Cohesive Zone Model Parameters Research Articles

Analysis of automotive mixed‐adhesive joints weakened by moist conditions: Experimental characterization and numerical simulation using cohesive zone model

AbstractThis paper is mostly concerned with an experimental and numerical study to clarify the behaviour and failure in the mono‐adhesive joints and mixed‐adhesive joints under different environmental conditions (dry [E0], 75.3% relative humidity [E1], 84.2% relative humidity [E2], and submerged in tap water [E3] at 25°C) and different strain rates (1 and 100 mm/min). Experimental investigations are compared with the numerical analysis, which is carried out by bilinear cohesive zone model (CZM). Through this work, degradations of cohesive parameters are calculated by using open‐faced double cantilever beam (DCB) and end notch flexure (ENF) specimens. The experimental data show that the cohesive parameters of Araldite 2015 have negative correlation to moisture content. Although Araldite AV138 parameters experience a decrease in mode I, in mode II, its cohesive parameter increases. First, it is found that the decrease in experimental failure load of mixed‐adhesive joints with regard to the dry condition is recorded as 32.6%, 54%, and 59.1% for E1, E2, and E3 conditions, respectively. Following this further, single lap joint (SLJ) that has non‐uniform moisture content distribution is modelled by engaging specific CZM parameters related to the specific moisture content. The results show a good agreement between experimental and numerical data.

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

In this work we develop a complete analytical solution for a double cantilever beam (DCB) where the arms are modelled as Timoshenko beams, and a bi-linear cohesive-zone model (CZM) is embedded at the interface. The solution is given for two types of DCB; one with prescribed rotations (with steady-state crack propagation) and one with prescribed displacement (where the crack propagation is not steady state). Because the CZM is bi-linear, the analytical solutions are given separately in three phases, namely (i) linear-elastic behaviour before crack propagation, (ii) damage growth before crack propagation and (iii) crack propagation. These solutions are then used to derive the solutions for the case when the interface is linear-elastic with brittle failure (i.e. no damage growth before crack propagation) and the case with infinitely stiff interface with brittle failure (corresponding to linear-elastic fracture mechanics (LEFM) solutions). If the DCB arms are shear-deformable, our solution correctly captures the fact that they will rotate at the crack tip and in front of it even if the interface is infinitely stiff. Expressions defining the distribution of contact tractions at the interface, as well as shear forces, bending moments and cross-sectional rotations of the arms, at and in front of the crack tip, are derived for a linear-elastic interface with brittle failure and in the LEFM limit. For a DCB with prescribed displacement in the LEFM limit we also derive a closed-form expression for the critical energy release rate, G_c. This formula, compared to the so-called ‘standard beam theory’ formula based on the assumptions that the DCB arms are clamped at the crack tip (and also used in standards for determining fracture toughness in mode-I delamination), has an additional term which takes into account the rotation at the crack tip. Additionally, we provide all the mentioned analytical solutions for the case when the shear stiffness of the arms is infinitely high, which corresponds to Euler–Bernoulli beam theory. In the numerical examples we compare results for Euler–Beronulli and Timoshenko beam theory and analyse the influence of the CZM parameters.

A cohesive zone model for the characterization of adhesion between cement paste and aggregates

The influence of an Interfacial Transition Zone on mechanical behavior of concrete has been established by many authors. Several experimental studies have highlighted the weak mechanical properties of Interfacial Transition Zone due mainly to higher porosity than other phases, or to the presence of initial damage at the interface between paste and aggregates. Thus, it is necessary to take this zone into account when modelling the mechanical behavior of concrete, particularly outside of the elastic domain. Various analytical or numerical methods have been proposed, and some of these replace the physical representation of an Interfacial Transition Zone, by an imperfect interface between paste and aggregates, and an adhesion model with specific mechanical properties. In this work a cohesive zone model coupling adhesion, friction and unilateral contact is applied to a finite element model of a cement paste-aggregate composite, designed to test interface mechanical properties. Cohesive zone model parameters are calibrated using an experimental study of the same composite, submitted to mechanical loading during hydration and leaching of cement paste. This numerical approach allows modelling of the mechanical behavior of a composite until the tensile strength is reached. Moreover evolution of cohesive zone model parameters during hydration and leaching, shows a partial adhesion on contact surfaces between cement paste and aggregate. This could explain initial interface damage.

Graphene Reinforced Epoxy Adhesive For Fracture Resistance

The fracture resistance of construction adhesive has attracted tremendous interests in the past decades. This paper conducts an experimental study on the mode I fracture resistance of epoxy construction adhesive reinforced with graphene nanoplatelets (GNPs) through double cantilever beam (DCB) specimens. The experimental results show that the mode I fracture toughness of nanocomposites increases compared with the neat epoxy. It is worth noting that the mode I fracture toughness of nanocomposites at a graphene content of only 0.25 wt% exhibits a 5 times enhancement compared with neat epoxy adhesive. When the graphene content continues to increase, the mode I fracture toughness of adhesive decreases as the aggregation of graphene in adhesive. The mechanical behavior of the DCB specimens with different nanocomposites adhesive are predicted using finite elements analysis (FEA). The mode I fracture properties of nanocomposites obtained from the experimental results are used as cohesive zone model parameters in FEA. The prediction agrees very well with the experimental results.

Experimental characterization of cohesive zone models for thin adhesive layers loaded in mode I, mode II, and mixed-mode I/II by the use of a direct method

The demand for designing lightweight structures without any loss of strength or stiffness has conducted many engineers and researchers to seek for alternative joining methods. In this context, adhesive bonding may appear as an attractive joining method. However the interest of adhesive bonding remains while the structural integrity of the joint is ensured. According to recent literature the cohesive zone model (CZM) appears as a suitable approach able to predict both static and fatigue strength of adhesively bonded joints. This approach of the fracture process of adhesive layers is based on the modeling of the adhesive mechanical behavior through a set of adhesive cohesive properties in either mode I, mode II or mixed-mode I/II. The strength prediction of adhesively bonded joints is then highly dependent on the CZM parameters. The methods used to experimentally characterize them are thus essential. A new methodology, termed direct method, is presented and tested. It is based on the measurement of displacement field of bonded adherends at the crack tip of classical specimens allowing for the loading of the adhesive layer in pure mode I, pure mode II and mixed-mode I/II. The tested adhesive is a methacrylate–based two-component adhesive paste found under the reference SAF30 MIB manufactured by AEC Polymers (ARKEMA group). The adherends are in aluminium 6060. It is shown that it is possible to characterize the cohesive properties of the adhesive layer using the direct method. The numerical tests involve both adherends and adhesive nonlinearities. Nevertheless, the presented experimental implementation passes by the development of a dedicated data pre-processing to interpret the experimental measurements, highlighting the significance of the choice of the measurement means linked to the design of specimen.

Cohesive zone modeling of the autoclave pressure effect on the delamination behavior of composite laminates

Current manufacturing processes using resin transfer molding or low-pressure prepreg curing may result in different defects and interfacial properties. The effect of autoclave pressure on the delamination behavior of T800/X850 composite laminates is explored. Cohesive zone model was used to model the delamination of unidirectional composite laminates under short-beam bending. Composites with various interlaminar properties were manufactured using autoclave under cure pressure from 0 MPa to 0.6 MPa. Cohesive zone model was validated using the material parameters of the composite cured under 0.6 MPa. The effect of cohesive zone model parameters including cohesive strength, mode I fracture toughness ([Formula: see text]), and mode II fracture toughness ([Formula: see text]) on the delamination behavior and load–displacement response was investigated. Parametric study shows that interlaminar cohesive strength and mode II fracture toughness dominated the initiation of yield and post-yield region, respectively. The correlation between autoclave pressure and mode II fracture toughness was predicted, which is mainly affected by void content.

Graphene nanoplatelets/epoxy composites with excellent shear properties for construction adhesives

Abstract The properties and bonding capabilities of construction adhesives have attracted tremendous interests in the past decades. This paper conducts an experimental study on the shear properties of epoxy construction adhesive reinforced with graphene nanoplatelets (GNPs) through thick adherend shear test (TAST). The experimental results show that the shear strength of nanocomposites increases with the increased graphene content. It is worth noting that the shear strength of nanocomposites at a graphene content of only 0.75 wt% exhibit a 102% enhancement compared with neat epoxy adhesive. Other shear properties, including shear modulus, shear strain at failure and toughness also deliver much better performances compared with neat epoxy, indicating the effectiveness of graphene on shear properties improvement. The mechanical behavior of the TAST specimens with different nanocomposites adhesive are predicted using 3D finite elements analysis (FEA). The shear properties of nanocomposites obtained from the experimental results are used as cohesive zone model parameters in FEA. The prediction agree very well with the experimental results.

Linear and nonlinear analyses of femoral fractures: Computational/experimental study

This paper describes two new methods for computational fracture analysis of human femur using Quantitative Computed Tomography (QCT) voxel-based finite element (FE) simulation. The paper also reports comprehensive mechanical testing for validation of the methods and evaluation of the required material properties. The analyses and tests were carried out on 15 human femurs under 11 different stance-type loading orientations. Several classical forms of subcapital, transcervical, basicervical, and intertrochanteric fractures plus a specific type of subtrochanteric fracture were created and analyzed. A new procedure was developed for prediction of the strengths and the fracture initiation patterns using a FE-based linear scheme. The predicted and observed fracture patterns were in correspondence, and the FE predictions of the fracture loads were in very good agreement with the experimental results. Moreover, the crack initiation and growth behaviors of two subtrochanteric fractures were successfully simulated through a novel implementation of the cohesive zone model (CZM) within a nonlinear FE analysis scheme. The CZM parameters were obtained through a series of experimental tests on different types of specimens and determination of a variety of material properties for different anatomic regions and orientations. The presented results indicated that the locations and patterns of crack initiation, the sequences of crack growth on different paths, and the compatibility of growth increments agreed very well with the observed specifications. Also, very good agreements were achieved between the measured and simulated fracture loads.

Mixed-mode cohesive zone parameters from integrated digital image correlation on micrographs only

Mixed-mode loading conditions strongly affect the failure mechanisms of interfaces between different material layers as typically encountered in microelectronic systems, exhibiting complex material stacking and 3D microstructures. The integrated digital image correlation (IDIC) method is here extended to enable identification of mixed-mode cohesive zone model parameters under arbitrary levels of mode-mixity. Micrographs of a mechanical experiment with a restricted field of view and without any visual data of the applied far-field boundary conditions are correlated to extract the cohesive zone model parameters used in a corresponding finite element simulation. Reliable or accurate force measurement data is thereby not available, which constitutes a complicating factor. For proof-of-concept, a model system comprising a bilayer double cantilever beam specimen loaded under mixed-mode bending conditions is explored. Virtual experiments are conducted to assess the sensitivities of the technique with respect to mixed-mode loading conditions at the interface. The virtual experiments reveal the necessity of (1) optimizing the applied local boundary conditions in the finite element model and (2) optimizing the region of interest by analyzing the model’s kinematic sensitivity relative to the cohesive zone parameters. From a single test-case, exhibiting a range of mode-mixity values, the mixed-mode cohesive zone model parameters are accurately identified with errors below 1%. The IDIC-procedure is shown to be robust against large variations in the initial guess values for the parameters.Real mixed-mode bending experiments are conducted on bilayer specimens comprising two spring steel beams and an epoxy adhesive interface, under different levels of mode-mixity. The mixed-mode cohesive zone model parameters are identified, demonstrating that IDIC is a powerful technique for characterizing interface properties of interfaces, imaged with a limited field of view, as is typically the case in microelectronic applications.

Determination of Mixed-Mode Cohesive Zone Failure Parameters Using Digital Volume Correlation and the Inverse Finite Element Method

The suitability of an optimisation workflow for the determination of the mixed-mode cohesive zone model parameters using digital volume correlation (DVC) data and the inverse finite element method was examined. A virtual compression experiment of a cylinder with a spherical inclusion was modelled using the finite element method. A bilinear traction separation law with a linear mixed-mode relationship was used to describe the interfacial behaviour. Known mode I and mode II fracture energies, = 20 J/m2 and = 40 J/m2 and damage initiation stress, = 0.09 MPa, were used to generate a target composite debonding behaviour. An objective function,, determined based on the debonding behaviour measurable by DVC was chosen. A full factorial experiment was carried out for the four cohesive parameters and showed that correlation between fracture energies/ damage initiation stresses and is non-linear and discontinuous with multiple local minima. Optimisations initiated at the local minima identified from the full factorial experiment correctly determined the target cohesive fracture energies and damage initiation stresses.

Ductile Fracture Study of Stainless Steel AISI 304L Thin Sheets Using the EWF Method and Cohesive Zone Modeling

The purpose of this study is to model the ductile fracture phenomenon using experimental and numerical methods. The stainless steel AISI 304L thin sheets are studied including two thicknesses (0.8 and 1.5 mm). A mechanical characterization is firstly done in order to obtain the main mechanical properties useful for the numerical modeling. In order to determine the essential work of fracture (EWF), DENT specimens are used involving the two thicknesses. The results obtained in terms of EWF for the two thicknesses are close; we find that the essential work of fracture can be considered as an intrinsic criterion for thin sheets. A cohesive zone modeling (CZM) is used in the present study; the model is represented by a traction–separation law (TS). The cohesive elements are implemented in the finite element model, and the material parameters of the model are determined by the mechanical and fracture characterizations. A satisfactory reproduction of the experimental tests is obtained. A good correlation is also obtained between the essential work of fracture determined experimentally and the work of separation used as cohesive zone model parameter.

Temperature Effects on Fracture Toughness Parameters for Pipeline Steels

The present article showcases a temperature dependent cohesive zone model (CZM)-based finite element simulation of drop weight tear test (DWTT), to analyse fracture behavior of pipeline steel (PS) at different temperatures. By co-relating the key CZM parameters with known mechanical properties of PS at varying temperature, a temperature dependent CZM for PS is proposed. A modified form of Johnson and Cook model has been used for the true stress–strain behavior of PS. The numerical model, using Abaqus/CAE 6.13, has been validated by comparing the predicted results with load–displacement curves obtained from test data. During steady-state crack propagation, toughness parameters (such as CTOA and CTOD) were found to remain fairly constant at a given temperature. These toughness parameters, however, show an exponential increase with increase in temperature. The present paper offers a plausible approach to numerically analyze fracture behavior of PS at varying temperature using a temperature dependent CZM.

A molecular dynamics based cohesive zone model for predicting interfacial properties between graphene coating and aluminum

A cohesive zone model (CZM) based on a traction–separation (T-S) relation is first developed to simulate the interfacial behavior between graphene coating and aluminum (Al) substrate. The CZM parameters, which are very difficult to obtain directly experimentally, are determined using molecular dynamics (MD) simulation. Specifically, the MD simulations under the normal and shear loadings are conducted on the graphene-coating/Al interface to derive its T-S relation and then the relevant interfacial behavior of the composite is identified. The MD results show that the behavior of the interface between graphene coating and Al substrate under normal and shear loading is temperature dependent. The maximum normal tensile stress at the interface decreases gradually while the temperature increases from 150 K to 600 K. But the maximum shear stress increases as the temperature increases from 150 K to 450 K and then decreases as the temperature increases from 450 K to 600 K. Finally, the CZM parameters are determined and then imported into a finite element (FE) model. The blister test results obtained by the FE method are in good agreement with those obtained by the MD simulations. These results suggest that the proposed approach is efficient in determining the CZM parameters of the interfacial behavior between the substrate and the ultrathin coating.

An Inverse Analysis-Based Optimal Selection of Cohesive Zone Model for Metallic Materials

Five different cohesive zone models (CZMs), including bilinear, polynomial, trapezoidal, exponential, and PPR (Park–Paulino–Roesler) models, which are commonly used in simulating fracture failure of metallic materials, are evaluated in this paper. The cohesive parameters of these CZMs are determined by an inverse analysis based on the modified Levenberg–Marquardt method. A finite element (FE) model is developed by employing these CZMs and used to predict fracture behaviors of steel grade 120, which is frequently used for the tool joints of drill pipes. Tensile and fracture tests are conducted to determine material properties and fracture behaviors of the steel grade 120, and the fracture behavior obtained from the experiment is used to determine the CZM parameters and validate the FE model. It is found that the five CZMs, with the cohesive parameters determined by the inverse analysis, can be used to simulate the ductile fracture process of the steel, and that among the five CZMs, the exponential CZM provides the closest results to the experimental data.

A Cohesive Zone Model for the Stamping Process Encountered During Three-Dimensional Printing of Fiber-Reinforced Soft Composites

Fiber-reinforced soft composites (FrSCs) are seeing increasing use in applications involving soft actuators, four-dimensional printing, biomimetic composites, and embedded sensing. The three-dimensional (3D) printing of FrSCs is a layer-by-layer material deposition process that alternates between inkjet deposition of an ultraviolet (UV) curable polymer layer and the stamping of electrospun fibers onto the layer, to build the final part. While this process has been proven for complex 3D geometries, it suffers from poor fiber transfer efficiencies (FTEs) that affect the eventual fiber content in the printed part. In order to address this issue, it is critical to first understand the mechanics of the fiber transfer process. To this end, the objective of this paper is to develop a cohesive zone-based finite element model that captures the competition between the “fiber–carrier substrate” adhesion and the “fiber–polymer matrix” adhesion, encountered during the stamping process used for 3D printing FrSCs. The cohesive zone model (CZM) parameters are first calibrated using independent microscale fiber peeling experiments involving both the thin-film aluminum carrier substrate and the UV curable polymer matrix. The predictions of the calibrated model are then validated using fiber transfer experiments. The model parametric studies suggest the use of a roller-based stamping unit design to improve the FTE of the FrSC 3D printing process. Preliminary experiments confirm that for a 0.5 in diameter roller, this new design can increase the FTE to ∼97%, which is a substantial increase from the 55% efficiency value seen for the original flat-plate stamping platen design. The model has broader applications for the transfer-printing of soft material constructs at the submicron scale.

Image-based interface characterization with a restricted microscopic field of view

Accurate characterization of adhesion properties in microelectronic systems is challenging due to (1) the far-field load application that often falls outside the microscopic field of view, (2) the ultra-small loads associated with specimen deformation, and (3) the load-case and specimen dependent interface response. To overcome these challenges, a generic method based on Integrated Digital Image Correlation (IDIC) is proposed, which identifies cohesive zone model parameters (of an arbitrary model not intrinsic to the identification method), by correlating images of a delamination process from a restricted field of view at the microscopic scale, whereby far-field loading data cannot be exploited.To quantify the effects of potential error sources on the performance of the proposed IDIC-routine, virtual experimentation is first conducted. Inaccurate application of boundary conditions in the FE-model of IDIC is thereby shown to be the most critical source of error. Subsequently, a real double cantilever beam (DCB) experiment has been analyzed as a well-defined test-case for characterization of adhesion properties. Since the Young’s modulus of the bulk material is generally well known, the imaged, elastically deforming bulk material acts as a force sensor. External load measurement can therefore be omitted from the identification process, thereby rendering the interface identification method independent of the particular test method. The implemented IDIC-algorithm is shown to be robust for accurately identifying the two cohesive zone parameters of interest: the work of separation Gc and the critical opening displacement δc.

A cohesive zone model for self-similar fractal crack propagation

Cracks in the nature have been proven to be fractal by many experiments. Despite the fractal fracture mechanics has been developed by many researchers, fractal geometry still has few applications in analysis of engineering structures. One of the reasons is that previous studies are somehow inconvenient when apply, e.g. to the finite element method. This study proposes a Cohesive zone model (CZM) for self-similar fractal crack propagation of material interfaces. The determination of the CZM parameters and the simulation of fractal crack propagation are developed by replace the fractal crack with the equivalent smooth crack. The fractal dimension has effects on both the crack extension resistance and the max traction stress. As shown by the simulation of a DCB specimen, the fractal dimension also affect the ultimate load and the crack propagation process. It is shown that it is possible to predict the propagation of fractal cracks without considering geometric modeling of the crack topology by our cohesive zone model.

Strain-rate dependent influence of adherend stiffness on fracture load prediction of BGA solder joints

Fracture experiments with ball grid array (BGA) specimens having different adherend rigidities were performed under bending loads at intermediate strain rates (0.2–1s−1) and a high strain rate of 30s−1. A cohesive zone model (CZM) was established and the predictive capability of the model was assessed for the specimens with different rigidities. The predicted fracture loads were within 12% of the measured forces when the CZM parameters were obtained using specimens with a similar degree of constraint. This suggests that in many practical cases, the effect of adherend stiffness can be neglected in predicting the strength of BGA solder joints.

Ductile fracture of solder-Cu interface and inverse identification of its interfacial model parameters

Interfacial failure is a crucial issue in the study of reliability in electronic packaging. The failure mechanism is complicated since ductile failure of the solders is generally accompanied with brittle fracture of the intermetallic compounds(IMCs). Besides, it is also greatly influenced by loading conditions. In this paper, fractures of SAC305-Cu interfaces under mode I and mode II loading conditions have been experimentally studied. Their interfacial micro-structures before and after failures have been analyzed using SEM and EDS. At the same time, numerical simulations of interfacial failure have also been performed using an improved cohesive zone model. Finally, the failure mechanisms for both mode I and mode II fractures were disclosed. In addition, though the cohesive zone models(CZM) were widely used to investigate the interfacial failure, their parameter identification is still an important concern, especially when considering both the accuracy and efficiency in the analysis. In our work, a parameter inverse analysis method has been developed, based on the Kalman filter algorithm and the response surface interpolation technique. This interpolation method can hugely improve the computational efficiency, but it will also introduce a large numerical error in the present cases, in which the interfacial failure is accompanied by large plastic deformation of solder, or the parameter searching ranges are set over-large. Aiming at this issue, a range-reduced inverse analysis scheme was further developed in our work. The developed method and scheme were validated robust and accurate through verifications of both pseudo and real experimental data. The cohesive zone model parameters acquired can be effective to simulate the interfacial failure of Cu and Pb-free solder. The whole inverse analysis is automatically achieved and can be easily applied to other complicated interfacial failure problems.

Silica–silane coupling agent interphase properties using molecular dynamics simulations

In this paper, strength of the interphase between silica and glycidoxypropyltrimethoxy silane (GPS) coupling agent has been studied using molecular dynamics (MD) simulations. Silica–GPS interphase model is created by coupling the hydroxylated silica surface with monolayer-hydroxylated GPS molecules. The interphase model is subjected to mode-I (normal), mode-II (shear) and mixed-mode (normal–shear) mechanical loading to determine the interphase cohesive traction–separation (T–S) response (i.e., cohesive traction law). In MD simulations, atomic interactions are modeled with the reactive force field ReaxFF. Effects of interphase thickness and GPS bond density on the T–S response are studied. Simulation results indicate that interphase strength decreases with increase in the interphase thickness before attaining a plateau level at higher thickness. For a particular thickness, strength improves significantly with increase in the GPS bond density with the silica surface. Damage mode is adhesive at the silica interface at lower thickness and transitions to mixed mode and cohesive failure within the silane interphase at higher thickness. Mixed-mode T–S responses are bounded by the mode-I and mode-II responses. Characteristic parameters of the continuum-level potential-based cohesive zone model (PPR–CZM) are determined by fitting the MD-based mode-I and mode-II T–S responses with PPR–CZM functional. Development of the PPR–CZM parameters enables bridging length scales from the MD to the continuum scale for fracture modeling of the fiber–matrix interphase in composites subjected to mixed-mode loading. Results on mode-I and mode-II unloading are also presented.