Cohesive Finite Element Method Research Articles

A three-dimensional finite strain volumetric cohesive XFEM-based model for ductile fracture

The verification/prediction by numerical simulation of the resistance of large-scale metal structures subjected to extreme loading (e.g. accidental mechanical overload) that can lead to failure constitutes a major issue in the transport, energy, and defense sectors. This work aims to develop a three-dimensional numerical methodology (i) capable of macroscopically accounting for the various dissipative mechanisms of plasticity and damage until failure, (ii) formulated within the framework of large deformation, (iii) implemented in a commercial computation code, and (iv) mesh-objective. The commercial computational code is ABAQUS-std, and the methodology is implemented as a user finite element (UEL). Geometric non-linearities are treated within the framework of an updated Lagrangian formulation (ULF). The more or less diffuse damage phase is described by the Gurson–Tvergaard–Needleman (GTN) microporous plasticity model with standard finite element (FE). The micro-void coalescence phase-induced dilation/shear band is described using an original volumetric cohesive extended finite element method approach (VCZM-XFEM). The progressive loss of cohesion leading to ultimate cracking is treated with extended finite element method (XFEM). Particular attention is paid to transition criteria (damage to localization, localization to cracking), to the orientation of the localization plane (especially in Mode II), to the cohesive zone model and to techniques for overcoming numerical difficulties (volumetric locking, numerical integration). The so-built 3D-FS-GTN-VCZM-XFEM unified methodology is capable of reproducing the degradation mechanisms, and, the failure surface shape and orientation in large elasto-plastic deformation of structures typical of laboratory tests, even for fairly coarse meshes.

Revealing the grain boundary effect on interfacial adhesion in polycrystal Fe/Ni interfaces by using a multi-scale CZM-CPFEM approach

In layered structure, interface plays a significant role in property improvement, whereas its multiple factors at various length scales restricted further understanding. Previous research found a novel grain boundary (GB)-interface interaction: crack initiation locally occurred at the junctions between pre-existing GBs and interface. This leads to decreased interfacial strength. To clarify the mechanisms of such GB-interface interaction, the present study proposed a multi-scale cohesive zone model-crystal plasticity finite element method (CZM-CPFEM) model to investigate the effect of pre-existing GB on intrinsic bonding strength at atomic scale and interfacial stress distribution at micro scale, respectively. At atomic scale, interfacial fracture criteria were modelled according to Molecular Dynamics (MD)-based traction-separation relationships. The accuracy of CZMs was improved by considering both isothermal holding and tilting configuration effects. At micro scale, a practical interfacial microstructure was used to construct CPFEM models. Tensile simulations showed that the local stress concentration occurred at junctions, attributed to the anisotropic plastic deformation behaviours across the GB. On the other hand, weak bonding adhesion at the junction only affects the local crack initiation strength, showing insignificant impacts on the overall interfacial fracture behaviour.

Numerical Simulation of Transverse Crack on Composite Structure Using Cohesive Element

Due to their anisotropic behavior, composite structures are weak in transverse direction loading. produces transverse cracks, which for a laminated composite, may lead to delamination and total failure. The transition from transverse crack to delamination failure is important and the subject of recent studies. In this paper, a simulation of transverse crack and its transition to delamination on cross-ply laminate was studied extensively using a cohesive element Finite Element Method (FEM). A pre-cracked [0/90] composite laminate made of bamboo was modeled using ABAQUS/CAE. The specimen was in a three-point bending configuration. Cohesive elements were inserted in the middle of the 90° layer and in the interface between the 0° and 90° layer to simulate transverse crack propagation and its transition to delamination. A load–displacement graph was extracted from the simulation and analyzed. As the loading was given to the specimen, stress occurred in the laminates, concentrating near the pre-cracked region. When the stress reached the tensile transverse strength of the bamboo, transverse crack propagation initiated, indicated by the failure of transverse cohesive elements. The crack then propagated towards the interface of the [0/90] laminates. Soon after the crack reached the interface, delamination propagated along the interface, represented by the failure of the longitudinal cohesive elements. The result of the numerical study in the form of load–displacement graph shows a consistent pattern compared with the data found in the literature. The graph showed a linear path as the load increased and the crack propagated until a point where there was a load-drop in the graph, which showed that the crack was unstable and propagated quickly before it turned into delamination between the 0o and 90° plies.

Multiscale modeling of unfolding and bond dissociation of rubredoxin metalloprotein

Mechanical properties of proteins that have a crucial effect on their operation. This study used a molecular dynamics simulation package to investigate rubredoxin unfolding on the atomic scale. Different simulation techniques were applied, and due to the dissociation of covalent/hydrogen bonds, this protein demonstrates several intermediate states in force-extension behavior. A conceptual model based on the cohesive finite element method was developed to consider the intermediate damages that occur during unfolding. This model is based on force-displacement curves derived from molecular dynamics results. The proposed conceptual model is designed to accurately identify bond rupture points and determine the associated forces. This is achieved by conducting a thorough comparison between molecular dynamics and cohesive finite element results. The utilization of a viscoelastic cohesive zone model allows for the consideration of loading rate effects. This rate-dependent model can be further developed and integrated into the multiscale modeling of large assemblies of metalloproteins, providing a comprehensive understanding of mechanical behavior while maintaining a reduced computational cost.

Splitting Mode-I fracture toughness of carbon fibers using nanoindentation

In this study, we conducted a thorough experimental and computational investigation to extend the pillar-splitting technique, developed initially for ceramics, to brittle fibers in reinforced composites. In pillar-splitting methodology, micropillars with circular cross-sections are tested to evaluate the load required to cause instability. The instability load is then correlated with the fracture toughness using the parameter γ which is evaluated using the cohesive zone finite element method (CZ-FEM). In reinforced composites, a unique opportunity arises due to the existence of already present micropillars (reinforcing fibers) for fracture toughness evaluation. In this work, the authors successfully applied the pillar-splitting technique to carbon fibers by investigating the effects of fiber/matrix assembly and the shape of the fiber upon the error in instability load. The minimum height required to avoid matrix effects is found to be equal to the diameter of the fiber reinforcements for a fiber–matrix system with a perfect interface. By contrast, the required protruding height is reduced to zero for a weak fiber–matrix interface. A new parameter, β, is introduced to quantify the deviation of the cross-sectional shape from circularity. An effective γ is then evaluated and used in the pillar-splitting experiments to correlate the instability load to Mode I fracture toughness. Finally, the results are validated experimentally, and the Mode I fracture toughness is evaluated for a range of Toray PAN carbon fibers. Fracture toughness is found to decrease as the modulus of the carbon fibers increases.

Damage behavior of high particle volume fraction composites with initial damage by finite element meso-modeling

Analyzing the deformation and damage processes of high particle volume fraction composites (HPVFCs) based on the meso-structure modeling plays an important role in their service lifetime and functional reliability. The reported mesoscopic structural models are usually ideal models without initial damage and apply to composites with the volume fraction of particles less than 80%. This work provides a new mesoscopic structure model called aggregate settlement-merging model to successfully simulate the mechanical behavior and damage mechanism of the polymer-bonded explosive (PBX) under quasi-static loads, and the macroscopic response is accurately predicted by the cohesive finite element method. This simulation commendably predicts the failure modes including interface debonding, binder filaments, and grain failure, which is consistent with the observation in micromechanical experiments. The multi-scale relationship between macroscopic mechanical properties and microscopic initial interface damage is quantitatively established in a form of an exponential function. This study shows a relationship between meso-structures and performance and provides strategy for designing next generation high-performance HPVFCs.

Three‐dimensional cohesive finite element simulations of mechanical behavior of polymer‐bonded explosives under quasi‐static tensile loading

AbstractMicrostructural features such as voids, microcracks and interfaces play an important role in the mechanical properties of polymer‐bonded explosives, which significantly decide the performance, safety and reliability. A series of micron‐scale 3D models were constructed, and a 3D cohesive finite element method in a commercial software was used to study the elastic properties and fracture development of HMX/Estane polymer‐bonded explosives under quasi‐static tension. The predicted Young's modulus of HMX/Estane PBX with particle volume fraction of 92.7 % at 0.01 s−1 is 2.24 GPa, which is only 7.4 % different from the experimental result. 3D models perform better than 2D models in the prediction of Young's modulus and Poisson's ratio, and the difference between 2D and 3D results can be up to 40 %. In addition, the effect of particle size on the mechanical properties is investigated. It is shown that 3D models can correctly describe the relationship of particle size with stress‐strain curves and fracture development of PBX. Results demonstrate that a 3D model is necessary in the study to delineate the relationships between microstructural features and the mechanical behavior of polymer‐bonded explosives.

Data science assisted cohesive finite element modelling of impact behaviour of AP‐HTPB crystal binder composite

AbstractIn this work, the response of an ammonium perchlorate (AP)‐hydroxyl‐terminated polybutadiene (HTPB) composite material under impact loading is presented, utilizing computational cohesive finite element method (CFEM) simulations that are validated with drop hammer experiments. This study examined the impact behaviour of AP crystal sizes between 200 and 400 μm by varying impact velocities between 3 and 10 m/s. Based on the outcome of CFEM simulations, analysis of variance (ANOVA) tests and a response surface method (RSM) were utilized to construct a mathematical model approximating the relationships between simulation inputs and outcomes. Both computational and experimental results show that the local strain rate has a considerable positive correlation with crystal size, and the rate of temperature change has positive correlations with both crystal size and impact velocity. Further, it was observed that stiffness and compression energy are the primary factors to variances in local strain rate and rate of change of temperature. RSM has been found to be an effective tool for modelling impact responses of materials under varying experimental conditions.

Relations of Microstructural Attributes and Strength-Ductility of Zirconium Alloys with Hydrides

As the first safety barrier of nuclear reactors, zirconium alloy cladding tubes have attracted extensive attention because of its good mechanical properties. The strength and ductility of zirconium alloy are of great significance to the service process of cladding tubes, while brittle hydrides precipitate and thus deteriorate the overall performance. Based on the cohesive finite element method, the effects of cohesive strength, interfacial characteristics, and hydrides geometric characteristics on the strength and ductility of two-phase material (zirconium alloy with hydrides) are numerically simulated. The results show that the fracture behavior is significantly affected by the cohesive strength and that the overall strength and ductility are sensitive to the cohesive strength of the zirconium alloy. Furthermore, the interface is revealed to have prominent effects on the overall fracture behavior. When the cohesive strength and fracture energy of the interface are higher than those of the hydride phase, fracture initiates in the hydrides, which is consistent with the experimental phenomena. In addition, it is found that the number density and arrangement of hydrides play important roles in the overall strength and ductility. Our simulation provides theoretical support for the performance analysis of hydrogenated zirconium alloys during nuclear reactor operation.

Could effective fracture toughness of polycrystalline aggregates exceed inner grain fracture toughness by adjusting toughness of grain boundary?

Obtaining intergranular and transgranular fractures through grain boundary engineering has been considered an efficient technique that improves the effective fracture toughness of polycrystalline aggregates. In this paper, the idealized hexagonal microstructure, random microstructures, and microstructures of grains with large aspect ratios are analyzed through a semi-analytical approach and the cohesive finite element method. The results indicate that when the aspect ratio of grains is not too large, the crack paths consisting of intergranular and transgranular fractures are approximately Mode I fracture morphologies among these microstructures. As the ratio of toughness between grain boundaries and grains varies, the effective fracture toughness of the microstructure can be increased more than the grain boundary fracture toughness but cannot exceed the inner grain fracture toughness.In contrast, the microstructure of grains with a large aspect ratio leads to deflected crack paths that are unexpectedly obtained, which implies that the approximate Mode-I intergranular fracture along transverse direction is almost impossible. The results demonstrate that the projected energy dissipation rate along the direction perpendicular to the loading axis can be significantly improved beyond the inner grain fracture toughness by enlarging the aspect ratio of the grains. Nevertheless, the mixed-mode effective fracture toughness is still limited to the grain fracture toughness. Corresponding experiments are also carried out to qualitatively verify the numerical results. The underlying mechanism for this deflection of fracture path is due to the strong anisotropy of fracture toughness. The higher the grain aspect ratio, the greater the anisotropy of the macroscopic effective fracture toughness. The energy favored fracture path is determined by the largest ratio between the driving force and the toughness of fracture over all directions. Therefore, cracks cannot propagate in the direction of the maximum fracture toughness when the aspect ratio of the grain is sufficiently large. The fracture diagrams that vary with the aspect ratio of grain and the ratio of fracture toughness between the grain and grain boundary are provided. The results can provide valuable guidance for designing microstructures and improving fracture toughness in materials.

Numerical modelling of the mechanical behaviour of Aluminosilicate Glass: A comparison between two simulation approaches

This paper presents a comparison between two numerical methods for modelling the mechanical and failure behaviour of aluminosilicate glass: Cohesive Elements Method (CEM) and Finite Element Method coupled to Smooth Particle Hydrodynamics (FEM-SPH). The failure behaviours, provided by these two approaches, are herein compared under i) quasi-static tests on material coupons, ii) dynamic tests (compressive and tensile tests) also on material coupons and iii) structural impact loading conditions in which the ballistic perforation of aluminosilicate glass tiles due to the impact of a flat-nosed steel projectile are considered. Both methods provide comparable results under quasi-static loading conditions, while more significant differences arise in the ballistic impact part, in which some limitations of CEM are shown.

A cohesive fracture model for predicting crack spacing and crack width in reinforced concrete structures

The cracking behavior analysis, in terms of crack spacing and crack width prediction, is essential to assess the damage and durability of a reinforced concrete (RC) structure. However, available numerical models cannot give satisfactory results in the cracking prediction due to the continuum representation of the concrete material often adopted in the numerical framework. Based on the cohesive finite element method, an interelement fracture model has been proposed here to investigate the cracking behavior, as well as its influence on the load-carrying capacity, of RC structural elements under static loading conditions. This fracture model is employed together with an embedded truss model for the rebars allowing them to be crossed by the cracks. Cracking analyses are performed on RC members subjected to tension and flexural loads. Comparisons with available experimental and numerical results have highlighted the effectiveness of the proposed model to investigate the cracking behavior in RC structures.

Numerical Investigation on Interference of Multiple Hydraulic Fractures in Layered Formation

Staged treatment in vertical wells is extensively applied in layered formation to obtain commercial exploitation of hydrocarbon resources. Large-sized heterogeneities always exist between multiple hydraulic fractures in different layers. To reveal the interference of multiple hydraulic fractures in layered formation, a series of numerical investigations were conducted based on the cohesive zone finite element method. The results show that the sole stress interference is too small to exert an effective impact on adjacent pay zones, which is quite different from those in horizontal wells. The flow distribution in one pay zone can reach 56.2%, which is more than five times the magnitude of the least 10.5% during the fracturing in three pay zones. The fracture size heterogeneities are mainly caused by the interference of the fluid flow into multiple perforation tunnels in different pay zones. To further clarify how the flow distribution in the pay zones is affected, five related factors, including perforating thickness, pay zone thickness, rock permeability, minimum horizontal stress of the pay zone, and rock strength, are analyzed. The results show that it is through the manner of flow distribution adjustment in each pay zone that the five factors affect the fracture size. This study is of critical importance to clarify how the multiple hydraulic fractures from vertical wells interfere in layered formation and explain why the hydraulic fractures we get in the field are far away from what we want ideally.

Microstructure-sensitive investigation on the mechanical behavior of CNT-reinforced composites considering debonding damage based on cohesive finite element method

In this paper, an analytical modeling and numerical approach based on the finite element (FE) method are introduced to study the influence of the real morphology (e.g., length and waviness) and distribution of carbon nanotubes (CNTs) on the mechanical behavior of the CNT-reinforced composites. The analytical model has considered the real morphology effect using the equivalent curved CNTs with perfect bonding. The equivalent chord length, diameter, and waviness have been computed using the abundance of different values of measured parameters in an actual microstructure of the CNTs in the matrix. In the FE method, a computational tool is used to map an actual composite microstructure onto a FE representative volume element (RVE) with the exact shape, size, distribution, and waviness of CNTs. FE analysis has been carried out in both well-bonded and interface-debonding conditions. The cohesive zone model (CZM) with bilinear traction-separation law for both opening and sliding modes has been utilized to capture the debonding at the CNT-matrix interface. Results indicate that in the presence of weak bonding, CNT waviness can enhance the composite stiffness rather than reduce it. A quite different conclusion to what can be obtained with the assumption of perfect adhesion. In the presence of poor bonding, the curvature has a positive effect on composite properties and improves the load transferring from the matrix. FE analysis for different RVEs highlights that the curvature and length of the CNTs are essential features of the microstructure, and they can effectively influence the mechanical properties of the material. Results demonstrate that the equivalent curved CNTs cannot appropriately represent the real microstructure.

A novel model of Z-pin insertion in prepreg based on fracture mechanics

Through-thickness reinforcement is a promising solution to the problem of delamination susceptibility in laminated composites. Modeling Z-pin–prepreg interaction is essential for accurate robotics-assisted Z-pin insertion. In this paper, a novel Z-pin insertion force model combining the classical cohesive finite element (FE) method with a dynamic analytical fracture mechanics model is proposed. The velocity-dependent cohesive elements, in which the fracture toughness is provided by the analytical model, are implemented in Z-pin insertion FE model to predict the crack initiation and propagation. Then Z-pin insertion experiments are performed on prepreg sample with metallic Z-pins at different velocities to identify the analytical model parameters and validate the simulation predictions offered by the model. Dynamics of Z-pin interaction with inhomogeneous prepreg is described and the effects of insertion velocity on prepreg contact force are studied. Results show that the force model agrees well with experiments and the fracture toughness rises with the increasing Z-pin insertion velocity.

The role of microstructure in the impact induced temperature rise in hydroxyl terminated polybutadiene (HTPB)–cyclotetramethylene-tetranitramine (HMX) energetic materials using the cohesive finite element method

In this work, microstructure dependent impact-induced failure of hydroxyl-terminated polybutadiene (HTPB)–cyclo-tetra-methylene-tetra-nitramine (HMX) energetic material samples is studied using the cohesive finite element method (CFEM). The CFEM model incorporates experimentally measured viscoplastic constitutive behavior, experimentally measured interface level separation properties, and phenomenological temperature increase due to mechanical impact based on viscoplastic and frictional energy dissipation. Nanoscale dynamic impact experiments were used to obtain parameters for a strain-rate dependent power law viscoplastic constitutive model in the case of bulk HTPB and HMX as well as the HTPB–HMX interfaces. An in situ mechanical Raman spectroscopy (MRS) setup was used to obtain bilinear cohesive zone model parameters to simulate interface separation. During analyses, the impact-induced viscoplastic energy dissipation and the frictional contact dissipation at the failed HTPB–HMX interfaces is found to have a significant contribution toward local temperature rise. Microstructures having circular HMX particles show a higher local temperature rise as compared to those with diamond or irregularly shaped HMX particles with sharp edges indicating that the specific particle surface area has a higher role in temperature rise than particle shape and sharp edges. Regions within the analyzed microstructures near the HTPB–HMX interfaces with a high-volume fraction of HMX particles were found to have the maximum temperature increase.

Multi-scale numerical simulation of fracture behavior of nickel-aluminum alloy by coupled molecular dynamics and cohesive finite element method (CFEM)

In the current study, a multi-scale investigation on the crack propagation of B2-NiAl alloy was performed by using coupled molecular dynamics (MD) and the cohesive finite element method (CFEM). In particular, by using python programming, a FE model with a zero-thickness cohesive element for batch insertion was established. The T-S curve obtained from MD simulation was adopted as the material input parameter for the zero-thickness cohesive element to investigate the micro crack propagation mechanism and realize the macro crack random propagation simulation. The results showed that in micro-scale, the crack propagation behavior of single crystal B2-NiAl was primarily caused by continuous coalescence of the main cracks and microvoids generated from the stress concentration at the crack front. Furthermore, the single crystal B2-NiAl experienced phase transition and followed the Bain path. Moreover, the T-S curves at different temperatures were compared with Needleman classical theoretical models, demonstrating the properness of the Needleman model. Afterwards, the macroscopic fracture toughness values of B2-NiAl alloys at different temperatures were calculated and compared with those obtained from experiments. Such comparisons demonstrated good agreement with each other and indicated that the T-S curve obtained via MD can be applied to the FE method. These results validated the rationality of this multi-scale method, which offers an alternative approach for fracture behavior simulation across macro and micro scales.

Biaxial fatigue crack growth in proton exchange membrane of fuel cells based on cyclic cohesive finite element method

During the operation of proton exchange membrane in fuel cells, cyclic mechanical loads are introduced due to the humidity cycles. The resulting fatigue crack is known to be the main source for its mechanical degradation. In this paper, we use a relation between damage evolution of the cohesive elements and Paris law to simulate the biaxial fatigue crack growth. The effects of various loading conditions are investigated. The predicted crack growth is in a good agreement with experimental studies. Both the transverse stress and the tensile overload have retardation effects. It is also found that the fatigue crack growth rate associated with a shorter pre-crack depends more on the load waveform. Moreover, fatigue crack grows faster under the low-high loading history than the high-low one. These simulation results have provided significant insights into the fatigue failure behavior of membranes during operation conditions and can help improve their durability.

A computational framework for predicting the fracture toughness of metals as function of microstructure

We present a simplified computational framework based on the cohesive finite element method (CFEM) for predicting the macroscale fracture measures such as KIC and JIC of ductile metals as functions of microstructural attributes. Currently, no systematic approach exists to explicitly quantify the effects of grain and grain boundary behavior on the fracture measures of polycrystalline materials. Our computational approach involves embedding a microstructure region around the crack tip in a compact tension specimen subjected to mode-I loading and explicitly resolving fracture processes in the microstructure. To track how the interplay between intergranular and transgranular fracture mechanisms affect the fracture processes and consequently KIC and JIC, a grain boundary misorientation dependent interfacial separation model is used. The framework allows exploration of the effects of microstructure on the macroscopic fracture measures via the manifestation of different fracture mechanisms. Calculations carried out for Mo capture and delineate the competing effects between (a) intergranular and transgranular fracture and (b) constituent plasticity and fracture on the overall fracture toughness of the material. The use of statistically equivalent microstructure sample sets (SEMSS) allows the statistical distributions of KIC to be predicted for Mo with different grain sizes. The results indicate that, as the minimum grain boundary interfacial strength decreases and the grain yield strength increases, intergranular fracture becomes more pronounced over transgranular fracture. Consequently, the plastic dissipation primarily associated with transgranular fracture is suppressed, resulting in lower overall fracture toughness. Microstructures with intermediate levels of grain size exhibit the toughest material response via a combination of tortuous crack paths and plastic dissipation. Finally, the results are analytically quantified in a manner that takes into account the effects of grain boundary characteristics, constituent plasticity, and stochasticity via the use of the SEMSS. Although the calculations here are performed on Mo in a simplified setting, the approach can be extended and applied to other material systems.

Enhancement of interface strength of carbon fiber/epoxy resin composites filled with low-dimensional materials

ABSTRACT Low-dimensional materials could improve the interface strength between the epoxy resin and carbon fibers (CFs) in the composites. Four type of low-dimensional powders were employed to functionalize the CFs/epoxy interface, and their reinforcement efficiency were compared by performing CF bundle pull out test. Two kinds of processing methods were adopted to introduce low-dimensional powders, one is coating powders onto the CF surfaces, and the other is adding powders in epoxy resin. It is shown that adding these nano-fillers into the matrix and coating them onto the CF surface resulted in a marked improvement in the interface adhesion. Moreover, the cohesive finite element method was employed to unveil the effect of some uncertain parameters on the measured results.