Cohesive Zone Elements Research Articles

On modeling tool performance while machining aluminum-based metal matrix composites

Tool performance while machining aluminum-based metal matrix composites has been investigated by developing finite element models based on particle size and volume fraction of the workpiece. Two types of finite element models are developed, i.e., with and without cohesive elements. The effects of varying cutting speed, feed rate, volume fraction, and size of reinforcement particles on tool performance are investigated using both models. It has been found that models without cohesive zone element can predict cutting forces, tool stresses, and temperatures to a reasonable degree of accuracy. The increase in tool stresses and temperatures due to cutting speeds, feed rate, particle size, and volume fraction can be visualized with these models. Models based on cohesive elements can predict localized effect of particle debonding and failure on tool stresses and machined surface. It has been noticed that increase in particle size and cutting speed increases the effects of particle rolling and sliding on the tool face due to increase in kinetic energy resulting in high wear.

Shear test on hard coated flip-chip bumps to measure back end of the line stack reliability

Introduction of ultra-low κ (ULK) material into advanced back end of line (BEOL) stacks has improved the electrical performance of the flip-chip microelectronic packages. However, the integration of the brittle and porous ULK materials presents several mechanical reliability challenges due to chip-package interaction effects. One of the primary failure modes in a organic flip-chip microelectronic package is delamination of interlayer dielectric (ILD) layers. Thermo-mechanical stresses that arise at the end of flip-chip assembly process can be high enough to cause fracture of the ILD layers in the vicinity of a solder bump. It has been observed from experiments that two bumps subjected to apparently same amount of thermo-mechanical stresses and same process history can exhibit difference in failure pattern. Current numerical models nor micro- scale interfacial fracture characterization experiments such as double cantilever beam (DCB) or four-point bend (FPB) tests are not capable of predicting such a failure. Such a behavior is possible only if the adhesion strength of the ILD layers are not constant but varies spatially from bump to bump. The difference in adhesion strength between adjacent bumps can be attributed to the difference in trace pattern layout or via distribution. In order to understand the failure at the bump level that is sensitive to capture differences in local trace patterns, microscale test techniques need to be developed.The focus of this work is to demonstrate a new reliable microscale test technique performed using nano-indenter to measure the mechanical reliability of BEOL stacks. A high-load spherical head is used to apply a known displacement on a solder bump coated with a ceramic. The force initial increases and suddenly drops indicating failure. Cross-sections of the tested bumps clearly indicate crack propagating through the BEOL stack while the coated bump remains intact. Since the forces subjected on the bump during the test is similar to the forces subjected on the bump during flip-chip assembly, the critical force can be used as a measure of fracture strength of the BEOL stack. The results from the test indicate that the critical force varies from bump to bump and the results are repeatable. Furthermore, finite-element model of the test is developed. The failure of the ILD layers is simulated using cohesive zone (CZ) elements and the mixed-mode traction-separation parameters required to characterize the CZ elements are extracted from macro-scale test techniques like DCB and FPB tests. The force-displacement (P-Δ) plot from the model mimics the experiment and predicts the average value of the critical force observed in experiment.

Evaluation of the interfacial strength of carbon-fiber-reinforced temperature-resistant polymer composites by the micro-droplet test

This paper presents an evaluation method for the fiber/matrix interfacial strength. The interfacial strength is determined by comparing experimental data with numerical simulations. The micro-droplet test is conducted, and the fiber axial stress at the point of interface debonding is obtained. A numerical simulation is performed with ABAQUS using an axisymmetric finite-element model. In the numerical simulation, an accurate value of the thermal residual stress based on the thermo-viscoelasticity and the damage to the resin around the blade-contacting point is considered to simulate the experimental phenomena ideally. In the thermal residual stress analysis, the actual thermal residual stress is calculated by considering the relaxation modulus and the time–temperature superposition principle for the resin. Damage initiation criteria for both dilatational and shear cases, based on continuum damage mechanics, are considered for the resin. Interfacial debonding is simulated using a cohesive zone model, and the interfacial strength is taken as the strength of the cohesive zone element at the simulated fiber maximum stress corresponding to the experimental value.

Verification of the performance of rotatable jig for a single cantilever beam method using the finite element analysis

The performance of new jig for single cantilever beam test method was verified by finite element analysis. Two types of jig were designed for a small specimen that had relatively short length compared to the width of cantilever; one was simple fixed jig and the other was specially designed rotatable jig. The rotatable jig has a rotatable seesaw which adjusts the experimental misalignments between the specimen and test machine. Among the three translational and three rotational misalignments, following three important factors were considered; rotation about x-axis, rotation about z-axis, and translation in y-axis. Adhesive layer was modeled by cohesive zone element, and crack propagation behavior and the deviation of energy release rate were investigated. The fixed jig showed undesired asymmetric crack propagation and large deviation of energy release rate when it had rotational misalignment about x-axis. However, the proposed new rotatable jig showed almost symmetrical crack propagation and small deviation of energy release rate regardless of misalignments. Rotational motion of the seesaw automatically compensated the rotational misalignment of the specimen. The rotatable jig also showed relatively small deviation of energy release rate compared with the fixed jig by the rotational misalignment about the z-axis. In contrast, the rotatable jig showed deviation of energy release rate by translational misalignments in the y-axis. However, the magnitude of the deviation was very small within the controllable range of experimental misalignment. In conclusion, it was found out that the proposed jig was appropriate for the measurement of adhesion of a small specimen by single cantilever beam method.

Modeling and Analysis of Composite Bonded Joints

The bonded joints in composite structures is a challenging point in both research study and industry application. Compared with homogeneous and isotropic material, there is higher chance of stress concentration and intrinsic weak for this anisotropic structures. It is most common source of failure in structural laminates. So it is important to model and analyze the composite bonded joint to get the mechanical response and estimate the damage evolution. In this review paper, composite bonded joint are categorized based on bonded methods, materials, loading methods and failure modes. Multiple widely used adhesive bonded joint models including cohesive zone element model (CZM), interface element model, multiple point constraint model, kinking crack model, and repeating RVE model are introduced and discussed. To estimate the damage evolution in the bonded joint, a series of damage criteria have been developed including displacement based, stress based, energy based and modulus based damage criteria. Those damage criteria of bonded joint are also discussed and compared. This review work is important for the development of modeling of composite bonded joint in future.

Prediction of fracture in grain boundaries of nano‐coatings using cohesive zone elements

AbstractA cohesive zone element technique (CZ) is applied to study grain boundary fracture in nano coating layers (see [1]). This goes along with the investigations of the delamination and fracture behavior of the coatings and the substrate interface. The main motivation is to investigate antiadhesive and wear resistant properties of coatings made of ceramics produced by the High Power Pulsed Magnetron Sputtering (HPPMS) technique [2]. Different physical conditions in HPPMS result into different grain morphologies with different mechanical properties. Therefore prediction of fracture and damage in such systems can lead to the optimum choice of process parameters in order to gain the best fracture resistance properties for the coatings. To illustrate the applicability of the model, several simulations with different mechanical and structural properties are performed. The developed CZ element model is capable of modeling the separation, the contact and also the irreversible reloading conditions in different directions [3]. The model is further developed to be applicable for geometrically complex interfaces including different bonding behaviors, with a high robustness. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

응집 영역 요소를 이용한 고분자 접착 테이프의 박리거동 모사

금속/고분자 샌드위치 복합재는 경량성과 제진, 방음 등의 다기능성의 측면에서 기존의 스틸 강판을 대체할 후보 중 하나로서 연구되고 있다. 금속/고분자 복합재의 활용하기 위해서는 접착력을 바탕으로 한 박리 거동 예측이 매우 중요한 요소이다. 본 연구에서는 응집요소를 사용하여 유한요소 해석을 통해 접착제를 사용한 고분자 테이프의 박리거동 해석을 수행하였다. 응집요소의 특성은 박리시험과 역학 관계로부터 도출한 파괴인성을 통해 정의하였고 이를 해석에 적용하였다. 스틸 강판에서 고분자 테이프를 박리하는 시험을 모사하였고, 해석결과와 시험결과를 비교하여 박리 거동 모사가 가능함을 확인하였다. Metal and polymer sandwich composites, which are made of sheet metal sheath and polymer or fiber reinforced plastic core, have been reconsidered as an alternative to sheet metal due to their lightness and multifunctional properties such as damping and sound-proof properties. For the successful applications of these composites, the delamination prediction based on the adhesion strength is important element. In this study, the numerical simulation of the delamination behavior of polymeric adhesive tapes with metallic surfaces was performed using cohesive zone elements and finite element software. The traction-separation law of the cohesive zone element was defined using the fracture energy derived from peel mechanics and experimental results from peel test and implemented in finite element software. The peel test of the polymeric adhesive film against steel surface was simulated and compared with experiments, demonstrating reasonable agreement between simulation and experiment.

Higher order Cauchy–Born rule based multiscale cohesive zone model and prediction of fracture toughness of silicon thin films

In this work, we extend the multiscale cohesive zone model (MCZM) (Zeng and Li in Comput Methods Appl Mech Eng 199:547–556, 2010), in which interatomic potential is embedded into constitutive relation to express cohesive law in fracture process zone, to include the hierarchical Cauchy–Born rule in the process zone and to simulate three dimensional fracture in silicon thin films. The model has been applied to simulate fracture stress and fracture toughness of single-crystal silicon thin film by using the Tersoff potential. In this study, a new approach has been developed to capture inhomogeneous deformation inside the cohesive zone. For this purpose, we introduce higher order Cauchy–Born rules to construct constitutive relations for corresponding higher order process zone elements, and we introduce a sigmoidal function supported bubble mode in finite element shape function of those higher order cohesive zone elements to capture the nonlinear inhomogeneous deformation inside the cohesive zone elements. Benchmark tests with simple 3D models have confirmed that the present method can predict the fracture toughness of silicon thin films. Interestingly, this is accomplished without increasing of computational cost, because the present model does not require quadratic elements to represent heterogeneous deformation, which is the inherent weakness of the previous MCZM model. Quantitative comparisons with experimental results are performed by computing crack propagation in non-notched and initially notched silicon thin films, and it is found that our model can reproduce essential material properties, such as Young’s modulus, fracture stress, and fracture toughness of single-crystal silicon thin films.

Effect of the size reduction on the bulk tensile and double cantilever beam specimens used in cohesive zone models

Cohesive zone elements used in finite element analysis are a reliable way to design and predict the behaviour of the joint. The characterisation of the traction separation law used in these models is done using tensile and fracture tests, and the parameters of such laws depend on humidity and temperature. Water diffusion tests are therefore necessary, which are dependent on specimen geometry, meaning a bigger specimen takes longer to fully saturate. To solve this problem and increase the efficiency of the ageing process, smaller tensile bulk and double cantilever beam (DCB) specimens are necessary. Another advantage of smaller DCB specimens is that they can be tested in smaller high-temperature chambers, where normal DCB specimens do not fit. Smaller geometries of the bulk tensile and DCB tests are analysed, and a proposed geometry for each test is shown to produce very satisfactory results, validating the use of these specimens.

Finite element modeling of periodic polycrystalline aggregates with intergranular cracks

The present study addresses the prediction of the mechanical response of model polycrystalline aggregates in which the anisotropy of individual crystals induces high internal stresses as well as microcracks. A novel procedure is proposed in order to automatically generate finite element (FE) meshes that conform to the polycrystalline microstructure. The meshes obtained are periodic in 3-D and they contain cohesive zone elements along all grain boundaries. The FE model is applied to two materials with significant elastic anisotropy at the crystal level: stainless steel and graphite. A self-consistent equivalent inclusion solution is shown to produce a valid mean-field estimate of the effective stiffness of the polycrystal. This reference solution is used in order to optimize the assignment of lattice orientations to individual grains prior to the FE simulations. It is demonstrated that relying on such model polycrystals increases the accuracy of FE predictions at an affordable computational cost. The influence of internal cracks on the macroscopic response depends on the anisotropy of individual crystals.

Failure mechanism based modelling of impact on fabric reinforced composite laminates based on shell elements

A shell element based modelling strategy for simulating impact on fabric reinforced laminated composites within the framework of the Finite Element Method is presented. Thereby, each ply of the laminate is represented by its own layer of shell elements. The interfaces in-between are discretised by cohesive zone elements. Material nonlinearities within plies, i.e. fibre rupture, matrix cracking and plasticity-like effects, and interfaces, i.e. delamination, are accounted for by appropriate constitutive laws. Impact simulations of a rectangular laminated composite plate with quasi-isotropic layup in a drop tower test setup are conducted. The predictions are based on material parameters partly from corresponding material data sheets and partly estimated from the literature. Thus, no inverse model calibration is applied. The acquired simulation results are validated with accompanying experiments. The predicted spatial distribution of ply damage and delaminations, as well as the associated energy absorption agree very well with the experimental results. The approach shows excellent performance in terms of computational efficiency such that simulations of the impact behaviour of structural composite components become feasible.

Mechanical behavior of fiber/matrix interfaces in CFRP sheets subjected to plastic deformation

The use of Carbon Fiber Reinforced Plastic (CFRP) is increasing markedly, partially in the aviation industry, but it has been considered that CFRP sheets cannot be formed by press-forming techniques owing to the low ductility of CFRP. Since the mechanical characteristics of CFRP are dominated by the microscale structure, it is possible to improve its formability by optimizing the material structure. Therefore, to improve the formability, the interaction between the carbon fibers and the matrix must be clarified. In this study, microscale analyses were conducted by a finite-element model with cohesive zone elements.

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

ABSTRACTThis 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.

Application of a cohesive zone element for the prediction of damage in nano/micro coating

AbstractMany tools in production technology are nowadays coated to obtain a satisfactory lifetime and degradation resistance. Therefore, the main goal of this study is to investigate antiadhesive and wear resistant coatings made of ceramics, plastics and metals produced by High Power Pulsed Magnetron Sputtering (HPPMS) technique [1]. A cohesive zone element technique (CZ) is applied to model the interactions of the coatings and the substrate surfaces (see [2]). This goes along with the investigations of the delamination and failure behavior of the involved surfaces. To illustrate the applicability of the model, several structural simulations are performed. The developed CZ element model is capable of modeling the separation, the contact and also the irreversible reloading conditions in both normal and tangential directions [3]. The model is further developed to be applicable for different structures including different bonding behaviors, with a higher stability. The talk concludes with a detailed discussion of the numerical results of different material and interface properties. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Finite element analysis of mode II delamination suppression in stitched composites using cohesive zone model

To provide an accurate prediction of mode II delamination properties of stitched composites, a single stitched laminate under pure shear load (interlaminar shear) is investigated. An interlaminar shear test (IST) is conducted, using a specially constructed fixture. A finite element model of the IST is developed, using a spring connector to represent the stitch thread. Furthermore, an end notch flexural test is simulated based on the IST model and with a cohesive zone element used to simulate crack propagation. The effects of the cohesive zone modelling parameters (interfacial strength, stiffness and viscosity coefficient) are also investigated. Close agreement is obtained between the simulated and experimental results. Finally, the verified model is extended to study the effect of the number of stitch rows in the crack region. The results confirm that the crack propagation starting point (peak load) depends on the number of stitch rows in the crack region.

Mapping Cohesive Fracture and Fragmentation Simulations to Graphics Processor Units

SummaryA graphics processor units(GPU)‐based computational framework is presented to deal with dynamic failure events simulated by means of cohesive zone elements. The work is divided into two parts. In the first part, we deal with pre‐processing of the information and verify the effectiveness of dynamic insertion of cohesive elements in large meshes in parallel. To this effect, we employ a novel and simplified topological data structure specialized for meshes with triangles, designed to run efficiently and minimize memory occupancy on the GPU. In the second part, we present a parallel explicit dynamics code that implements an extrinsic cohesive zone formulation where the elements are inserted ‘on‐the‐fly’, when needed and where needed. The main challenge for implementing a GPU‐based computational framework using an extrinsic cohesive zone formulation resides on being able to dynamically adapt the mesh, in a consistent way, by inserting cohesive elements on fractured facets. In order to handle that, we extend the conventional data structure used in the finite element method (based on element incidence) and store, for each element, references to the adjacent elements. This additional information suffices to consistently insert cohesive elements by duplicating nodes when needed. Currently, our data structure is specialized for triangular meshes, but an extension to tetrahedral meshes is feasible. The data structure is effective when used in conjunction with algorithms to traverse nodes and elements. Results from parallel simulations show an increase in performance when adopting strategies such as distributing different jobs among threads for the same element and launching many threads per element. To avoid concurrency on accessing shared entities, we employ graph coloring. In a pre‐processing phase, each node of the dual graph (bulk elements of the mesh as graph nodes) is assigned a color different from the colors assigned to adjacent nodes. In that fashion, elements of the same color can be processed in parallel without concurrency. All the procedures needed for the insertion of cohesive elements along fracture facets and for computing nodal properties are performed by threads assigned to triangles, invoking one kernel per color. Computations on existing cohesive elements are also performed based on adjacent bulk elements. Experiments show that GPU speedup increases with the number of nodes and bulk elements. Copyright © 2015 John Wiley & Sons, Ltd.

Influence of fiber length on the tensile behavior of fiber metal laminates with discontinuous reinforcement

In this paper, the influence of fiber length on the tensile behavior of fiber metal laminate, which is fabricated with unidirectionally arrayed chopped strand plies and aluminum sheets and named as unidirectionally arrayed chopped strand/aluminum laminate, was investigated based on finite element analysis and experiment. The unidirectionally arrayed chopped strand ply is made by introducing slits into carbon fiber reinforced plastic prepreg where continuous fibers are arrayed unidirectionally. The fiber length is one of the most fundamental factors in tailoring the unidirectionally arrayed chopped strand/aluminum laminate to achieve the desired mechanic behaviors for specific applications. With longer fiber length, the mechanical behaviors of the bulk laminate should be more favorable, while the formability would be better with short fiber. Two-dimensional finite element models, with intra-laminar cohesive zone elements inserted into the slits of unidirectionally arrayed chopped strand plies and inter-laminar cohesive zone elements inserted into the all interfaces of unidirectionally arrayed chopped strand/aluminum laminate, respectively, were developed for the analysis of unidirectionally arrayed chopped strand/aluminum laminates with different fiber lengths under tension. Typical numerical results were validated by experimental results, which confirm that the tensile behaviors of the unidirectionally arrayed chopped strand/aluminum laminates with various different fiber lengths can be well predicted by present numerical modeling method.

An enriched shell element formulation for efficient modeling of multiple delamination propagation in laminates

In the modeling of progressive damage in fiber reinforced polymers, the kinematical representation of delamination is normally treated in one of two ways. Either efficient or accurate modeling of delamination is considered. In the first case, delamination is disregarded or implicitly included in the material modeling. In the second case, delamination is explicitly modeled at a significant numerical cost where all plies are represented by separate elements in the thickness direction, connected by interlaminar cohesive zone elements. In this paper, we therefore aim to take one step closer to more efficient FE analyses by presenting a modeling concept which supports laminate failure analyses requiring only one shell element through the thickness. With this concept, arbitrary delamination propagation is accounted for only in areas where it is needed. In addition, by using this concept, the model preparation time is reduced. We show that the current shell formulation proposed can be utilized to accurately simulate propagating delamination cracks as well as to accurately describe the kinematics of a laminate containing multiple delaminations through the thickness. Thus, we see significant potential for this modeling concept in analyses in which computationally efficiency is of major importance, such as for large scale crash analyses.

Finite Element Modelling of Cracks as Acoustic Emission Sources

This paper presents results for a new acoustic emission crack source model based on a finite element modelling approach which calculates the dynamic displacement field during crack formation. The specimen modelled is statically loaded until conditions for crack growth as defined by a failure criterion are fulfilled. Subsequently, crack growth is modelled by local degradation of the material stiffness utilizing a cohesive zone element approach. The displacements due to crack growth generate the acoustic emission signal and allow detailed examination of the principles of acoustic emission sources operation. Subsequent to crack growth signal propagation is modeled. The signal propagation is modeled superimposed on the static displacement field. The presented model comprises a multi-scale and multi-physics approach to consider the signal propagation from source to sensor, the piezoelectric conversion of the elastic wave to an electric signal and the interaction to the acquisition electronics. Validation of the modeling approach is done by investigating the acoustic emission signals of micromechanical experiments. Using a specifically developed load stage, carbon fiber filament failure and matrix cracking can be prepared as model sources. A comparison of the experimental signals to the modeled signals shows good quantitative agreement in signal amplitude and frequency content. A comparison between the present modeling work and analytical theories demonstrates the substantial differences not considered in previous modeling work of acoustic emission sources.

Modeling machining of particle-reinforced aluminum-based metal matrix composites using cohesive zone elements

Finite element modeling for the machining of heterogeneous materials like particle-reinforced metal matrix composites has not been much successful as compared to homogeneous metals due to several issues. The most challenging issue is to deal with severe mesh distortion due to nonuniform deformation inside the workpiece. Other problems are related to the modeling of the interface between reinforcement particles and matrix and tool-reinforcement particle interaction. In this study, different strategies are adopted for finite element models (FEM) to cope with the above issues and comparative analyses have been performed. These 2D FE models are based on plane strain formulations and utilize a coupled temperature displacement method. The workpiece is modeled using reinforcement particle size and volume fraction inside the base matrix. The interface between the reinforcement particles and the matrix is modeled by using two approaches, with and without cohesive zone elements, and the chip separation is modeled with and without using a parting line. This allows models to simulate the local effects such as tool-reinforcement particle interaction and reinforcement particle debonding. In addition, the models can predict cutting forces, chip morphology, stresses, and temperature distributions. The effects of different methodologies on the model development, simulation runs, and predicted results have been discussed. The results are compared with experimental data, and it has been found that the utilization of cohesive zone elements (CZE) with the parting line approach seems to be the best one for the modeling of metal matrix composite (MMC) machining.