The numerical technique has been used to study the initiation and propagation of a crack in a double cantilever beam under mode I and mixed mode in-plane loadings. Computed results are found to agree well with the corresponding experimental findings. Significant contributions of the work include the determination of optimum values of CZM parameters, and simulating mode I, mode II and mixed mode failures using a meshless method with the SSPH basis functions.     

The mixed-mode fracture behavior of epoxy by the compact tension shear test

In this study, pure mode I, pure mode II and mixed mode fracture behavior of an epoxy were investigated. Specifically, the mixed mode values of fracture toughness and critical strain energy release rate (CSERR) were measured. Specimens were subjected to mixed mode loading using compact tension shear (CTS) test. Some experimental modifications were found to be necessary to eliminate rotation and ensure crack propagation at the notch when testing epoxy specimens at high mode II loading. A failure criterion for the mixed mode loading of polymer is developed and its predictions are compared with the experimental results. The crack propagation direction in epoxy was investigated in this research as well. A detailed study of failure mechanisms on the fracture surface was performed. The results indicate that the increase in the value of toughness can be directly related to the fracture morphology.     

Direct numerical simulations on crack formation in ceramic materials under thermal shock by using a non-local fracture model

In this work, a non-local failure model was proposed and implemented into a finite element code. It was then used to simulate the crack evolution in ceramic materials subjected to thermal shock. By using this numerical model, the initiation and propagation of cracks in water quenched ceramic specimens were simulated. The numerical simulations reproduced faithfully the crack patterns in ceramic specimens underwent quenching tests. The periodical and hierarchical characteristics of the crack patterns were accurately predicted. The numerical simulations allow a direct observation on whole the process of crack initiation and growth, which is quite a difficult task in experimental studies. The failure mechanisms and the fracture procedure are discussed according to the numerical results obtained from the simulations. It is shown that the numerical model is simple, robust, accurate and efficient in simulating crack evolution in real structures under thermal shock.     

Crack Path Selection in Adhesively-Bonded Joints: The Role of Material Properties

This paper investigates the role of material properties on crack path selection in adhesively bonded joints. First, a parametric study of directionally unstable crack propagation in adhesively-bonded double cantilever beam specimens (DCB) is presented. The results indicate that the characteristic length of directionally unstable cracks varies with the Dundurs' parameters characterizing the material mismatch. Second, the effect of interface properties on crack path selection is investigated. DCB specimens with substrates treated using various surface preparation methods are tested under mixed mode fracture loading to determine the effect of interface properties on the locus of failure. As indicated by the post-failure analyses, debonding tends to be more interfacial as the mode II fracture component in the loading increases. On the other hand, failures in specimens prepared with more advanced surface preparation techniques appear more cohesive for given loading conditions. Using a high-speed camera to monitor the fracture sequence, DCB specimens are tested quasi-statically and the XPS analyses conducted on the failure surfaces indicate that the effect of crack propagation rate on the locus of failure is less significant when more advanced surface preparation techniques are used. The effect of asymmetric interface property on the behavior of directionally unstable crack propagation in adhesive bonds is also investigated. Geometrically-symmetric DCB specimens with asymmetric surface pretreatments are prepared and tested under low-speed impact. As indicated by Auger depth profile results, the centerline of the crack trajectory shifts slightly toward the interface with poor adhesion due to the asymmetric interface properties. Third, through varying the rubber content in the adhesive, DCB specimens with various fracture toughnesses are prepared and tested. An examination of the failure surfaces reveals that directionally unstable crack propagation is more unlikely to occur as the toughness of the adhesive increases, which is consistent with the analytical predictions that were discussed using an energy balance model.     

Crack Path Selection in Adhesively-Bonded Joints: The Role of Material Properties

This paper investigates the role of material properties on crack path selection in adhesively bonded joints. First, a parametric study of directionally unstable crack propagation in adhesively-bonded double cantilever beam specimens (DCB) is presented. The results indicate that the characteristic length of directionally unstable cracks varies with the Dundurs' parameters characterizing the material mismatch. Second, the effect of interface properties on crack path selection is investigated. DCB specimens with substrates treated using various surface preparation methods are tested under mixed mode fracture loading to determine the effect of interface properties on the locus of failure. As indicated by the post-failure analyses, debonding tends to be more interfacial as the mode II fracture component in the loading increases. On the other hand, failures in specimens prepared with more advanced surface preparation techniques appear more cohesive for given loading conditions. Using a high-speed camera to monitor the fracture sequence, DCB specimens are tested quasi-statically and the XPS analyses conducted on the failure surfaces indicate that the effect of crack propagation rate on the locus of failure is less significant when more advanced surface preparation techniques are used. The effect of asymmetric interface property on the behavior of directionally unstable crack propagation in adhesive bonds is also investigated. Geometrically-symmetric DCB specimens with asymmetric surface pretreatments are prepared and tested under low-speed impact. As indicated by Auger depth profile results, the centerline of the crack trajectory shifts slightly toward the interface with poor adhesion due to the asymmetric interface properties. Third, through varying the rubber content in the adhesive, DCB specimens with various fracture toughnesses are prepared and tested. An examination of the failure surfaces reveals that directionally unstable crack propagation is more unlikely to occur as the toughness of the adhesive increases, which is consistent with the analytical predictions that were discussed using an energy balance model.     

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.     

Damage prediction of sintered α-SiC using thermo-mechanical coupled fracture model

A three-way coupled thermo-mechanical fracture model is presented to predict the damage of brittle ceramics, in particular α-SiC, over a wide range of temperatures (20–1400°C). Predicting damage over such a range of temperatures is crucial for thermal protection systems for many systems such as spacecraft. The model, which has been implemented in MOOSE, is divided into three modules: elasticity, damage phase field, and heat conduction. Analytical approaches for determining crack lengthscales are presented for both simple tension and simple shear. Validation tests are conducted for both flexural strength and fracture toughness over the specified range of temperatures. Flexural strength simulation results fall within the uncertainty region of the experimental data, and mode I fracture toughness simulation results are also in agreement with the experimental data. Mode II and mixed mode fracture toughness simulations results are presented with the modified G-criterion. Finally, the parallel computing capabilities of the model are considered in various scalability tests.     

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     

Experimental Study of the Fracture Toughness of a Ceramic/Ceramic-Matrix Composite Sandwich Structure

A hybrid experimental–numerical approach has been used to measure the fracture resistance of a sandwich structure consisting of a 304 stainless steel/partially stabilized zirconia ceramic-matrix composite crack-arresting layer embedded in a partially stabilized zirconia ceramic specimen. The mode I fracture toughness increases significantly when the crack propagates from the ceramic into the ceramic-matrix composite region. The increased toughening due to the stainless steel particles is explained reasonably well by a toughening model based on processing-induced thermal residual stresses. In addition, several experimental modifications were made to the chevron-notch wedge-loaded double cantilever beam specimen to overcome numerous problems encountered in generating a precrack in the small, brittle specimens used in this study.     

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.     

Study on mixed‐mode fracture characterization in functionally graded materials

The fracture characterizations on mixed‐mode crack of functionally graded materials (FGMs) are investigated using digital speckle correlation method (DSCM). The stress intensity factors at mixed‐mode crack tip are obtained from digital speckle displacements fields. In combination with finite elements simulation results, the influences of gradient coefficients on fracture behavior of mixed‐mode cracks are analyzed. All the results show that the influence of gradient coefficients on fracture modes is not noticeable, and the stress intensity factor at the crack tip in graded materials are clearly influenced by the gradient coefficients, i.e., the stress intensity factors decrease with the increasing of gradient coefficients. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Mixed-Mode Fracture Toughness of Ceramic Materials

An experimental technique whereby pure mode I, mode II, and combined mode I-mode II fracture toughness values of ceramic materials can be determined using four-point bend specimens containing sharp, through-thickness precracks is discussed. In this method, notched and fatigue-precracked specimens of brittle solids are subjected to combined mode I-mode II and pure mode II fracture under asymmetric four-point bend loading and to pure mode I under symmetric bend loading. A detailed finite element analysis of the test specimen is performed to obtain stress intensity factor calibrations for a wide range of loading states. The effectiveness of this method to provide reproducible combined mode I-mode II fracture toughness values is demonstrated with experimental results obtained for a polycrystalline Al₂O₃. Multiaxial fracture mechanics of the Al₂O₃ ceramic in combined modes I, II, and III are also described in conjunction with the recent experimental study of Suresh and Tschegg (1987). While the mode II fracture toughness of the alumina ceramic is comparable to the mode I fracture toughness K _Ic, the mode III fracture initiation toughness is 2.3 times higher than K _Ic. The predictions of fracture toughness and crack path based on various mixed-mode fracture theories are critically examined in the context of experimental observations, and possible effects of fracture abrasion on the apparent mixed-mode fracture resistance are highlighted. The significance and implications of the experimental methods used in this study are evaluated in the light of available techniques for multiaxial fracture testing of brittle solids.     

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.     

Quantitative Characterization of the Fracture Surface of Si Single Crystals by Confocal Microscopy

Experiments are conducted to study the dislocation nucleation conditions at the crack tip in {110}〈110〉 oriented Si single crystals. Specimens with surface cracks are first statically loaded at elevated temperatures for a prolonged period of time to initiate and move dislocations away from the crack tip, then cooled down to room temperature and loaded to fracture to measure the fracture toughness. Fractographic analysis of the fracture surfaces is performed. Distinct wavy patterns on the fracture surface at the initial cleavage crack front are observed, which is attributed to the existence of local mixed mode I/mode III stresses resulting from the inhomogeneous dislocation activity. Confocal microscopy is employed to quantify the fracture surface roughness. The results show that the increase of fracture toughness is directly associated with the increased area of the rough surface, which is characterized by the roughness number or the fractal dimension increment. Our results also demonstrate that dislocation nucleation can occur only at discrete sites. The spacing between these dislocation nucleation sources is of the order of 1 μm. A simple model is developed for the relationship between the fracture toughness and the surface roughness parameters, which is in good agreement with the experimental results.     

Cohesive Zone Modeling of Propellant and Insulation Interface Debonding

The reliability of the bonding of propellant to insulation is a key part of the analysis of rocket motor structural integrity. In this study, the debonding of the propellant/insulation interface was investigated by combining experiment and simulation. The improved exponential cohesive zone model and the bilinear cohesive zone model were used to predict the fracture properties of the adhesive interface. Double cantilever sandwich experiments and uniaxial tensile tests were performed to determine the corresponding model parameters. Furthermore, cohesive parameters were calibrated by applying an inverse analysis based on Hooke-Jeeves optimization algorithm. Good agreement was observed between the numerical simulation of double cantilever sandwich beam tests and the experimental curves. These results demonstrate that cohesive zone models can simulate the crack initiation and propagation of propellant/insulator interface in mode I. The bilinear law was shown to be more suitable for simulating fracture of the propellant/insulation interface in a strict sense than the exponential law. The numerical load-displacement curve was found to be sensitive to all cohesive parameters.     

Finite elements based approaches for the modelling of radial crack formation upon Vickers indentation in silicon nitride ceramics

By having superior properties silicon nitride ceramics can be considered as the state-of-the-art material in the bearing industry. Vickers indentation of this material is typically accompanied by formation of cracks visible on surface. Two Finite Elements models are developed in the current work: the first model is based on fracture mechanics and the second on cleavage stress criterion. Plastic behavior of silicon nitride is included in the modeling, and since little is known on the plasticity of this material, the Drucker-Prager model (used for non-metallic materials) along with the classical J₂-plasticity are explored. The results of the fracture mechanics based model correlate well with experimental results in terms of surface crack length. The numerical results in terms of the morphology of the indented zone (including cracks and plastic zone) are provided by the stress criterion based model, and these results correlate well too, with the experimental data.     

In-situ characterization on crack propagation behavior of SiCf/SiC composites during monotonic tensile loading

The microstructure and crack propagation path of 2.5D SiC_f/SiC composites were observed by synchrotron radiation x-ray computed micro tomography (SR-μCT) equipped with in-situ tensile device. The results showed that the pore morphologies of the SiC_f/SiC composites are mainly divided into three types in three-dimension space: interconnected pores, isolated pores and micro pores in fiber bundles. The crack initiation occurred at the root of the defects under in-situ tensile load and the crack was perpendicular, parallel to the stress axis or mixed mode to propagate. At the interface scale between fiber and matrix, the crack deflection will be controlled by physical parameters such as fracture energy release rate and the modulus of elasticity. At the fiber bundle scale, the crack is easy to shear propagate along the interface between weft and warp fiber bundles due to the existence of the mechanical bonding and residual tensile stress.     

Calibration of cohesive parameters for a castable refractory using 4D tomographic data and realistic crack path from in-situ wedge splitting test

Crack propagation in an alumina castable refractory with mullite-zirconia aggregates was investigated in-situ using a wedge splitting test performed inside a laboratory tomograph. Four-dimensional (i.e., 3D space and time) data from digital volume correlation were used to investigate the influence of a realistic crack path on the simulation of the fracture process. A cohesive law was chosen, since toughening mechanisms were present, and calibrated via finite element model updating. When a straight crack path was assumed instead of the experimental crack path, a 10% higher fracture energy and a 35% higher cohesive strength were calibrated. Although the force alone could be used in the minimized cost function, the kinematic information gives valuable insight into the trustworthiness of the geometrical hypotheses assumed in the finite element model. Such framework can be applied to study nonlinear fracture processes for different materials with complex toughening mechanisms such as crack deflection or branching.     

Fracture toughness of silicon nitride balls via thermal shock

A new method for fracture toughness determination of ceramic balls is presented. The starter crack is introduced into the surface of the ball by a Knoop indentation followed by grinding off the deformed zone. The loading through surface tensile stresses is realized by water quenching, i.e. dropping the heated ball into water. The temperature difference is stepwise increased to find the critical temperature difference for the initiation of crack growth. The geometric factor is calculated in a parametric finite element study, whereas the temperature distribution in the ball was previously determined by using the Biot concept. Combining experimentally measured critical temperature differences for different cracksizes and ball diameters with numerical results of the geometric factor, the fracture toughness of the silicon nitride balls is evaluated. For the evaluation, the knowledge of several material properties (e.g. the CTE) and other parameters is necessary, which have influence on the precision of the measurement. The overall measurement uncertainty is estimated to be about ± 10 %, what roughly corresponds to the value determined with standard measurement procedures. There is an excellent agreement with published fracture toughness results of these balls determined by the modified Surface Crack in Flexure procedure.     

Fracture Criteria for Piezoelectric Ceramics

Fracture criteria for piezoelectric materials were investigated. Mode I and mixed mode fracture tests were performed on PZT-4 piezoelectric ceramics to verify the validity of the mechanical strain energy release rate as a fracture criterion. Experimental results indicated that crack extension could be aided or impeded by an electric field, depending on the field direction. Further, the direction of crack extension was studied. A crack closure method, together with finite element analysis, was introduced to calculate the mechanical strain energy release rate. The maximum mechanical strain energy release rate was used to predict fracture loads under combined mechanical and electrical loads. It was found that the mechanical strain energy release rate criterion is superior to other fracture criteria and predicts fracture loads fairly accurately.