Cohesive/adhesive failure interaction in ductile adhesive joints Part II: Quasi-static and fatigue analysis of double lap-joint specimens subjected to through-thickness compressive loading

This paper proposes a new methodology for the finite element (FE) modelling of failure in adhesively bonded joints. Cohesive and adhesive failure are treated separately which allows accurate failure predictions for adhesive joints of different thicknesses using a single set of material parameters. In a companion paper (part I), a new smeared-crack model for adhesive joint cohesive failure was proposed and validated. The present contribution gives an in depth investigation into the interaction among plasticity, cohesive failure and adhesive failure, with application to structural joints. Quasi-static FE analyses of double lap-joint specimens with different thicknesses and under different levels of hydrostatic pressure were performed and compared to experimental results. In all the cases studied, the numerical analysis correctly predicts the driving mechanisms and the specimens’ final failure. Accurate fatigue life predictions are made with the addition of a Paris based damage law to the interface elements used to model the adhesive failure.     

Strain energy release rate based damage analysis of functionally graded adhesively bonded tubular lap joint of laminated FRP composites

Strain energy release rate (SERR) based damage analyses of functionally graded adhesively bonded tubular lap joints of laminated fiber reinforced plastic (FRP) composites under varied loadings have been studied using three-dimensional geometrically non-linear finite element (FE) analyses. FE simulations have been carried out when a tubular joint is subjected to axial and pressure loadings. SERR is utilized as the characterizing and governing parameter for assessing damages emanating from the critical location. Individual and total SERR over the damage front have been computed using modified crack closure integral (MCCI) based on the concept of linear elastic fracture mechanics. Results reveal that damage initiation locations in tubular joints subjected to axial and pressure loadings are entirely different. Furthermore, modes responsible for propagation of such damages in tubular joints under axial and pressure loadings are also different. Based on the FE simulations, tubular joints under pressure loading are found to be more vulnerable for damage initiation and its propagation. Furthermore, the damage propagation behavior of tubular joints with pre-embedded damages at the critical location has been compared between conventional mono-modulus adhesives and functionally graded adhesives with appropriate material gradation profile. Results indicate that material gradient profile of the adhesive layer offers excellent reduction in SERR for shorter interfacial failure lengths in tubular joints under axial loading which is desired to delay the damage growth. Improved crack growth resistance in the joint enhances the structural integrity and service life of the tubular joint structure. However, considerable reduction in SERR has not been noticed in the said joint when subjected to pressure loading. Hence, the use of functionally graded adhesive along the bond layer is recommended for the designer/technologist while designing tubular joint under general loading condition.     

Toughening epoxy adhesives with multi-walled carbon nanotubes

In this paper, the effect of adding multi-walled carbon nanotubes (MWCNTs) with an outer diameter of less than 8 nm to an epoxy adhesive was studied on the adhesive fracture resistance and damage behaviour. The fracture energies of the neat and toughened adhesives were measured by testing double-cantilever beam specimens. Moreover, a cohesive zone model (CZM) was used to numerically study the effect of MWCNTs on the damage behaviour of the toughened adhesives. The maximum improvement of 58.4% in the adhesive fracture energy was obtained when the adhesive was toughened with 0.3 wt% of MWCNTs. The fracture surfaces were analysed using the scanning electron microscopy (SEM) technique. It was found that the presence of MWCNTs in the toughened adhesives caused rougher fracture surfaces. Moreover, some fracture mechanisms including nanotube pull-out and de-bonding were observed in the fracture surfaces. The numerical analyses showed that the damage process zone length was also influenced by MWCNTs. The longest damage process zone was obtained for the toughened adhesive with 0.3 wt% of MWCNTs.     

Low speed impact behaviour of adhesively bonded foam-core sandwich T-joints

This paper investigates the effects of foam core density and aluminum skin plates on the low speed impact behaviour of adhesively bonded sandwich T-joints having a PVC foam core and aluminum face-sheets. The dynamic response of adhesively bonded sandwich T-joints was analyzed by the explicit finite element method. Two different material models were implemented to the foam core material: a hyperelastic model and a crushable foam material with ductile damage whereas the aluminum face-sheets were modelled as an elasto-plastic material. The cohesive response of adhesive interfaces was included using three dimensional cohesive element based on cohesive zone model. Adhesively bonded sandwich T-joint specimens were manufactured and tested to validate the numerical model. A very good agreement between the experimental and FE results were achieved. The density of the foam core material of adhesively bonded sandwich T-joint played important role on the joint failure mechanism. The joint having a stiffer foam core experienced more damage in both stiffener panel and adhesive layers.     

Geometrical study of mixed adhesive joints for high-temperature applications

The use of adhesives for high-performance structural applications has significantly increased in the last decades. However, the use of adhesive joints in adverse environmental conditions is still limited due to the reduced capability of adhesives to withstand large thermal gradients. Dual adhesive joints, which contain two adhesives with remarkably different mechanical behaviours, are a technique suitable for being used in extreme temperatures. The object of this study is a ceramic–metal joint, representative of the thermal protection systems of some aerospace vehicles. In this paper, several joint-mixed joint geometries are presented, studied with recourse to finite element analysis. In a first phase, the three-dimensional finite element models and the material properties are validated against experimental data. In a second phase, the model geometry is modified, with the aim of understanding the effect of several changes in the joints’ mechanical behaviour and comparing the merits of each geometry. The models’ presented good agreement was found between experimental and numerical data and the alternative geometries allowed the introduction of additional flexibility on the joint but at the cost of lower failure load.     

Comparison of the Shear Stress-strain Behaviour of some Structural Adhesives

The shear stress-strain behaviour of structural adhesives provides important data for the designer. Shear modulus, strength, and elastic and plastic strain to failure have been determined using a torsional butt joint technique which is relatively quick to perform and is believed to be very accurate. A range of structural adhesives have been compared, which has highlighted some important differences in their behaviour. Increasing the bond line thickness of an adhesive lowers the plastic strain to failure.     

Strength of epoxy adhesive-bonded stainless-steel joints

The strength of stainless-steel joints bonded with two epoxy adhesives was investigated. The experimental programme included tests on single-lap and butt joints, as well as thick-adherend and napkin ring shear tests. Results suggested that the tensile and shear strengths of the epoxy adhesives were quite similar. However, finite element (FE) analyses raised doubts on the true adhesive strengths, due to the complex stress state in joint tests and pressure-dependent adhesive behaviour. In spite of some uncertainties, FE analyses showed that failure could be fairly well predicted by a maximum shear strain criterion.     

Comparison of cohesive zone and continuum damage approach in predicting the static failure of adhesively bonded single lap joints

The paper presents a comparison of the cohesive zone model (CZM) and the continuum damage mechanics approach in predicting the static failure of a single lap joint (SLJ). The effect of mesh size and viscosity were studied to give more understanding on the failure load and computational time. Both the load–displacement response and the backface strain technique were utilised to compare the validity of predictions. Peel and shear stress and damage distributions along with the damage progression are compared to understand the behaviour of the models in predicting the static failure response. In general, both approaches show good accuracy in predicting the failure load; however, the cohesive zone approach requires shorter computation time than the continuum damage approach. The continuum damage approach shows some mesh-dependency particularly for elements with high aspect ratios, whereas the cohesive zone approach is not. The continuum damage approach is less sensitive than the cohesive zone approach to the artificial damping required to achieve convergence. Another interesting finding is using the same ultimate stress level of damage in the continuum damage approach at the peak load is much lower than that in the cohesive approach; but the failure process in this approach is faster.     

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.     

Strength prediction of bonded single lap joints by non-linear finite element methods

A non-linear finite element technique has been used to predict the mode of failure and failure load of single lap joints made from three aluminium alloys and four epoxy adhesives, and the results compared with those obtained from experiment and closed-form analyses. The finite element program used was able to account for the large displacement rotations that occur in a single lap joint under load, and allowed the effects of elasto-plasticity in both the adhesive and adherends to be modelled. A failure criterion based on the uniaxial tensile properties of the adhesive was used: for two untoughened adhesives a maximum stress criterion was found to be appropriate while for two toughened adhesives a maximum strain criterion was employed.     

Analysis on low velocity impact damage of laminated composites toughened by structural toughening layer

The intralaminar and interlaminar damages of U3160/3266 laminated composites toughened by polyamide nonwoven fabric (PNF) under low velocity impact are investigated through a numerical model which considers both the three‐dimensional continuum damage mechanics (CDM) and the bilinear cohesive zone model (CZM). The analysis of the intralaminar damage is implemented by the ABAQUS/Explicit finite element code coupled with a user‐defined subroutine VUMAT where the longitudinal failure, transverse matrix cracking, and nonlinear shear of the material are taken into account. Then the effects of the thickness and strength of PNF/3266 interlayer on the damage of composites are numerically analyzed. The results reveal that damage morphology can be simulated qualitatively compared to the experimental counterparts. With the decreasing interlayer thickness or the increasing interlayer strength, the damage area is effectively reduced. This work provides an effective model to predict the low velocity impact damage of composites, and is helpful for the optimization of interlayer toughened composites. POLYM. COMPOS., 38:1280–1291, 2017. © 2015 Society of Plastics Engineers     

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.     

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.     

Nonlinear Stress Analysis of an Adhesive Tubular Lap Joint

The analysis of adhesive bonded joints have been based, generally, on the assumption that the adhesive behaves as a linearly elastic material. Many adhesives, however, exhibit nonlinear stress-strain behaviour, particularly near failure. This article reports an attempt on the analysis of an adhesive tubular lap joint with the adhesive obeying a nonlinear stress-strain law. The Finite Element method has been employed for the solution.     

Effect of Joint Geometry on the Behavior and Failure Modes of Sandwich T-Joints Under Transverse Static and Dynamic Loads

Due to wide spread application of adhesive T-joints in various industries, a review of properties and strength of their fracture modes under static and dynamic loadings is required. By defining the ability of failure in the joint material and fracture of adhesive in the numerical model, fracture modes of sandwich T-joints have been investigated. This paper presents numerical results on the performance of sandwich T-joints subjected to static tensile, static transverse, and dynamic transverse loading. The results of available experiments in the literature have been used to validate the detailed numerical models capable of simulating the damage processes observed. In general, the failure load predicted by the finite element (FE) analysis is within 5% of the experimental results.     

Modeling of high strength steel joints bonded with toughened adhesive for vehicle crash simulations

Improvement of the structural adhesive increases the difficulties in crash simulations of adhesive-bonded vehicle structures. In this paper, a simplified finite element model is recommended for modeling of the toughened adhesive-bonded joint. Solid elements and shell elements are respectively used to represent the adhesive and the base metal. To better predict the impact response of adhesive, an isotropic elastoplasticity model in LS-DYNA 971 is modified, in which the strain rate effect of both the pre-failure material properties and the failure criterion can be characterized. A method that can correct the variation of adhesive thickness is developed. The input failure parameters of the material model are identified with simulations of adhesive-bonded coach-peel and lap-shear coupon tests. It is found that adhesive failure parameters in the simplified model are independent of the base metal thickness.To improve the simplified model, several issues associated with its practical application, e.g., influence of spewed-out adhesives, variations of adhesive layer representation, have also been addressed in this paper. The recommended simplified model is then used in simulation of the adhesive-bonded tube axial impact test, which validates well its characterization capability and computational efficiency.     

Anisotropic continuum damage model for prediction of failure in flax/polypropylene fabric composites

An anisotropic continuum damage modeling approach was applied to model failure of a composite of unidirectional flax in a polypropylene matrix under quasi‐static tensile loading. Tensile, compressive and shear stiffness, and strength values of the composite were characterized according to ASTM standards, and the damage was quantified by optical microscopy. Based on the experimental strength and damage values, an anisotropic strain‐dependent material damage model was developed and implemented in the finite element program ABAQUS. This was combined with geometric models of the fabric composites incorporating the yarn geometry. Good agreement was observed between the experimental and numerical stress–strain curves, and the failure strength prediction by the model was within 3.1% of the experimental value. This study shows that combining a geometric model closely incorporating the actual geometry of a fabric composite with an experimentally determined material degradation model can yield good predictions of the mechanical behaviour of the composite. POLYM. COMPOS., 37:2588–2597, 2016. © 2015 Society of Plastics Engineers     

Investigating tensile behaviour of toughened epoxy paste adhesives using circumferentially notched cylindrical bulk specimens

Toughened epoxy adhesives are frequently used to bond metals and polymer-matrix composite materials in many structural applications. The mechanical properties of adhesives are often characterised by testing either bulk adhesive specimens or bonded joints (i.e. in-situ form). In this paper, cylindrical bulk specimens with circumferential notches were manufactured and tested to investigate the tensile behaviour of an epoxy paste adhesive toughened with hollow glass microspheres. Bulk specimens were manufactured from the paste adhesive using injection moulding. Tensile tests were conducted for strain-rate and stress triaxiality effects by varying displacement rates and notch radii, respectively. Fracture surfaces were examined using optical and scanning electron microscopy to identify failure mechanisms. The results obtained from the toughened paste adhesive indicate that strain-rate and stress triaxiality influence its tensile fracture behaviour.     

Effect of Adherend Recessing on the Tensile Strength of Single Lap Joints

Bonded joints are gaining importance in many fields of manufacturing owing to a significant number of advantages to the traditional methods. The single lap joint (SLJ) is the most commonly used method. The use of material or geometric changes in SLJ reduces peel and shear peak stresses at the damage initiation sites. In this work, the effect of adherend recessing at the overlap edges on the tensile strength of SLJ, bonded with a brittle adhesive, was experimentally and numerically studied. The recess dimensions (length and depth) were optimized for different values of overlap length (L _O), thus allowing the maximization of the joint's strength by the reduction of peak stresses at the overlap edges. The effect of recessing was also investigated by a finite element (FE) analysis and cohesive zone modelling (CZM), which allowed characterizing the entire fracture process and provided joint strength predictions. For this purpose, a static FE analysis was performed in ABAQUS® considering geometric nonlinearities. In the end, the experimental and FE results revealed the accuracy of the FE analysis in predicting the strength and also provided some design principles for the strength improvement of SLJ using a relatively simple and straightforward technique.