Cohesive Traction Separation Law Research Articles

A computational homogenization approach for the study of localization of masonry structures using the XFEM

A computational homogenization method is presented in this article, for the investigation of localization phenomena arising in periodic masonry structures. The damage of the macroscopic, structural scale is represented by cohesive cracks, simulated by the extended finite element method. The cohesive traction–separation law along these cracks is built numerically, using a mesoscopic, fine scale, masonry model discretized by classical finite elements. It consists of stone blocks and the mortar joints, simulated by unilateral contact interfaces crossing the boundaries of the mesoscopic structure, assigned a tensile traction–separation softening law. The anisotropic damage induced by the mortar joints can be depicted by this method. In addition, the non-penetration condition between the stone blocks is incorporated in the averaging relations. Sophisticated damage patterns, depicted by several continuous macro-cracks in the masonry structure, can also be represented by the proposed approach. Finally, results are compared well with experimental investigation published in the literature.

Damage of the Bone-Cement Interface in Finite Element Analyses of Cemented Orthopaedic Implants

In orthopedic surgery and particularly in total hip arthroplasty, fixation of femoral implant is generally made by the surgical cement. Bone–cement interface has long been implicated in failure of cemented total hip replacement (THA), it is actually a critical site that affect the long-term stability and survival of prosthetic implants after implantation. The main purpose of this study is to investigate the effect of cement penetration into the bone on damage scenario at the interface. Previously most researchers have been performed to study damage accumulation in the cement mantle for different amount of cement penetration. In this work, bone–cement interface integrity has been studied for different mechanical properties. Cohesive traction separation law is used to detect contact damage between cement and bone. Results showed that a larger debonded area was predicted proximally and distally. Adhesion between bone and cement is affected mainly by cement penetration into the bone. Higher cement penetration into the bone leads to a good load transfer. A lower strength of the bone–cement interface due to a lower mechanical property results in faster interface damage. So we advise surgeons to well perpetrate the bone for long-term durability of cemented THA.

Analytical investigation of interfacial debonding in graphene-reinforced polymer nanocomposites with cohesive zone interface

ABSTRACTA shear-lag analysis is performed to investigate the interfacial debonding in graphene-reinforced polymer nanocomposites. The interface behavior is simulated using a cohesive traction-separation law. The applied stresses which lead to damage and debonding initiation at the interface are obtained. The progression of damage along the interface is investigated by considering the length variation of the damaged and the debonded zone against the applied stress. Also, a parametric study is performed to examine the influences of graphene volume fraction and main interface parameters including the interfacial shear strength and interfacial fracture energy on damage progress at the interface.

On the numerical simulation of crack interaction in hydraulic fracturing

In this paper, we apply the enhanced local pressure (ELP) model to study crack interaction in hydraulic fracturing. The method is based on the extended finite element method (X-FEM) where the pressure and the displacement fields are assumed to be discontinuous over the fracture exploiting the partition of unity property of finite element shape functions. The material is fully saturated and Darcy’s law describes the fluid flow in the material. The fracture process is described by a cohesive traction-separation law, whereas the pressure in the fracture is included by an additional degree of freedom. Interaction of a hydraulic fracture with a natural fracture is considered by assuming multiple discontinuities in the domain. The model is able to capture several processes, such as fracture arrest on the natural fracture, or hydraulic fractures that cross the natural fracture. Fluid is able to flow from the hydraulic fracture into the natural fracture. Two numerical criteria are implemented to determine whether or not the fracture is crossing or if fluid diversion occurs. Computational results showing the performance of the model and the effectiveness of the two criteria are presented. The influence of the angle between a hydraulic fracture and a natural fracture on the interaction behaviour is compared with experimental results and theoretical data.

Modelling peeling- and pressure-driven propagation of arterial dissection

An arterial dissection is a longitudinal tear in the vessel wall, which can create a false lumen for blood flow and may propagate quickly, leading to death. We employ a computational model for a dissection using the extended finite element method with a cohesive traction-separation law for the tear faces. The arterial wall is described by the anisotropic hyperelastic Holzapfel–Gasser–Ogden material model that accounts for collagen fibres and ground matrix, while the evolution of damage is governed by a linear cohesive traction-separation law. We simulate propagation in both peeling and pressure-loading tests. For peeling tests, we consider strips and discs cut from the arterial wall. Propagation is found to occur preferentially along the material axes with the greatest stiffness, which are determined by the fibre orientation. In the case of pressure-driven propagation, we examine a cylindrical model, with an initial tear in the shape of an arc. Long and shallow dissections lead to buckling of the inner wall between the true lumen and the dissection. The various buckling configurations closely match those seen in clinical CT scans. Our results also indicate that a deeper tear is more likely to propagate.

The influence of skin-core residual stress and cooling rate on the impact response of carbon fibre/polyphenylenesulphide

This study investigates the influence of macroscale skin-core residual stress and cooling rate on the impact response of aerospace grade carbon fibre/polyphenylenesulphide (CF/PPS). Numerical simulations are developed which analyse the thermal shrinkage and residual stress development of unidirectional (UD) lay-up configurations. Macroscale skin-core residual stresses are then incorporated into low-velocity impact simulations based on an orthotropic elastic material model. Interlaminar delamination is modelled using a bilinear cohesive traction–separation law, and intralaminar failure is modelled using the Chang–Chang strength-based failure criterion. The simulation results are compared with the results of drop tower impact tests showing qualitative agreement in terms of maximum impact force and delamination. The results of this work highlight the importance of cooling rate on the interlaminar delamination and intralaminar failure of CF/PPS.

Micromechanical boundary element modelling of transgranular and intergranular cohesive cracking in polycrystalline materials

In this paper a cohesive formulation is proposed for modelling intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model uses a multi-region boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour and specific material orientation. Transgranular surfaces are inserted as the simulation evolves and only in those grains that experience stress levels high enough for the nucleation of a new potential crack. Damage evolution along (inter- or trans-granular) interfaces is then modelled using cohesive traction separation laws and, upon failure, frictional contact analysis is introduced to model separation, stick or slip. This is the first time inter- and trans-granular fracture are being modelled together by BEM, and DBEM is being extended to include cohesive approach for anisotropic materials. Finally numerical simulations are presented to demonstrate the validity of the proposed formulation in comparison with experimental observations and literature results.

Nanomechanical modeling of interfaces of polyvinyl alcohol (PVA)/clay nanocomposite

We study interfacial debonding of several representative structures of polyvinyl alcohol (PVA)/pyrophillite-clay systems – both gallery-interface (polymer/clay interface in the interlayer region containing polymer between clay layers stacked parallel to each other) and matrix-interphase (polymer/clay interphase-region when individual clay layers are well separated and dispersed in the polymer matrix) – using molecular dynamics simulations, while explicitly accounting for shearing/sliding (i.e. Mode-II) deformation mode. Ten nanocomposite geometries (five 2-D periodic structures for tension and five 1-D periodic structures for shearing) were constructed to quantify the structure-property relations by varying the number density of polymer chains, length of polymer chains and model dimensions related to the interface deformation. The results were subsequently mapped into a cohesive traction–separation law, including evaluation of peak traction and work of separation that are used to characterise the interface load transfer for larger length scale micromechanical models. Results suggest that under a crack nucleation opening mode (i.e. Mode-I), the matrix-interphase exhibits noticeably greater strength and a greater work of separation compared to the gallery-interface; however, they were similar under the shearing/sliding mode of deformation. When compared to shearing/sliding, the tensile peak opening mode stresses were considerably greater but the displacement at the peak stress, the displacement at the final failure and the work of separation were considerably lower. Results also suggest that PVA/clay nanocomposites with higher degree of exfoliation compared with nanocomposites with higher clay-intercalation can potentially display higher strength under tension-dominated loading for a given clay volume fraction.

Ab initio determination of the traction–separation curve for a metal grain boundary: a critical assessment of strategies

We have performed a uniaxial tensile test on the Σ5 [1 0 0] 36.87° twist grain boundary (GB) in face-centred cubic Al within the framework of density functional theory in order to derive an atomistic cohesive traction–separation law. Addressing the importance of kinetics to GB breakage, we accompanied our energy-separation curve calculations by two additional studies. Firstly, using the nudged elastic band method, we determined for a series of GB separations the heights of the zero temperature barriers separating intact and broken GB configurations. Secondly, a representative subset of these transition paths was examined at finite temperature with ab initio molecular dynamics. Contrasting prevalent conclusions on GB breakage behaviour, our results suggest that the GB likely stays intact at room temperature well into the range of separations where a broken GB represents the thermodynamically favourable configuration. Given the non-negligible resulting influence on critical tensile stress and work of separation, our findings may be viewed as stressing the need for a kinetic analysis in a general first principles based uniaxial tensile test.

Modelling of the damage process of interfaces inside the WC/Co composite microstructure: 2-D versus 3-D modelling technique

The paper relates to a numerical analysis of the damage process of interface inside the WC/Co composite microstructure under tensile load by the finite element method. The focus is on comparing two modelling techniques for the damage process of interface material: flat (2-D) modelling and three-dimensional (3-D) modelling of RVEs. The damage process of metallic interface inside the Co composite is described by XFEM (eXtended Finite Element Method), based on a cohesive traction-separation law. The applied numerical tool is the commercial ABAQUS® package, where the non-linear problem is solved by the Newton-Raphson method. The use of 3-D modelling to describe the failure of WC/Co composite metallic interface enabled investigation of the damage process, starting from the moment of damage initiation to the total loss of rigidity of interface elements in a vast area of the examined microstructure.

Micromechanical Boundary Element Modelling of Transgranular and Intergranular Cohesive Cracking in Polycrystalline Materials

In this paper a cohesive formulation is proposed for modelling intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model uses a multi region boundary element approach combined with a dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour and specific material orientation. Transgranular surfaces are inserted as the simulation evolves and only in those grains that experience stress levels high enough for the nucleation of a new potential crack. Damage evolution along (inter-or trans-granular) interfaces is then modelled using cohesive traction separation laws and, upon failure, frictional contact analysis is introduced to model separation, stick or slip. Moreover some physical consideration based on cohesive energies were made, in order to guarantee the cohesive model in consideration was appropriate for the purpose of this work. Finally numerical simulations have been performed to demonstrate the validity of the proposed formulation in comparison with experimental observations and literature results.

Impact damage and residual strength predictions of 2D woven SiC/SiC composites

Lightweight, Ceramic Matrix Composites (CMC) are very attractive alternatives to superalloys for applications in hot turbine sections. However, debris, such as dirt, ice and metallic particles may be ingested by aero-engines and impact from them may cause serious damage and/or degradation to CMC components of the engines. It is important to develop predictive models and computational tools that would address this problem. The objective of this paper is to develop a progressive damage model for Ceramic Matrix Composite and implement it into ABAQUS Explicit to numerically predict impact damage and residual strength of a CMC component. To achieve this objective, experimental data on 2D woven SiC/SiC beams subjected to high velocity impact and subsequent four-point-bending tests were used. Modified Hashin–Rotem criteria were assumed for damage initiation and specialized cohesive traction-separation laws were developed to address the fiber toughening mechanism experienced by the CMC in tension and shear modes. Impact damage and four-point-bending of the SiC/SiC specimens were simulated in ABAQUS Explicit, and relatively good agreement was found between FEA predictions and test results, including the impact zone shape and size, as well as the load-deflection response and residual bending strength from the four-point-bending tests.

The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

In this paper, we present an enhanced local pressure model for modelling fluid pressure driven fractures in porous saturated materials. Using the partition-of-unity property of finite element shape functions, we describe the displacement and pressure fields across the fracture as a strong discontinuity. We enhance the pressure in the fracture by including an additional degree of freedom. The pressure gradient due to fluid leakage near the fracture surface is reconstructed based on Terzaghi’s consolidation solution. With this numerical formulation we ensure that all fluid flow goes exclusively in the fracture and it is not necessary to use a dense mesh near the fracture to capture the pressure gradient. Fluid flow in the rock formation is described by Darcy’s law. The fracture process is governed by a cohesive traction–separation law. The performance of the numerical model for fluid driven fractures is shown in three numerical examples.

Modeling of interface cracking in copper–graphite composites by MD and CFE method

Molecular dynamics (MD) method was used to study mechanical properties of copper–graphite composite interface. Mode I fracture of the interface of copper–graphite composite was modeled by considering fixed and free boundary conditions, which means slipping constraint conditions for atomic layers in the composite. The stress near crack tip and the energy changes of the system are obtained. Then a cohesive traction–separation law of copper–graphite interface can also be obtained by using the MD simulation. For the purpose of comparisons, a modeling of interfacial fracture of the composite by using a zero-thickness cohesive finite element (CFE) was carried out. It is found that there is a stress concentration but no singularity for the normal stress at the crack tip in interface obtained by using the present MD simulation and CFE method. While in the interface away from the crack tip, the obtained stress is consistent with the solution of classical interfacial fracture mechanics.

Finite element analysis of the microdroplet test method using cohesive zone model of the fiber/matrix interface

This paper presents a finite element (FE) modeling methodology to simulate and assess the importance of various factors affecting the failure mechanisms in the microdroplet test used to measure the interface shear strength (IFSS) of S-glass fiber epoxy matrix. These factors include the effect of processing-induced residual thermal stresses, progressive debonding with interfacial friction, unstable crack propagation and frictional fiber sliding on mixed-mode loading at the interface. Cohesive zone modeling approach is employed to simulate the crack propagation and interfacial failure. Mode II dominated traction separation laws are determined through numerical simulations of microdroplet test results. The importance of including the effect of residual stresses and interfacial friction in determining the cohesive traction–separation laws is illustrated. The sensitivity of the results for mode I traction–separation parameters is studied. The developed holistic modeling methodology allows for accurate determination of traction–separation behavior of the interface. This modeling effort also attempts to identify improvements to the microdroplet test method which is widely used to assess the degree of fiber/matrix adhesion.

Cohesive traction–separation laws for tearing of ductile metal plates

The failure process ahead of a mode I crack advancing in a ductile thin metal plate or sheet produces plastic dissipation through a sequence of deformation steps that include necking well ahead of the crack tip and shear localization followed by a slant fracture in the necked region somewhat closer to the tip. The objective of this paper is to analyze this sequential process to characterize the traction–separation behavior and the associated effective cohesive fracture energy of the entire failure process. The emphasis is on what is often described as plane stress behavior taking place after the crack tip has advanced a distance of one or two plate thicknesses. Traction–separation laws are an essential component of finite element methods currently under development for analyzing fracture of large scale plate or shell structures. The present study resolves the sequence of failure details using the Gurson constitutive law based on the micromechanics of the ductile fracture process, including a recent extension that accounts for damage growth in shear. The fracture process in front of an advancing crack, subject to overall mode I loading, is approximated by a 2D plane strain finite element model, which allows for an intensive study of the parameters influencing local necking, shear localization and the final slant failure. The deformation history relevant to a cohesive zone for a large scale model is identified and the traction–separation relation is determined, including the dissipated energy. For ductile structural materials, the dissipation generated during necking prior to the onset of shear localization is the dominant contribution; it scales with the plate thickness and is mesh-independent in the present numerical model. The energy associated with the shear localization and fracture is secondary; it scales with the width of the shear band, and inherits the finite element mesh dependency of the Gurson model. The cohesive traction–separation laws have been characterized for various material conditions.

An Investigation into the Fracture Mechanical Behavior of Bone Cement: Simulation Using Cohesive Zone Models (CZMs)

In this investigation, we propose a new concept to embed cohesive zone into the continuum structure of bone cement, an example of brittle material, in investigating the mechanical behavior and fracture mechanism and to predict the fracture which elastic fracture mechanics (EFM) is unable to. Four finite element (FE) models with embedded cohesive zones for the simulations of tensile, compression, double shear and 3-point bending tests have been implemented. Cohesive zones (CZ) are embedded at high risks of fracture with orientations determined by fracture mode. A bilinear cohesive traction-separation law (TSL) is applied. The fracture parameters in traction-separation curve are validated and justified in the simulations to agree well with the force-displacement curves in the four practical tests. Apart from the maximum load, the perpetual safe working load (SWL) in theory also can be predicted by tracing the history of the stiffness degradation of fractured cohesive zone by means of simulation. A distinct advantage of our numerical model is that it is able to extend to investigate the mechanical behavior and fracture mechanism of other brittle materials. The proposed method with embedded cohesive zones in FE models can be introduced to predict the fracture and to forecast the maximum load and safe working load (SWL) of the continuum structure in more complicated loading conditions.

Suggestions to the cohesive traction–separation law from atomistic simulations

The cohesive model becomes popular in crack analysis for its clear physical background and flexible implementation. The cohesive traction–separation law, however, is a critical point and will generally be empirically assumed. In the present paper the cohesive traction–separation law is investigated based on constrained three-dimensional atomistic simulations. The computations under mode I conditions show that crack growth even in the nano-scale single-crystal aluminum is in the form of void nucleation, growth and coalescence, which is similar to ductile fracture at meso-scale. The concentrations of the atomic tensile stress and the atomic hydrostatic stress at a certain distance from the crack tip characterize void nucleation and final crack growth. The Mises stress does not play a role in the material failure in the nano-scale. This implies that ductile failure under mode I loading condition is dominated by the normal traction, which agrees with the assumption of the cohesive zone model. Variations of the atomic stresses near the crack tip provide the theoretical background for the cohesive zone model and can be used to identify the cohesive traction–separation law. The traction curve is very sensitive to the distance to the crack tip, which is related with the stress triaxiality. The atomistic simulations show tendentious agreement with the known cohesive traction–separation laws, whereas the scattering of the atomic stress versus separation implies effects of the hydrostatic stress in the traction–separation law. The computation provides important information for constructing the cohesive zone model.

Time-dependent cohesive zone modelling for discrete fracture simulation

The cohesive crack tip model became very popular in fracture and failure mechanics, starting with the original publications of (Dugdale, 1960) [1] and (Barenblatt, 1962) [2] and first practical applications in the early 1980s. A compact representation of the fracture mechanical basis, kinematic and constitutive issues as well as some special characteristics of the related finite element formulation are given in the first part of this contribution. The main part is dedicated to the presentation and discussion of recent developments of cohesive finite element methods for time-dependent fracture. On the basis of a rheological model assumption, a novel viscoelastic extension for cohesive traction separation laws is presented and the resultant characteristic behaviour is depicted and compared for different loading conditions. Adopting an industrial application of a peel foil specimen, the time-dependent characteristics as well as some aspects of parameter identification and application of the material model are shown.

An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture

AbstractThis paper describes an adaptive numerical framework for cohesive fracture models based on a spacetime discontinuous Galerkin (SDG) method for elastodynamics with elementwise momentum balance. Discontinuous basis functions and jump conditions written with respect to target traction values simplify the implementation of cohesive traction–separation laws in the SDG framework; no special cohesive elements or other algorithmic devices are required. We use unstructured spacetime grids in a h‐adaptive implementation to adjust simultaneously the spatial and temporal resolutions. Two independent error indicators drive the adaptive refinement. One is a dissipation‐based indicator that controls the accuracy of the solution in the bulk material; the second ensures the accuracy of the discrete rendering of the cohesive law. Applications of the SDG cohesive model to elastodynamic fracture demonstrate the effectiveness of the proposed method and reveal a new solution feature: an unexpected quasi‐singular structure in the velocity response. Numerical examples demonstrate the use of adaptive analysis methods in resolving this structure, as well as its importance in reliable predictions of fracture kinetics. Copyright © 2009 John Wiley & Sons, Ltd.