Cohesive Zone Approach Research Articles

A combined ALE-cohesive fracture approach for the arbitrary crack growth analysis

This work introduces an advanced numerical model, based on a cohesive zone approach and the moving mesh technique, for simulating fracture propagation in quasi-brittle materials. The proposed procedure involves two stages: first, a mesh boundary representing the crack is selected and aligned with the crack growth direction by using the Arbitrary Lagrangian-Eulerian (ALE) methodology; next, a zero-thickness interface cohesive element, equipped with a traction-separation law, is adaptively inserted along the previously selected mesh boundary, in order to describe the nonlinear fracture process. The proposed model allows for multiple crack onset and propagation without requiring mesh-updated procedures and sensibly reduces the well-known mesh dependency issues of the standard discrete fracture approaches. Numerical analyses of mixed-mode fracture in concrete specimens are performed and suitable comparisons with experiments show the effectiveness and reliability of the proposed model in predicting arbitrary crack growth.

Modeling of 2D thermo-elastic brittle fracture using smoothed floating node method

This paper presents an extension of the recently developed smoothed floating node method (SFNM) with cohesive zone approach to model crack growth in elastic materials under thermo-elastic loading conditions. The SFNM utilizes floating nodes to accurately model the crack by activating dormant nodes at intersection points of crack path and the corresponding element edges. Through the activation of floating nodes, the cracked element transforms into sub-elements, facilitating separate integration of each sub-element. A smoothing cell-based integration technique is employed to convert the area integral to line integral which mitigates the element distortion issues. The temperature distribution is initially determined across the entire domain, and then imposed as thermal loads in the 2D domain. The thermal stress intensity factor is calculated for both homogeneous and bi-material specimens using the interaction energy integral approach, and the crack propagation is predicted using circumferential stress criterion. The accuracy of the proposed framework is demonstrated with several benchmark problems of fracture mechanics. The develop framework yields comparable results with the available literature with less modeling complexity.

Phase field-based cohesive zone approach to model delamination in fiber-reinforced polymer composites

In the present work, a unified phase field-based cohesive zone model (PF-CZM) has been utilized to predict bulk fracture and most importantly interfacial delamination in carbon fiber-reinforced polymer composites (CFRP). The formulation is based on the classical phase-field approach of energy minimization, with a rational degradation function and a polynomial-type crack geometric function. Incorporation of those provides the PF theory to integrate various traction–separation behaviors by choosing optimal constitutive functions and makes the theory capable of predicting the quasi-brittle type of fracture. Since the interfacial delamination in composites occurs either due to adhesive failure or decohesion between stacked lamina, the PF-CZM model is used to predict such failure by exploiting the cohesive zone flavor of the model. Further, the model inherently incorporates the strength of the material without any additional calibration. Various standard simulations are performed considering CFRP geometry where delaminations due to adhesive failure or interface decohesion occur in a mode-I and mode-II fashion. The model is observed to predict mode-I and mode-II separation accurately. To test the accuracy of the model an experimental validation is also performed. In addition to the delamination, open hole tension (OHT) simulations of CFRP lamina for different fiber orientations are considered to validate the anisotropic crack growth predictions, and the results are compared with experiments.

Prediction of fracture evolution in the TiN/Al thin films based on a full-field modelling approach

The classical approach to fracture simulation in a thin film for bioengineering applications neglects the underlying complex morphology of the deposited layer, leading to inaccurate numerical predictions. That may carry high risks during product development and its further exploitation, especially in biomedical applications. Therefore, here, we demonstrate the new approach to numerical investigation of the fracture evolution in pulsed laser-deposited (PLD) titanium nitride (TiN) thin films under loading conditions based on the full-field model of layer columnar morphology. We use the TiN film deposited on the aluminium (Al) substrate as a case study. Based on the nanoindentation test, we first determine the flow stress characteristics of the Al substrate and TiN/Al structure. An inverse analysis technique allowed us to precisely recalculate measured load–displacement values into the required stress–strain curve. Then, we developed a full-field model based on the digital material representation (DMR) concept for further investigation. The DMR was generated to replicate major morphological features of the deposited thin film identified under transmission electron microscop (TEM). Finally, we incorporated the TiN/Al full-field model into the finite element analysis with a cohesive zone approach for local analysis of fracture behaviour. Inverse analysis based on the developed direct model and experimental measurements allowed us to identify the parameters of the fracture model. As a result, we proved that the full-field model based on the digital material representation concept could be used for reliable predictions of local fracture development along the morphological features of the deposited thin film.

Snap-through Crack Propagation in Architected Bonded Interfaces Analyzed Using a Mechanoluminescent SAO/E Coating.

We investigate the mechanics of crack propagation in architected adhesive joints whose adherends are inspired to the base plate of the barnacle Amphibalanus (=Balanus) amphitrite, and feature an array of buried hollow cylindrical channels located perpendicularly to the direction of crack growth. Selective laser sintering is used to obtain the adherends that are subsequently bonded in the double cantilever beam configuration to ascertain the mechanics of crack growth. Finite element (FE) simulations are deployed to determine the strain energy release rate (ERR) and to elucidate the salient features of the fracture process. It is shown that the channels induce a modulation of the ERR and enable a crack tip shielding mechanism. Besides, FE simulations based on a cohesive zone approach indicate the occurrence of crack pinning/depinning cycles that are validated via experiments. A highlight of the present study is the use of a mechanoluminescent (ML) coating to unravel the evolution of the transient stress field in the crack tip region. The coating comprises an optical epoxy resin loaded with doped strontium aluminate phosphors (SrAl2O4/Eu2+) and converts mechanical energy into light emission with intensity proportional to the magnitude of mechanical stress. By combining the ML emission patterns with the stress distribution obtained from FEA, we unveil interesting details of snap-through cracking in architected bio-inspired adhesive joints.

Effect of moisture on the delamination properties of fractured PVB-laminated glass: A joint experimental and numerical study

In practical applications of laminated glass, local moisture exchange may occur through panel edges or glass cracks and leads to a significant impact on the post-fracture behavior of laminated glass. In this paper, the effect of moisture on the interfacial delamination properties of PVB-laminated glass is studied. At the experimental level, quasi-static uniaxial tensile tests on pure PVB and through-cracked tensile tests on PVB-laminated glass were conducted at room temperature, considering four initial moisture levels, i.e., 0.2%, 0.4%, 0.6%, and 0.8%, corresponding to relative humidity of 13.6%, 25.6%, 36.1%, and 44.5%, respectively. It is worth noting that for each laminated glass specimen used in the TCT tests, a controlled moisture content was uniformly introduced into the interlayer during the manufacturing process, which is different from traditional aging tests. This allowed for characterization of the moisture-dependent material properties of PVB and interfacial delamination properties of fractured PVB-laminated glass under controlled and uniform moisture conditions. At the numerical level, the moisture-dependent material behavior of the PVB interlayer was first calibrated with 5-parameter Mooney-Rivlin hyperelastic material laws. The moisture-dependent material laws and through-cracked tensile (TCT) test results were then used for an inverse determination of the cohesive strength and interfacial fracture energy at PVB-glass interface through a numerical cohesive zone approach. This study found that the moisture content can significantly affect the interfacial properties of the PVB-laminated glass, with the cohesive strength and interfacial fracture energy decreasing by approximately 70% and 50%, respectively, as the moisture content increases from 0.2% to 0.8%. The changes of the above interfacial parameters can be approximated by linear relationships. In addition, the energy absorption of fractured PVB laminated glass decreases significantly with increasing moisture content due to the degradation of PVB interlayer performance and reduced interfacial adhesion. Therefore, the effect of moisture content should be considered in the practical design of certain laminated glass applications to ensure post-fracture load-bearing capacity.

Phase field model for mixed mode fracture in concrete

Concrete is a quasi-brittle material and generally fails in mixed mode I-II fracture. The fracture energy release in mode I and mode II during crack propagation is usually different. However, the tensile test fracture toughness has generally been considered in most of the numerical models to study fracture in concrete. In this paper, a phase field model is presented which considers the fracture energy of mode I and mode II for mixed mode I-II fracture simulation in concrete. In addition, it uses a fracture mode controlling parameter χ which, in a sense, controls the governing failure criterion. The post-peak material response is modeled using a cohesive zone approach. The effect of the length scale parameter, mesh size and χ is investigated. For validation, a single-edge notch beam with a notch at various eccentricities is considered. It is shown that the model is mesh independent for a sufficiently fine mesh in cracking region. Also, the effect of the length scale parameter on global response is insignificant. It is observed that χ≥1 gives satisfactory results both for mode I and mixed mode I-II fracture in single edge notch concrete beam. The numerical results for the load–displacement curve are compared with the experimental data both qualitatively and quantitatively. It is concluded that the proposed phase field model can simulate mode I and mixed mode I-II fracture in concrete with sufficient accuracy.

The Influence of Time, Atmosphere and Surface Roughness on the Interface Strength and Microstructure of AA6061–AA1050 Diffusion Bonded Components

Diffusion bonding experiments followed by tensile testing were conducted on cylindrical pairs of AA6061-AA1050 aluminum alloys. The influence of bonding time, atmosphere and surface roughness on the resulting interface strength was studied. Metallurgical characterization was performed to study the quality of the bonded interface for different process conditions, and also to investigate the process of oxide formation on the specimen surface. Finite element analysis of the bonding experiments was used to study the thermo-mechanical fields during the bonding process. Using a cohesive zone approach for modelling the bonded interface, the bond strength for the different process parameters was quantified. The results demonstrate that high bond strength can be obtained even for specimens bonded in an air furnace, provided the surface roughness is low. When the surface roughness increases, specimens bonded in air show a reduction in interface strength, which is not observed for specimens bonded in vacuum. Inspection of the bonded interface suggests that this reduction in interface strength can be attributed to oxidation and pockets of air trapped between the asperities of the contact surface, which hinder diffusion and plastic flow.

Smoothed floating node method for modelling cohesive fracture in quasi-brittle materials

This paper presents a numerical framework for implementation of cohesive zone model with smoothed floating node method (SFNM) for failure analysis of quasi-brittle materials. The nonlinear behavior of material inside the fracture process zone in front of the crack tip is modeled with a potential-based intrinsic cohesive zone approach. Here, SFNM is used to represent the kinematics of crack and the crack front inside the domain without the requirement of remeshing and discontinuous enrichment functions during crack growth, hence resolves the issues associated with the existing discrete numerical methods. A strain smoothing technique is adopted over the domain through which classical domain integration changes to line integration along each boundary of the smoothing cell, hence derivative of shape functions are not required in the computation of the field gradients, thus resolves the issue of element distortion. The proposed numerical framework is firstly verified using the patch test of the two-dimensional specimen under mode I and mode II loading conditions and subsequently extended for solving the two-dimensional standard fracture problems. The effectiveness of the proposed framework is checked by comparing the computational results with the available literature results.

Finite elements analyses of early-stage crack propagation in aluminum wire bonds due to power cycling

This paper focuses on the thermomechanical behaviour and the consecutive damage of the bond-wire contacts in power semiconductors. Electro-thermal-mechanical finite element analysis of power cycle loads was used to model realistic transient temperature loadings as well as mechanical stresses. Mechanical damage modelling using the cohesive zone approach was used in conjunction with coupled finite element analysis. Parallel to the theoretical research, a pulse width modulation power cycling test bench was realized, and thermal cycles tests were carried out on power modules with temperature swing ∆Tj = 30°C and minimal temperature Tj, min = 55°C. Electron Back Scatter Diffraction was used to investigate crack early-stage crack propagation and crack propagation of the samples. Fatigue cracks were found to be always initiated from the interface wire –metallization and propagate exactly at the contact.

A temperature- and conversion-dependent cohesive zone approach for the calculation of process-induced damage in adhesive bondlines of multi-material structures

Adhesive bondlines in multi-material car bodies underlie various influences from the production process. Especially the mismatch of the coefficient of thermal expansion during the oven process of cathodic dip coating can cause damage and weaken the joint strength. Temperature-dependent mechanical properties and the increasing conversion that describes the degree of cure of the adhesive are important parameters affecting the adhesive bondlines during production. To take these effects into account in numerical simulations, a cohesive zone approach, which is commonly used to model adhesive bondlines in structural simulations, is adapted to a one-component, hot curing, structural epoxy adhesive for body-in-white manufacturing and is extended with a reaction kinetic model of the curing reaction, conversion-dependent material properties, and temperature dependency. The investigation of the material properties using a rheometer and differential scanning calorimetry experiments is described. Furthermore, the cohesive zone model is presented and an experimental validation of the model using customized tapered-double-cantilever-beam specimens to investigate the crack opening behavior of incompletely cured adhesives shows a good agreement with the numerical data.

A smoothed particle hydrodynamics approach for phase field modeling of brittle fracture

Fracture is a very challenging and complicated problem with various applications in engineering and physics. Although it has been extensively studied within the context of mesh-based numerical techniques, such as the finite element method (FEM), the research activity within the Smoothed Particle Hydrodynamics (SPH) community remains scarce. SPH is a particle-based numerical method used to discretize equations of continuum media. Its meshfree nature makes it ideal to simulate fracture scenarios that involve extreme deformations. However, to model fracture, SPH researchers have mostly relied on ad-hoc empirical local damage models, cohesive zone approaches, or pseudo-spring models, which come with a set of drawbacks and limitations. On the other hand, phase field models of brittle fracture have recently gained popularity in academic circles and provide significant improvements compared to previous approaches. These improvements include the derivation from fundamental fracture theories, the introduction of non-locality, and the ability to model multiple crack initiation, propagation, branching, and coalescence, in situations where no prior knowledge of the crack paths is available. Nevertheless, phase field for fracture has not been studied within SPH. In this proof-of-concept paper we develop and implement a phase field model of brittle fracture within the context of SPH. Comprehensive mathematical and implementation details are provided, and several challenging numerical examples are computed and illustrate the proposed method’s ability to accurately and efficiently simulate complex fracture scenarios.

An integrated inverse numerical–experimental approach to determine the dynamic Mode-I interlaminar fracture toughness of fibre composites

A combined numerical–experimental methodology is presented to determine the dynamic Mode-I fracture properties of Fibre-Reinforced Polymer (FRP) composites. The experimental aspect consists of a modified Wedge-Double cantilever Beam (WDCB) test using a Split Hopkinson Pressure Bar (SHPB) set-up followed by a numerical inverse modelling strategy using cohesive-zone approach. The proposed method is inherently robust due to the use of three independent comparison metrics namely, the strain–displacement response, the crack length history and the crack opening history to uniquely determine the delamination properties. More importantly, the complexity of dealing with the frictional effects between the wedge and the DCB specimen is effectively circumvented by utilising appropriate acquisition techniques. The proposed methodology is applied to extract the high-rate interlaminar fracture properties of a carbon fibre reinforced composite, IM7/8552 and it is further shown that a high level of confidence in the calibrated data can be established by adopting the proposed methodology.

A microstructure informed and mixed-mode cohesive zone approach to simulating hydrogen embrittlement

Hydrogen induced failure under uniaxial tension is simulated in a duplex stainless steel considering microstructural feature of the material. There are three key ingredients in the modelling approach: image processing and finite element representation of the experimentally observed microstructure, stress driven hydrogen diffusion and diffusion coupled cohesive zone modelling of fracture considering mixed failure mode. The microstructure used as basis for the modelling work is obtained from specimens cut in the transverse and longitudinal directions. It is found that the microstructure significantly influences hydrogen diffusion and fracture. The austenite phase is polygonal and randomly distributed in the transverse direction, where a larger effective hydrogen diffusion coefficient and a lower hydrogen fracture resistance is found, compared to the specimen in the longitudinal direction, where the austenite phase is slender and laminated. This indicates that the proper design and control of the austenite phase help improve hydrogen resistance of duplex stainless steel. The strength of the interface in the shear direction is found to dominate the fracture mode and initiation site, which reveals the importance of considering mixed failure mode and calibrating the hydrogen induced strength reduction in shear.

Development of a microstructural cohesive zone model for intergranular hydrogen environmentally assisted cracking

During the initial stages of hydrogen environmentally assisted cracking (HEAC), including crack incubation, initiation and microstructurally short cracking, the geometrical configuration of the microstructure greatly influences the crack growth behaviour. Therefore, there is a big incentive to generate a model which can replicate intergranular HEAC at a microstructural scale. This report provides a general framework to implement a microstructural intergranular HEAC model by using a cohesive zone approach in Abaqus. The parameters of the phenomenological model were fitted by using in-situ synchrotron tomography observations of crack initiation and propagation during HEAC of AA7449-T7651. After fitting the parameters, the real HEAC behaviour of the aluminium alloy 7449-T7651 has been replicated accurately. Several characteristic HEAC features were achieved, including crack segmentation, preferential cracking along grain boundaries with a high resolved normal stress and cracks slowing down at grain boundary triple junctions. Comparisons with experimental observations show the suitability of this approach for the prognosis of crack initiation and propagation at a microstructural scale under HEAC conditions.

Integration of an adaptive cohesive zone and continuum ductile fracture model to simulate crack propagation in steel structures

Damage mechanics continuum criteria have been shown to provide an effective alternative to conventional fracture mechanics parameters to simulate ductile crack initiation in mild steel under large scale yielding and variable stress states. In this study, a damage mechanics initiation criterion, called the Stress Weighted Damage Model, is extended to simulate ductile crack propagation through an Adaptive Cohesive Zone model. The proposed approach regularizes the crack tip singularity using features of conventional cohesive zone methods, while adaptively updating the traction separation relationship to model crack propagation based on the continuum damage criterion. The proposed model is implemented in the finite element platform WARP3D and demonstrated using a set of fourteen coupon scale fracture experiments of two structural steels. The tests include Circumferentially Notched Tensile bars and sharp-cracked Compact Tension specimens, where the response is represented by load-deformation response and J-R curves, respectively. Comparisons with test results demonstrate that the combined Stress Weighted Damage Model and Adaptive Cohesive Zone approach can accurately simulate crack propagation with consistent mesh convergence. Examples are included to contrast the proposed model capabilities with a conventional (stress-based) Cohesive Zone model and the Gurson-Tvergaard model.

A hysteresis cohesive approach for predicting mixed-mode delamination onset of composite laminates under cyclic loading: Part I, model development

A new approach is proposed to predict onset of fatigue-induced delamination in composite laminates under cyclic loading by progressive interface degradation. Based on the hysteresis cohesive zone approach, a new damage parameter is defined to construct an irreversible cohesive zone model. Residual displacement jump is introduced and used along with mixed-mode bilinear traction-separation law parameters for calculating the damage parameter. Fatigue-induced delamination onset is then predicted by proposing a damage criterion. 3-D Finite Element (FE) formulation is developed with proper elements for plies and also proper elements for the interface. Cyclic loading is also simulated mimicked by the MIN-MAX method. The current research is conducted in two parts as Part I and Part II. While this article focuses on the theoretical framework of the developed modeling, the numerical implementation of the modeling and also a comparison of the outputs with experimental observations will be presented in the companion paper as Part II.

On the delamination of polyvinyl butyral laminated glass: Identification of fracture properties from numerical modelling

This work investigates the delamination behaviour of polyvinyl butyral (PVB) laminated glass under quasi-static loading based on a cohesive zone model (CZM) with an isotropic bilinear traction - separation (T – δ) law. It presents a 2D model of a through-cracked tensile (TCT) test within an implicit finite element framework of the commercial software ANSYS. Test results from literature are used to calibrate the adhesion properties of the PVB-glass interface in a numerical cohesive zone approach. The previous TCT tests were performed at a loading rate of 6 mm/min and a temperature of approx. 22 °C. Three different PVB adhesion grades, i.e., BG R10 (low), BG R15 (medium) and BG R20 (high) are considered. Given the uncertainty in the identification of adhesion parameters, including interfacial fracture energy, cohesive strength and stiffness, a parametric analysis is conducted quantifying the influences of model parameters on the simulation results. The study allows for decoupling of individual parameters in the calibration. Then, interfacial fracture energies and cohesive strengths of the PVB-laminated glass are calibrated by matching the force – displacement curves of the numerical simulations with those from the TCT experiments. One representative case was chosen for each adhesion grade. We obtain interfacial fracture energies of 425 J/m2, 650 J/m2 and 1000 J/m2 for BG R10, BG R15 and BG R20 PVBs, respectively, while the corresponding cohesive strengths are 3 MPa, 5 MPa and 10 MPa, respectively. Moreover, based on numerical simulation results, the conversion of energy during the delamination process is extracted and discussed. The mixed-mode delamination mechanism is investigated by calculating the mode I and mode II energy release rates with respect to different PVB thicknesses and adhesion. The results show that the proportion of the mode I energy release rate is around 30%∼40% of the total energy release rate at the stable delamination stage and increases with PVB thickness. The presented study contributes to the adhesion properties of various types of PVB interlayers reported in open literatures and proposes a methodology for the unique identification of adhesion properties.

Modeling anisotropic fracture in a metal-fiber reinforced composite system

Hybrid structures consisting of metal and composites can be applied to specific requirements of different applications. The computational modeling of composites is quite complex compared to homogeneous and isotropic materials like metals because of the heterogeneity introduced due to the presence of different phases such as matrix, fiber and matrix-fiber interface, and anisotropy due to the fiber alignment. The crack propagation in a composite material depends on a combination of various damage modes, namely, fiber pull-out, matrix cracking, delamination. The strength and stiffness of the composite depend on the mechanical and fracture properties of the individual phases, and the fiber inclination. The metal-composite interface is modeled using the cohesive zone approach. A nonlocal diffused approach is proposed to model the anisotropic failure in composites reinforced with unidirectional and woven fibers and the interaction of the crack with the interface. Parametric studies are conducted to understand the role of fiber orientation and interface fracture properties of the system. The proposed model is illustrated through numerical examples to understand various failure mechanisms in a metal-composite system.

Modeling of failure at the interface of ductile materials by applying the cohesive discontinuous Galerkin method

In this study, the failure behavior at the interface of ductile materials is investigated. In order to capture the degradation of the tractions at the interface, a cohesive zone (CZ) model is applied. The choice of the type of the CZ approach, i.e. either intrinsic or extrinsic, brings about different drawbacks. The former includes an elastic regime at the interface prior to the failure, which can result in numerical difficulties whereas the latter necessitates the re-meshing of the structure during crack propagation. In order to overcome these problems, the incomplete interior penalty Galerkin variant of the discontinuous Galerkin (DG) method is applied both at the interface and in the bulk instead of the standard conforming finite element method. In addition, the application of the DG method enables to use nonmatching meshes in the discretized model. To treat the bulk, an elastoplastic material model with isotropic hardening as well as different hardening rules for small strains is incorporated into the DG framework. Two numerical examples are computed to study the convergence behavior of the new cohesive discontinuous Galerkin (CDG) method in comparison to that of the conventional models. The new CDG method outperforms the conventional CZ continuous Galerkin elements in the presence of locking effects as well as hanging nodes.