Cohesive Zone Modelling Technique Research Articles

Measurement of the interfacial energy release rate (ERR) and cohesive law parameters of polyvinyl butyral laminated glass using a novel beam-type test specimen

The polyvinyl butyral (PVB) laminated glass (LG) structures are widely used in architectural and automotive sectors. Determination of the interfacial fracture energy (i.e. G) between the PVB layer and glass is one of the most vital procedures for ensuring the structural safety and fracture resistance of these kinds of components. The present study investigates the adhesion characteristics between glass and PVB interface in a LG composite structure. A new simple test fixture is introduced to measure the mixed-mode fracture energy from pure mode I (i.e. GI) to pure mode II (i.e. GII). By making use of the concept of Equivalent material Concept (EMC), linear elastic fracture mechanics (LEFM) formulations together with finite element (FE) analysis can be used to compute the compliance parameter of the system and pure modes I/II fracture energies. Besides, the interaction of cohesive forces between the PVB layer and glass are simulated by using a FE method based on a bi-linear cohesive zone model (CZM) technique. In this regard, the cohesive law parameters are computed for mode I and mode II in an iterative process. Then, the obtained pure mode cohesive law parameters are utilized to predict the mixed-mode load–displacement diagrams. The obtained results demonstrate the satisfactory accuracy of the cohesive law parameters and fracture energies in predicting the mixed-mode loading results across four different loading rates (i.e. LR = 2, 5, 10, and 15 mm/min).

Compression after impact (CAI) failure mechanisms and damage evolution in large composite laminates: High-fidelity simulation and experimental study

This study focuses on developing and validating a high-fidelity finite element model for predicting damage evolution and residual strength in fiber-reinforced composite panels. Impact and compression after impact (CAI) tests were conducted at both barely visible impact damage (BVID) and clearly visible impact damage (CVID) levels. The ASTM D7137 standard 100 mm × 150 mm CAI coupons were inadequate to cover the range of experimental studies required for model validation. Therefore, larger 254 mm × 304.8 mm laminates were investigated under two CAI testing conditions: one a scaled-up version of ASTM standard coupon, and the other with additional anti-buckling support plates to reduce unsupported areas to 127 mm × 177.8 mm. The model captured inter- and intra-laminar failure modes, including fiber breakage, splitting, kinking, pull-out, and crushing as well as matrix cracking, delamination, and their interactions. This was achieved by cohesive zone modeling technique and enhancement of the LaRC05 failure criteria through modeling the fiber damage evolution and utilizing an efficient search algorithm to determine the matrix fracture plane and fiber kink band angle. This study underscores the efficacy of the high-fidelity modeling approach in accurately predicting both impact damage and CAI strength in typical aircraft impact damage scenarios. Additionally, it provides insights into complex CAI failure mechanisms and energy release associated with various damage modes and highlights the effect of global buckling on the failure behavior and compressive strength of composite laminates. Furthermore, it shows that the proposed fixture with support plates is suitable for testing a broader range of impact scenarios without experiencing global buckling.

A Numerical Assessment of the Influence of Local Stress Ratio in the Fatigue Analysis of Post-Buckled Composite Single-Stringer Specimen

This paper presents a numerical approach for investigating fatigue delamination propagation in composite stiffened panels loaded in compression in the post-buckling field. These components are widely utilized in aerospace structures due to their lightweight and high-strength properties. However, fatigue-induced damage, particularly delamination at the skin–stringer interface, poses a significant challenge. The proposed numerical approach, called the “Min–Max Load Approach”, allows for the calculation of the local stress ratio in a single finite element analysis. It represents the ratio between the minimum and maximum values of the stress along the delamination front, enabling accurate evaluation of the crack growth rate. The methodology is applied here in conjunction with the cohesive zone model technique to evaluate the post-buckling fatigue behavior of a composite single-stringer specimen with an initial delamination. Comparisons with experimental data validate the predictive capabilities of the proposed approach.

Application of the effective crack length method to model delamination of unidirectional composite laminates under Mode II shear loadings

Damage modelling of composite material delamination is an intense field of research to understand the complex composite failure behaviour and predict the residual strength of damaged structures. One of the widely employed methods to simulate delamination is the cohesive zone modelling (CZM) technique. To successfully utilize this approach, accurate characterisation of the interlaminar fracture toughness is crucial, while the composite delamination is dominated by Mode I and Mode II fracture in most cases. Numerous studies have been conducted on composite materials delamination under Mode I loadings using double cantilever beam (DCB) tests. Accordingly, the ASTM standard testing procedure and data reduction scheme to obtain Mode I fracture toughness (GIc) have been well established and widely accepted. However, it is still challenging to characterize the composite Mode II delamination resistance due to the susceptibility problems inherent to the existing testing methods and the lack of robust data reduction schemes to accurately identify the initial crack tip and monitor the crack growth. This study attempts to find a reliable solution to obtain the Mode II fracture toughness (GIIC) and an effective modelling strategy to simulate Mode II delamination in laminated composites. First, we reviewed the existing testing set-ups and surveyed the data reduction schemes conventionally used to obtain GIIC. The advantages and drawbacks of the three most used test methods, and particularly the standard end-notched flexure (ENF) test (ASTM D7905/D7905M) and the end-loaded split (ELS) test (ISO 15114:2014) were examined. Second, the advantages of the effective-crack-length-based data reduction schemes against the classical data reduction schemes were empirically studied with the ENF tests conducted on G40-800/5276-1 carbon-fibre reinforced composite laminate coupons. Although many studies have studied the accuracy of the effective-crack-length-based approaches from different aspects, there is a lack of direct comparison between the numerical results and experimental data. Our modelling study demonstrates that among the five data reduction schemes that are examined, the compliance calibration method (CCM) required by ASTM D7905 yields the most conservative GIIC values, which is suitable for establishing material property for a design purpose. The compliance-based beam method (CBBM) may generate the least conservative GIIC values, which are deemed to be the most accurate ones for modelling and simulation validation purposes. Finite element (FE) modelling of the ENF tests using the CZM technique was carried out and comprehensive parametric studies were conducted to achieve an efficient and robust strategy for delamination modelling of composite laminates under Mode II shear loadings.

Analysis of adhesively bonded joints of laser surface treated composite primary components of aircraft structures

The performance of the adhesively bonded aerospace structures highly depends on the adhesion strength between the adhesive and adherents, which is affected by, in particular, the condition of the bonding surface. Among the various surface treatment methods, as state of the art, laser surface treatment is a suitable option for the CFRP composite structures to enhance the adhesion performance, adjusting the roughness and surface free energy with relatively minimizing the damage to the fibers. The aim of this study is the validation and evaluation of the adhesive bonding behavior of the laser surface-treated CFRP composite structures, using the finite element technique to perform a conservative prediction of the failure load and damage growth. Such objectives were achieved by executing both experimental and numerical analyses of the secondary bonded CFRP parts using a structural adhesive. In this regard, to complement physical experiments by means of numerical simulation, macro-scale 3D FEA of adhesively bonded Single Lap Joint and Skin-Spar Joint specimens has been developed employing the Cohesive Zone Model (CZM) technique in order to simulate bonding behavior in composite structures especially skin-spar relation in the aircraft wing-box.

Mixed mode fracture toughness of epoxy molding compound/printed circuit board interface of semiconductor packages with respect to temperature and moisture

Interfacial delamination is a critical factor for dissimilar bi-material interfaces in terms of structural mechanical behavior and reliability. In this study, the mixed mode interfacial fracture toughness of a thin epoxy molding compound/printed circuit board bilayer with different mixities was measured via the asymmetric double cantilever beam test with a reinforced metal jig. Additionally, mode II fracture toughness properties were measured through the end notched flexure test. All tests were performed under various temperature and moisture absorption conditions below 100℃/85 %RH. Then, a finite element simulation was performed with the cohesive zone model technique to validate the experimentally measured fracture toughness values by comparing the load–displacement curves from the experiment and simulation. Additionally, the single leg beam test and its finite element simulation were conducted and compared for validation of the measured mixed mode fracture toughness values. It was demonstrated that the developed mixed mode fracture toughness measurement method could provide accurate fracture toughness, which could effectively predict the overall load–displacement curve and damage propagation behavior.

Design Concepts for Peel-Dominant Adhesive Joints in Aeronautic Applications

The adhesive bonding technique is employed from the aeronautical/aerospace industry to current house products. To comply with the requirements of distinct applications, different joint configurations are available to the designer. While single-lap joints (SLJ) are the most common in application and research, double-lap joints, scarf joints and T-joints find specific applications. T-joints are seldom studied in the literature, but these are used, for instance, in aircraft to bond the stiffener beams to the skin, or in the cars between the B-pillar and the rocker. Due to the high stress concentrations, T-joints often fail under average stresses much lower than the adhesive strengths, giving rise to the necessity for proper design and strength improvement methodologies. This work initially aims to validate the cohesive zone modelling (CZM) technique with experiments, and then use it to numerically evaluate and optimize the performance of T-joints subjected to peel loads. CZM is nowadays regarded as the most powerful strength prediction tool for adhesive joints, and can be a valuable tool to improve T-joints. Different features are addressed for a complete analysis: adhesive type, geometrical parameters, dual-adhesive technique for strength improvement, and composite joints. The evaluated geometrical parameters are the base adherend thickness (a), T-part thickness (t), overlap or bonding length (l) and curvature radius (r). As a result of this work, the model was successfully validated, and clear design guidelines were provided to define the ideal geometric and material (adhesive) conditions for best performance.

Static strength prediction of curved composite joints under internal pressure

ABSTRACT Nowadays, adhesive joints are largely applied in the automotive, aircraft and aerospace, civil, and naval industries. Although several applications involve flat (plane) adherends, curved joints play an important role in many engineering applications like civil and aircraft construction. This work aims to investigate three structural adhesives, ranging from brittle to ductile, applied in curved joggle-lap joints between carbon fibre reinforced polymer adherends and subjected to internal pressure, to validate a robust design procedure and provide project guidelines for this complex structural, geometrical, and loading system, which constitute the main novelty of the proposed work. A numerical cohesive zone model parametric analysis was undertaken by varying the overlap length, thickness of the adherends, and adherends’ curvature, including the evaluation of peel and shear stresses in the adhesive, failure mode comparison, maximum load, and energy dissipated after failure. Validation of the cohesive zone model technique was initially performed using flat single-lap joint under tensile loads. A significant effect of the overlap length and thickness of the adherends on the maximum load was found, while the adherends’ curvature effect on the maximum load was negligible. Ductile adhesives, although less strong, generally performed better in terms of maximum load and dissipated energy.

Cohesive zone modeling of I–II mixed mode fracture behaviors of hot mix asphalt based on the semi-circular bending test

Low temperature cracking is a major distress form of asphalt pavement. In this study, I–II mixed mode fracture test was conducted using cohesive zone modeling technique under −10 °C. Laboratory tests and virtual finite element modeling (FEM) tests were both conducted on semi-circular bending (SCB) specimens with the notch angle varying from 0 to 75° to yield the mixed fracture behaviors. Different loading rates, including 5 mm/min, 10 mm/min, 20 mm/min and 30 mm/min, were applied to investigate the influence of loading rate on the fracture resistance. Results indicated that the peak load increased with the increase of notch angle, which was caused by the increased alignment cracking area. Mode I critical stress intensity factor (KIC) decreased, while mode II critical stress intensity factor (KIIC) increased firstly and decreased subsequently from 1.25 MPa·m1/2 to 0.35 MPa·m1/2 with the increase of notch angle. Compared to KIC tested under the loading rate of 5 mm/min, KIC obtained at 30 mm/min increased by 12.6 %, 8.5 %, 8.4 %, 7.3 %, 7.4 % and 10.4 % for specimens with the notch angles of 0, 15°, 30°, 45°, 60° and 75°, respectively. For KIIC, the increments were 8.5 %, 8.4 %, 7.3 %, 7.4 % and 10.4 %, respectively. The mixity parameter, Me, was adopted to characterize the contribution of each fracture mode on the overall fracture behaviors. It was found that with the increase of notch angle, the mode II contribution on the overall fracture increased. However, the influence of loading rate on Me was very slight, indicating the loading rate could not play any impact on the respective contributions of mode I and II fracture on the overall fracture resistance. Moreover, a linear relationship was found between Me and the notch angle.

Cohesive zone parametric analysis in the tensile impact strength of tubular adhesive joints

The use of tubular adhesive joints has considerably grown, including applications in truss/vehicles frames and fluid transportation pipelines, but the impact performance of these joints is under addressed in the literature. It thus becomes pertinent to propose modelling techniques to predict and characterize tubular joints to withstand these loads, which involve a higher modelling complexity than the static loading case. This work evaluates, by cohesive zone modelling (CZM), the tensile impact strength of tubular joints between AW6082-T651 aluminium alloy adherends and bonded with different adhesives. Initially, CZM validation was accomplished with single-lap joint (SLJ) data. For the tubular joints, the influence of geometric parameters was evaluated by changing the overlap length ( LO) and outer tube thickness ( tSE). The analysis begins with an elastic stress analysis to the adhesive layer, followed by maximum load ( Pm) and dissipated energy at failure ( U) predictions using CZM, impact velocity effect and comparison with static analytical solutions. With this study, it was possible to evaluate the different geometrical parameters, select the optimal geometry and adhesive type, and to validate the CZM technique for the impact strength prediction of tubular adhesive joints.

Numerical evaluation of tensile-loaded tubular scarf adhesive joints

Tubular adhesive joints are widely employed when joining tubes and rods. The loads to which these joints are subjected may be axial or torsional. When loaded in the axial direction, cylindrical joints present stress concentrations in the adhesive layer, as is the case of lap joints. To improve the joint strength in the axial direction, the cross-section of the tubes can be chamfered to produce a scarf tubular joint. The geometrical variations produced by machining the chamfers increase the overall bonding area, leading to higher joint strength. This study aims to compare the tensile performance of tubular scarf joints (TSJ) with aluminium (AW6082-T651) adherends, considering the variation of the scarf angle (α) from 45° to 3.43°; the joints were bonded with a moderately ductile adhesive, the Araldite® 2015. Firstly, through the comparison of experimental tests and numerical analysis of tubular lap joints (TLJ), the cohesive zone model (CZM) technique and respective cohesive parameters were validated. A CZM analysis was then performed on the TSJ to analyse peel (σy) and shear stresses (τxy) in the adhesive layer. Damage and joint strength analyses were also carried out, as well as the study of the dissipated energy for the different joint configurations. The CZM technique was validated, and the numerical analysed showed a major α effect, with benefits for smaller α, and improved stress distributions over TLJ.

Adhesively-bonded T-joint cohesive zone analysis using dual-adhesives

At the present time, adhesive joints are widely used in the industry, replacing mechanical and welding joints in many applications. T-joints are used in many applications such as automotive, marine, and aerospace industries. Several methodologies have been proposed to reduce the stress concentration at bonding ends and to obtain a more uniform stress distribution along the bondline, such as optimization of the overlap length (LO) or the adhesives’ thickness, adding outer or inner chamfers, using adhesive fillets, and dual-adhesives. Aiming to improve the strength of T-joints, in this work the dual-adhesive technique is studied, consisting of using two adhesives, placing a more flexible adhesive at the overlap ends and a stiffer one in the central area. To test this method in T-joints, different adhesive ratios were applied. To evaluate this concept, a numerical study was carried out using the cohesive zone modelling (CZM) technique, in the ABAQUS® software, including a study of failure modes, stresses, strength or maximum load (Pm) and dissipated energy (U). With the present work, it was initially possible to validate the CZM technique with experimental results. The numerical work that followed showed that the strength of T-joints significantly depends on the combination of adhesives used and that it is possible to achieve increases in Pm and U in relation to single-adhesive joints (SAJ).

Mixed mode fracture analysis in a ductile adhesive using semi-circular bend (SCB) specimen

An improved semi-circular bend (SCB) specimen is introduced to obtain the mixed mode fracture envelope of a ductile adhesive with a considerable fracture process zone ahead of the crack tip. This specimen has been used for brittle adhesives fracture energy measurement. The proposed test procedure is very simple to implement and does not require any special loading fixture. The specimen is able to cover the whole mixed-mode ratios from pure mode I to pure mode II. Experiments are carried out on the manufactured specimens and the fracture loads are used in an inverse approach to obtain the fracture energy of the adhesive joints. The cohesive zone modelling (CZM) technique is employed as the data reduction method. Proper geometrical parameters for SCB joints are chosen through a wide-range of numerical simulations based on a linear elastic formulation. It is shown that the crack growth does not affect the mixed-mode ratio for the proposed adhesive joint. Another advantage of this specimen compared to the existing beam-based approaches (such as end-notched flexure (ENF), mixed-mode bend (MMB), etc.) is its lower risk of plastic deformation in the adherends. The mixed mode fracture envelope in the tested adhesive is obtained and the results of fracture energy under pure mode I loading are validated with the results of double cantilever beam (DCB) tests successfully.

A modified degradation technique for fatigue life assessment of adhesive materials subjected to cyclic shear loads

Understanding the fatigue response of adhesive joints under cyclic shear stress is important to avoid fatigue failure of the bonded structures. Recently, a cohesive zone modelling (CZM) technique was developed where the cohesive properties of the elements were degraded by a proposed empirical relation. However, based on this degradation approach, the fatigue life of the joints should be known before running the analysis. The aim of the current study is to improve the numerical method in which the fatigue life of the joints will be automatically estimated during the analysis. To achieve this, the concepts of fracture mechanics are considered by using the Paris’ law combined with the degradation model. A user material subroutine is developed to conduct the numerical calculations based on the concepts of CZM. End notched flexure (ENF) tests were carried out to evaluate the numerical data. Based on the results, it was found that the modified approach, in which the total fatigue life is obtained automatically, can be employed for fatigue life assessment of adhesive joints subjected to cyclic shear stresses.

Tensile fatigue life prediction of adhesively bonded structures based on CZM technique and a modified degradation approach

Due to their inherent advantages, the use of adhesive joints is widely increasing in advanced industrial sectors such as automotive and aircraft structures, where the lightweight components play a significant role in the efficiency of the products. These structural adhesively bonded connections mostly experience cyclic stress conditions during their service life. One of the most critical fatigue loading conditions for adhesive joints is the tensile cyclic loading. To design against tensile fatigue conditions recently a cohesive zone modelling (CZM) technique combined with a degradation approach was proposed in the literature. However, to apply this degradation method on cohesive elements, the total fatigue life of the joints should be known before the analysis. The aim of the current work is to improve this degradation approach to calculate the fatigue life automatically. To achieve this, a combination of Paris law and degradation model were considered in a numerical procedure. Using the Paris law and the experimental results obtained out of the fatigue crack propagation tests of DCB (double cantilever beam) specimens, the tensile fatigue life of each integration point (IP) during the analysis is estimated automatically. The model was validated and calibrated by experimental data.

Collapse analysis of a large plastic pipe using cohesive zone modelling technique

Polypropylene (PP) plastic pipes have recently gained widespread application in non-pressurized gravity pipes used for seawater intake lines in the petrochemical industry. These pipes consist of a solid wall base pipe, on which an outer reinforcement called the omega-profile is spirally winded and hot fusion bonded. The omega-profile is usually filled with grout to provide on-bottom stability for subsea installation. It is of high importance that the bond between the omega-profile and the base pipe has sufficient strength to provide resistance against buckling of the pipeline system. The objective of this study is to investigate the collapse behaviour of such large-diameter PP pipes subjected to a negative internal pressure. The bond is modelled with cohesive zone modelling technique with the aim to determine the failure mode that governs the collapse behaviour of the pipe, e.g. buckling or delamination. Experiments where conducted on single cantilever beam (SCB) specimens cut from the pipe to determine the cohesive bond strength between the omega-profile and base pipe. The findings from the experiments are implemented in a full pipe model, where the surface between the omega-profile and base pipe is assigned bond strength characteristics in accordance with the experimental results. The FEA results of the non-linear collapse analysis of the full pipe model show that for the range of grout stiffness values considered (0 ≤ Eg ≤ 30 GPa), the governing failure mode of the pipe is initiated by buckling and proceeded by delamination. For delamination to govern the failure mode, a grout stiffness greater than 36 GPa in combination with a weaker bond strength than the experimentally measured would be required. The methodology presented in this study gives a rather accurate tool for the design and analysis of this type of structures, and can reliably assess the bond strength level required in view of the governing failure modes, e.g. buckling and delamination.

Bonding dissimilar materials via adhesively bonded spot-welded joints: cohesive zone model technique

This study investigates the single-strap joints (adhesively bonded spot-welded) under static loading. Experimental tensile tests are carried out to validate the numerical analyses. For this purpose, the specimens of dissimilar materials were prepared by joining them with a thin layer of a two-component epoxy-based adhesive at one side and spot welding at the other side. Then, they were tested under tensile-loading conditions. The numerical analyses were performed according to the cohesive zone model (CZM) to estimate the failure loads of the joints. The failure loades of the joints with different dimensions were studied to evaluate the conditions causing the cohesive failure of either the adhesive layer or the weld nugget. It is shown that with minor changes in the bondline and weld designs, the joining process of the dissimilar materials will be more feasible.

Fatigue analysis of a post-buckled composite single-stringer specimen taking into account the local stress ratio

The fatigue life prediction of post-buckled composite structures represents still an unresolved issue due to the complexity of the phenomenon and the high costs of experimental testing. In this paper, a novel numerical approach, called “Min-Max Load Approach”, is used to analyze the behavior of a composite single-stringer specimen with an initial skin-stringer delamination subjected to post-buckling fatigue compressive load. The proposed approach, based on cohesive zone model technique, is able to evaluate the local stress ratio during the delamination growth, performing, in a single Finite Element analysis, the simulation of the structure at the maximum and minimum load of the fatigue cycle. The knowledge of the actual value of the local stress ratio is crucial to correctly calculate the crack growth rate. At first, the specimen is analyzed under quasi-static loading conditions, then the fatigue simulation is performed. The results of the numerical analysis are compared with the data of an experimental campaign previously conducted, showing the capabilities of the proposed approach.

Effect of Mesh Sensitivity and Cohesive Properties on Simulation of Typha Fiber/Epoxy Microbond Test

The microbond test for natural fibers is difficult to conduct experimentally due to several challenges including controlling the gap distance of the blade, the meniscus shape, and the large data spread. In this study, a finite element simulation was performed to investigate the effects of the bonding characteristics in the interface between the fiber and matrix on the Typha fiber/epoxy microbond test. Our aim was to obtain the accurate mesh and cohesive properties via simulation of the Typha fiber/epoxy microbond test using the cohesive zone model technique. The axisymmetric model was generated to model the microbond test specimen with a cohesive layer between the fiber and matrix. The cohesive parameter and mesh type were varied to determine the appropriate cohesive properties and mesh type. The fine mesh with 61,016 elements and cohesive properties including stiffness coefficients Knn = 2700 N/mm3, Ktt = 2700 N/mm3, and Kss = 2700 N/mm3; fracture energy of 15.15 N/mm; and damage initiation tnn = 270 N/mm2, ttt = 270 N/mm2, and tss = 270 N/mm2 were the most suitable. The cohesive zone model can describe the debonding process in the simulation of the Typha fiber/epoxy microbond test. Therefore, the results of the Typha fiber/epoxy microbond simulation can be used in the simulation of Typha fiber reinforced composites at the macro-scale.

Tool development for automating the structural integrity assessment of aircrafts’ components

During the aircraft’s maintenance, it is essential that its structural inspection as well as potential found damages to be assessed in an effective manner within a limited time frame. To reduce the required time, for the aforementioned procedure, an innovative tool is developed. For the first time, a structural integrity assessment tool integrates image processing algorithms and FE models. The tool processes data from Non Destructive Testing (NDT), via image processing algorithms, and then provide pieces of information regarding the residual strength of the examined component in an automated way. The data acquired, from the NDT, are interpreted using the threshold method, in order to generate an accurate map of the component with its damages (size and location). This information automatically feeds a parametric Finite Element (FE) model, which forms an FE model of the damaged component ready for analysis. The parametric FE model can construct models for isotropic and laminated monolithic components using the XFEM method and the Cohesive Zone Modelling (CZM) technique respectively. For the case of laminated components, Progressive Damage Modelling (PDM) is also considered. In this study, simple geometries as the upper and lower wing skin, are analysed under static tension or compression. Aim is to examine the effectiveness and feasibility of the developed tool. The main benefits obtained from the application of the tool is that the image processing data are manipulated automatically and fast providing all the information regarding the location and size of damage in the examined component. Moreover, from the obtained numerical results the strength reduction of the component can be predicted well, by just comparing them with the respective numerical results of the reference undamaged component. Overall, the developed tool is very promising, since time saving can be gained.