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.     

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.     

A Rate-Dependent Cohesive Zone Model for Adhesively Bonded Joints Loaded in Mode I

The present work investigates the rate-dependent failure behaviour of structural adhesive joints loaded in mode I. Butt joint and tapered double cantilever beam (TDCB) specimens were tested at velocities ranging over more than six orders of magnitude. A rate-dependent extension of the bi-linear cohesive zone model is proposed and implemented into the finite element code LS-DYNA via an user-defined subroutine. The parameters for the implemented cohesive zone model are found directly by evaluation of experimental data. The comparison of simulations with experimental results for different specimen types and test velocities validates the proposed model. The critical energy release rate of adhesively bonded joints is usually measured in (tapered) double cantilever beam tests, and evaluated using the Irwin–Kies equation. In this paper a different evaluation method is proposed, which provides additional information on the energy dissipated during crack initiation. The results of this method agree with the results obtained using the Irwin–Kies equation. The investigations have focussed on thin adhesive layers. Parameter identification and validation have been performed using the crash-optimized adhesive Terokal 5077 from Henkel.     

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.     

Strength Prediction of Adhesively Bonded Single Lap Joints Under Salt Spray Environment Using a Cohesive Zone Model

The aim of this research was to develop an experimental–numerical approach to characterize the effect of salt spray environment on adhesively bonded joints and predict the degradation in joint strength. Experiments were conducted on bulk adhesive specimens and single lap joints (SLJs) under salt spray condition and the corresponding experimental results were reported. The environment degradation factor, Deg, was incorporated into a bilinear cohesive zone model (CZM) to simulate the degradation process of the joints. The degraded CZM parameters, determined from static tests on bulk adhesive, were imported into the CZM using an approximate moisture concentration gradient approach. The reduction in residual strength of SLJ under salt spray environment was successfully predicted through comparing the experimental and numerical results.     

The simulation of a double cantilever beam test using the virtual crack closure technique with the cohesive zone modelling

The fracture of an adhesively bonded joint is a complicated process of crack nucleation and propagation. In this work, a method for modelling the fracture process with separate nucleation and propagation phases is presented. The method combines the virtual crack closure technique (VCCT) with the cohesive zone modelling (CZM) on the finite element basis to take into account the development of fracture toughness. The method is applied to simulate a double cantilever beam (DCB) test as an example. Experiments using a butt joint specimen are carried out to support the adhesive characterization. The analysis focuses on the physical validity of the VCCT-CZM coupling and on the determination of applicable simulation parameter values. By using experimental data as a reference, the simulation results are compared to the results of traditional CZM and VCCT simulations. The comparison indicates that the applied combined CZM-VCCT method reproduces the DCB test cycles more accurately than the CZM and VCCT models.     

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.     

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.     

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

Abstract

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

Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints

The objective of this work is to discuss the adequacy of cohesive and continuum damage models for the prediction of the mechanical behaviour of bonded joints. A cohesive mixed-mode damage model appropriate for ductile adhesives is presented. The double cantilever beam and the end-notched flexure tests are proposed in order to evaluate the cohesive properties of the adhesive as a thin layer under mode I and mode II, respectively. A new data reduction scheme based on the crack equivalent concept is also proposed to overcome crack-monitoring difficulties during propagation in these fracture characterization tests. An inverse method to determine the cohesive parameters of the trapezoidal softening law is discussed. A continuum mixed-mode damage model is developed in order to better simulate the cases where adhesive thickness plays an important role. The model is applied to evaluate the effect of adhesive thickness on fracture characterization of adhesive joints. Some important conclusions about the advantages and drawbacks of cohesive and continuum damage models are reported.     

Tensile behaviour of three-dimensional carbon-epoxy adhesively bonded single- and double-strap repairs

An experimental and numerical study of the tensile behaviour of three-dimensional carbon-epoxy adhesively bonded strap repairs is presented. Experimentally, the failure mode, elastic stiffness and strength were evaluated for different overlap lengths and patch thicknesses. The numerical simulations, performed in ABAQUS^®, allowed obtaining the elastic stiffness and the patch debonding load, used to understand the repairs behaviour. The adhesive layer was simulated with cohesive elements including a mixed-mode cohesive damage model with trapezoidal traction-separation laws in pure modes I and II, to account for the ductile behaviour of the adhesive used. These laws were determined by an inverse method, which consists on the estimation of the cohesive parameters with a fitting procedure of the experimental and numerical load–displacement curves of the respective fracture characterization test. The pure mode III cohesive law was equalled to the pure mode II one. This numerical methodology was found adequate to reproduce the experimentally observed behaviour of these repairs.     

Determination of Traction Separation Law for Interfacial Failure in Adhesive Joints at Different Loading Rates

Cohesive zone modeling (CZM) has been extensively used in recent years to simulate failure in adhesive joints. Accurate determination of the traction–separation law (TSL) (or parameters of the CZM) is very crucial to the success of this approach. Recent experimental investigations have indicated that loading rate influences the TSL/CZM parameters. In this work we have attempted to measure the TSL using two different approaches for an adherend/adhesive system which always fails by interfacial failure. In the first approach, the TSL is obtained by differentiating the experimentally measured J integral by the opening displacement. The second, an inverse approach, involves a finite element (FE) analysis in which the adhesive layer is also modeled and cohesive elements are used to model the interfacial failure. The TSL is then obtained iteratively by matching the numerical load–displacement data to that obtained in experiments. We show that the first approach yielded TSLs which are dependent on both adhesive layer thickness and the loading rate, whereas the second approach yielded a TSL which is independent of the adhesive layer thickness and the loading rate. Therefore, the TSL obtained from the second approach is intrinsic to the adhesive/adherend pair and in that sense is unique.     

Rate effects for mixed-mode fracture of plastically-deforming,adhesively-bonded structures

Mixed-mode fracture of an adhesively-bonded structure made from a commercial adhesive and a dual-phase steel has been studied under different rates. Since mixed-mode fracture occurs along the interface between the steel and the adhesive, the cohesive parameters for the interface were required. The mode-II interfacial properties were deduced in earlier work. In this paper the mode-I interfacial toughness and the mode-I interfacial strength were determined at different rates. The mode-I interfacial strength was not affected by rate up to crack velocities at levels associated with impact conditions, and was essentially identical to the cohesive strength appropriate for crack growth within the adhesive layer. The mode-I toughness was reduced by about 40% when the crack propagated along the interface rather than within the adhesive. Furthermore, transitions to a brittle mode of failure occurred in a stochastic fashion, and were associated with a drop in interfacial toughness by a factor of about five. The mode-I interfacial parameters were combined with the previously-determined mode-II interfacial parameters within a cohesive-zone model to analyze the mixed-mode fracture of the joints which exhibited both quasi-static and unstable fracture. The mixed-mode model and the associated cohesive parameters for both quasi-static and unstable crack propagation provide bounds for predicting the behavior of the bonded joints under various rates of loading, up to the impact conditions that could be appropriate for automotive design.     

Behavior and failure of adhesive bonds in pin fin heat sinks using cohesive zone model

Adhesive bonding is a versatile material joining method that tends to distribute the load over the bonded area and provide more flexibility in selecting the base material without worrying about the joining process and its effects. To improve the performance of heat sinks, polymer composite pin fin are used to improve the thermal conductivity. Adhesives are usually used in bonding composite fins to their metal base plate. In this work we provide a methodology for estimating the fatigue life of the adhesive joint. A thermo-mechanical cohesive zone model (CZM) is used at the interfaces to measure the softening of the bond under thermal cyclic loading which in turn decreases the critical stress for failure. A summary of the fatigue crack initiation (FCI) life prediction model is presented before a qualitative study is performed to estimate the effect of convection environment on the life and behavior of the adhesive bond.     

Study on the effect of post curing on the mode II fracture energy of structural adhesive using a parameter identification approach

In this work, a parameter identification approach was developed based on a combined experimental-numerical approach to determine the optimal set of adhesive parameters in adhesively bonded specimen subjected to various post curing treatments. End-Notched Flexure (ENF) testing was conducted to characterise the Mode II fracture property under both recommended and post curing conditions, providing benchmark data for the numerical analysis stage. Experimental results revealed that Mode II fracture energy was effectively affected by the post curing history, with higher temperature and longer curing duration leading to enhanced fracture resistance. The numerically identified Cohesive Zone Model (CZM) parameters using multi-island genetic algorithm provided good correlation in Mode II fracture energies between Finite element (FE) modelling and experimentally measured values, thus extensive experimental characterisation work to determine the adhesive parameters can be effectively eliminated.     

Direct determination of a new mode-dependent cohesive zone model to simulate metal-to-metal adhesive joints

In this paper, a new mode-dependent cohesive zone model for the simulation of metal to metal adhesive joints is directly determined. Three consecutive steps have been taken into account for this end. First, double cantilever beam (DCB) and end-notched flexure (ENF) specimens are utilized for the direct experimental extraction of the traction-separation laws (TSLs) for adhesive bonded joints subjected to pure mode I and mode II, respectively. Next, the results are implemented to obtain the relative cohesive zone parameters for defining the simplified Park-Paulino-Roesler cohesive zone model (S-PPR CZM). Finally, mixed-mode characteristics parameters are derived for an arbitrary mode-mixity ratio based on pure mode TSLs. The model is further implemented in ABAQUS® commercial software to be verified against the experimental results of pure mode loadings which leads to the direct extraction of TSLs. The experiments conducted on the strength of single lap joint (SLJ) and scarf joint (SJ) specimens, commonly tested for mixed-mode loading, confirm the accuracy of the developed mixed-mode S-PPR model for different mode-mixity conditions.     

Evaluation of different modelling conditions in the cohesive zone analysis of single-lap bonded joints

Cohesive Zone Models (CZM) are widely used for the strength prediction of adhesive joints. Different simulation conditions, such as damage initiation and growth criteria, are available for use in CZM analyses to provide the mixed-mode behaviour. Thus, it is highly relevant to understand in detail their influence on the simulations’ outcome. This work studies the influence of different conditions used in CZM simulations to model a thin adhesive layer in single-lap joints (SLJ) under a tensile loading, for an estimation of their influence on the strength prediction under diverse geometrical and material conditions. Validation with experimental data is considered. Adhesives ranging from brittle to highly ductile and overlap lengths (L_O) between 12.5 and 50 mm were considered. Different studies were considered: Variation of the elastic stiffness of the cohesive laws, different mesh refinements, study of the element type, and evaluation of several damage initiation and growth criteria. The analysis carried out in this work confirmed the known suitability of CZM for static strength prediction of bonded joints and pointed out the best set of numerical conditions for this purpose. Inaccurate results can be obtained if the choice of the modelling conditions is not the most suitable for the problem.     

The tension failure mechanisms of composite stepped bonding repairs and joints for the aircraft primary load-bearing structures

Stepped and scarf topology are still the preferred choices for repairs and joints of composite primary load-bearing structures. The stepped bonding scheme is easy to be implemented in real engineering process. The precise stress distribution, load capacity, damage mode and failure mechanism are not adequately clear. This paper adopts static stress analysis of FEM (Finite Element Method), experimental studies and CDM (Continuum Damage Mechanics) to reveal the tension failure mechanism for composite stepped bonding structures. In the static stress analysis, the mesoscale FEM model considered the adhesive thickness was created. It investigated the detail stress distribution and concentration of the step topology adhesive. Then seven specimens with tensile load were studied experimentally through relation of load-deformation and the appearance of damage. For more details, the adhesive damage was simulated by using CZM (Cohesive Zone Model) which includes the mix-mode fracture of normal force and sliding shear force. The process of damage propagation evolution can be clearly observed in the simulation results. The damage initiates at the vertical location of steps adhesive and propagates to the horizontal overlaps adhesive. Simulation for predicting the ultimate load capacity coincides with experiments. This paper’s work will be useful for designing and analyzing the full composite materials airframe and wing repaired by stepped bonding technique.