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.     

Simulation of Mixed-Mode I/II Fatigue Crack Propagation in Adhesive Joints with a Modified Cohesive Zone Model

A model to predict fatigue crack growth in bonded joints under mixed mode I/II conditions is developed in this work. The model is implemented in the finite element software ABAQUS using the related USDFLD subroutine. The present model is based on the cohesive zone (CZ) concept, where damage develops according to the value of the opening/sliding at the bondline under static loading, and according to a cyclic damage accumulation law under fatigue loading. The damage accumulation law is obtained by distributing the cyclic crack area increment over the process zone ahead of the crack tip, where the cyclic crack area increment is calculated according to a Paris-like law that relates the crack growth rate to the applied loading. In this way, the experimental crack growth rate is related directly to damage evolution in the cohesive zone, i.e., no additional parameters have to be tuned besides the quasi-static cohesive zone parameters.     

Fatigue Growth of Cohesive Defects in T-Peel Joints

This paper uses 2D and 3D finite element models to predict the stresses within bonded and weld-bonded T-peel joints. Epoxy adhesive is modelled as a homogeneous layer providing a perfect bond between aluminium adherends. Knowledge of the critical tensile stresses enables the likely region of fatigue crack initiation to be predicted. The long term reliability and durability of a joint depend directly on its fatigue strength. This research elucidates the region of cohesive crack initiation, the subsequent direction of crack propagation and the relative duration of the different stages of fatigue crack growth. The various stages of embedded, surface and through-width fatigue growth of cohesive defects within a T-peel joint are compared. This establishes fatigue life from crack initiation to final joint fracture for typical bonded and weld-bonded T-peel joints.     

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.     

Testing different cohesive law shapes to predict damage growth in bonded joints loaded in pure tension

ABSTRACT

Adhesive bonding is a widely used joining method because of specific advantages compared to the traditional fastening methods. Cohesive zone modelling (CZM) is currently the most widely used technique for strength prediction. CZM supposes the characterization of the CZM laws in tension and shear. This work evaluated the tensile fracture toughness (G_IC) and CZM laws of bonded joints with three adhesives by the double-cantilever beam (DCB) test. The experimental work consisted of the adhesives’ tensile fracture characterization by the J-integral technique. As the main novelty of this work, the precise shape of the cohesive law of adhesives ranging from brittle to highly ductile was defined by the direct method, using a digital image correlation method to evaluate the tensile relative displacement (δ_n) of the adhesive layer at the crack tip and adherends’ rotation at the crack tip (?_o). Moreover, finite element (FE) simulations permitted assessing the accuracy of triangular, trapezoidal and linear-exponential CZM laws in predicting the experimental behaviour of the DCB bonded joints with markedly distinct behaviours. As output of this work, fracture data and information regarding the applicability of these CZM laws to each type of adhesive is provided, allowing the subsequent strength prediction of bonded joints.     

Fatigue analysis of composite bonded repairs

Abstract

The present work intends to describe all procedures developed in order to predict the fatigue/fracture behaviour of single-strap repairs of carbon-epoxy composites. The main goal is to validate a mixed-mode I + II cohesive zone model for high-cycle fatigue based on the modified Paris law. A preliminary static fracture characterisation in mode I, mode II and mixed-mode I + II is necessary in order to achieve the static energetic criterion describing fracture of the bonded joint. Subsequently, the same tests were carried out under high-cycle fatigue loading in order to determine the evolution of the modified Paris law parameters as function of mode ratio. These fatigue/fracture characterisation tests were also used to validate the cohesive mixed-mode I + II zone model appropriate for high-cycle fatigue. The model was then used to predict fatigue life of the single-strap repairs and revealed good performance when compared with experimental results. Finally, the model was utilised to assess the influence of specimen geometry on the fatigue life of these structural repairs. It was concluded that such type of models can be considered appealing tools concerning the optimisation of repaired structures fatigue life.     

Low-speed bending impact behavior of adhesively bonded single-lap joints

This study addresses the low-speed impact behavior of adhesively bonded single-lap joints. An explicit dynamic finite element analysis was conducted in order to determine the damage initiation and propagation in the adhesive layers of adhesive single-lap joints under a bending impact load. A cohesive zone model was implemented to predict probable failure initiation and propagation along adhesive–adherend interfaces whereas an elasto-plastic material model was used for the adhesive zone between upper and lower adhesive interfaces as well as the adherends. The effect of the plastic deformation ability of adherend material on the damage mechanism of the adhesive layer was also studied for two aluminum materials Al 2024-T3 and Al 5754-0 having different strength and plastic deformation ability. The effects of impact energy (3 and 11 J) and the overlap length (25 and 40 mm) were also investigated. The predicted contact force-time, contact force-central displacement variations, the damage initiation and propagation mechanism were verified with experimental ones. The SEM and macroscope photographs of the adhesive fracture surfaces were similar to those of the explicit dynamic finite element analysis.     

Analysis and design of adhesively bonded joints for fatigue and fracture loading: a fracture-mechanics approach

An experimental–computational fracture-mechanics approach for the analysis and design of structural adhesive joints under static loading is demonstrated by predicting the ultimate fracture load of cracked lap shear and single lap shear aluminum and steel joints bonded using a highly toughened epoxy adhesive. The predictions are then compared with measured values. The effects of spew fillet, adhesive thickness, and surface roughness on the quasi-static strength of the joints are also discussed. This fracture-mechanics approach is extended to characterize the fatigue threshold and crack growth behavior of a toughened epoxy adhesive system for design purposes. The effects of the mode ratio of loading, adhesive thickness, substrate modulus, spew fillet, and surface roughness on the fatigue threshold and crack growth rates are considered. A finite element model is developed to both explain the experimental results and to predict how a change in an adhesive system affects the fatigue performance of the bonded joint.     

Predicting the strength of adhesively bonded joints of variable thickness using a cohesive element approach

One major characteristic of bonded structures is the highly localised nature of deformation near sharp corners, ply-terminations, and ends of joints where load transfer occurs. This paper presents an investigation of the use of a cohesive zone model in predicting the strong effects of stress concentration due to varying adherend thickness on the pull-off strength measured by the Pneumatic Adhesion Tensile Testing Instrument. A comparison is made with the point-strain-at-a-distance criterion, where the plastic deformation of the adhesive is analysed using a modified Drücker–Prager/cap plasticity material model. The fracture properties of the cohesive zone model were determined using double-cantilever and end-notch flexural specimens, and the cohesive strengths were measured using tensile and lap shear tests. Comparisons with experimental results reveal that the cohesive zone model with perfectly plastic (or non-strain-softening) cohesive law provides accurate predictions of joint strengths.     

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.     

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.     

Taguchi analysis of bonded composite single-lap joints using a combined interface–adhesive damage model

The mechanical behaviour of bonded composite joints depends on several factors, such as the strength of the composite–adhesive interface, the strength of the adhesive and the strength of the composite itself. In this regard, a finite element model was developed using a combined interface–adhesive damage approach. A cohesive zone model is used to represent the composite–adhesive interface and a continuum damage model for the adhesive bondline. The influence of the composite–adhesive interfacial adhesion and the strength of the adhesive on the performance of a bonded composite single-lap joint was investigated numerically. A Taguchi analysis was conducted to rank the influence of material parameters on the static behaviour of the joint. It was found that the composite–adhesive interfacial fracture energy and the mechanical properties of the adhesive predominantly govern the static performance of the joints. A parametric study was performed by varying the most important material parameters, and a response surface equation is proposed to predict the joint strength. It is shown that the influence of experimental parameter variations, e.g. variation in adhesive curing and surface preparation conditions, can be numerically accommodated to investigate the static behaviour of bonded composite joints by combining finite element and statistical techniques. The methods presented could be used by practicing engineers to describe the failure envelope of adhesively bonded composite joints.     

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.     

The Static Failure of Adhesively Bonded Metal Laminate Structures: A Cohesive Zone Approach

Adhesively bonded metal laminates are used in aerospace applications to achieve low cost, light weight structures in the aerospace industry. Advanced structural adhesives are used to bond metal laminae to manufacture laminates, and to bond stringers to metal laminate skins. Understanding the failure behaviour of such bonded structures is important in order to provide optimal aircraft designs. In this paper, the static failure behaviour of adhesively bonded metal laminate joints is presented. A cohesive zone model was developed to predict their static failure behaviour. A traction–separation response was used for the adhesive material. Three joint configurations were considered: a doubler in bending, a doubler in tension and a laminated single lap. The backface strains and static failure loads obtained from experimental tests were used to validate the results from finite element modelling. The models were found to be in good agreement with experiments.     

Determination of traction-separation laws on an acrylic adhesive under shear and tensile loading

Structural acrylic adhesives are of special interest because those adhesives are cured at room temperature and can be bonded to oily substrates. To use those adhesives widely for structural bonding, it is necessary to clarify the methodology for predicting strengths of bonding structures with those adhesives. Recently, cohesive zone models (CZMs) have been receiving intensive attentions for simulation of fracture strengths of adhesive joints, especially when bonded with ductile adhesives. The traction-separation laws under mode I and mode II loadings require to estimate fracture toughness of adhesively bonded joints. In this paper, the traction-separation laws of an acrylic adhesive in mode I and mode II were directly obtained from experiments using Arcan type adhesively bonded specimens. The traction-separation laws were determined by simultaneously recording the J-integral and the opening displacements in the directions normal and tangential to the adhesive layer, respectively.     

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.     

Analysis of the fracture process zone and effective crack length in the adhesively bonded end-notched flexure specimen

The mode II fracture of adhesive joints is well-known to involve large fracture process zones. Their effect in fracture energy measurements can be taken into account by the effective crack length approach. Moreover, fracture process zones can be simulated by cohesive zone models, which are increasingly used for structural analysis of adhesive joints. This paper aimed at evaluating the influence of the traction-separation law on the fracture process zone and on the effective crack length in end-notched flexure tests. Novel analytical cohesive zone models were developed for the bilinear and trapezoidal traction-separation laws. The latter were shown to affect significantly the energy dissipation rate versus effective crack length curve prior to crack initiation. Therefore, this effect seems to provide a simple approach for evaluating approximate traction-separation laws. The models here developed are easy to apply and provide simple approximate expressions useful for specimen selection.     

FE simulation of the curing behavior of the epoxy adhesive Hysol EA-9321

Cold-curing adhesives, characterized by an unsteady curing degree, present various advantages for assembling large scale structures set up under outdoor conditions. Thus various applications can be found in aerospace and automotive industries where structures are affected by thermal and mechanical loads. Hence, the curing state of the adhesive must be known to evaluate the lifetime of such bonded structures. The evolution of the polymerization of the adhesive Hysol EA-9321 during the curing process was examined in this paper. To that end, the curing degree of the adhesive was experimentally and analytically investigated for different curing cycles with a view to a potential application in the aerospace domain, where structures are assembled at low temperatures. Existing dynamic and isothermal curing models were applied to simulate the curing behavior of the adhesive. Then, an FEM model was developed to simulate the process of adhesive curing by taking into account a thermo-kinetic coupling.     

Contents Lists and Abstracts from the Journal of the Adhesion Society of Japan

Double cantilever beam fracture specimens were used to investigate rate dependent failures of model epoxy/steel adhesively bonded systems. Quasi-static tests exhibited time dependent crack growth and the maximum fracture energies consistently decreased with debond length for constant crosshead rate loading. It was also possible to cause debonding to switch between interfacial and cohesive failure modes by simply altering the loading rate. These rate dependent observations were characterized using the concepts of fracture mechanics. The time rate of change of the strain energy release rate, dG/dt, is introduced to model and predict failure properties of different adhesive systems over a range of testing rates. An emphasis is placed on the interfacial failure process and how rate dependent interfacial properties can lead to cohesive failures in the same adhesive system. Specific applications of the resulting model are presented and found to be in good agreement when compared with the experimental data. Finally, a failure envelope is identified which may be useful in predicting whether failures will be interfacial or cohesive depending on the rate of testing for the model adhesive systems.     

Experimental and numerical analysis on fatigue durability of single-lap joints under vibration loads

Fatigue is one of the most common yet complicated failures that can cause damage to mechanical structures. Structural adhesively bonded joints are not exempt from this deleterious phenomenon and have to be assessed under vibration loads. In this work, fatigue characteristics of single-lap joints (SLJ) made of steel and carbon fibre reinforced plastic (CFRP) laminates under vibration loads are primarily investigated by experiments. The aim of this work is to analyze the changes in the ultimate load of the SLJ under vibration loads. The experimental results showed that SLJ will face cohesive failure after the uniaxial tensile loading test. In addition to the increase of vibration cycles, the ultimate load and failure displacement gradually decrease. In order to model the adhesive between joint components and simulate the damage propagation, a new traction–separation law called the embedded process zone (EPZ) and a damage factor are introduced and developed within the framework of cohesive zone Modeling (CZM) techniques. Meanwhile, the stress variations in the adhesive layer of SLJ in different vibration cycles are researched using the finite element method in ABAQUS.