Shape Of Cohesive Law Research Articles

A general solution to the maximum detachment force in thin film peeling

While it is well known that the steady-state detachment force during 90° peeling of an elastic film on a rigid substrate provides a simple and powerful method to determine the interfacial work of adhesion, the situation is less clear for the maximum detachment force associated with the peeling process. Here, we propose a general solution to this maximum detachment force during 90° peeling, which is shown to depend on the interfacial work of adhesion, interfacial strength, bending modulus of the film, as well as an interfacial cohesive law shape factor. Combining this solution with Kendall’s classical model provides a method that allows the interfacial work of adhesion and interfacial strength of a film-substrate system to be simultaneously determined via peeling test.

Cohesive zone parameter influence on the impact strength of composite adhesive joints

Adhesive bonding is a process of permanent bonding between the components of a structure that uses an adhesive to join the components after curing. Adhesive joints have increasingly been used in many applications. Thus, it is important to assess their behavior when subjected to static or impact loads. In this sense, cohesive zone models (CZM) have been used to predict the strength of adhesive joints and to simulate the growth of damage in structures after the definition of the cohesive laws. This work studies the different CZM conditions used to model an adhesive layer in a single-lap joint (SLJ) subjected to impact loading. The numerical results were validated using experimental data. In this study, four overlap lengths (LO) were considered. The evaluated modelling conditions were the decoupling of loading modes with triangular law, cohesive law shape, damage initiation criteria and damage propagation criterion. This analysis allowed to conclude that CZM is a reliable technique to predict the adhesive joint strength under impact. On the other hand, the numerical analysis made it possible to understand in detail the influence of the modelling conditions used in the cohesive models in the results.

A comparison of crack propagation theories in viscoelastic materials

Crack propagation in viscoelastic materials cannot be understood with the use of classical fracture mechanics, which predicts no dependence on the speed of propagation, unless cohesive models like Barenblatt or Dugdale are introduced, as done by Knauss & Schapery first in the 1970s. However, there is another approach, suggested qualitatively by deGennes in 1996, and quantitatively by Persson and Brener in 2005, which attempts an energy (power) balance by considering viscoelastic dissipation in the bulk of the material. Here, we revisit the main results of the two theories and show that they lead to approximately the same scaling laws not just for the standard material, but also for power law materials (which have a continuous spectrum of relaxation times). Recent findings by Schapery have concluded that the shape of the cohesive law results essentially in a shift in velocity which depends both on cohesive law shape and viscoelastic properties. Therefore, the Persson-Brener cutoff radius in the integral of dissipation can be chosen to fit approximately the cohesive model results to match the shift of the reference velocity.

On the R-curve and cohesive law of glass/epoxy end-notch flexure specimens with 0//θ interface fiber angles

In the current paper, the effects of interface fiber angles on the characteristics of R-curve and the cohesive law shape of end-notch-flexure specimens are investigated using numerical and empirical methods. To this aim, laminated composites manufactured by E-glass/epoxy with 0//θ interface where θ = 0, 15, 45, 60, and 90 were fabricated and tested. The mode II laminated fracture toughness and the cohesive shear traction-separation model were obtained irrespective of the impact of the remote-ply orientation. The empirical results showed that as the interface fiber angle rises, the crack growth behavior in the samples becomes more stable which is evident in the augmented length of the steady-state fracture process zone. Furthermore, the maximum bearable load of specimens drops considerably. Also, the delamination toughness propagation is approximately identical for all specimens. This is the case even if the initiation of delamination toughness is significantly reduced by increasing the interface fiber angle. After parameter identification of the cohesive zone model and conducting numerical analyses, it was demonstrated that this model with the proposed linear-exponential softening behavior can estimate the load-displacement response of samples that display a pronounced R-curve behavior.

On the energy release rate extraction and mixed mode behavior of fatigue cohesive model

This paper presents a comprehensive study on the energy release rate (ERR) extractions and mixed mode behavior of fatigue cohesive model. The development of the non-linear cohesive zone ahead of a crack tip is influenced by multiple factors, where the extractions of ERRs and mode ratios are crucial for accurate fatigue analysis in Paris law-based models. Investigations into the effects of different parameters e.g. interfacial strengths, shapes of the cohesive laws and element sizes on the extracted ERRs are conducted. In addition, two novel mixed mode bending models i.e. multi-stage mode ratio (MSMR) and continuously various mode ratio (CVMR) models are proposed for mixed-mode behavior study. All results are compared to the theoretical fracture mechanics analysis and to each other. It is found that if the interfacial strength becomes too low, an excessively long cohesive zone can form, where the mode ratio could significantly deviate from the true value and negatively impact the accuracy. The shape of cohesive laws is also found to influence the ERRs and mode ratios to some extent but are not the dominating factor.

A Comparative Study of Cohesive Law Shapes in Analytical Modeling of Interfacial Debonding in Lithium-Ion Battery Electrodes

To determine the impact of cohesive law shapes on the modeling of interfacial debonding in lithium-ion battery electrodes, analytical methods based on different cohesive models for the debonding process have been developed individually. Three different cohesive laws, namely, triangular, trapezoidal, and rectangular laws, have been employed. To ensure comparability, the cohesive strength and the fracture toughness have been set to be identical for different cohesive laws. The evaluation of debonding onset has suggested that the cohesive law shape affects the modeling results only when the interface is ductile. The largest possible difference for the triangular law and the rectangular law on the debonding onset has been estimated. A discussion for specific electrodes has also been provided.

Subcritical and critical states of a crack with failure zones

• A new semi-analytical technique is developed to solve the problems of crack mechanics within the cohesive zone model . • Proposed technique implicitly takes into account the finite stress condition. • New dependencies for critical crack lengths are obtained for the non-uniform traction-separation laws. The problem on the stress–strain state near a mode I crack in an infinite plate is solved in the frame of a cohesive zone model. The complex variable method of Muskhelishvili is used to obtain the crack opening displacements caused by the cohesive traction , which models the failure zone at the crack tip, as well as by the external load. The finite stress condition and logarithmic singularity of the derivative of the separation with respect to the coordinate at the tip of a physical crack are taken into account. The cohesive traction distribution is sought in a piecewise linear form, nodal values of which are being numerically chosen to satisfy the traction-separation law. According to this law, the cohesive traction is coupled with the corresponding separation and fracture toughness . The tips of the physical crack and cohesive zone (geometric variables) along with the discrete cohesive traction are used as the problem parameters determining the stress-strain state. If the crack length is included in the set, then the critical crack size can be found for the given loading intensity. The obtained determining system of equations is solved numerically. To find the initial point for a standard numerical algorithm, the asymptotic determining system is derived. In this system, the geometric variables can be easily eliminated, which make it possible to linearize the system. In the numerical examples, the one-parameter traction-separation laws are used. Influence of the shape parameters of the law on the critical crack size and the corresponding cohesive length is studied. The possibility of using asymptotic solutions for determining the critical parameters is analysed. It is established that the critical crack length slightly depends on the shape parameter, while the cohesive length shows a strong dependence on the shape of cohesive laws .

Effect of the cohesive law shape on the modelling of adhesive joints bonded with brittle and ductile adhesives

Cohesive Zone Models (CZMs) have been increasingly used for the fracture prediction of adhesively bonded joints. In order to better understand the relation between the fracture behaviors of the different geometry/adhesive combinations and the shape of CZMs, the butt-joint uniaxial tension, shear and the double cantilever beam (DCB) fracture experiments were conducted using two distinct adhesives, an epoxy-based brittle adhesive and a VHBTM tape ductile adhesive. Three shapes of CZMs were adopted, including the exponential, bilinear, and trapezoidal models, to numerically predict the experimental performance. The comparisons between the numerical predictions and the experiments results demonstrated that the bilinear CZM is suitable for modelling the brittle adhesive bonding butt-joints in the uniaxial tensile and shear fracture processes, and the exponential CZM is suitable for modelling the ductile adhesive bonding ones. The critical stresses, the fracture energy and the shape of the CZMs have significant effects on the numerical results of the butt-joints uniaxial tension and shear for the two types of adhesives. In addition, for the DCB specimen fracture processes, it is shown that the bilinear CZM and the trapezoidal CZM predicted the brittle adhesive bonding joints better, and the trapezoidal CZM fitted the experimental data best for the two types of adhesives bonding joints. The overall results demonstrate that the selection of the shapes of CZM depend on the properties of the adhesive to obtain an accurate fracture processes prediction.

Experimental and numerical analysis of scarf aluminum adhesive joints

This work consists of a validation of Cohesive Zone Model (CZM) laws in traction and shear, estimated by the application of the direct method, in the strength prediction of joints under a mixed-mode loading. In this context, scarf joints with different scarf angles (α) and adhesives of different ductility were tested. Pure-mode cohesive laws served as the basis for the creation of simplified triangular, trapezoidal and exponential laws that were tested for each of the adhesives. Their validation was accomplished by comparing the numerical predictions with the experimental results. The use of the direct method allowed obtaining very precise maximum load (Pm) predictions, indicating the cohesive law shape more suitable for each adhesive /geometry set. For the geometric and material conditions considered, this study has led to the conclusion that no significant Pm errors are incurred by the choice of a less appropriate law.

On the strength prediction of adhesively bonded FRP-steel joints using cohesive zone modelling

The variety of failure modes that are likely to occur in fibre-reinforced polymer (FRP)/steel joints used in the construction industry adds to the complexity associated with the design of these joints. This variation in possible failure modes is mainly attributed to the lack of a controlled application environment and to rather insufficient quality assurance protocols and procedures. The use of energy-based methods such as, cohesive zone modelling (CZM), can be a solution to circumvent such complexities. This paper investigates a number of issues related to CZM analyses of FRP/steel adhesive joints using various test configurations and a comprehensive numerical study. Parameters such as the effect of shape and type of cohesive law, crack path location, length of damage process zone, variations of adhesive and FRP properties, and different failure modes including cohesive, interfacial debonding and FRP failure on the strength of joints are investigated. The results show that the behaviour of the tested joints is accurately predicted provided that the variation of failure modes are taken into account. Moreover, it is shown that the damage process zone in adhesive layer is directly proportional to the shape of cohesive laws. This feature can be employed in the design phase to ensure sufficient overlap length and to account for important in-service parameters such as temperature and moisture.

Specimen geometry and specimen size dependence of the $${\mathcal {R}}$$ R -curve and the size effect law from a cohesive model point of view

An analytic model has been developed for a Compact Tension specimen subjected to a controlled displacement and corresponding load within a cohesive model framework. The model is able to capture the material response while the Fracture Process Zone is being developed, obtaining the evolution of multiple variables such as the crack opening and the cohesive stresses, for an arbitrary Cohesive Law shape. The crack growth prediction based on the $${\mathcal {R}}$$ -curve and the nominal strength prediction based on Bažant’s Size Effect Law have been implemented using the output variables available from the proposed analytic model. The minimum specimen size has been found in order to properly apply $${\mathcal {R}}$$ -curve based methods. The study has concluded that only the cohesive model is able to properly capture the changes of the Specimen Geometry and Specimen Size, as unlike in other theories, no Linear Elastic Fracture Mechanics assumptions are made.

Cohesive fracture of elastically heterogeneous materials: An integrative modeling and experimental study

A combined modeling and experimental effort is made in this work to examine the cohesive fracture mechanisms of heterogeneous elastic solids. A two-phase laminated composite, which mimics the key microstructural features of many tough engineering and biological materials, is selected as a model material system. Theoretical and finite element analyses with cohesive zone modeling are performed to study the effective fracture resistance of the heterogeneous material associated with unstable crack propagation and arrest. A crack-tip-position controlled algorithm is implemented in the finite element analysis to overcome the inherent instability issues resulting from crack pinning and depinning at local heterogeneities. Systematic parametric studies are carried out to investigate the effects of various material and geometrical parameters, including the modulus mismatch ratio, phase volume fraction, cohesive zone size, and cohesive law shape. Concurrently, a novel stereolithography-based three-dimensional (3D) printing system is developed and used for fabricating heterogeneous test specimens with well-controlled structural and material properties. Fracture testing of the specimens is performed using the tapered double-cantilever beam (TDCB) test method. With optimal material and geometrical parameters, heterogeneous TDCB specimens are shown to exhibit enhanced effective fracture energy and effective fracture toughness than their homogeneous counterparts, which is in good agreement with the modeling predictions. The integrative computational and experimental study presented here provides a fundamental mechanistic understanding of the fracture mechanisms in brittle heterogeneous materials and sheds light on the rational design of tough materials through patterned heterogeneities.

An experimental analysis of the fracture behavior of composite bonded joints in terms of cohesive laws

Modeling adhesive joints by means of cohesive models relies on the definition of cohesive laws. Although cohesive laws are known to be dependent on the loading mode, there is a lack of experimental evidences to describe this dependence. At the same time, the adherend and adhesive thicknesses are known to affect the fracture toughness of the bond, but their effect on the cohesive law has not been clarified. In this work, an experimental characterization of an epoxy adhesive is presented. The effect that the mode mixity has on the bond toughness and its cohesive law is compared against the effect of the adhesive and adherend thicknesses. The impact of these two latest parameters is shown to be minor if compared to the influence of the mode mixity, which mainly defines the cohesive law shape. Finally, the implications of these experimental findings on the numerical simulation of adhesive joints are discussed.

Characterization of the translaminar fracture Cohesive Law

Quasi-brittle materials such as fibre-reinforced composite materials develop a relatively large Fracture Process Zone where material toughening mechanisms such as matrix cracking, fibre-bridging and fibre pull-outs take place. The damage onset and damage propagation are well defined from a cohesive model point of view, although no standard procedure has been yet developed to characterize the translaminar Cohesive Law. The present work proposes an objective inverse method for obtaining the Cohesive Law with the use of an analytic model capable of predicting the load–displacement curve of a Compact Tension specimen for any arbitrary Cohesive Law shape. The softening law has been obtained for two laminates, providing an excellent agreement with the experimental results. With the obtained softening function, the nominal strengths of a Center Cracked Specimen and an Open Hole specimen have been predicted for a wide range of specimen sizes.

Influence of the cohesive law shape on the composite adhesively-bonded patch repair behaviour

Abstract In this study, the cohesive failure of the adhesive layer of an adhesively-bonded joint under uniaxial tensile loads in static conditions is discussed as an approximation to the behaviour of adhesively-bonded repairs. A three-dimensional finite-element model of a single-lap joint was developed using the commercial code Abaqus. Cohesive Zone Models (CZM) coupled to Finite Element Analysis, were used to study the failure strength of the joint. They allowed the prediction of the initiation of the crack and its growth. CZM are governed by a traction-separation law, which can acquire different shapes. The numerical model, considering a linear cohesive law, was validated with 2D numerical and experimental results available in the literature. The effect of different cohesive law shapes, such as exponential and trapezoidal, on the failure load of the joint was studied. In addition, a cohesive parametric analysis was performed, varying the adhesive toughness and cohesive strength. The most suitable cohesive law was the trapezoidal, since the failure load results were close to the experimental data taken from the literature. The cohesive strength is identified as the most influential parameter on the studied variable.

Fracture Analysis of Cohesive Soils Using Bilinear and Trilinear Cohesive Laws

AbstractTensile cracking of soil is an important issue that affects the strength and permeability of soil in many geotechnical applications, such as in soil dams and landfill liners. When the size of the fracture process zone is not negligible compared to specimen dimensions, a nonlinear fracture mechanics approach, such as a cohesive crack model, should be used to simulate the experimental results. A critical issue in the simulation of cohesive failure mechanism is the definition of cohesive interactions along fracture surfaces. In this study, bilinear and trilinear cohesive laws are examined based on data sets available in the literature. The inverse method is used for the definition of the cohesive parameters. As a result of this study, some conclusions are established to assess the importance of using a suitable cohesive law shape for a given soil that accurately predicts the cohesive fracture parameters under different material conditions. Finally, based on a tensile strength model of granular soil, ...

On the parametric sensitivity of cohesive zone models for high-cycle fatigue delamination of composites

This article investigates the sensitivity of cohesive zone models (CZMs) for high-cycle fatigue delamination in relation to constituent static parameters, namely, the cohesive strength and stiffness, whose values are frequently calibrated by curve fitting or selected for convenience without any physical basis. After reviewing the damage mechanics formulation of mixed-mode CZMs for static (monotonic) loading in bilinear, exponential, and polynomial cohesive laws, the source of uncertainty arising from the calibration or selection of static parameters is remarked. The formulation of the CZMs for high-cycle fatigue loading using interface separation, strain, and strain energy release rate (SERR) based fatigue damage rate functions is discussed. Several numerical studies are conducted to explore the sensitivity of CZMs for fatigue delamination in relation to static cohesive parameters and to the shape of the cohesive law under mode I and mixed-mode loading. The performance of the CZMs is also investigated for additive and non-additive decomposition of total damage into its static and fatigue components, and for constrained and unconstrained damage update strategies in the vicinity of the crack tip. Numerical studies illustrate that a CZM employing the separation or strain based fatigue damage rate function is highly sensitive to phenomenological cohesive strength and stiffness parameters, whereas a CZM employing the SERR based damage rate function is minimally sensitive to the same static parameters. While the shape of the static cohesive law does not affect fatigue crack growth rate predictions, studies show that cohesive laws with higher-order smoothness can better describe linear Paris regime behavior. The main conclusion of this article is that incorporating a SERR based fatigue damage rate function into a CZM with higher-order smoothness leads to a more robust approach for simulating high-cycle fatigue delamination of laminated composite materials.

응집 요소를 사용한 균열 진전 유한요소 해석에서 응집 법칙의 영향에 대한 연구

In this paper, the effect of cohesive laws on the finite element analysis of crack propagation using cohesive elements is investigated through three-point bending and double cantilever beam problems. The cohesive elements are implemented into ABAQUS/Standard user subroutines(UEL), and the shape of cohesive law is varied by changing parameters in polynomial functions of cohesive traction-separation relations. In particular, crack propagation behaviors are studied by comparing load-displacement curves of the analysis models which have different shapes of cohesive laws with the same values of fracture energy and cohesive strength. Furthermore, the influence of the element size on crack propagation is discussed in this study.

Mesh dependence of transverse cracking in laminated metals with nanograined interface layers

Combination of surface mechanical attrition treatment (SMAT) and co-rolling can produce large-scale laminated nanostructured metals with both high strength and high ductility. For the co-rolled SMATed metals with nanograined interface layers, numerical investigation based on the cohesive finite element method focuses on effects of shape of the cohesive law and mesh size. Simulations show that the shape of the bilinear cohesive law varies peak stress and normal opening displacement significantly and that larger thickness of brittle phase allows use of coarser meshes while not to consider lower bound of the mesh size may lead to unreasonable results.

Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer

Adhesively-bonded joints are extensively used in several fields of engineering. Cohesive Zone Models (CZM) have been used for the strength prediction of adhesive joints, as an add-in to Finite Element (FE) analyses that allows simulation of damage growth, by consideration of energetic principles. A useful feature of CZM is that different shapes can be developed for the cohesive laws, depending on the nature of the material or interface to be simulated, allowing an accurate strength prediction. This work studies the influence of the CZM shape (triangular, exponential or trapezoidal) used to model a thin adhesive layer in single-lap adhesive joints, for an estimation of its influence on the strength prediction under different material conditions. By performing this study, guidelines are provided on the possibility to use a CZM shape that may not be the most suited for a particular adhesive, but that may be more straightforward to use/implement and have less convergence problems (e.g. triangular shaped CZM), thus attaining the solution faster. The overall results showed that joints bonded with ductile adhesives are highly influenced by the CZM shape, and that the trapezoidal shape fits best the experimental data. Moreover, the smaller is the overlap length (LO), the greater is the influence of the CZM shape. On the other hand, the influence of the CZM shape can be neglected when using brittle adhesives, without compromising too much the accuracy of the strength predictions.