Cohesive Zone Model Approach Research Articles

Characterization and Numerical Modelling of Through-Thickness Metallic-Pin-Reinforced Fibre/Thermoplastic Composites under Bending Loading

Through-Thickness Reinforcement (TTR) technologies are well suited to improving the mechanical properties in the out-of-plane direction of fibre-reinforced composites. However, besides the enhancement of delamination resistance and thus the prevention of overall catastrophic failure, the presence of additional reinforcement elements in the composite structure affects also the mechanical properties in in-plane direction. In this work, the flexural behaviour of a glass-polypropylene (GF/PP) hybrid yarn-based composite with TTR in form of metallic pins has been investigated experimentally and numerically. The insertion of the metallic pins is realized via thermoactivated pinning technology (TAP). In four-point-bending tests, it is shown that the flexural stiffness and strength decreases with an increase of the overall pin density. Hereby, it is observed that the pins act as crack initiators. For numerical modelling on specimen level, a continuum damage mechanic (CDM) model is used to predict the nonlinear deformation response of the composite, as well as fibre fracture and matrix cracking. A debonding and slipping phenomena of the pin in the composite is modelled by a cohesive zone modelling approach for the interface between pin and composite.

3D Finite‐Element Simulation of Wedge Splitting Test of Non‐Standard Ceramic Double Cantilever Beam with Chevron Notch

Small‐scaled non‐standard specimens with chevron notch (CN) from Zirconia ceramics are probed both numerically and experimentally by wedging. The original construction in the form of double cantilever beam (DCB) with CN is considered for the fracture toughness determination of ZrO2 specimens. The fracture toughness is determined in experiment on wedging of DCB with CN, with application of analytical formula derived by one of the authors and maximum force, bending the cantilever's arm. The 3D finite‐element simulations of wedge splitting test are performed using two approaches: cohesive zone modeling (CZM) approach and element elimination technique (EET). The specific fracture energy defined in experiments is taken as the input parameter for CZM simulations of crack propagation. The effect of parameters, namely, cohesive strength, and friction coefficient, between ceramic wedge and ceramic cantilever, is considered. Different traction–separation laws are implemented, and the resulting force–displacement curves are compared with experimentally obtained ones. In the CZM approach, considering the fracture energy and the predefined crack path, matching of experimental and numerical results is not achieved. In EET, in which the restrictions on the crack paths and the requirements for inputting the fracture energy are not imposed, a good match with the experimental results is achieved.

Effect of elevated temperatures and humidity on glass/steel adhesive joints

Glass/steel adhesive joints are being used increasingly in the construction industry as they offer significant structural advantages. While humidity and elevated temperatures are known to lead to the degradation of both the bulk adhesive materials and the bonded interfaces, quantification and prediction of the degradation effects are currently lacking. In this paper, the effects of elevated temperatures and humidity were determined and predicted by employing a combined experimental and numerical methodology. Bulk material and interface characterisation tests were performed to quantify the degradation of the bulk material properties and the glass/steel interfaces. Two numerical methodologies were devised and compared based on their ability to predict failure of glass/steel adhesive joints following environmental exposure, namely a continuum mechanics approach based on the bulk properties of the adhesive, and a cohesive zone modelling approach that assesses damage and failure based on the glass/steel interface properties. The results highlight the significantly different relative contributions of bulk property and interface degradation depending on the type of adhesive used.

Structural integrity analysis and damage assessment of a long composite wind turbine blade under extreme loading

The high demand of low cost wind energy needs to design large scale turbine blades with reduced weight which poses great challenges to their structural integrity while prone to extreme wind gusts. The loading can cause large-deflection bending and damage leading to significant drop in the load-bearing ability of long composite wind turbine (WT) blades. In this study, a comprehensive finite element (FE) modelling procedure is developed to simulate structural integrity and damage in composite blade using ANSYS software. The three-dimensional blade model is analyzed by carrying out geometrically nonlinear FE analysis to investigate the blade deformation and highly stressed regions leading to possible failure modes. The results show that the blade suction side is subjected to high compressive stress causing local skin buckling, which is further investigated using linear buckling analysis. Such local buckling drives interfacial debonding between skin and spar joined with a weak adhesive. Subsequently, the interfacial damage in the identified critical region is modelled by developing a damage submodel employing cohesive zone model (CZM) approach at the skin-spar interface. The analysis results indicate that buckling driven skin-spar debonding at adhesive interface is initial damage mode which can lead to progressive failure of the blade structure. Consequently, the ultimate load bearing capacity of WT blade is governed by a coupled buckling and debonding phenomenon even at load level below the ultimate design load. The simulation methodology adopted in this study can be employed to develop reliable and cost-effective computational tools for analyzing structural integrity and assessing damage in blade structure than expensive experimental testing.

Processing and out-of-plane properties of composites with embedded graphene paper for EMI shielding applications

This study focuses on the evaluation of the effects of incorporating a thin layer (‘paper’) of Graphene nanoplatelets (GnP) between the lamina on the processability and out-of-plane performance of glass fiber composites for EMI shielding applications. Various thicknesses of GnP paper (50, 120, and 240 µm) were embedded within layers of glass fabric for subsequent resin infusion. The out-of-plane failure surfaces were evaluated using a purpose-built fixture. In all experiments, the separation was observed within the graphene layers of the GnP paper rather than at composite/GnP interface. In comparison to pristine samples, decreases of 252%, 305%, and 386% respectively were recorded in the out-of-plane strength of embedded GnP papers. Numerical simulations were completed using a bilinear traction separation law based on the cohesive zone modeling approach. All composites were tested for electromagnetic interference (EMI) shielding properties. The EMI shielding was improved significantly by embedding GnP paper within glass fiber composites.

Interfacial fatigue damage behavior of fiber reinforced rubber—A combined experimental and cohesive zone model approach

AbstractThe interfacial damage behavior of short fiber reinforced rubber sealing composites (SRRC) under fatigue load is researched in this article, where an experimental and cohesive zone model approach are employed. The fiber mass fractions of samples are 2%, 5%, and 10%, respectively. The curves of the fatigue strain (ε n) varying with the fatigue cycle number (n) were obtained by the fatigue test. The damage patterns of SRRC with different fiber mass fractions were confirmed by scanning electron microscope. A finite element model (FEM) was established to predict interfacial fatigue damage, where the cohesive element was imbedded in the interface between fiber and matrix. The results show that the ε n‐n curves of SRRC predicted by FEM agree well with experimental data when fiber mass fractions are high. The samples with 5% fiber mass fraction are optimal to restrain the origination of the interfacial abhesion, and a possible damage path of SRRC is obtained.

Failure Analysis of Unidirectional Ceramic Matrix Composite Lamina and Cross-Ply Laminate under Fiber Direction Uniaxial Tensile Load: Cohesive Zone Modeling and Brittle Fracture Mechanics Approach

The current research work presents the computational micromechanical analysis of the room temperature tensile failure behavior of unidirectional (UD) and cross-ply (0/90) ceramic matrix composites (CMCs). For computational micromechanical analysis, three-dimensional (3D) representative volume element (RVE) and multi-fiber multilayer RVE (M2 RVE) models are generated that are representative of the lamina and the laminate under investigation. The RVE and M2 RVE models are generated by replicating the fiber distribution, and the placement of the fibers observed in a microscopic image of an actual CMC laminate. The generated RVE models consist of the discrete representation of individual constituent phases of the CMC such as fibers, interphase, matrix, and the fiber–interphase interface region. Under the applied external tensile load, the fiber–interphase interface interactions are modeled using the cohesive elements that follow the bilinear traction separation law. The matrix, fiber, and interphase materials failure behavior is captured using a brittle cracking model. In order to validate the proposed numerical methodology, the predicted average stress–strain curve at the UD laminate level is compared to the experimental stress–strain curve reported in the literature. In addition, the observed different phases in the predicted stress–strain curve are validated with the literature data. Using the proposed numerical methodology, a detailed local stress–strain and damage analysis leads to an observation that the so-called ductile stress–strain behavior (kink in the stress–strain curve) of a CMC UD laminate under uniaxial fiber direction tensile loads is mainly caused by the matrix damage initiation. Apart from the SiC material properties such as strength and fracture energy, it is also observed that the RVE size influences the average strength and failure strain predictions using computational micromechanics.

A cohesive zone model approach to interlaminar behaviour of carbon/epoxy laminated curved beams

This study analytically investigates the behaviour of carbon/epoxy laminated curved beams subjected to interlaminar tensile stress by means of a four-point-bending test, carried out in compliance with ASTM D6415 Standard. A Cohesive Zone Model (CZM) has been used to analyse the interlaminar tensile strength (ILTS) and the post-failure behaviour for lay-ups in several thicknesses, as well as the location of first and subsequent predicted delamination. In this study, the model behaviour is described by a bilinear constitutive model. Initially, a law of traction-separation governs the elastic behaviour, until satisfying a quadratic criterion that establishes the failure and degradation starting at the interface. Finally, a law describes the evolution of the damage and the interaction in mixed-mode conditions, which leads to the final failure of the interface and delamination onset. Two-dimensional finite element models (FEM) have been created to apply the CZM and analyse the influence of several cohesive model parameters, such as, cohesive element stiffness, cohesive element size and critical energy release rate. Predicted load–displacement curves have been compared with the experimental results obtained and strong correlation has been observed. The ILTS values predicted by the two-dimensional models show deviations no greater than 5.6% in comparison with the experimental results. These models and the influence of their parameters play an important role in the prediction of the interlaminar tensile strength and the post-failure behaviour of laminated curved beams.

Numerical analysis of mixed-mode fatigue crack growth of adhesive joints using CZM

With the increased use of adhesive joints in industrial environments, the need for improvement of this bonding technology arises. Namely, a reliable fatigue life estimation is essential to prevent catastrophic failure in adhesively bonded structural components. The cohesive zone model (CZM) approach has been used in numerical models to assess degradation by fatigue under pure mode conditions. However, in real life, components are subjected to multiaxial loads, the aim of this paper is to perform a numerical estimation of the fatigue behavior of an epoxy-based adhesive subjected to mixed mode loading conditions. To achieve this, the mixed mode was split into the corresponding components of mode I and mode II. For each mode, the adhesive’s cohesive properties were degraded by fatigue, according to a relation previously published for pure mode I and which has also been validated for pure mode II. Fatigue tests were performed on DCB specimens to calibrate the degradation model which, along with a triangular shaped CZM, was included in an Abaqus user material subroutine (UMAT) to perform a simulation of the fatigue behavior. Results showed that such approach can be applied to estimate the fatigue life of adhesive joints under mixed mode loading conditions.

Mode II and Mixed Mode Delamination Growth in Composite Materials Using Peridynamic Theory

This paper presents a method using Peridynamic Theory (PD) to model delamination failure in a unidirectional (UD) composite specimen under Mode II and mixed mode loading conditions. The original brittle damage model in PD is modified as a bilinear law in order to capture progressive softening. The proposed constitutive relations are implemented in bond-based PD formulation under plane stress conditions. The PD model of the End Notched Flexure (ENF) and Mixed Mode Bending (MMB) test specimens are generated using a MATLAB code. The PD model of the specimens are implemented in Finite Element Analysis (FEA) software ABAQUS. PD solutions of force displacement curves are obtained with explicit time integration scheme in ABAQUS. The PD solutions are verified using the analytical and FEA results from the literature and the analytical solutions of ENF and MMB problems using Corrected Beam Theory (CBT). In addition to PD solutions, FEA of the ENF and MMB problems are performed using Cohesive Zone Modelling (CZM) approach. It is observed that the PD results obtained with bilinear material law are in good agreement with both FEA, analytical results and the results from the literature.

Peel testing of a packaging material laminate studied by in-situ X-ray tomography and cohesive zone modeling

Peel testing is used to study adhesive fracture in packaging material laminates. The focus is on improved understanding of the mechanisms that provide a laminate's adhesive properties, as measured by standard macroscopic tests. Using a specially-designed peel test load rig, peel tests are performed in-situ in a laboratory X-ray tomograph. The peel test results are analyzed using a combination of theoretical models for the adhesive fracture and 3D finite element simulations based on a cohesive zone model approach. Complementary experiments are performed to characterize the properties of the peel arm material. Relaxation of the material is found to occur during image acquisition in the in-situ tests. Despite this, it is possible to obtain 3D reconstructions with good quality during peeling. Peel test properties like the peel arm's root rotation angle and peel arm thinning are quantified. In the present 90° peel tests, it is found that the delamination progresses in an inhomogeneous manner, with the edges delaminating before the center. A number of issues and mechanisms during the peel test are identified. As an example, the peel arm itself can sometimes split, leaving residues of adhesive on the substrate surface. Such phenomena indicate the ambiguities involved in assessing adhesion properties from standard macroscopic force-displacement measurements, without accounting for the mechanisms involved on finer length scales.

Numerical Simulation of Crack Propagation in Flexible Asphalt Pavements Based on Cohesive Zone Model Developed from Asphalt Mixtures.

To give engineers involved in planning and designing of asphalt pavements a more accurate prediction of crack initiation and propagation, theory-based models need to be developed to connect the loading conditions and fracture mechanisms present in laboratory tests and under traffic loading. The aim of this study is to develop a technical basis for the simulation of fracture behavior of asphalt pavements. The cohesive zone model (CZM) approach was applied in the commercial FE software ABAQUS to analyze crack propagation in asphalt layers. The CZM developed from the asphalt mixtures in this study can be used to simulate the fracture behavior of pavements and further optimize both the structure and the materials. The investigations demonstrated that the remaining service life of asphalt pavements under cyclic load after the initial onset of macro-cracks can be predicted. The developed CZM can, therefore, usefully supplement conventional design methods by improving the accuracy of the predicted stress states and by increasing the quality, efficiency, and safety of mechanical design methods by using this more realistic modeling approach.

Experimental and numerical characterization of Mode I fracture in unidirectional CFRP laminated composite using XIGA-CZM approach

This article presents an effective study for characterization of interlaminar Mode I fracture process zone (FPZ) in unidirectional CFRP laminated composite structure. Mode I fracture toughness testing has been carried out on double cantilever beam (DCB) specimens. Experimental studies have been carried out on non-precraked DCB specimens in order to obtain the amount of energy released during crack initiation from the natural crack front. The energy release rate (ERR) is obtained from experimental data as a function of crack growth (Δa) and pre-crack tip opening displacement (δ∗) by utilizing five data reduction schemes. The analytical function between ERR and δ∗ is used to construct fibre bridging law using J-integral approach. The obtained traction separation laws from each data reduction scheme is implemented into cohesive zone modelling (CZM) for numerical simulation. Fractured surfaces have been examined by means of Scanning electron microscope (SEM). Numerical studies have been carried out for both non-precracked and precracked specimens using combined framework of fracture mechanics using extended isogeometric analysis (XIGA) and damage mechanics using CZM approach. It has been observed that crack travels catastrophically in non-precracked (NPC) specimens due to fast dissipation of excess energy. Introduction of fibre bridging law, obtained from experimental investigation, into CZM in combined framework of XIGA methodology shows a good agreement with experimental results.

Simulations of fracture tests of uncharged and hydrogen-charged additively manufactured 304 stainless steel specimens using cohesive zone modeling

Fracture tests of uncharged and hydrogen-charged single edge bend specimens of additively manufactured 304 stainless steels are simulated using the cohesive zone modeling (CZM) approach. Two-dimensional plane strain finite element analyses without cohesive elements are conducted to identify the values of cohesive energy. Similar analyses using CZM with the trapezoidal traction-separation laws are then conducted. The best-fit cohesive parameters show the values of cohesive strength for the uncharged specimens are higher than those for the hydrogen-charged ones whereas the value of cohesive energy for the uncharged specimens can be either slightly lower or higher than that for the hydrogen-charged ones.

Numerical evaluation of crack stopping mechanisms in composite bonded joints due to corrugation and bolts

In this paper, the crack stopping mechanisms in corrugated composite bonded joints and hybrid bonded/bolted joints were evaluated numerically using the cohesive zone modeling approach. For the study, the DCB (double-cantilever beam) and the CLS (crack-lap shear) specimens were modelled. The first two specimens were subjected to static loads and the latter both to static and fatigue loads. The analysis was performed using the LS-DYNA explicit FE code. Fatigue crack growth simulation was performed using an in-house developed user-defined subroutine (UMAT). The numerical results reveal a crack stopping in the corrugated DCB, no crack stopping in the corrugated CLS and a reduction of crack growth rate in the bonded/bolted CLS for both static and fatigue loads. The methods and the findings of the present study can be used for the design of crack stopping features in adhesively bonded primary composite aircraft structures.

An evaluation of mode-decomposed energy release rates for arbitrarily shaped delamination fronts using cohesive elements

Computing mode-decomposed energy release rates in arbitrarily shaped delaminations involving large fracture process zones has not been previously investigated. The J-integral is a suitable method for calculating this, because its domain-independence can be employed to reduce the integration domain to a cohesive interface, and reduce it to a line integral. However, the existing formulations for the evaluation of the mode-decomposed J-integrals rely on the assumption of negligible fracture process zones. In this work, a method for the computation of the mode-decomposed J-integrals in three-dimensional problems involving large fracture process zones and using the cohesive zone model approach is presented. The formulation is applicable to curved fronts with non-planar crack faces. A growth driving direction criterion, which takes into account the loading state at each point, is used to render the integration paths and to decompose the J-integral into loading modes. This results in curved and non-planar integration paths crossing the cohesive zone. Furthermore, its implementation into the finite element framework is also addressed. The formulation is validated against virtual crack closure technique (VCCT) and linear elastic fracture mechanics (LEFM)-based analytical solutions and the significance and generality of the formulation are demonstrated with crack propagation in a three-dimensional composite structure.

STATIC FAILURE OF THE ADHESIVE AND COMBINATION JOINTS ON COLD-FORMED STEEL JOINT USING A COHESIVE ZONE MODEL APPROACH

A research of new connection method due to axially static loading on the cold-formed steel in civil engineering structures has been investigated. Joint failure was modeled with a cohesive zone model (CZM) approach where the governing parameters were determined from fracture mechanics test specimens. The incremental in capacity strength of cold-formed steel single lap joints (SLJs) was successfully predicted. Video microscope records carried out on the failure surface of the joints in experimental works. The modeling results have a good correlation with the experimental works. Strength capacity deviation of experimentation to FEM are 21.93%, 18.5%, 36.3%, 12.47% and 4.03% for srew, epoxy resi adhesive, polyester resin adhesive, combination screw with epoxy resin and combination screw with polyester resin connections.

Micro-mechanics based cohesive zone modeling of full scale ductile plate tearing: From initiation to steady-state

Ductile plate tearing, where the crack propagates multiple plate thicknesses, is targeted by the micro-mechanics based Gurson-Tvergaard-Needleman (GTN) model. The focus is on extracting detailed information on the fracture process that governs ductile crack initiation from a blunt pre-crack until the crack reaches steady-state propagation in order to enhance accuracy of the traditionally used cohesive zone traction-separation relations. The aim is to facilitate an accurate representation of the tearing process within the cohesive zone modeling framework as such simplistic models are largely exploited by engineers worldwide. Unfortunately, accuracy in the representation of crack propagation is often sacrificed for computation speed, but the present work allows correlating the cohesive zone modeling to a much more accurate, though computational expensive, micro-mechanics based (full 3D) model response. In the modeling of large-scale plate tearing, shell elements are typically employed to represent the engineering scale of the structure while the cohesive zone represents the micro-scale in terms of crack initiation and growth process. Thus, the cohesive zone essentially has to take over at the onset of the first localization (thinning far ahead of the crack tip). Calibration of the cohesive zone parameters has earlier been made in accordance with experimental observations such that the overall response of the system is well reproduced. But, the present work takes the calibration of the cohesive zone one step further and exploits details from a large-scale GTN model calculation. The goal is to match the response from the GTN model with the much less computation demanding cohesive zone modeling approach by incorporating knowledge of the loading history for individual cross-sections, in front of the pre-crack, through which the tearing crack propagates. The full 3D micro-mechanics based model set-up allows tracking of key parameters, such as peak traction and tearing energy, which goes into the cohesive traction-separation relation. The dependency on distance from the crack initiation site of the cohesive zone parameters is determined - from crack initiation to steady-state propagation - and followed up by a discussion on how to construct a traction-separation relation for ductile plate tearing.

Finite Element Simulation of Interlaminar and Intralaminar Damage in Laminated Composite Plates Subjected to Impact

Abstract Here In this study, the composite laminates subjected to transverse impact with consideration interlaminar and intralaminar damage based on Cohesive Zone Model (CZM) and Progressive Damage Model (PDM) are investigated by numerical analysis using ABAQUS commercial finite element code. The delamination in stacking ply with the same fiber orientation is considered as interlaminar damage and the delamination in an inner layer of any cluster is ignored. Hashin criterion is used for intralaminar damage initiation and evolution without using any subroutine. First, the appropriate procedure for delamination on composite specimen was suggested based on CZM approach in double cantilever beam to verify the intralaminar damage simulation. Then by considering several case studies with different impact energies, the results of present simulation is verified with the relevant and available experimental results and numerical references in the existing literature. According to the available experimental results the present simulation results are more acceptable and accurate than the results of similar numerical works, especially in higher impactor velocity.

A history-dependent cohesive zone model in elastic and visco-elastic materials under constant and variable loading

A history-dependent cohesive zone model approach is used to study the crack behaviour in elastic and visco-elasto materials. The cohesive (yield) stress at the cohesive zone points is related to the nonlinear normalised equivalent stress functional over the stress history at these points, and is expressed in the form of an Abel-type (fractional) integral. We analyse the cohesive zone length evolution in time and the crack tip opening during the stationary crack stage as well as during the propagating crack stage. We consider the external load increasing linearly with time and compare the solution with the case of the constant load. We obtain the solution numerically and analyse the influence of the viscoelasticity by comparing with the case of purely elastic behaviour of the bulk of the material.