Cohesive Zone Model Approach Research Articles

Numerical investigation of patch geometry effect on the fatigue life of aluminum panels containing cracks repaired with CFRP composite patch using XFEM and CZM approach

This study investigated numerically the effect of using composite patches with various geometric shapes to improve the fatigue life of aluminum panels of AA7075-T6 and AA2024-T3 containing cracks and compared with the available experimental results. The Cohesive Zone Model (CZM) and Extended Finite Element Method (XFEM) were applied to static and fatigue analyses. Four types of rectangular, trapezoidal, left-oriented and right-oriented triangular composite patches were used in the numerical analysis. With the combination of XFEM and CZM methods, and using the Paris equation, the fatigue crack propagation and fatigue life of aluminum panels containing cracks can be reasonably predicted. A composite patch with a suitable shape and geometry, fatigue life of the repaired panel can be improved considerably. With a 204% improvement in fatigue life in comparison to the unrepaired panel, the repaired sample made of aluminum alloy AA2024-T3 alloy achieved the most significant improvement in fatigue life. In AA7075-T6 alloy samples repaired with composite patches, the samples repaired with rectangular and trapezoidal patches experienced the highest fatigue life increases, respectively with 342 and 290% compared to the unrepaired samples. The comparison of numerical simulation results with the available experiment results shows a good agreement.

Enhancement of interfacial shear strength of shape memory alloy–polylactic acid composite and predictive modeling through cohesive zone modeling approach for 4D printing

Enhancement of interfacial shear strength of shape memory alloy–polylactic acid composite and predictive modeling through cohesive zone modeling approach for 4D printing

Bending of fusion-bonded thermoplastic single lap joints

The assembly of thermoplastic composites is one of the most important issues for their reliable use in the aerospace and automotive industries. Assembly through co-curing is a process that enables simultaneous bonding and curing of adherends and is a preferable option for these industries. This paper presents a study of fusion-bonded, co-cured single lap joints with thermoplastic adherends that were subjected to four-point bending. Processing of the joint created a 45° notch at one edge of the overlap. The effect of this notch on the strength of the joint was assessed in tension and compression by flipping the joint. Compared to samples without such notches, experiments indicated that the tensile stresses in the vicinity of the notch decreased the maximum load and applied displacements at failure initiation by about 30 % and 33 %, respectively. In order to better understand this behavior, the joints were also analyzed using finite element simulations. The initial failure was predicted using the Maximum Stress Theory. Both experimental and numerical results were consistent up to the initial failure. The analysis did not account for the subsequently observed interlaminar delamination in the adherends. This type of failure would most likely be approached using measured interlaminar traction-separation relations in a cohesive zone modelling approach.

Combined loading of unreinforced and Z-pin reinforced composite pi joints: An experimental and numerical study

Blind predictions of experimental responses of non-reinforced and z-pin reinforced composite pi joints were established using a progressive damage and failure model. The finite element model used a novel mixed-mode cohesive formulation to model intra-laminar and inter-laminar damage. A deliberate meshing strategy was used for cohesive interlayers to capture the interaction between intra- and inter-laminar damage modes. A smeared cohesive zone modeling approach was implemented to efficiently include the effects of z-pinning for the z-pin reinforced specimens. Using material properties obtained through experimental correlation of simpler joint configurations, blind predictions for large element specimens subjected to combined loading (axial compression and push-off loading) were established. To assess the predictive capabilities of the model, experimental and numerical comparisons were made in terms of load-displacement response, critical loads, and failure progression. Comparisons between the experimental results and predictions for the unreinforced joints were found to be in good agreement across the range of compressive loads tested. For the z-pin reinforced joints, initial responses were accurately predicted; however, ultimate loads and the toughening effect of the z-pin reinforcement was overpredicted.

Characterization and analysis of conduction welded thermoplastic composite joints considering the influence of manufacturing

Thermoplastic composite welding is a key technology that can help to make the aviation industry more sustainable, while at the same time enable high-volume production and cost-efficient manufacturing. In this work, characterization, testing and analysis of thermoplastic composite conduction welded joints is performed while accounting for the influence of the manufacturing process. Test specimens are designed from welds of a half a meter long welding tool that is developed to weld the stiffened structures of the next-generation thermoplastic composite fuselage. In the design, special attention is paid to the weldability of the laminates, while ensuring fracture occurs only at the welded interface. Two specimen configurations are evaluated for the Double Cantilever Beam and End-Notched Flexure characterization tests. Moreover, Single Lap-Shear specimens are tested in tension and in three-point-bending. Finally, the characterized material properties are introduced in finite element analyses to demonstrate that the cohesive zone modeling approach can be used to conservatively predict the strength of these welded joints. New insights are obtained in the relation between the manufacturing process, the quality of the weld and the mechanical properties of the joints, which are significantly different compared to autoclave consolidated composites.

Numerical Evaluation of Hydroformed Tubular Adhesive Joints under Tensile Loads

Adhesive joints are widespread in the aerospace, aeronautics, and automotive industries. When compared to conventional mechanical joints, adhesive joints involve a smaller number of components, reduce the final weight of the structure, enable joining dissimilar materials, and resist the applied loadings with a more uniform stress state distribution compared to conventional joining methods. Hydroformed tubular adhesive joints are a suitable solution to join tubes with identical cross-sections, i.e., tubes with the same dimensions, although this solution is seldom addressed in the literature regarding implementation feasibility. This work aims to numerically analyze, by cohesive zone modelling (CZM), hydroformed tubular adhesive joints between aluminum adherends subjected to tensile loads, considering the variation of material parameters (type of adhesive) and geometrical parameters. Initially, a validation of the proposed CZM approach is carried out against experimental data. Next, the aim is to numerically evaluate the tensile characteristics of the joints, measured by the maximum load (Pm) and energy of rupture (ER), considering the main geometrical parameters (outer tube diameter of the non-hydroformed adherend or dENHA, overlap length or LO, tube thickness or tAd, and joggle angle or q). CZM validation was successfully performed. The numerical study determined that the optimal geometry uses the adhesive Araldite® AV138, higher dENHA and LO highly benefit the joint behavior, tAd has a moderate effect, and q has negligible influence on the results.

Structural behaviour of adhesive bonds in 3D printed adherends

Additive manufacturing (AM) processes, also known as 3D printing, are experiencing growth and more industries are seeking solutions in these types of processes due to their advantages, including reducing the manufacturing time, sustainability, and the freedom to execute complex geometries. However, the dimensions of components are still quite small. Thus, it is necessary to find solutions for cases where assembly and joining of manufactured components are necessary. This work studies the tensile performance of adhesively bonded single-lap joints (SLJ) between AM adherends of polylactic acid (PLA), Polyethylene Terephthalate Glycol-modified (PETG), and Acrylonitrile Butadiene Styrene (ABS), bonded with the adhesives Araldite® 2015 and Sikaforce® 7752. The adherends’ mechanical elastic, plastic and fracture properties are determined prior to the assessment of the adhesive performance in SLJ. Failure modes, joint strength, assembly stiffness, and failure energy are obtained experimentally and compared to Cohesive Zone Model (CZM) predictions, aiming to provide the best material/adhesive combination that maximises the joint performance. In terms of strength and stiffness, PLA joints bonded with the Araldite® 2015 provided the best results, although the behaviour was different for the dissipated energy. The CZM approach showed to be a reliable design approach for bonded AM joints.

Experimental and numerical investigation on crack propagation in biomimetic nacreous composites with gradient structures

Combining interlocking structures and gradient design, this paper proposes a 2D biomimetic nacreous composite material with a gradient interlocked structure. Experimental and numerical simulation methods are employed to investigate the initiation and propagation behavior of cracks in the regular interlocking and gradient interlocked biomimetic nacreous composite materials. Samples of biomimetic nacreous composite materials with pre-existing cracks are manufactured using 3D printing technology, and uniaxial tensile tests are conducted to explore their crack propagation behavior. For biomimetic nacreous composite materials with periodic interlocking structures, the interlocking angle is found to play an important role in the toughening mechanism of composites. In biomimetic composite materials with large interlocking angles, crack inhibition effects are achieved through structural gradient design, effectively preventing catastrophic failure. Within the numerical analysis framework, a cohesive zone modeling approach is employed to represent the softer phase of the material, and the numerical simulation are validated by direct comparison with experimental results. In addition, a comprehensive numerical analysis is carried out to comprehend how the structural gradient affects the spread of cracks in these nacreous composites. This research not only illuminate the underlying deformation and toughening mechanisms intrinsic to interlocking nacreous composites but also pave the way for innovative strategies in the design of biomimetic materials through the incorporation of structural gradients.

Progressive failure analysis of z-pin reinforced composite pi joints

A finite element model of a z-pin reinforced composite pi joint has been developed and correlated against experimental results. A smeared cohesive zone modeling approach was implemented to represent the effect of z-pinning in an efficient and scalable manner. In the smeared approach, cohesive properties governing the traction–separation response of the z-pin reinforced areas were defined to account for the effective fracture toughness caused by z-pinning in an averaged sense. The crack band method was used to account for diffuse damage and failure in the weave of the pi preform. The damage in the preform developed due to delamination suppression caused by the z-pinning. The numerical model was calibrated using experimental data from pristine and defective z-pinned pi joints subjected to pull-off and side-bend loading. Comparisons of experimental and numerical results show good agreement in terms of structural response, critical loads, and failure modes.

A model for the response of unreinforced and z-pin reinforced composite pi joints

Experimental data obtained from Narrow Element and Wide Element pi joints was used to motivate the development of a mechanics-based model to predict the quasi-static response of non-reinforced and z-pin reinforced composite pi joints. The progressive failure modeling approach used a novel cohesive formulation to include intra- and inter-laminar damage modes and their interactions. A smeared cohesive zone modeling approach was implemented in which effective fracture toughness and cohesive strength values were defined in the areas corresponding to the z-pin fields in the reinforced joints. Properties defining the cohesive responses were calibrated at the narrow element level and subsequently used in the wide element model to establish blind predictions prior to experimental testing. Unreinforced (unpinned) and z-pin reinforced pi joint specimens were tested in pull-off loading. Experimental and numerical comparisons were made in terms of load–displacement response, critical loads, damage modes, and failure progression. Comparisons between the experimental results and blind predictions for the unpinned joints were found to be in good agreement; however, discrepancies for the z-pin reinforced joint emphasize the challenges associated with physics-based simplified modeling techniques intended to capture complex z-pin behavior.

Cohesive Properties of Bimaterial Interfaces in Semiconductors: Experimental Study and Numerical Simulation Using an Inverse Cohesive Contact Approach.

Examining crack propagation at the interface of bimaterial components under various conditions is essential for improving the reliability of semiconductor designs. However, the fracture behavior of bimaterial interfaces has been relatively underexplored in the literature, particularly in terms of numerical predictions. Numerical simulations offer vital insights into the evolution of interfacial damage and stress distribution in wafers, showcasing their dependence on material properties. The lack of knowledge about specific interfaces poses a significant obstacle to the development of new products and necessitates active remediation for further progress. The objective of this paper is twofold: firstly, to experimentally investigate the behavior of bimaterial interfaces commonly found in semiconductors under quasi-static loading conditions, and secondly, to determine their respective interfacial cohesive properties using an inverse cohesive zone modeling approach. For this purpose, double cantilever beam specimens were manufactured that allow Mode I static fracture analysis of the interfaces. A compliance-based method was used to obtain the crack size during the tests and the Mode I energy release rate (GIc). Experimental results were utilized to simulate the behavior of different interfaces under specific test conditions in Abaqus. The simulation aimed to extract the interfacial cohesive contact properties of the studied bimaterial interfaces. These properties enable designers to predict the strength of the interfaces, particularly under Mode I loading conditions. To this extent, the cohesive zone modeling (CZM) assisted in defining the behavior of the damage propagation through the bimaterial interfaces. As a result, for the silicon-epoxy molding compound (EMC) interface, the results for maximum strength and GIc are, respectively, 26 MPa and 0.05 N/mm. The second interface tested consisted of polyimide and silicon oxide between the silicon and EMC layers, and the results obtained are 21.5 MPa for the maximum tensile strength and 0.02 N/mm for GIc. This study's findings aid in predicting and mitigating failure modes in the studied chip packaging. The insights offer directions for future research, focusing on enhancing material properties and exploring the impact of manufacturing parameters and temperature conditions on delamination in multilayer semiconductors.

Cohesive zone evaluation of different design solutions for adhesive joints in canoeing boats

The canoeing boat industry is focused on providing the best possible characteristics to the users. Currently, the fabrication of canoeing boats is based on composite materials, which find advantage in joining by adhesive bonding. The present work numerically studies, by cohesive zone modelling (CZM), an adhesive joint applied in a canoeing boat, namely the hull/deck joint. The numerical workplan includes the currently used joint configuration and adhesive in the analysis, while different joint configurations and adhesives were also tested. Initially, the CZM approach was validated with experimental results taken from the literature. As a result, CZM was positively validated, followed by numerical assessment of the best geometry-adhesive combination, which significantly improved on the current used joint.

Cohesive Zone Modeling of the Interface Fracture in Full-Thermoplastic Hybrid Composites for Lightweight Application.

With the increasing demand for lightweight and high-performance materials in the automotive and aerospace industries, full-thermoplastic hybrid composites have emerged as a pivotal solution, offering enhanced mechanical properties and design flexibility. This work aims to numerically model the fracture strength in full-thermoplastic hybrid composites made by forming and overmolding organosheets. The mode I fracture was investigated by modeling the behavior of T-joint specimens under a tensile test following the cohesive zone modeling (CZM) approach. The sample was designed to replicate the connection between the laminate and the overmolded part. Double cantilever beam (DCB) specimens were manufactured with organosheets and tested to mode I opening to determine the interlaminar fracture toughness. The fracture toughness out of the mode I test with DCB specimens was used to define the CZM parameters that describe the traction-separation law. Later, due to the particular geometry of the T-join specimens that under tensile load work close to pure mode I, the cohesive parameters were determined by inverse analysis, i.e., calibrating the theoretical models to match experimental results. The fracture resistance T-joint specimens appeared dependent on the fiber-bridging phenomenon during the delamination. In particular, the presence of fiber-bridging visible from the experimental results has been replicated by virtual analyses, and it is observed that it leads to a higher energy value before the interface's complete breakage. Moreover, a correspondence between the mode I fracture toughness of the DCB specimen and T-joint specimens was observed.

Mode I and Mode II fracture behavior in pultruded glass fiber-polymer – Experimental and numerical investigation

Many recent works have shown that the capacity of pultruded glass fiber-polymer structural members is governed by interlaminar failure. However, there is still a lack of information regarding the fracture properties associated and the best techniques to be adopted. This paper aims to propose a testing methodology and to evaluate the interlaminar fracture of pultruded glass fiber-polymer specimens extracted from a composite bridge deck system. Both Modes I and II were investigated, through Double Cantilever Beam (DCB) and End-Loaded-Split (ELS) tests, respectively. The starter crack (or initial separation) was introduced via a water jet machine and the crack length was measured with the video extensometer technique. In all, nine different methods were applied to obtain the fracture toughness properties. The results are discussed and compared with 2D non-linear finite element models, where the cohesive zone model (CZM) approach was used. The Modified Beam Theory method (MBTASTM) presented the best results for crack propagation in Mode I, whereas differences lower than 1% from experiments were obtained when using the Corrected beam theory using effective crack length (CBTE) and the Experimental compliance method (EMC) methods for Mode II.

Predicting Interfacial Failure in Laminate Composite by using the Finite Element Method (FEM) : A Cohesive Zone Modeling Approach for Delamination

This study explores the interfacial failure modes of laminate composite, focusing ondelamination and debonding. To simulate these failures, a cohesive zone model (CZM) is employed, witha key component being the traction-separation law that characterizes softening near the delamination tip.The study demonstrates the modeling of debonding using the COMSOL® 5.6 software based on theFinite Element Method (FEM) decohesion model. The CZM's effectiveness in predicting mixed-modesoftening and delamination propagation is showcased through a model of mixed-mode bending in acomposite beam. By subjecting the beam to various loading conditions, the CZM accurately predictssoftening behavior and delamination progression. This research highlights the CZM's value inunderstanding and predicting interfacial failure, enabling improved design and structural integrity oflaminate structures.

Solving Some Problems of Crack Mechanics for a Normal Edge Crack in Orthotropic Solid Within the Cohesive Zone Model Approach

Solving Some Problems of Crack Mechanics for a Normal Edge Crack in Orthotropic Solid Within the Cohesive Zone Model Approach

Assessment of failure mechanism of double-strap 3D-FML adhesively bonded joints under tensile and compressive loadings using cohesive zone modelling approach

Despite the widespread applications of Fiber Metal Laminates (FMLs), there is a clear lack of information regarding the performance of bonded joints mating 2D-FMLs and the recently-developed 3D-FMLs, particularly when considering their performances under compressive loading. Therefore, as a follow-up to the authors’ recent investigations, an extensive series of numerical analyses are conducted in the present study to simulate the tensile and compressive (i.e., buckling, and post-buckling) responses of double-strap adhesively bonded joints mating 3D-FMLs. The 3D-FMLs are joined using carbon fiber-reinforced plastic (CFRP) straps and structural epoxy resin. The damage initiation and evolution in the bonded regions are modelled by seven different FE models, which incorporated the mixed-mode trapezoidal Cohesive Zone Modelling (CZM) approach in conjunction with continuum elements. Firstly, the effects of different numbers of CZM layers and thicknesses on simulating the damage mechanism are investigated. Subsequently, the influence of CFRP straps’ thickness and length on the performance of the adhesive joints is parametrically studied. The distributions of peel and shear stresses along the length of the bonded regions are also systematically explored. Based on the results, the optimal joint configuration is established, and the most effective modelling framework is highlighted by comparing numerically predicted results against experimental results.

A mixed-mode fatigue crack growth model for co-consolidated thermoplastic joints

In this work, a mixed-mode fatigue crack growth model for simulating interfacial fracture of co-consolidated thermoplastic joints was developed. The model is based on the cohesive zone modeling approach and was specifically designed to account for any I + II mode-mixity, requiring only pure mode I and II loading data as input. The fatigue crack growth rate is constantly updated using a function of the energy release rates and the computed mode-mixity ratio. A linear mode-mixity law is applied. Both force-controlled and displacement-controlled loads can be modeled in specimens ranging from coupon-scale sizes to larger structural elements. Implementation of the model was done for the low-melt polyaryletherketone (LM-PAEK) material by developing a user-defined subroutine in the LS-Dyna FE software. To feed the model, mode I and mode II fatigue tests were conducted using double-cantilever beam and end-notch flexure specimens, respectively, while to validate the model mixed-mode single lap shear (SLS) tests were conducted. The model reproduces accurately the mode I and II fatigue crack growth while it predicts also accurately the mixed-mode fatigue crack growth of the SLS specimens.

A novel cohesive zone modelling approach to represent mixed mode loading and bond line thickness effects

ABSTRACT Accurate representation of the traction–separation response for mixed mode loading in a cohesive zone model (CZM) is critical to predicting the response of adhesive joints in a number of applications, including transportation and vehicle crashworthiness. Traditionally, the Mode I and Mode II responses are treated independently, with mixed mode response determined by relationships between the degree of mode mixity and separation, potentially leading to overprediction of the plateau traction and underprediction of the plateau length in mixed mode loading. This poor fit is due to the indirect relationship between mixity and traction and having minimal fitting options for separation-to-plateau and softening. To address this limitation, a mixed mode CZM approach is proposed, based on measured mixed-mode traction–separation results for a toughened epoxy adhesive. The effects of bond-line thickness were considered, to examine the ability of the proposed approach to include additional effects (beyond mode mixity) that are known to affect the traction–separation response. The CZM implementation was assessed using the original test data and was shown to capture the measured experimental traction–separation response across a range of mixed mode loading and bond line thickness more accurately compared to traditional CZM treatments.

On the evaluation of strain energy release rate of cement-bone bonded joints under mode II loading

Bone cements based on poly(methylmethacrylate) (PMMA) are primarily used in joint replacement surgeries. In the fixation of joint replacement, the self-curing cement fills constitutes a very important interface. To understand and improve the interaction between cortical bone and bone cement it is essential to characterize the mechanical properties of cement-bone bonded joints in full detail. In this study, the end-notched flexure test was used in the context of pure mode II fracture characterisation of cement-bone bonded joints. A data reduction scheme based on crack equivalent concept was employed to overcome the difficulties inherent to crack length monitoring during damage propagation. A finite element method combined with a cohesive zone model was first used to validate numerically the adopted method. The procedure was subsequently applied to experimental results to determine the fracture toughness of cement-bone bonded joints under pure mode II loading. The consistency of the obtained results leads to the conclusion that the adopted procedure is adequate to carry out fracture characterisation of these joints under pure mode II loading. The innovative aspect of the present work lies in the application of cohesive zone modelling approach to PMMA-based cement-bone bonded joints.