Cohesive Zone Approach Research Articles

Boundary conditions of implicit affective influences on effort-related cardiovascular response

A large percentage of oil paintings in museum collections suffers from chemo-mechanical degradation phenomena that are primarily due to metal soap formation. Metal soaps result from the chemical reaction between metal ions present in the pigments and saturated fatty acids released by the oil paint. They appear as large protrusions that disfigure the surface texture, possibly triggering mechanical damage and flaking of the painting. Despite that these phenomena have been widely observed in situ, the interaction between chemical and mechanical degradation processes is far from being understood. This paper proposes a chemo-mechanical model to predict metal soap formation and the resulting chemo-mechanical damage in historical oil paintings. The chemical process is described by means of a diffusion-reaction model, whereby the spatial growth of the metal soap crystal takes place in a small reaction zone at the boundary of the crystal. Metal soap crystallization and growth, driven by the diffusion of saturated fatty acids and metal ions, result in a chemically-induced volumetric growth strain. This introduces stresses in the paint, ultimately promoting crack nucleation and propagation. The fracture process is simulated with a cohesive zone approach, using interface elements equipped with a traction-separation law. The mass flux-concentration relation at the interfaces is consistently specified as a function of the mechanical damage. A set of numerical simulations illustrates the capability of the model to predict metal soap crystallization and growth and the fracture induced in the paint. The study finally illustrates the influence of various chemical and mechanical parameters (i.e., the size of the metal soap nucleus, the mismatch in elastic stiffness parameters between the metal soap and paint materials, the fracture length scale of the paint material, the chemical growth strain and the reaction rate) on the chemo-mechanical degradation of the paint layer.

Conditions controlling kink crack nucleation out of, and delamination along, a mixed-mode interface crack

This paper analyzes the competition between kink nucleation and interface fracture for an interface crack (without a putative kink flaw) subject to mixed-mode loading. The simulations utilize a distributed cohesive zone approach that embeds cohesive elements throughout the entire mesh; dynamic crack path evolution occurs through a loss of cohesive traction associated with a critical separation between elements. The simulations identify mesh densities that lead to mesh-independent results for randomly oriented triangular meshes, and provide clear guidelines regarding parameters that recover toughness-controlled cracking (i.e. linear elastic fracture mechanics). The results demonstrate that, when the when the normalized bulk toughness is far from the transition between kinking and delamination, crack direction and critical loads are identical to those predicted by He and Hutchinson, who analyzed cracking from a putative flaw associated with the maximum energy release rate. Near the transition between fracture modes, kink nucleation depends on the relative size of the interface and bulk process zones, such that additional criteria are needed (beyond those postulated by He and Hutchinson). Regime maps are presented which indicate regions of kink nucleation versus delamination as a function of controlling cohesive parameters.

XFEM-based cohesive zone approach for modeling near-wellbore hydraulic fracture complexity

Near-wellbore fracture tortuosity has important impacts on the productivity of fractured oil and gas wells and the injectivity of CO2 or solids disposal injectors. Previous models for simulating near-wellbore fracture tortuosity usually assume fracture growth in linear-elastic media, without considering the effects of porous features of the rock. In this paper, a 2D fully coupled model is developed to simulate near-wellbore fracturing using the XFEM-based cohesive segment method. The model takes into account a variety of crucial physical aspects, including fracture extension and turning, fluid flow in the fracture, fluid leak-off through wellbore wall and fracture surfaces, pore fluid flow, and rock deformation. The proposed model was verified against two sets of published experimental results. Numerical examples were carried out to investigate the effects of various parameters on near-wellbore fracture trajectory, injection pressure, and fracture width. Results show that near-wellbore fracture behaviors are not only dependent on rock elastic properties and field stresses, but also greatly influenced by porous properties of the rock, such as permeability and leak-off coefficient. Some field implications were provided based on the simulation results. By overcoming some limitations of the previous models, the proposed model predicts more realistic fracture evolution in the near-wellbore region and provides an attractive tool for design and evaluation of many field operations, for which near-wellbore fracture behaviors play an important role on their successes.

A micromechanical scratch model to investigate wear mechanisms in UD-GFRP composites

This study suggests a micromechanical approach to scrutinize the glass fiber reinforced polyester (GFRP) composite tribological behavior. A single indenter scratch test (SST) using spherical tip conical indenter was adopted. The 3D finite element (FE) model was developed into ABAQUS/Explicit commercial code. Both material behavior and damage of polyester matrix and glass fiber was modeled using the Johnson Cook behavior law. Nevertheless, the fiber/matrix interface behavior is described using the cohesive zone approach via the cohesive elements. The elementary wear mechanisms owing to the SST were appraised at different attack angle and normal load by the mean of scanning electron microscope (SEM). In this work, the material removal map was built to emphasize the correlation between the tribological parameters, particularly the attack angle and the normal load, and the material removal process. The numerical results emphasized the significant effects of the attack angle and the penetration depth on the transition of the wear mechanisms from ploughing to composite damage. The experimental wear mechanisms and the predicted elementary wear mechanisms seem to be in a good agreement.

Review and benchmark study on the analysis of low-velocity impact on composite laminates

For the analysis of low-velocity impact damage, many analytical and numerical models were developed by various authors. These models range from simple approaches with a single degree of freedom up to finite element models on micro-scale. The prediction of delamination, fiber failure, and inter-fiber damage, as well as a physically sound kinematic behavior, are usually the objectives of these simulations. However, achieving satisfactory results requires massive computation and modeling efforts. In the present paper, we review the capability to capture impact damage on the coupon and the structural level. For this purpose, a large compendium of analytical and numerical analysis methods from various authors is considered. Based on existing works, six representative modeling approaches of different abstraction scales are derived and considered on a qualitative and quantitative benchmark study. We analyze all models regarding their advantages and deficiencies. With two experimental coupon impacts, all approaches are tested on their predictive capabilities on the coupon level. The applicability of these methods on the structural level is evaluated according to the benchmark results. Modeling approaches included in the benchmark range from high-fidelity models on meso-scale, macro-scale shell models, and analytical estimations. The focus is put on stacked layer models with solid or shell elements and various cohesive zone approaches. With this paper, we also present guidelines for impact analysis strategies on the structural level. These guidelines aim for a good balance between accuracy and computation effort and involve various simplifications of impact scenarios. In this regard, the range of low-velocity has to be monitored. The energy distribution over the eigenmodes of the impact system suitably indicates the limit of low-velocity impact.

Mesoscale models of interface mechanics in crystalline solids: a review

Theoretical and computational methods for representing mechanical behaviors of crystalline materials in the vicinity of planar interfaces are examined and compared. Emphasis is on continuum-type resolutions of microstructures at the nanometer and micrometer levels, i.e., mesoscale models. Grain boundary interfaces are considered first, with classes of models encompassing sharp interface, continuum defect (i.e., dislocation and disclination), and diffuse interface types. Twin boundaries are reviewed next, considering sharp interface and diffuse interface (e.g., phase field) models as well as pseudo-slip crystal plasticity approaches to deformation twinning. Several classes of models for evolving failure interfaces, i.e., fracture surfaces, in single crystals and polycrystals are then critically summarized, including cohesive zone approaches, continuum damage theories, and diffuse interface models. Important characteristics of compared classes of models for a given physical behavior include complexity, generality/flexibility, and predictive capability versus number of free or calibrated parameters.

Simulation of arterial dissection by a penetrating external body using cohesive zone modelling

In this paper, we study the dissection of arterial layers by means of a stiff, planar, penetrating external body (a ‘wedge’), and formulate a novel model of the process using cohesive zone formalism. The work is motivated by a need for better understanding of, and numerical tools for simulating catheter-induced dissection, which is a potentially catastrophic complication whose mechanisms remain little understood. As well as the large deformations and rupture of the tissue, models of such a process must accurately capture the interaction between the tissue and the external body driving the dissection. The latter feature, in particular, distinguishes catheter-induced dissection from, for example, straightforward peeling, which is relatively well-studied. As a step towards such models, we study a scenario involving a geometrically simpler penetrating object (the wedge), which affords more reliable comparison with experimental observations, but which retains the key feature of dissection driven by an external body, as described. Particular emphasis is placed on assessing the reliability of cohesive zone approaches in this context. A series of wedge-driven dissection experiments on porcine aorta were undertaken, from which tissue elastic and fracture parameters were estimated. Finite element models of the experimental configuration, with tissue considered to be a hyperelastic medium, and evolution of tissue rupture modelled with a consistent large-displacement cohesive formulation, were then constructed. Model-predicted and experimentally measured reaction forces on the wedge throughout the dissection process were compared and found to agree well. The performance of the cohesive formulation in modelling externally driven dissection is finally assessed, and the prospects for numerical models of catheter-induced dissection using such approaches is considered.

Abaqus2Matlab: A suitable tool for finite element post-processing

A suitable piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from the image processing and the integrated graph-plotting features of Matlab but also opens up new opportunities in results post-processing, statistical analysis and mathematical optimization, among many other possibilities. The software architecture and usage are appropriately described and two problems of particular engineering significance are addressed to demonstrate its capabilities. Firstly, the software is employed to assess cleavage fracture through a novel 3-parameter Weibull probabilistic framework. Then, its potential to create and train neural networks is used to identify damage parameters through a hybrid experimental–numerical scheme, and model crack propagation in structural materials by means of a cohesive zone approach. The source code, detailed documentation and a large number of tutorials can be freely downloaded from www.abaqus2matlab.com.

Progressive failure analysis of DCB bonded joints using a new elastic foundation coupled with a cohesive damage model

A new analytical model to predict progressive failure in a double cantilever beam (DCB) bonded joint is proposed. The model is based on the Winkler elastic foundation theory and coupled with a damage model based on the cohesive zone approach. The elastic behaviour of the adhesive layer is accounted for defining a new general stiffness foundation function. The model is compared and validated against experimental and finite element simulations using cohesive elements. Bonded DCB specimens with flexible and stiff adhesives and different width to thickness ratios have been tested and simulated. The new coupled model accurately predicts the load-displacement curve, damage process zone, crack propagation and stress-strain distribution response of the DCB test, whatever the thickness or stiffness of the adhesive layer. Moreover, a very low computational cost/time is required in comparison with finite element simulations.

Modeling of intergranular thermal fatigue cracking of a lead-free solder joint in a power electronic module

Fatigue of lead-free solder joints remains the most critical concern in thermo-mechanical reliability of high power modules. Due to size miniaturization requirements, fatigue properties become strongly affected by features of the solder joint microstructure. Phenomenological fatigue models based on effective material properties at macro-scale only grossly predict the engineering lifetime for some specific boundary conditions while ignoring the important effects of the microstructural mechanisms of deformation. In this study, a 3D microstructure-informed model for reproducing the intergranular fatigue crack in the solder joint of a power module is developed. The submodeling technique is applied in order to investigate accurately the critical zone of the solder joint with reasonably reduced computational time. In the submodel, the anisotropic elasticity and crystal plasticity constitutive laws are integrated for the bulk grain material, while the decohesion at grain boundaries is modeled by the cohesive zone approach. The needed crystal plasticity parameters are calibrated using the Berveiller–Zaoui transition rule to fit tensile test data for the so-called InnoLot solder alloy, and physically-based concepts are used to estimate the cohesive zone parameters at the grain scale. Simulations demonstrate how fatigue cracking occurs and propagates at grain boundaries in the solder joint. A criterion is then presented to estimate the fatigue lifetime of the entire solder joint, based on specific quantities predicted numerically.

Cohesive zone and level set method for simulation of high cycle fatigue delamination in composite materials

This paper deals with high cycle fatigue delamination in composite materials. The cohesive zone approach along with the level set method is used to simulate fatigue-driven delamination growth. The cohesive zone method is used for calculation of the energy release rate at the crack front because of its superiority over the virtual crack closure technique (VCCT) for bi-material interfaces and non self-similar crack growth. Evolution of the crack front in 3D during fatigue growth is handled with the level set method. The damage variable in the cohesive zone formulation is changed according to the updated level set field. Benchmarks are used to evaluate the performance of the proposed approach in simulation of 3D delamination growth under fatigue loading.

Viscous regularization for cohesive zone modeling under constant displacement: An application to hydrogen embrittlement simulation

The convergence problem during the cohesive zone modeling of hydrogen embrittlement in constant displacement scenario is attributed to the numerical instability which is studied analytically in the present work. The property of numerical stability is directly associated with the number of solutions for the controlling equations from the failure initiation point. It is shown that all the cases with a non-unique solution are numerically unstable thereby having convergence problem. Linear elastic and elasto-plastic material models are considered in the derivation, and the convergence properties for both models are proved essentially the same. The viscous regularization proposed by Gao and Bower (2004) proves effective in solving the convergence problem with good accuracy under constant displacement, provided that the viscosity is small enough. This is further supported by a pipeline engineering case study where the viscosity regularized cohesive zone approach is applied to the hydrogen embrittlement simulation. The stabilizing mechanism of the viscous regularization is attributed to its capacity to enforce a single solution by modifying the controlling equations. The influence of viscous regularization on symmetry modeling is also discussed.

Comparison of cohesive zone and continuum damage approach in predicting the static failure of adhesively bonded single lap joints

The paper presents a comparison of the cohesive zone model (CZM) and the continuum damage mechanics approach in predicting the static failure of a single lap joint (SLJ). The effect of mesh size and viscosity were studied to give more understanding on the failure load and computational time. Both the load–displacement response and the backface strain technique were utilised to compare the validity of predictions. Peel and shear stress and damage distributions along with the damage progression are compared to understand the behaviour of the models in predicting the static failure response. In general, both approaches show good accuracy in predicting the failure load; however, the cohesive zone approach requires shorter computation time than the continuum damage approach. The continuum damage approach shows some mesh-dependency particularly for elements with high aspect ratios, whereas the cohesive zone approach is not. The continuum damage approach is less sensitive than the cohesive zone approach to the artificial damping required to achieve convergence. Another interesting finding is using the same ultimate stress level of damage in the continuum damage approach at the peak load is much lower than that in the cohesive approach; but the failure process in this approach is faster.

Exploring the influence of micro-structure on the mechanical properties and crack bridging mechanisms of fibrous tufts

A constitutive model for tufts bridging a mode I delamination is presented. The tuft is modelled as a rod, laterally supported by an elastic medium and clamped at both ends. A fracture mechanics approach is introduced to describe the progressive debonding of the tuft from the embedding laminate. The debonding model requires the identification of stiffness, strength and toughness properties, which depend both on the laminate/tuft architecture and the constituent materials. Such identification is carried out via experimental data obtained from tensile tests on single tufts inserted in a pre-delaminated non-crimp fabric composite. The experimental results are complemented by micro-scale finite element analysis. The mode I bridging law obtained from the constitutive model is implemented into a meso-scale cohesive zone formulation. This formulation is applied to predict the response to delamination of tufted Double Cantilever Beam (DCB) coupons. The cohesive zone approach is validated by means of experimental data from DCB tests. It is shown that the proposed micro- to meso-scale modelling approach yields results in good agreement with the experiments.

Rate-dependent elastic and elasto-plastic cohesive zone models for dynamic crack propagation

To overcome deficiencies with existing approaches a new cohesive zone model is introduced and trialled in this paper. The focus is on rate-dependent cohesive zone models which have appeared in the recent literature but can be shown to suffer unrealistic behaviour. Different combinations of material response are examined with rate effects appearing either in the bulk material or localised to the cohesive zone or in both. A benefit of using a cohesive-zone approach is the ability to capture plasticity and rate effects locally. Introduced is a categorisation of bulk-material responses and cohesive zone models with particular prominence to the role of rate and plasticity. The shape of the traction separation curve is shown to have an effect and captured in this paper with application of a trapezoidal cohesive zone model. Rate dependency for the cohesive zone model is introduced in terms of a rate-dependent dashpot models applied either in parallel and/or in series. Traditionally, two possible methods are adopted to incorporate rate dependency, which are either via a temporal critical stress or a temporal critical separation. Applied singularly, tests reveal unrealistic crack behaviour at high loading rates. The new rate-dependent cohesive model introduced here couples the temporal responses of critical stress and critical displacement and is shown to provide for a stable realistic solution to dynamic fracture. Dynamic trials are performed on a cracked specimen to demonstrate the capability of the new approach.

An investigation of the step-wise propagation of a mode-II fracture in a poroelastic medium

In this paper we use an eXtended Finite Element Method based model for the simulation of shear fracture in fully saturated porous materials. The fracture is incorporated as a strong discontinuity in the displacement field by exploiting the partition of unity property of finite element shape functions. The pressure is assumed to be continuous across the fracture. However, the pressure gradient, i.e. the fluid flow, can be discontinuous. The failure process is described by the cohesive zone approach and a Tresca fracture condition without dilatancy. We investigate the propagation of a shear fracture under compression asking the question whether or not a Tresca criterion can result in stepwise propagation in a poroelastic medium. In order to evaluate possible numerical artefacts, we also look at the influence of the element size and the magnitude of a time increment. The performance of the X-FEM model and the influence of the pore pressure on the fracture propagation are addressed. Our simulations do not show evidence for step wise progression in mode II failure.

Fracture of eutectoid steel bars under tensile loading: Experimental results and numerical simulation

Construction steel bars tested under tension usually show a cup-cone fracture pattern. Nevertheless, some steels, such as the eutectoid one used for manufacturing prestressing steel wires, show a different pattern: a flat fracture surface with a dark region inside. This paper presents experimental work performed to identify the fracture mechanisms that trigger this particular flat fracture pattern and numerical simulations where it is reproduced numerically. The experimental tests are carried out on cylindrical specimens of three diameters, 3, 6 and 9mm, subjected to tension. In order to analyse the fracture mechanism, numerical simulations are performed by using the finite element method and the cohesive zone approach. To that end, a cohesive interface element with mechanical properties that depend on the stress triaxiality is presented and assessed. This approach provides reasonably good agreement with the experimental results. In addition, when compared with other popular models such as the GTN model, it presents certain advantages since it requires a smaller number of parameters to be defined.

Modeling the effect of rate and geometry on peeling and tack of pressure-sensitive adhesives

A model is developed for predicting separation along interfaces of pressure sensitive adhesives. Many authors have used the cohesive zone approach to solve such problems but the parameter calibration of such models remains uncertain. This study reports a novel method for determining such parameters. In addition, it provides crucial evidence for the suitability of the cohesive zone model approach in modelling interface fractures.Peel tests were performed at various rates using specimens which consisted of a polyester backing membrane supporting an acrylic pressure-sensitive adhesive (PSA) adhered to a polyethylene substrate. Interfacial separation of the PSA from the polyethylene substrate was observed. Finite element (FE) peeling simulations were conducted which modeled the backing-membrane as an elasto-plastic power-law material, the adhesive as a viscoelastic material and the interfacial properties with a cohesive zone model (CZM). The material properties of the backing membrane and the pressure-sensitive adhesive were measured from tensile and stress relaxation experiments. The rate-dependent CZM parameters were measured directly from poker-chip probe-tack tests which were performed at pull-off speeds which corresponded to the rates employed for the peel tests. The effect of the PSA thickness and test rate on both tack and peel was investigated experimentally, as well as modeled numerically. Good agreement was found between the experimentally measured and numerically predicted peel forces for different peel angles, speeds and PSA thicknesses. In addition, it was proven that the rate dependence observed in the peel and probe-tack data was dominated by the rate dependence of the interface properties, i.e. the time dependence of the two CZM parameters of maximum stress and fracture energy, rather than the time-dependent bulk viscoelasticity of the PSA peel arm.

Finite element simulation of dynamic brittle fracture in pipeline steel: A XFEM-based cohesive zone approach

Leaking in a CO2 pipeline could escalate to sudden crack propagation, due to a large temperature drop. The resulting drop in fracture toughness together with the pressure stresses at the defect plane leads to pipeline brittle fracture. The main objective of this study is to monitor and predict brittle fracture behaviour of API X70 pipeline steel by means of experimental and numerical approaches, respectively. Dynamic fracture properties of CO2 line pipe steels are generally assessed using the Charpy impact test. To this end, Charpy V-notch tests are performed at different temperatures in order to study the resistance of materials subjected to impact loading conditions. The Charpy test provides valuable indications on the impact properties of materials. Using the experimental results the ductile to brittle transition temperature curve is presented. The extended finite element method based cohesive zone approach is introduced to model the brittle fracture at low temperature. After validation of the developed model against experimental observation significant results from the simulation are graphically presented and discussed.

A two-scale damage model for high cycle fatigue delamination in laminated composites

In this paper a model for predicting fatigue delamination growth in laminated composites under high cycle fatigue is proposed. The model uses the cohesive zone approach and a two-scale continuum damage mechanics model. The behavior of the interface material is considered quasi-brittle at the macro scale while plastic deformations are allowed at the scale of micro-defects. The validity of the proposed model is investigated through several standard tests using experimental data from literature. Good agreement between the numerical and experimental results is observed. The model is also capable of simulating fatigue under variable amplitude loading. This feature of model is shown through several sample simulations.