Use Of Cohesive Zone Model Research Articles

Numerical investigation on the fatigue life of non‐cracked metallic plates repaired with bonded CFRP

AbstractIn Europe, a large number of old riveted metallic bridges approach the end of their fatigue life. Past research has shown that the application of CFRP can be very efficient in delaying the crack growth rate of deficient structural elements with existing crack. However, little attention is given to the fatigue resistance of non‐damaged metallic members approaching the end of their fatigue life. This is particularly relevant for old metallic riveted bridges, where many critical components do not have existing cracks. This paper presents a numerical investigation on the fatigue behavior of non‐cracked metallic plates bonded with CFRP using epoxy resin. Nonlinear finite element analyses are performed using the commercial software ABAQUS. The cyclic elasto‐plastic behavior and the fatigue strain life of puddle iron metal are obtained from previous experimental results conducted on specimens extracted from Luiz I Bridge (Porto, Portugal). Debonding failure of the adhesive joint is simulated through the use of cohesive zone model with traction separation law. The cohesive behavior was calibrated using fracture mechanic tests results on the adhesive, conducted in a previous related study. The fatigue crack initiation life was estimated using local approach based on material fatigue strain life. Fatigue resistance curves that relate the number of cycles to failure and the applied nominal stress for unreinforced and reinforced elements are derived. The results show that the application of CFRP can significantly increase the fatigue crack initiation life of a metallic structural component significantly.

Selected Aspects of Cohesive Zone Modeling in Fracture Mechanics

This review paper discusses the basic problems related to the use of cohesive models to simulate the initiation and development of failure in various types of engineering issues. The most commonly used cohesive zone models (CZMs) are described. Recent achievements in the field of cohesive modeling are characterized, with particular emphasis on the problem of mixed mode loading, the influence of the strain rate, the stress state triaxiality, and fatigue. A separate chapter of the work is devoted to the identification of cohesive parameters. Examples of the use of CZMs for the analysis of the fracture and failure process in various applications, both on the macro and microscopic scale, are given. The directions of CZMs development were indicated as well as the issues that are currently under particularly intensive development.

Numerical analysis of elasto-plastic adhesively single step lap joints with cohesive zone models and its experimental verification

Adhesive bonding method is used as an alternative to mechanical bonding methods, and it is frequently used in automotive, space and aviation industries. In the present study; the displacement and failure load capacity characteristics of single step lap joint was measured experimentally and compared with results of finite element (FE) analysis. In addition, the change in the length and the thickness of the material and adhesive in this joint type, stresses on the adhesive was examined by numerical analysis that have affected. Also, the effects of overlap length and material thickness on the stresses in adhesive were examined with numerical analysis for the single step lap joint. AA2024-T3 aluminum alloy adhered material and double component DP460 structural adhesive was used as adhesives in the single step lap joint. In the numerical analysis of this joint type, two different material models including multilinear isotropic hardening (MISO) and cohesive zone model (CZM) were used in the adhesive layer. During the experimental tests, two cameras were used to measure the displacements and crack propagations. As a result, the data obtained from the numerical analysis were compared to the experimental data of the single step lap joint type, the use of CZM in the adhesive region was found to be very important in terms of compliance. Thus, the difference between CZM and MISO results in terms of damage load in adhesive is 7 %, while this difference is 32 % in terms of displacement. Also, it has a great importance to get the displacement data via a video extensometer for the compatibility of FE and experimental analyses. Another result obtained from the study is that changing the material thickness, the adhesive thickness and the overlap length in the joint, changes the stress concentrations and shear stresses at the ends of the overlap area.

An efficient method to extract a mode I cohesive law for bonded joints using the double cantilever beam test

Cohesive Zone Models (CZM) are widely used for modeling bonded joints. The main difficulty concerning the use of CZM is the obtention of the interface cohesive law. To measure the cohesive law of bonded joints, experimental methods have been developed which are tedious and expensive because they require the use of additional measurement techniques in addition to the basic test outputs (load and displacement) to measure the J-integral and the crack opening displacement, essential parameters that obtain the cohesive law. In this work, a method is presented to obtain the cohesive law directly from the load-displacement curve of a DCB test. The method combines a model based on Dugdale's condition with an inverse method. The method is compared to the measurements from other authors who used the aforementioned more costly existing methods, and a good agreement between them is obtained. The method presented reduces the instrumentation needed during the test and it is very useful when testing under extreme conditions requiring the use of environmental chambers.

Prediction of fretting fatigue crack initiation location and direction using cohesive zone model

Abstract Contact stresses distributions may substantially reduce the fatigue life of components subject to fretting, leading to early unexpected failures. Accurately predicting the components lives is, therefore, an important topic to be addressed, in particular from a design point of view. This topic has received great attention in the past decades and several numerical tools that better estimate these components lives have been proposed. In this paper, the focus is in the crack initiation phase. At this stage, it is important to correctly predict the crack initiation location and orientation, which is often achieved by using critical plane approaches. Instead, the use of cohesive zone model (CZM) as an alternative approach to accurately estimate those parameters is investigated. Cohesive zone model as well as two of its common initiation criteria, namely quadratic traction-separation criterion and maximum nominal stress criterion, are used to study crack initiation location and orientation under fretting conditions. Our results are compared with the traditional critical plane approaches and with experimental data, suggesting that cohesive approaches can accurately be used in crack initiation prediction.

Numerical Representation of Multiple Premature Failures in Steel-Plated RC Beams

Realizing the importance of widely used technique of plating for flexural retrofitting of reinforced concrete (RC) beams and its drawbacks due to premature failure(s), present work concentrates in developing a finite element tool model capable of successfully capturing multiple premature failure modes and their corresponding behaviors. The model is simple but focused; the capability and accuracy of the results have been validated through test literature, particularly focusing on the load capacities of beams at progressive stages of failure modes; which is from crack initiation through to complete failure, such as the load of crack initiation, first crack and complete failure. Acceptable accuracy is shown in terms of crack type(s), crack patterns, sequence, location and direction of propagation through the innovative use of cohesive zone model (CZM). The model clearly explains that debonding and peeling, although originating from a same location for most cases, are extensions of different types of cracks.

Multiple solutions in cohesive zone models of fracture

The use of cohesive zone models (CZM) for studying crack initiation and propagation can lead to non-unique deformed configurations. This situation can lead to solution branches that may be non-physical, leading to difficulty in interpreting computed results. These aspects are studied in this paper using the double cantilever beam (DCB) specimen first and next in the context of a mode I center crack in a thin sheet of infinite extent subjected to remote tensile loading. Analytical solutions to the CZM that employ constant stress and linear softening laws are presented, and it is shown that when the linear softening cohesive law is used, two cohesive zone sizes are valid for the same external loads, leading to two equally possible deformed configurations, satisfying all the field equations and boundary conditions. The smaller of the two cohesive zones has a lower energy which proposed as a criterion to render a unique solution.

Capturing failures in steel-plated RC beams through a combination of discrete and continuum models

In recent decades, a significant research has been conducted towards understanding the behaviour of plated beam. Initially designed to achieve a desired capacity, the plated beams prematurely fail in undesirable modes of failure, such as debonding and peeling. The uncertainty related with such modes of failure poses a real challenge towards quantifying them. This field is far from being clearly understood. Realising the importance of widely used technique for flexural retrofitting of reinforced concrete (RC) beams and its drawbacks due to premature failure(s), present work concentrates in developing a finite element tool model capable of successfully capturing multiple premature failure modes and their corresponding behaviours related to RC beam retrofitted with steel plates at their soffits. The capability and accuracy of the results has been validated through test literature in terms of load capacities of beams at progressive stages of failure type(s) through crack patterns, location, and direction of propagation. Numerical beams are showing expected load/displacement behaviour with the ability to predict further direction of propagation of cracks especially at concrete-plate interface with the use of Cohesive Zone Model (CZM).

Slip and wear at a corner with Coulomb friction and an interfacial strength

Traditional analyses of slip at corners of contacts, based on linear elasticity and a Coulomb friction law, are very sensitive to the details of local geometries, owing to the effects of elastic singularities. Following the use of cohesive-zone models to address such issues in mode-II fracture, we present analyses of slip and wear at corners of contacts when a finite interfacial shear strength is incorporated with a Coulomb friction law. We show that the concept of an instantaneous cohesive-length scale, borrowed from the field of fracture mechanics, can be used to describe the nature of stress fields around corners, and defines when linear-elasticity and Coulomb friction can provide an accurate description of the interfacial behavior. We also show that the sensitivity of slip analyses to geometrical details decreases when the cohesive-length scale increases. We also show that the cohesive strength of an interface plays a crucial role in the propagation of a wear scar across an interface. If only Coulomb slip is assumed to occur, a wear scar may not progress beyond the original stick-slip boundary. If a finite interfacial shear strength is introduced into the analysis, the wear scar can propagate along the interface.

Use of cohesive zone models to design automotive bonded joints

Cohesive-zone models have been widely used for the analysis of interface debonding. In this paper, three of these models are used to study a set of debonding problems. A comparative analysis of the three models is carried out; results are presented and discussed for numerical simulations referring to both single-mode and mixed-mode situations. The results show that the differences between the load-deflection curves obtained for the three models considered, become more evident by increasing the stiffness of the specimen. Considering that the most common joint configuration in automotive industry is the lap-shear joint, the main conclusion of this work is that the joint stiffness will not affect the computational response obtained with the three different models studied here.

The proper generalized decomposition for the simulation of delamination using cohesive zone model

ABSTRACTThe use of cohesive zone models is an efficient way to treat the damage especially when the crack path is known a priori. It is the case in the modeling of delamination in composite laminates. However, the simulations using cohesive zone models are expensive in a computational point of view. When using implicit time integration or when solving static problems, the non‐linearity related to the cohesive model requires many iteration before reaching convergence. In explicit approaches, an important number of iterations are also needed because of the time step stability condition. In this article, a new approach based on a separated representation of the solution is proposed. The proper generalized decomposition is used to build the solution. This technique coupled with a cohesive zone model allows a significant reduction of the computational cost. The results approximated with the proper generalized decomposition are very close the ones obtained using the classical finite element approach. Copyright © 2014 John Wiley & Sons, Ltd.

Investigating Some Technical Issues on Cohesive Zone Modeling of Fracture

This study investigates some technical issues related to the use of cohesive zone models (CZMs) in modeling the fracture of materials with negligible plasticity outside the fracture process zone. These issues include: (1) why cohesive laws of different shapes can produce similar fracture predictions, (2) under what conditions CZM predictions have a high degree of agreement with linear elastic fracture mechanics (LEFM) analysis results, (3) when the shape of cohesive laws becomes important in the fracture predictions, and (4) why the opening profile along the cohesive zone length (CZL) needs to be accurately predicted. Two cohesive models were used in this study to address these technical issues. They are the linear softening cohesive model and the Dugdale perfectly plastic cohesive model. Each cohesive model uses five cohesive laws of different maximum tractions. All cohesive laws have the same cohesive work rate (CWR) defined by the area under the traction–separation curve. The effects of the maximum traction on the cohesive zone length and the critical remote applied stress are investigated for both models. The following conclusions from this study may provide some guidelines for the prediction of fracture using CZM. For a CZM to predict a fracture load similar to that obtained by an LEFM analysis, the cohesive zone length needs to be much smaller than the crack length, which reflects the small-scale yielding condition requirement for LEFM analysis to be valid. For large-scale cohesive zone cases, the predicted critical remote applied stresses depend on the shape of the cohesive models used and can significantly deviate from LEFM results. Furthermore, this study also reveals the importance of accurately predicting the cohesive zone profile for determining the critical remote applied load.

Adhesive Contact: A Few Comments on Cohesive Zone Models and Self-Consistency

The use of cohesive zone models in the context of the adhesive contact of spheres is discussed. An alternative derivation of the double Hertz cohesive zone model is proposed other than the one by Greenwood and Johnson [10]. Based on this example, and the derivation method used, some features of adhesive contact models, are discussed with emphasis on the role of the additional, physically motivated, lengthscale introduced by the cohesive zone.

A new theoretical framework for the formulation of general, nonlinear, multiscale plate theories

A new type of general, theoretical framework for the development of comprehensive, nonlinear, multiscale plate theories for laminated structures is presented. The theoretical framework utilizes a generalized two scale description of the displacement field based on a superposition of global and local effects where the functional forms for the global and local displacement fields are arbitrary. The two scale nature of theory allows it to explicitly consider the layered nature of the structure. The subsequent development of the governing equations for the theory is carried out using the general nonlinear equations of continuum mechanics referenced to the initial configuration. The equations of motion and the lateral surface boundary conditions for the theory are derived using the method of moments over the different scales subject to an orthogonality constraint. The theory satisfies the interfacial constraints and the top and bottom surface boundary conditions in a strong sense. Delamination effects are incorporated into the theory through the use of cohesive zone models (CZMs). Arbitrary CZMs can be incorporated into the theory without the need for reformulation of the governing equations. The theory is formulated in a sufficiently general fashion that any type of history-dependent material can be used to describe the inelastic response of the materials composing the layers. Furthermore, as a result of the multiscale nature of the theory it can be specialized to single scale theories of the equivalent single layer (ESL) or discrete layer (DL) types in a unified fashion and without the need for any reformulation. While the starting point for the proposed theory is the same as used by Williams [Williams, T.O., 1999. A generalized multilength scale nonlinear composite plate theory with delamination. Int. J. Solid Struct. 36, (20) 3015–3050; Williams, T.O., 2001. Efficiency and accuracy considerations in a unified plate theory with delaminations. Comp. Struct. 52, (1) 27–40; Williams, T.O., 2005. A generalized, multilength scale framework for thermo-diffusionally-mechanically coupled, nonlinear, laminated plate theories with delaminations. IJSS 42, (5–6) 1465–1490] the subsequent formulation is significantly different. The differences in the two theories allow the currently proposed theory to improve on the capabilities of the previous theory; particularly in the satisfaction of the traction continuity constraints at the interfaces. It is shown that the theory is capable of providing accurate predictions for all of the fields in perfectly bonded and delaminated plates even for relatively low orders of displacement approximations. In particular, the theory is shown to provide accurate predictions for the transverse stresses that are continuous across the interfaces directly from the constitutive relations.

Competing failure mechanisms in mixed-mode fracture of an adhesively bonded polymer-matrix composite

In this paper, the use of cohesive-zone models to analyze crack-path selection in adhesive joints made from a polymer-matrix composite is demonstrated. Cohesive-zone parameters for the adhesive and composite obtained in a previous work were used without any modifications to make the predictions presented in this study. The results of numerical simulations of two mixed-mode geometries, single-lap shear and asymmetrical double-cantilever beam specimens, are compared to experimental observations. It is shown that the numerical simulations provided reasonably good predictions for the strength and failure mechanisms of the joints, allowing the nature of the competition between failure of the composite and failure of the interface to be determined.