Bilinear Cohesive Law Research Articles

An XFEM/CZM based inverse method for identification of composite failure parameters

An experimental–numerical methodology for identification of mode I failure parameters, namely the critical strain energy release rate (GIc) and the strength (σc) of unidirectional carbon/epoxy composite is proposed. Using an inverse procedure, the experimental results of a double cantilever beam (DCB) test are used in conjunction with a counterpart extended finite element method (XFEM) cohesive zone model (CZM). In the developed numerical model, the notch and the crack path are located and enriched implicitly by a level set function and the crack propagation is controlled by a bi-linear cohesive law. The cost function accounts for the error between the numerical and the experimental results, and it is minimised in a least squares sense by updating the values of the two independent parameters. The determined critical strain energy release rate is then compared with the one obtained using the corrected beam theory (CBT), and the identified strength is compared with the one estimated experimentally. Globally, the results are very well in agreement and the proposed methodology seems to be efficient to determine accurately the composite failure parameters.

Fatigue crack growth study of CFRP patch repaired Al 2014-T6 panel having an inclined center crack using FEA and DIC

In this work, the fatigue life of unrepaired and repaired Al-2014-T6 panels with an inclined center crack is investigated. Cracked panels are repaired through single- and double-sided adhesively bonded carbon fiber reinforced polymer (CFRP) patch. The fatigue crack growth is monitored experimentally using digital image correlation and numerically using 3D finite element analysis. The adhesive-interface between the panel and patch is modeled using bilinear cohesive law. The CFRP/Al-2014-T6 adhesive-interface properties are obtained from the baseline tests. Fatigue life of double-sided repaired panel is observed to be twice that of single-sided. And non-uniform crack front is observed in single-sided repaired panels.

Investigation of delamination and damage due to free edge effects in composite laminates using cohesive interface elements

Composite materials due to high strength and stiffness to their weight ratio are widely used in different structures. Hence, it is necessary to predict their failure behavior under loading. The delamination due to interlaminar stresses at free edges is one of the most important damage modes in laminated composites. In this study, this mode in cross-ply and angle-ply laminates has been investigated using a cohesive zone model. The advantage of this method is the possibility of modeling the delamination initiation and propagation without requirement to the presence of initial crack and remeshing. Hence, at first an interface element based on bilinear cohesive law was implemented in Ansys. Next, laminated plates with different lay-ups under uniaxial tension loading were modeled. Also Hashin’s failure criteria were used to predict ply damage initiation. Numerical results show that in angle-ply laminates with small fiber angle orientation, delamination in the shear mode is the dominant mode in the loss of structural strength. The numerical and experimental results for global load-displacement response show a good agreement. Also numerical results show that in cross-ply laminates even under in-plane loading, the damage behavior extremely depends on the stacking sequence. Studies show that in cross-ply laminates under uniaxial tension, if 90o plies are inserted in top and bottom surface of the laminate, the mode I delamination and matrix cracking will start later.

Editorial TS: 2nd international conference on structural adhesive bonding

© A m This special issue of Applied Adhesion Science (AAS) contains selected papers presented at the 2nd International Conference on Structural Adhesive Bonding (AB 2013). AB 2013 was chaired by the two of us and was held in Porto, Portugal during July 4–5, 2013. The goal of the conference was to provide a unique opportunity to exchange information, present the latest results as well as to discuss issues relevant to structural adhesive bonding research today. Approximately 130 papers were presented by researchers from more than 20 countries. In order to share the work presented at the conference, a selection of papers was made which resulted in the present Special Issue. The first paper by Quintino et al. is related to training and qualification of adhesive bonding personnel at the European level by the European Welding Federation (EWF). The courses are offered, namely European Adhesive Engineer, European Adhesive Specialist and European Adhesive Bonder. These courses are useful for companies to benefit from improved competitiveness in the global market place and from an increased likelihood of trouble-free production and service performance of their products. In the next paper, Paiva et al. study the importance of the surface treatment in the peeling strength of joints for the shoe industry. The authors considered the following materials: natural leather, thermoplastic rubber (TR), polyurethane (PU) and a polyurethane non structural adhesive solvent based. This work allows manufacturers of footwear to minimize the number of operations in the manufacture of shoes, while still being capable of satisfying the minimum requirements for the sector. In the third paper, Zhang et al. analysed the strength of adhesive joints of riser pipes in deep sea environment loadings such as external pressure, internal pressure, tension, torsion, bending loadings. The authors conclude that singular stress fields exist around the end of the interface. The riser pipe under external pressure, internal pressure and tension loading is more prone to break than under bending and torque loading. The last paper by Valoroso and De Barros is related to adhesive joint computations using cohesive zones. Numerical results are presented for a double cantilever beam geometry with varying thickness for which bilinear and exponential cohesive laws are considered. The authors conclude that the size of the process zone is found to be quite sensitive to the specimen characteristic size. The preparation of this Special Issue has been an interesting experience for the guest editors. The review process gave a deeper insight into the various aspects of adhesive joints and the chance to discuss in detail the manuscripts directly with the authors. We would like to thank the authors for their patience with the process and the

A continuum constitutive model for the simulation of fabric-reinforced composites

Fibre-reinforced polymer-based composite materials fail due to a wide variety of interacting damage mechanisms, which require complex constitutive models in order to develop Finite Element (FE) predictive analysis. In this paper, a constitutive behaviour model based on Continuum Damage Mechanics (CDM) is proposed for the simulation of fabric-reinforced composites. The model uses simplified loading functions in order to minimise the computational time required to obtain the numerical solution. To reduce the influence of mesh refinement on the numerical solutions, the Crack Band Model (CBM) algorithm is implemented. In this way, the energy dissipated at each point in the material is regularized for the different damage mechanisms. This newly-formulated constitutive model is implemented by means of a user-defined material subroutine in Abaqus/Explicit FE code. The model is validated by comparing the results of FE predictions with experimental data from open hole specimens, under quasi-static tensile loading conditions. A good correlation between the numerical and experimental results is achieved when using a bilinear cohesive law, for different combinations of hole diameter and specimen width.

Cohesive zone model for high-cycle fatigue of adhesively bonded joints under mode I loading

A cohesive zone model adequate for simulating the behaviour of adhesively bonded joints subjected to high-cycle fatigue and pure mode I loading is presented. The bilinear cohesive zone law with linear softening relationship was considered. The main advantage of the proposed formulation is the use of a unique damage parameter accounting for cumulative damage resulting from static and fatigue loading. The method was implemented in a user subroutine of the commercial finite element software Abaqus®. Two-dimensional numerical simulations of the double cantilever beam test using different representative combinations of the modified Paris law coefficients were performed. It was verified that the results of the model simulate with excellent agreement the several Paris laws used as input, thus demonstrating the good performance of the method as a predictive tool.

Interface analysis and design in carbon nanotube array composite based on cohesive finite element approach

Mechanical properties of composites can be significantly improved by using well-aligned carbon nanotube array (CNTA) as reinforcements. However, damage and cracks at the interface between carbon nanotubes (CNTs) and matrix are still major factors hampering the desired reinforcement effect of the CNTA. In this paper, a micromechanics-based bilinear cohesive law was applied in cohesive finite element model to characterize CNT/matrix interface. The interfacial properties were described by varying the values of cohesive strength and fracture energy of the interface. Then numerical simulation for the interfacial fracture and macroscopic properties of the CNTA composites under transverse loadings was conducted based on the present cohesive finite element method. Remarkable influences of interfacial properties on the overall properties of the CNTA composites were verified. The brittle failure mode of the CNTA composites was found to be shifted to the ductile mode as the interface became more expandable. Moreover, it is proved that the CNTA composites have a potential improvement with increased CNTA volume fraction and optimized interfacial cohesive parameters.

Temperature dependence of cohesive laws for an epoxy adhesive in Mode I and Mode II loading

The influence of the temperature on the cohesive laws for an epoxy adhesive is studied in the glassy region, i.e. below the glass transition temperature. Cohesive laws are derived in both Mode I and Mode II under quasi-static loading conditions in the temperature range $$-30\le T \le 80^{\,\circ }$$ C. Three parameters of the cohesive laws are studied in detail: the elastic stiffness, the peak stress and the fracture energy. Methods for determining the elastic stiffness in Mode I and Mode II are derived and evaluated. Simplified bi-linear cohesive laws to be used at any temperature within the studied temperature range are derived for each loading mode. All parameters of the cohesive laws are measured experimentally using only two types of specimens. The adhesive has a nominal layer thickness of 0.3 mm and the crack tip opening displacement is measured over the adhesive thickness. The derived cohesive laws thus represent the entire adhesive layer as having the present layer thickness. It is shown that all parameters, except the Mode I fracture energy, decrease with an increasing temperature in both loading modes. The Mode I fracture energy is shown to be independent of the temperature within the evaluated temperature span. At $$80^{\,\circ }$$ C the Mode II fracture energy is decreased to about 2/3 of the fracture energy at $$-30^{\,\circ }$$ C. The experimental results are verified by finite element analyses.

Size Effect Analysis in Laminated Composite Structure using General Bilinear Fit

Abstract A bilinear cohesive law analyzes the in-plane nominal strength of Quasi-brittle material containing a single hole in which damage around the open hole is represented by a line crack loaded on its faces. This analysis of quasi-brittle structures has been done by taking into account the geometry and length of fracture processing zone and the shape of the cohesive law. The nominal strength based on size effect is analyzed for similarly shape specimen geometry. Simple design tables for the bilinear cohesive law have been developed respect to the specimen types offering a very useful for engineering designers.

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.

Delamination of an elastic film from an elastic–plastic substrate during adhesive contact loading and unloading

Adhesive contact between a rigid sphere and an elastic film on an elastic–perfectly plastic substrate was examined in the context of finite element simulation results. Surface adhesion was modeled by nonlinear springs obeying a force-displacement relationship governed by the Lennard–Jones potential. A bilinear cohesive zone law with prescribed cohesive strength and work of adhesion was used to simulate crack initiation and growth at the film/substrate interface. It is shown that the unloading response consists of five sequential stages: elastic recovery, interface damage (crack) initiation, damage evolution (delamination), film elastic bending, and abrupt surface separation (jump-out), with plastic deformation in the substrate occurring only during damage initiation. Substrate plasticity produces partial closure of the cohesive zone upon full unloading (jump-out), residual tensile stresses at the front of the crack tip, and irreversible downward bending of the elastic film. Finite element simulations illustrate the effects of minimum surface separation (i.e., maximum compressive surface force), work of adhesion and cohesive strength of the film/substrate interface, substrate yield strength, and initial crack size on the evolution of the surface force, residual deflection of the elastic film, film-substrate separation (debonding), crack-tip opening displacement, and contact instabilities (jump-in and jump-out) during a full load–unload cycle. The results of this study provide insight into the interdependence of contact instabilities and interfacial damage (cracking) encountered in layered media during adhesive contact loading and unloading.

A fracture mechanics model to describe the buckling behavior of lightly reinforced concrete columns

In order to correctly model the behavior of slender columns made of lightly reinforced concrete (RC) subjected to buckling load, both tensile fracture and compressive damage should be taken into account. In this work, we propose to consider both failure types as cohesive cracks, governed by a bilinear cohesive law for traction or a linear-decreasing softening equation for compression. Since the columns are lightly reinforced, we assume only one single crack is to propagate at the column central section. The resulted two-dimensional FEM model is implemented in a commercial software for large deformations to take into account geometry changes in each iteration. The model is validated against experimentally obtained results. In addition, parametric studies are carried out to study the sensitivity on slenderness ratio, reinforcement ratio and concrete compressive strength. Good agreement for the comparison with both experimental data and ACI code is achieved. Due to its simplicity, the developed model provides a useful tool for the design of structural elements.

Predicting low-velocity impact damage in composites by a quasi-static load model with cohesive interface elements

AbstractA numerical model is developed for predicting low-velocity impact damage in laminated composites. Stacked shell elements are employed to model laminate plies with discrete interface elements in pre-determined zones to model the onset and propagation of matrix cracks and delamination. These interface elements are governed by a bi-linear cohesive failure law. Cohesive element zone size is determined by a separate finite element analysis using solid elements to identify the stress concentration sites. In order to save the computational effort, low-velocity impact load is modelled by quasi-static loading. Influence of contact force induced friction on shear driven mode II delamination is modelled by a friction model. For a clustered cross-ply laminate, calculated impact force and damage area are in good agreement with the test results. It is shown that matrix cracks should be included in the model in order to simulate delamination in adjacent interface. The practical outcome of this research is a validated modelling approach that can be further improved for predicting low-velocity impact damage in other stacking sequences.

Micromechanical-based criteria for the calibration of cohesive zone parameters

This paper presents a new micromechanical model for a collection of cohesive zone models embedded between each mesh of a finite element-type discretization. It aims to fully extend the previous linear results of Blal et al. (2012) [11] to the calibration of damageable cohesive parameters (cohesive peak stress, critical opening displacement, cohesive energy, etc). The main idea of the approach consists in replacing the underlying cohesive-volumetric discretization by an equivalent ‘matrix-inclusions’ composite. The overall behavior of this equivalent composite is estimated using homogenization schemes (Hashin–Shtrikman estimate and the modified secant method) and is given in a closed-form as function of both cohesive and bulk properties and the mesh density. In the particular case of a bilinear cohesive law a micromechanical damage model for quasi-brittle materials is derived. The corresponding local-to-global relationships are obtained for any overall triaxiality loading ratio.

Crack simulation of nano-bioceramic composite microstructures with cohesive failure law: Effects of sintering, loads and time

Crack behaviour of zirconia toughened alumina (ZTA) microstructures are simulated with a two-dimensional finite element simulation. Finite element models are developed using actual microstructure images of zirconia toughened alumina and a bilinear cohesive zone law. Simulation conditions are similar to those found at frictional contact between a femoral head and an acetabular cup of hip prosthesis. Effects of microstructures and contact stresses are investigated in terms of crack generation. Moreover, fatigue behaviour of a microstructure is determined by performing simulations under cyclic loading conditions. It is identified that total crack length observed in a microstructure increases with increasing the magnitude of applied contact stress. Cyclic simulation results show that progressive crack growth occurs with respect to number of fatigue cycles. In addition, it is demonstrated that zirconia grains resist crack growth in microstructures.

Bilinear approximations to the mode II delamination cohesive law using an inverse method

Cohesive zone modelling has proved to be a powerful tool to model delamination problems in high performance composites. Application to mode II delamination is of particular interest due to the large fracture process zone. In this paper, bilinear approximations to the mode II delamination cohesive law were determined for two carbon/epoxy composites. This was achieved by an inverse method that consisted of making Finite Element Analyses fit experimental load–displacement curves measured in well-known End-Notched Flexure tests. The optimal parameters of the bilinear cohesive law were determined by a genetic algorithm. The results showed the adequacy of the bilinear cohesive law and of the methodology employed.

Two-dimensional finite element simulation of fracture and fatigue behaviours of alumina microstructures for hip prosthesis

This paper describes a two-dimensional (2D) finite element simulation for fracture and fatigue behaviours of pure alumina microstructures such as those found at hip prostheses. Finite element models are developed using actual Al2O3 microstructures and a bilinear cohesive zone law. Simulation conditions are similar to those found at a slip zone in a dry contact between a femoral head and an acetabular cup of hip prosthesis. Contact stresses are imposed to generate cracks in the models. Magnitudes of imposed stresses are higher than those found at the microscopic scale. Effects of microstructures and contact stresses are investigated in terms of crack formation. In addition, fatigue behaviour of the microstructure is determined by performing simulations under cyclic loading conditions. It is shown that crack density observed in a microstructure increases with increasing magnitude of applied contact stress. Moreover, crack density increases linearly with respect to the number of fatigue cycles within a given contact stress range. Meanwhile, as applied contact stress increases, number of cycles to failure decreases gradually. Finally, this proposed finite element simulation offers an effective method for identifying fracture and fatigue behaviours of a microstructure provided that microstructure images are available.

Novel cohesive beam model for the End-Notched Flexure (ENF) specimen

This paper presents a new Cohesive Beam Model (CBM) for the mode II interlaminar fracture End-Notched Flexure (ENF) specimen. The ideal linear elastic solution agrees with a recent analysis and is similar to the well-known Corrected Beam Theory. However, the cohesive zone is known to be particularly important for modelling the large mode II fracture process zone. CBM with a bilinear cohesive law agreed very well with finite element analyses. Comparison with experimental results for two carbon/epoxy laminates indicated that the bilinear cohesive law provides a fairly good conservative approximation.

Strength prediction of adhesive joints after cyclic moisture conditioning using a cohesive zone model

This paper presents a methodology to predict the strength of adhesive joints under variable moisture conditions. The moisture uptake in adhesive joints was determined using a history dependent moisture prediction methodology where diffusion coefficients were based on experimental cyclic moisture uptake of bulk adhesive samples. The predicted moisture concentrations and moisture diffusion history were used in a structural analysis with a cohesive zone model to predict damage and failure of the joints. A moisture concentration and moisture history dependent bilinear cohesive zone law was used. The methodology was used to determine the damage and failure in aluminium alloy – epoxy adhesive single lap joints, conditioned at 50 °C and good predictions of failure load were observed. The damage in the adhesive joints decreased the load carrying capacity before reaching the failure load and a nonlinear relationship between the load and displacement was observed. Changes in crack initiation and crack propagation were also observed between different types of joints. The presented methodology is generic and may be applied to different types of adhesive joint and adhesive.

The Effect of Interface Damage on Macroscopic Constitutive Behavior of Composite Materials

Base on the finite element method, the effect of interface damage on macroscopic constitutive behavior of composite materials subjected to uniaxial tension was studied. A bilinear cohesive law, which relates the traction and displacement jumps, was adopted to model the debonding of particle/matrix interface. Stress-strain curves for a material with different interface properties, particle size and volume fraction were discussed in detail. The results show that the damage due to debonding of particle/matrix interfaces can significantly affect the macroscopic response of composite materials, and that the interaction of particles is innegligible in multi-particle structure.