Cohesive Zone Elements Research Articles

A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal superalloys

A numerical analysis using cohesive zone model under cyclic loading is proposed to develop a coupled predictive approach of crack growth in single crystal. The process of material damage during fatigue crack growth is described using an irreversible cohesive zone model, which governs the separation of the crack flanks and eventually leads to the formation of free surfaces. The cohesive zone element is modeled to accumulate fatigue damage during loadings and no damage during unloadings. This paper presents the damage model and its application in the study of the crack growth for precracked specimens. The use of cohesive zone approach is validated through a convergence study. Then, a general procedure of parameters calibration is presented in pure fatigue crack growth. In the last section, an extension of the cohesive zone model is presented in the case of creep–fatigue regime at high temperature. The model showed its capability to predict with a good agreement the crack growth in the case of complex loading and complex specimen geometries.

Evaluation and simulation of the peel behavior of polyethylene/polybutene‐1 peel systems

AbstractThe peel characteristics of sealed low‐density polyethylene/isotactic polybutene‐1 (PE‐LD/iPB‐1) films, with different contents of iPB‐1 up to 20 m.‐% (mass percentage), were evaluated and simulated in dependence on the iPB‐1 content, and in dependence on the peel rate. Sealing involves close contact and localized melting of two films for a few seconds. The required force, to separate the local adhered films, is the peel force, which is influenced, among others, by the content of iPB‐1. The peel force decreases exponentially with increasing iPB‐1 content. Transmission electron microscopy studies reveal a favorable dispersion of the iPB‐1 particles within the seal area, for iPB‐1 concentrations ≥6 m.‐%. Here, the iPB‐1 particles form continuous belt‐like structures, which lead to a stable and reproducible peel process. The investigation of the peel rate‐dependency on the peel characteristics is of important interest for practical applications. The peel force increases with increasing peel rate by an exponential law. A numerical simulation of the present material system proves to be useful to comprehend the peel process, and to understand the peel behavior in further detail. Peel tests of different peel samples were simulated, using a two‐dimensional finite element model, including cohesive zone elements. The established finite element model of the peel process was used to simulate the influence of the modulus of elasticity on the peel behavior. The peel force is independent of the modulus of elasticity, however, the peel initiation value increases with increasing modulus of elasticity. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Finite element analysis of stress distribution in thermal barrier coatings

A numerical simulation of crack development within APS TBC systems is presented. The TGO thickening and creep deformation of all system constituents is modelled. Two dimensional periodic unit cell is used to examine the effect of interfacial asperity on stress distribution and subsequent delamination of APS TBC. A study of cyclic loading and of creep of the base material on the stress distribution close to the asperity at the TGO/BC interface is made, revealing a small influence influence of both on the stress state in the thermal barrier coating system subjected to temperature loading. Cohesive zone elements at the oxide/ceramic interface model the development of the interfacial micro-crack. The finite element analysis shows that the development of the interfacial crack allows for a micro-crack formation within APS TBC. Subsequent TGO growth results in a tensional zone within the oxide layer. Linking of the micro-cracks at the interface and within TBC through TGO could lead to a coating delamination in the unit cell.

Determination of interfacial mechanical parameters for an Al/Epoxy/Al 2o 3 system by using peel test simulations

Peel test measurements and simulations of the interfacial mechanical parameters for the Al/Epoxy/Al2O3 system are performed in the present investigation. A series of Al film thicknesses between 20 and 250 microns and three peel angles of 90, 135 and 180 degrees are considered. Two types of epoxy adhesives are adopted to obtain both strong and weak interface adhesions. A finite element model with cohesive zone elements is used to identify the interfacial parameters and simulate the peel test process. By simulating and recording normal stress near the crack tip, the separation strength is obtained. Furthermore, the cohesive energy is identified by comparing the simulated steady-state peel force and the experimental result. It is found from the research that both the cohesive energy and the separation strength can be taken as the intrinsic interfacial parameters which are dependent on the thickness of the adhesive layer and independent of the film thickness and peel angle.

Finite Element Modeling of the Effects of Delamination Damage on the Natural Frequencies of Composite Panels

Abstract This paper describes the analysis and experimental effort undertaken to determine damage detection in composite beams. Finite element analysis of delamination and its effect on the natural frequencies of the composite beam is determined using cohesive zone elements of a commercial finite element software material model ANSYS. Numerical simulations are carried out to analyze typical cases of a delaminated composite beam with different boundary conditions. It is found that an increase in the delaminated region ratio increases the percent deviation in the natural system frequencies. The amount of deviation was different for different types of delamination. The frequency charts of the present study may be useful for engineering design and non-destructive testing analysis. It can be used as a tool for diagnosis, detection, and identification of delaminations in engineering applications by monitoring the frequency change.

Determination of interfacial properties between metal film and ceramic substrate with an adhesive layer

Peel test measurements and inverse analysis to determine the interfacial mechanical parameters for the metal film/ceramic system are performed, considering that there exist an epoxy interface layer between film and ceramic. In the present investigation, Al films with a series of thicknesses between 20 and 250 μm and three peel angles of 90, 135 and 180° are considered. A finite element model with the cohesive zone elements is used to simulate the peel test process. The finite element results are taken as the training data of a neural network in the inverse analysis. The interfacial cohesive energy and the separation strength can be determined based on the inverse analysis and peel experimental result.

Inverse analysis determining interfacial properties between metal film and ceramic substrate with an adhesive layer

In the present study, peel tests and inverse analysis were performed to determine the interfacial mechanical parameters for the metal film/ceramic system with an epoxy interface layer between film and ceramic. Al films with a series of thicknesses between 20 and 250 mu m and three peel angles of 90 degrees, 135 degrees and 180 degrees were considered. A finite element model with the cohesive zone elements was used to simulate the peeling process. The finite element results were taken as the training data of a neural network in the inverse analysis. The interfacial cohesive energy and the separation strength can be determined based on the inverse analysis and peel experimental result.

On using a penalty-based cohesive-zone finite element approach, Part II: Inelastic peeling of an epoxy-bonded aluminum strip

Previous work has demonstrated the use of a penalty methodology for enhancing the use of cohesive-zone elements to simulate double cantilever beam (DCB) and flexible-arm peeling problems, both involving elastic arm deformation. This approach is extended to the general case of inelastic peel arm deformations. Refinements to the original penalty selection methodology are included to account for the influence of plasticity in the peel arms. Accuracy of the method is demonstrated by comparing simulation results to experimental data of epoxy-bonded aluminum arms being peeled at different angles from a rigid substrate. This work addresses significant complexities in the analysis that arise due to the inelastic deformation of the aluminum peel arms.

Cohesive zone modeling of hydrogen-induced stress cracking in 25% Cr duplex stainless steel

Hydrogen-influenced cohesive zone elements are implemented in finite element models of rectangular notched tensile specimens of 25% Cr stainless steel. A three-step procedure consisting of stress analysis, diffusion analysis and cohesive zone fracture initiation analysis was performed. A linear traction separation law gives a good fit with experimental results for stress levels just below the material yield stress. Hydrogen concentrations of 40 ppm at the surface and 1 ppm in bulk always produces crack initiation at the surface.

Modeling of interfacial crack velocities in snow

Weak layers sandwiched between strong layers are found within a snowpack. The interface between the layers may have regions that are weakly bonded which act as stress raisers from where propagation of crack can take place, in mode II, along the interface. Damage ahead of the crack tip is modeled using a cohesive zone model. The crack propagation along the interface under a shear and compressive load (due to the weight of skier and snow) is studied using a finite element model with cohesive zone elements to describe the interface between the weak and strong layers. Four properties of the interface namely fracture energy in normal separation, fracture energy in shear separation, tensile and shear strengths are needed to characterize the cohesive elements. Tension and shear experiments on sieved snow with an 'ice lens' and shear experiments on natural snow with a weak interface are performed to get an estimate of the cohesive zone properties. The cohesive model, incorporated in a finite element mesh, is used to determine the speed of crack growth along the interface. The average cracks speed depends on modulus of the layers on either side of interface and for the modulus values studied here, is between 50 m/s and 300 m/s. The nature of crack propagation changes with thickness of the snowpack.

On the development of a 3D cohesive zone element in the presence of large deformations

Delamination is typically modelled using cohesive zone models. In this paper, it is shown that the validity of most models is limited to small displacements and/or deformations at the interface and the surrounding bulk materials. A large displacement formulation (LDF) is proposed that overcomes issues of the classical formulation with large displacements and deformations at the interface. Subsequently, a 3D cohesive zone element with this LDF is introduced and its numerical implementation is elaborated. Then, a 3D FEM model is proposed and the determination of several model parameters is substantiated. Finally, the implementation is validated by comparing numerical results with experimental observations.

Integrated numerical–experimental analysis of interfacial fatigue fracture in SnAgCu solder joints

In ball grid array (BGA) packages, solder balls are exposed to cyclic thermo-mechanical strains arising from the thermal mismatch between package components. Thermo-mechanical fatigue crack propagation in solder balls is almost always observed at the chip side of the bump/pad junction. The objective of the experimental part of this study is to characterize the bump/pad interface under fatigue loading. Fatigue specimens are prepared by reflowing Sn3.8Ag0.5Cu lead-free solder alloy on Ni/Au substrates. Obtained results show that fatigue damage evolution strongly depends on the microstructure. Applied strain and solder volume both have an influence on the fatigue damage mechanism. In the numerical part of the study, fatigue experiments are modeled using the finite element technique. A cohesive zone approach is used to predict the fatigue damage evolution in soldered connections. Crack propagation is simulated by an irreversible linear traction–separation cohesive zone law accompanied by a non-linear damage parameter. Cohesive zone elements are placed where failure is experimentally observed. Damage evolution parameters for normal and tangential interaction are scrutinized through dedicated fatigue tests in pure tensile and shear directions. The proposed cohesive zone model is quantitatively capable of describing fatigue failure in soldered joints, which can be further extended to a numerical life-time prediction tool in microelectronic packages.

Effect of material uncertainties on fatigue life calculations of aircraft fuselages: A cohesive element model

The present paper deals with the effect of uncertainties on the prediction of fatigue failure of aerospace and mechanical components. Typically the design of such structures has been based on costly experiments or modified versions of Paris’ law which are applicable to very restricted range of conditions. The present formulation employs cohesive zone elements in order to resolve the fractured zone in combination with an extrapolation scheme that makes the analysis over hundred of thousands of cycles computationally efficient. The effect of randomness in the cohesive strength is examined with respect to the total lifetime of the specimen.

Overview of trends in advanced composite research and applications in Japan

Recent research activities in advanced composites technologies conducted in Japan are reviewed and introduced. New research topics in reinforcing fibers described are low modulus pitch-based carbon fiber and PBO fiber. The second of these is very topical at the present time: nano-technology based composites use materials such as carbon nanotube, or carbon nano-fiber, or nanoclay. Because the Composites Technology Center in the Japan Aerospace Exploration Agency (JAXA) leads many new research fields in composites, the present review paper shows a slight bias towards the outputs of JAXA. The most remarkable outcome in this field at present is a compression strength improvement by loading cup-stack type carbon nano-fiber (CSCNF). Prepreg containing this CSCNF has been developed and has already been rerleased into the market. The third topic is related to newly developed high performance polymers including heat resistant polyimide, Tri A-PI and its family. The most recent product is a heat resistant polyimide that is highly soluble in some organic solvents; this material is suitable for preparation of imide wet prepreg. Composites fabricated through this prepreg route exhibit no voids and defects compared to the traditional amid-acid polyimide prepreg route. Another new topic in polymers is related to Japan's national project, radiation cure polymers and their processing. Electron beam cure, ultra-violet cure and visual light cure resins and their processing technologies have been developed in this national project. The next topic is a development of the low cost composites technology mainly for aircraft components. JAXA's activities related to this field are introduced first based on two new key technologies — Z-anchor® and stitching. New findings about the mechanism of interlaminar reinforcement by stitching are slightly focused. Finally, remarkable theoretical findings about composite mechanics in recent years are described. A clarification of mechanics of compression after impact behavior by using a newly developed cohesive zone element is reviewed first in this category. Matrix crack growth theories in the laminae adjacent to the initially cracked layer are introduced next where a motivation of this research is a cryogenic composite tank for future space transportation systems. The final topic is a development of the theory of structural health monitoring by using small diameter FBG sensor. By an evolution of these theories structural health monitoring has almost reached the level of practical applications.

Numerical simulation of segmentation cracking in thermal barrier coatings by means of cohesive zone elements

The paper presents comparative experimental and numerical studies of segmentation cracking of thermal barrier coatings (TBCs) during three point bending tests. The finite element simulation of failure development was performed using a cohesive zone approach. Acoustic emission (AE) technique and in situ observations by a charge-coupled device (CCD) camera allowed to determine critical strain values correlated with the damage evolution. Location of crack initiation and crack propagation paths up to macroscopic failure were investigated for as-received and annealed specimens. The results of the numerical simulations and of the experiment were quantitatively similar. The influence of critical energy release rate on crack patterns was examined, resulting in the increase of crack numbers due to decreased value of G I . This explains the good spallation resistance of electron beam-physical vapour deposition (EB-PVD) coatings, where G I is lower than in the case of air plasma sprayed (APS) thermal barrier coatings. Lower value of G I stimulates segmentation cracking and reduces delamination, as observed within electron beam-physical vapour deposition coatings.

Constraint effects in adhesive joint fracture

Constraint effects in adhesive joint fracture are investigated by modelling the adherents as well as a finite thickness adhesive layer in which a single row of cohesive zone elements representing the fracture process is embedded. Both the adhesive and the adherents are elastic–plastic with strain hardening. The bond toughness Γ (work per unit area) is equal to Γ 0 + Γ p , where Γ 0 is the intrinsic work of fracture associated with the embedded cohesive zone response and Γ p is the extra contribution to the bond toughness arising from plastic dissipation and stored elastic energy within the adhesive layer. The parameters of the model are identified from experiments on two different adhesives exhibiting very different fracture properties. Most of the tests were performed using the wedge-peel test method for a variety of adhesives, adherents and wedge thicknesses. The model captures the constraint effects resulting from the change in Γ p : (i) the plastic dissipation increases with increasing bond line thickness in the fully plastic regime and then decreases to reach a constant value for very thick adhesive layers; (ii) the plastic dissipation in the fully plastic regime increases drastically as the thickness of the adherent decreases. Finally, this model is used to assess a simpler approach which consists of simulating the full adhesive layer as a single row of cohesive elements.

Local fracture criteria : Lengthscales and applications

Cohesive zone elements for the modeling of fracture generally use fixed cohesive properties to describe the process of material separation. Results of crack growth simulations by the use of the modified Gurson relation demonstrate that in case of ductile fracture the separation parameters cohesive strength and characteristic length, however, do not remain constant throughout a crack growth analysis and their values are not known a priori This finally leads to the need of further developments in cohesive zone models where both cohesive zone parameters are adjusted by triaxiality. In the present paper such a model is presented, its material parameters are derived and an application to the simulation of crack growth in a ductile metal is demonstrated. This application shows that the triaxiality dependent cohesive zone model can in detail reflect the changes in lengthscale of separation and cohesive strength as the crack propagates through the ductile metal.