Bilinear Cohesive Zone Model Research Articles

Predicting interlaminar damage behaviour of fibre-metal laminates containing adhesive joints under bending loads

This study includes experimental and numerical investigations on fibre-metal laminate structures containing adhesive joints under static bending loads. Experimental tests were carried out on Glare® 4B specimens manufactured in-house and containing doubler joint features. Numerical analyses were performed using Abaqus software including damage in the glass fibre reinforced polymer layers, ductile damage in the resin pockets (FM94 epoxy) and plasticity in the metal layers. A new cohesive zone model coupling friction and interfacial shear under through-thickness compressive stress has been developed to simulate delamination initiation and growth at the metal/fibre interfaces with the adhesive joint under flexural loading. This model is implemented through a user-defined VUMAT subroutine in the Abaqus/Explicit software and includes two main approaches, firstly, combining friction and interfacial shear stresses created in the interlaminar layers of the fibre-metal laminate as a result of through-thickness stresses and secondly, considering elastic-plastic damage behaviour using a new cohesive zone model based on the trapezoidal law (which provides more accurate results for the simulation of toughened epoxy matrices than the commonly used bilinear cohesive zone model). Numerical results have been validated against experimental data from 4-point bending tests and a good correlation observed with respect to both crack initiation and evolution. Delamination and shear failure were noted to be the predominant failure modes under bending stresses as expected. This is due to the higher mode-II stresses introduced during bending which cause different damage evolution behaviour to that seen for axial stresses. Finite element results revealed that both friction and shear strength parameters generated from through-thickness compression stresses have a significant effect in predicting damage in fibre-metal laminate structures under this type of loading.

On the Pull-out Behavior of Hooked-End Shape Memory Alloys Fibers Embedded in Ultra-High Performance Concrete

This study presents a three-dimensional non-linear finite element investigation on the pull-out behavior of straight and hooked-end Shape Memory Alloys (SMA) and steel fibers embedded in Ultra-High Performance Concrete (UHPC) using a single fiber pull-out model. A bilinear cohesive zone model is used to characterize the interfacial traction separation relationships. The Concrete Damage Plasticity (CDP) model is used to simulate UHPC, and the mechanical behavior is obtained through experimental tests. Parametric studies are conducted to evaluate the effects of fiber materials, fiber diameters, and hook angles on the load-displacement behavior. A good agreement between the numerical and experimental results is obtained. It is found that the hooked-end fibers with a smaller diameter and a hook angle of 40° can be a better choice for structural application. Furthermore, it is observed that the use of SMA fibers significantly improves the pull-out performance between fibers and UHPC.

Simulation of Delamination Evolution of Slab Ballastless Track under Vertical Impact

During the running of a high-speed train, the wheel may bounce on the rail due to the track irregularity. The wheel bounce could generate a vertical impact, leading to the initiation and expansion of delamination between layers of the track structure. In this paper, the evolution of the interfacial damage and delamination subjected to the vertical impact is simulated using finite element analysis (FEA). In the FEA, a bilinear cohesive zone model (CZM) is adopted to simulate the interface between the track slab and the CA mortar layer. For different levels of impact energy, the contact force, vertical deformation, absorbed energy, area of interfacial damage, and area of delamination are calculated and compared. The effects of the tangential and normal stiffness of the interface on the distribution of interfacial damage and delamination are investigated. The results show that the contact force, vertical deformation, absorbed energy, area of interfacial damage, and area of delamination increase with the increase of the impact energy. The area of interfacial damage in the compression stage is closely related to the tangential stiffness, whereas the area of delamination depends on the normal stiffness. The normal stiffness that gives the largest area of delamination is recommended to be taken as the lower bound of the normal stiffness for both controlling the delamination and preventing an exceedance of the track irregularity limit.

The role of ply angle in interlaminar delamination properties of CFRP laminates

The paper describes the fracture toughness of biomimetic architected carbon fiber reinforced polymer (CFRP) laminates via experimental and numerical methods. High-fidelity Finite Element (FE) models in conjunction with modified Mises criteria have been developed to evaluate the effect of the interlaminar architectures on the fracture toughness of bio-inspired helicoidal composites. A bi-linear cohesive zone model (CZM) with Hashin damage criterion has been used here to simulate the interlaminar and intralaminar damage behaviors during quasi-static three-point bending (3 PB) tests of biomimetic architected CFRP laminates, and 3 PB test results extracted from open literature and obtained in this work have been used to validate the load-displacement response of the specimens predicted from the proposed FE model. Mode I and mode II interlaminar fracture toughness of these layered composites have also been identified as semi-analytical functions of the stacking angle of two adjacent layers, and the predictions show a good agreement with the corresponding experimental data. This work provides guidelines about the use of the bionic design CFRP composite in applications where toughness is critical.

Interlaminar mechanical properties of nano- and short-aramid fiber reinforced glass fiber-aluminum laminates: a comparative study

Delamination damages limit the application potential of Fiber metal laminates, hence improving the interlaminar mechanical properties has always been a research focus and challenge in this field. The toughening effect of two fillers, i.e., nano-aramid fibers (ANFs) and short-aramid fibers (ASFs), which are used at the interface of glass fiber-aluminum laminates, have been investigated. Chemical pretreatments of aluminum alloy surface were conducted to ensure the better adherence between the fiber composites and metal sheets. Results revealed that Mode-I and Mode-II fracture toughness of the laminates could be simultaneously improved when using the two fillers at the interface of glass fiber-aluminum laminates. Attributed to the better dispersion of ANFs in epoxy matrix, the toughening performance of ANFs is better than that of ASFs in this case. The mechanism of interlaminar toughening was revealed with electron microscopic observation of fracture morphology. Meanwhile, the finite element analysis based on bilinear cohesive zone model was adopted to predict the increased interlaminar tensile and shear strength.

The Mechanical Mechanism and Influencing Factors of Ice Adhesion Strength on Ice-Phobic Coating

Ice accretion can cause problems on polar ships, ocean platforms, and in other marine industries. It is important to understand the interface debonding behavior between ice and the surface of equipment. In this work, we created a mechanical model to analyze the interface debonding behavior between a square-based ice cuboid and an elastic coating base, using contact mechanics and fracture mechanics. Three-dimensional (3D) finite element (FE) simulation was used to simulate the interface debonding for normal and shear separation. A bilinear cohesive zone model (CZM) was used to simulate the interface between the ice cuboid and the elastic coating. We investigated the effect of the elastic modulus E of an elastic film on the critical detachment force Fc for normal and shear separation. The results showed that Fc increases with an increase of the elastic modulus of the elastic film. When E exceeds a certain level, Fc achieves a constant value and then remains stable. Finally, a series of epoxy/polydimethylsiloxane (PDMS) interpenetrating polymer-network (IPN) gel coatings with different elastic moduli were prepared. The ice tensile and shear adhesion strengths (σice and τice) of the coatings were measured. The results were roughly consistent with the results of the numerical simulation when E < 1 MPa.

Finite element modeling of mode I fatigue delamination growth in composites under large-scale fiber bridging

In this study, the Turon et al. and Kawashita-Hallett fatigue damage models are extended with a trilinear cohesive law to simulate mode I fatigue delamination in the composites undergoing large-scale fiber bridging. The trilinear cohesive zone model (CZM) is constructed by superposition of two bilinear CZMs. In order to implement the developed models, a user defined element (UEL) subroutine is prepared in the Abaqus software and finite element analyses are conducted based on the envelope loading technique to simulate the 3D double cantilever beam (DCB) specimens under high-cycle fatigue loading. The finite element models are assessed through the experimental data from the literature and also five available fatigue damage models based on the bilinear CZM. It is concluded that the trilinear CZMs has more accuracy than the bilinear ones in prediction of fatigue delamination with fiber bridging effects. A parametric study is performed on the two extended models and sensitivity of models to the fitting parameters and quasi-static CZM parameters are comprehensively investigated.

Effect of adhesive layer properties on the shear strength of single-lap structures of dissimilar materials based on the cohesive zone model

An analysis method for improving the shear strength for the single-lap joints of dissimilar materials based on the cohesive zone model (CZM) is presented in this paper. The shear-lag model is established for the single-lap joint, and the stress distribution of joints is derived on the basis of this model, which is verified by simulation. The bilinear CZM is constructed to simulate the fracture process of joints, and the influence of lap length and adhesive layer thickness on the stress distribution of adhesive layers is comprehensively analyzed through simulation. Therefore, the effects of different properties of adhesive layers on the bonded structure strength are discussed with experiments. Results show that the reasonable lap length and thickness in this work are, respectively, 20–22 and 0.4–0.6 mm. The research results will serve as a guide for the parameter design, fracture prediction, and performance optimization of bonded joints.

Push Plate Test of CRTS II Slab Ballastless Track: Theoretical Analysis, Experiments, and Numerical Simulation

Push plate test is a powerful tool to evaluate the interfacial bond performance of China railway track structure type‐II slab ballastless track structure (CRTS II SBTS). However, there is still a lack of theoretical explanation of the push plate test. In this paper, a linear proportional distribution method is proposed in terms of a series of analytical formulas to describe the interfacial force‐displacement variation of CRTS II SBTS in different damage stages of the horizontal push plate test. The force‐displacement relationship established by the linear proportional distribution method agrees well with that observed in full‐scale test. The horizontal push plate test is then simulated, in which a bilinear cohesive zone model (CZM) was adopted to simulate the interface within track structure. The parameters of the CZM are calculated based on the force‐displacement curves obtained from scale push plate test. Particularly, the normal cohesive parameters are determined based on the scale vertical push plate test instead of the traditional splitting tensile test. The simulation proves that both the maximum affected length in the undamage stage and the maximum damaged length in the damage stage depend rather on the interfacial stiffness and the material parameters of SBTS than the horizontal load. These two lengths given by the simulation are close to those defined by the proposed linear proportional distribution method. This indicates the reliability of the proposed method and the capability of scale push plate test in determining cohesive parameters.

Modelling Adhesive Using Non-Linear Truss Elements in Mode I Delamination Problems

A fast and simple finite element model is presented in this paper to simulate the crack propagation in notched beam structures with two layers and one interface medium in Mode I delamination. The truss elements from FEAP element library are endowed with a user material law describing the bilinear cohesive zone model (CZM) with the material unloading path defined by embedding a history variable in the response. The layer is modelled with linear elastic Timoshenko beam elements. The method is used for damage growth and damage propagation simulations in interfaces with both ductile and brittle materials. The method is robust for ductile interfaces, but for brittle interfaces more specific numerical techniques are required. The results are evaluated using available analytical and numerical solutions and a good agreement is achieved.

A self-contained element for modeling crack propagation in beams

The Cohesive Zone Model (CZM) has been used to model the propagation of cracks through beams and slabs, which is of practical application in a variety of fields. CZMs have been successfully incorporated into Finite Element (FE) models however, this involves significant pre-processing effort to develop a sufficiently fine mesh around cohesive elements, which also increases the required computational effort. To overcome this limitation, a self-contained’crack element,’ consisting of cohesive elements surrounded by pre-meshed bilinear bulk elements, was developed. A linear interpolation scheme to connect this crack element to adjoining beam elements, as well as a solution procedure using static condensation to solve crack propagation in beams was developed and implemented. Bilinear and non-linear CZMs were implemented to model the behavior of the cohesive elements. Under simple Mode I tension and flexure problems, the results were in-line with the expected behavior. It was found that the crack element was convergent with increasing mesh resolution, and needed to be only as long as its thickness, with the remainder of the beam being modeled by beam elements with just a handful of DOFs, reducing the size of the problem substantially. The element was also used to verify a theoretical model for the variation of modulus of rupture of a beam with its thickness, as well as a mixed-mode problem. In both those cases, the crack element showed good results.

Finite strain elasticity based cohesive zone model for mechanoluminescent composite interface: Part II. Interface damage characteristics

The need to estimate the micromechanical properties of elastico-mechanoluminescent (EML) composites was established in Part A of this paper. The particle–matrix interface was identified to be poorly understood towards building accurate EML models and to predict functional life estimates of the EML devices. Towards this, Part A of this paper defined the mechanical behavior of the interface as a softening spring through a bilinear cohesive zone model (CZM). Macroscale stress measurements were combined with material properties to estimate undamaged stiffness of the interface spring (). In Part B of this paper, the damage characteristics of the interface spring are estimated through an experimental approach to complete the CZM. This is achieved by first establishing the finite strain behavior of the macroscopic EML–PDMS composite from uniaxial tensile testing. Secondly, a controlled tear is induced in the composite and the microscale displacement fields around the tear tip are captured using digital image correlation technique. Tear tip displacements and finite strain behavior are combined to estimate cohesive stresses in the tear-tip region of the composite. The contribution of particle–matrix interfaces towards resisting propagation of the tear is isolated from experimental results to obtain interface-CZM damage parameters. The interface CZM parameters are subsequently utilized in an FEM model to simulate macroscopic composite behavior to find good correlation. The experimental framework established in this paper can be utilized to estimate interface parameters of any particulate-elastomer composites that exhibit finite strain behavior.

The role of microstructure in the impact induced temperature rise in hydroxyl terminated polybutadiene (HTPB)–cyclotetramethylene-tetranitramine (HMX) energetic materials using the cohesive finite element method

In this work, microstructure dependent impact-induced failure of hydroxyl-terminated polybutadiene (HTPB)–cyclo-tetra-methylene-tetra-nitramine (HMX) energetic material samples is studied using the cohesive finite element method (CFEM). The CFEM model incorporates experimentally measured viscoplastic constitutive behavior, experimentally measured interface level separation properties, and phenomenological temperature increase due to mechanical impact based on viscoplastic and frictional energy dissipation. Nanoscale dynamic impact experiments were used to obtain parameters for a strain-rate dependent power law viscoplastic constitutive model in the case of bulk HTPB and HMX as well as the HTPB–HMX interfaces. An in situ mechanical Raman spectroscopy (MRS) setup was used to obtain bilinear cohesive zone model parameters to simulate interface separation. During analyses, the impact-induced viscoplastic energy dissipation and the frictional contact dissipation at the failed HTPB–HMX interfaces is found to have a significant contribution toward local temperature rise. Microstructures having circular HMX particles show a higher local temperature rise as compared to those with diamond or irregularly shaped HMX particles with sharp edges indicating that the specific particle surface area has a higher role in temperature rise than particle shape and sharp edges. Regions within the analyzed microstructures near the HTPB–HMX interfaces with a high-volume fraction of HMX particles were found to have the maximum temperature increase.

Mechanical response of thin hard coatings under indentation considering rough surface and residual stress

The mechanical response of a system composed of a DLC coating on a steel substrate under indentation considering real conditions is investigated by using finite element method. The primary consideration is the mechanics of indentation induced coating cracking and interfacial delamination. A bilinear cohesive zone model with prescribed mechanical properties is applied to simulate evolutions of the crack and delamination. The effects of the rough surface and residual stress on the indentation results are evaluated. It is found that the surface roughness can reduce both the initial contact stiffness and maximum indentation load when the indenter is on an asperity peak. The compressive residual stress results in a greater indentation load level for a fixed penetration depth. Under the influence of rough surface and residual stress, the indentation elicited cracking and delamination occur in loading shear stress and unloading tensile stress modes, respectively. Moreover, the phenomenon of pop-in and pop-out on the load-displacement curve during the loading and unloading stages is individually monitored once the crack and delamination initiate. Additionally, the interface delamination is weakened by the coating cracking. Numerical results are also compared with previous studies, and can establish a reference for checking the results of actual indentation experiment.

Molecular Dynamics-Based Cohesive Zone Model for Mg/Mg17Al12 Interface

The fracture of the Mg/Mg17Al12 interface was investigated by molecular dynamics simulations. The interface crack extends in a brittle manner without noticeable plasticity. The distributions of normal stress and separation along the interface were examined to render a quantitative picture of the fracture process. A normal traction–separation curve was extracted from simulation and compared with three cohesive zone models, i.e., cubic polynomial cohesive zone model, exponential cohesive zone model, and bilinear cohesive zone model. The exponential cohesive zone model exhibits the best agreement with simulation results, followed by the bilinear cohesive zone model.

Study on the mechanical performance and interface damage of CRTS II slab track with debonding repairment

In this work, the effect of the carrying-out debonding repairment on the mechanical performance and interface damage of China Railway Track System (CRTS) II slab track was studied. The bilinear cohesive zone model (CZM) based on the stress-displacement relationships for describing the interface behaviors of the debonding repaired CRTS II slab track was obtained through the experimental tests. A finite element model (FEM) of the CRTS II slab track incorporating the debonding repairment between the track-slab and the mortar layer was established, which was applied in the simulations under the vertical temperature gradient load. The results show that the temperature deformation of the track-slab could be well restored and no structural damage occurred under the vertical temperature gradient load. The damage only initiates and develops at the edge of the interface between the track-slab and the mortar layer (T-M interface) under the vertical positive temperature gradient. However, the evolutions of the maximum damage variable and the damage area indicate that the influence of the interface damage emerging at the T-M interface is relatively limited.

In-situ strength effects in long fibre reinforced composites: A micro-mechanical analysis using the phase field approach of fracture

Transverse intralaminar cracks in layers with perpendicular orientation referred to the main loading direction have a significant effect on the apparent ultimate strength of the corresponding composite laminate. This effect stems from the fact that such transverse cracks generally promote the occurrence of other failure mechanisms leading to the specimen collapse in subsequent stages of the loading process. With the aim of conducting a careful investigation regarding the onset and progression of transverse intralaminar cracking events, a micro-mechanical analysis of cross-ply laminates is herein proposed. Particularly, the cross-ply laminates belonging to the family [0°2/90°n/0°2] are considered via the generation of high-fidelity micro-mechanical models, which reproduce the internal fiber arrangements related to the reference results in Saito et al. 2012, Experimental evaluation of the damage growth restraining in 90° layer of thin-ply CFRP cross ply laminates, Adv. Comp Mat, 21:1,57–66. Differing from alternative approaches, current predictions are equipped with the combined used of two fracture-based modeling methods: (i) the variational phase field (PF) approach for triggering crack events into the matrix, and (ii) the bilinear cohesive zone model (CZM) for the simulation of fibre-matrix decohesion failures. Relying on this computational methodology, the focus of this work is to analyze the influence of the transverse ply thickness (n) on the onset and propagation of damage under tensile conditions, in conjunction with the transition from micro-cracking to meso-scale damage states. For this purpose, several models are generated into the FE package ABAQUS using user-defined capabilities, replicating configurations of specimens included in previous experimental investigations, i.e. through the consideration of different transverse ply thickness (n = 1, 2, 4). Present results show the potential of the proposed methodology to predict the transverse matrix cracking phenomena and the ability and reliability for capturing the delay of the crack with thinner plies, a phenomenon which is usually denominated as in-situ effect in the related literature.

On the strength and interfacial properties of square wave joints with defects and mismatches

ABSTRACT In the present paper, the strength and interfacial properties of square-wave joints under tension are analyzed. By using the bilinear cohesive zone model, three main factors in practice, including geometric parameters, preexisting defects and mismatches, are considered. It is found that the strength and fracture toughness of the joints can be improved by proper adjustment of geometric parameters of the joint. What is more, the length of defect has a great influence on the mechanical properties of the adhesive joints, different from the defect’s location. Compacting adherends tightly during glue consolidation, making the bonding part as symmetrical as possible and introducing some protuberances on square-wave plug are found to be helpful to improve the joints’ mechanical behavior. The findings should be useful for the design of square-wave joints and the assessment of mechanical properties of adhesive joints in practical and potential applications.

Theoretical modelling of a vehicle-slab track coupled dynamics system considering longitudinal vibrations and interface interactions

Traction or braking operations are usually applied to the motor cars or locomotives for acceleration and deceleration, especially in perilous mountain high-speed railways that have complex and large gradient sections. Under such a circumstance, the wheel-rail longitudinal interactions may become more intense, which could induce longitudinal impact on the track structure. In this paper, some new concepts are introduced to account for this rarely concerned issue. Two typical interface interactions for a slab track system are fully considered, involving the longitudinal resistance between the rail and rail pad based on the Dahl friction model, and the longitudinal cohesive force between the prefabricated slab and CA (cement asphalt) mortar layer based on the bilinear cohesive zone model. By introducing system longitudinal vibrations and implementing the interface interactions into the classical vehicle-track system, a novel vehicle-slab track vertical-longitudinal coupled dynamics model is established, and investigated under the combined excitation of rail irregularities and polygonal wheel wear in traction conditions. Results indicate that the developed model is capable of capturing the longitudinal interactions between the track structures and enables considering initiation or evolution of the damage at the interface between the track slab and CA mortar subjected to complex train dynamic loads.

Investigation on Interface Damage between Cement Concrete Base Plate and Asphalt Concrete Waterproofing Layer under Temperature Load in Ballastless Track

The interfacial bond between cement concrete base plate (CCBP) and asphalt concrete waterproofing layer (ACWL) is a weak portion in the newly developed Chinese high-speed railway ballastless track. The interface damage caused due to fluctuating temperature load and dynamic train load is one of the most critical problems in Northern China. This paper aims to investigate the interface damage evolution process under temperature load via experimental and simulation analysis. Full-scale transverse shear tests were performed to explore the interface bond-slip mode of the adjacent ACWL and CCBP. Then, a finite element model of a ballastless track structure was built and a cohesive zone model (CZM) was utilized to model the interface damage initiation, crack propagation, and delamination process under uniform/gradient temperature load. Furthermore, the dynamic response of the ballastless track where CCBP and ACWL were partly/totally debonded was investigated and compared with the perfectly bonded structure. The results demonstrate that bilinear CZM is capable of revealing the interface damage initiation, crack propagation, and delamination process under temperature load. The interface state between the adjacent CCBP and ACWL was greatly affected by temperature changes and the interface bonding state had a great impact on the dynamic response of ballastless track.