Cohesive Zone Finite Element Research Articles

The strength of an adhesive contact in the presence of interfacial defects

Adhesive contacts which possess a dominant stress concentration, such as at the contact edge in spherical junctions or at the detachment front in a peeling film, are well studied. More complex adhesive junction geometries, such as mushroom-shaped fibrils in bioinspired micropatterned dry adhesives, have exhibited a complex dependence of adhesive strength on the presence of interfacial defects within the contact. This has led to the emergence of statistical variation of the local behavior among micropatterned sub-contacts. In order to examine the interplay between geometry and interfacial defect character in control of the adhesive strength, the model system of a stiff cylindrical probe on an elastic layer is examined. Both experiments (glass on PDMS) and cohesive zone finite element simulations are performed, with analytical asymptotic limits also considered. The thickness of the elastic layer is varied to alter the interfacial stress distribution, with thinner layers having a reduced edge stress concentration at the expense of increased stress at the contact center. The size and position of manufactured interfacial defects is varied. It is observed that for the thickest substrates the edge stress concentration is dominant, with detachment propagating from this region regardless of the presence of an interfacial defect within the contact. Only very large center defects, with radius greater than half of that of the contact influence the adhesive strength. This transition is in agreement with analytical asymptotic limits. As the substrate is made thinner and the stress distribution changes, a strong decay in adhesive strength with increasing center defect radius emerges. For the thinnest substrate the flaw-insensitive upper bound is approached, suggesting that this decay is dominated by a reduction in the contact area. For penny-shaped defects at increasing radial positions, the adhesive strength for the thinnest substrates becomes non-monotonic. This confirms an intricate interplay between the geometry-controlled interfacial stress distribution and the size and position of interfacial defects in adhesive contacts, which will lead to statistical variation in strength when defects form due to surface roughness, fabrication imperfections, or contaminant particles.

Incorporation of compaction effects in the automated generation of 3D woven composites representative volume elements by geometrical modelling

Advanced 3D woven composites have become an enabling technology in many industrial applications due to their proven benefits, particularly the improvement of the out-of-plane mechanical behavior with respect to other reinforcement schemes. The latter property has been shown to be strongly affected by the effects of compaction during manufacturing. The present study proposes an automated framework, based on heuristic procedures, for the generation of representative volume elements (RVEs) of 3D woven composites, allowing to include global and local geometrical features induced by transverse compaction, such as overall thickness reduction, changes in yarn cross-sections and consistent global/local fiber fractions. The methodology is illustrated for three types of reinforcement, namely a plain weave, an angular through-thickness interlock and a 3D orthogonal RVE. The resulting geometries generated by the proposed method compare favourably with typical observations from the literature in a quantitative manner. Finally, the proposed framework is integrated with a previously developed meshing strategy to allow damage studies for a selected architecture (plain weave) under torsional loading, presenting a complete computational chain by building cohesive zone finite element models from compacted RVEs. The torque-angle response curves obtained after the damage simulations show a decrease in stiffness and an increase of damage levels with compaction, which is in line with the expectations.

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.

Machine learning/finite element analysis - A collaborative approach for predicting the axial impact response of adhesively bonded joints with unique sandwich composite adherends

Despite the increasing usage of adhesively bonded joints (ABJs) in various industries, optimization of their bond strength in a cost-effective manner remains a challenging task, particularly when complex loading scenarios such as static and dynamic compressive loadings are considered. The task becomes even more challenging in bonded joints with sandwich composite adherends. This study focuses on the performances of double-strap ABJs configured by unique sandwich composite adherends, carbon fiber-reinforced plastic straps, and a room-cured structural epoxy resin under axial impact loading. A Finite Element-Cohesive Zone (FE-CZ) model is developed to simulate the response of the joints, and its integrity is validated against the experimental tests at three impact energy levels. The model is used to simulate the response of various ABJ configurations under axial impact loading, taking into account 13 material, geometrical, and testing-related parameters that influence joint strength, thereby generating 410 data sets. Subsequently, three Machine Learning (ML) models, including deep neural networks and genetic evolution (i.e., genetic programming and genetic algorithms) are developed and trained by the data sets to predict the ABJs load-bearing capacity. The ML models explore the relationship between the design parameters and the joint's ultimate load-bearing capacities, leading to the development of cost-effective and accurate empirical equations, and optimized joint configurations.

Effect of geometrical structure variations on strength and damage onset of cortical bone using multi-scale cohesive zone based finite element method

Three-dimensional multi-scale finite element models were designed to examine the effects of geometrical structure variations on the damage onset in cortical bone at multiple structural scales. A cohesive zone finite element approach, together with anisotropic damage initiation criteria, is used to predict the onset of damage. The finite element models are developed to account for the onset of microdamage from the microscopic length scales consisting of collagen fibres, to the macroscopic level consisting of osteons and the Haversian canals. Numerical results indicated that the yield strain at the initiation of microcracks is independent of variations in the local mineral volume fraction at each structural scale. Further, the yield strain and strength properties of cortical bone are dependent on its structural anisotropy and hierarchical structure. A positive correlation is observed between bone strength and mineral content at each length scale.

Effects of randomly distributed interface cohesive strength on the delamination of the REBCO tapes

This paper investigates the effect of randomly distributed interface cohesive strength on the initiation and propagation of delamination of the REBCO tapes. A three-dimensional cohesive zone finite element model (FEM) is established with consideration of randomly distributed interface cohesive strength satisfied three-parameter Weibull distribution, which is used to analyze the influence of the randomness of interface cohesive strength on the delamination performance of tapes under transverse tensile. The simulation results show that the boundary for delamination beginning predicted by the model, considering the randomly distributed interface cohesive strength, has a random character and is closer to the actual situation. Furthermore, parameters that are important to the random Weibull distribution are also investigated. It is shown that the scale parameter and the minimum interface cohesive strength have negligible influence on the delamination strength. Meanwhile, it has a significant impact on the peak value of the stress at delamination initiation in the REBCO layer and its position. For a particular Weibull distribution, its median can be used as constant interface cohesive strength to simulate the macroscopic delamination behavior of the tapes, accurately and efficiently.

Investigation on insertion mechanism of ultrasound guided insertion process based on numerical simulation

AbstractThe insertion of finer Z‐pins is the key factor for increasing the reinforcement effects of Z‐pinned composite laminates. This paper presents a three‐dimensional cohesive zone finite element (FE) model for revealing the insertion mechanism of the ultrasound guided insertion process of fine Z‐pins. The prepreg fracture is modeled based on the cohesive elements, where fracture toughness is obtained from the double insertion method. The contact between the needle and prepreg is simulated by LuGre dynamic friction model. According to model simulation and relevant experiments, compared with nonvibratory insertion, smaller insertion force, earlier surface fracture and slighter ply crimp can be observed in the ultrasound guided insertion process. In addition, the prepreg forms an initial crack firstly after needle insertion, followed by a final crack due to needle extraction and prepreg springback. The effects of needle diameter on the insertion force and crack length are discussed. It can be concluded that larger needle diameter can lead to greater insertion force and initial crack length, but has little effect on the final crack length.

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.

Determination of Mechanical and Fracture Properties of Silicon Single Crystal from Indentation Experiments and Finite Element Modelling.

It is well-known that cracks are observed around the impression during indentation of brittle materials. The cracks inception depends on load conditions, material and indenter geometry. The paper aims to use experimental micro-indentation data, FE simulations with cohesive zone modelling, and an optimisation procedure to determine the cohesive energy density of silicon single crystals. While previous studies available in the literature, which use cohesive zone finite element techniques for simulation of indentation cracks in brittle solids, tried to improve methods for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, this study focuses on the evaluation of the cohesive energy density 2Γ from which the material toughness can be easily determined using the well-known Griffith-Irwin formula. There is no need to control the premise of the linear fracture mechanics that the cohesive zone is much shorter than the crack length. Hence, the developed approach is suitable also for short cracks for which the linear fracture mechanics premise is violated.

Effects of randomly distributed defects on Mode-I interlaminar fracture of composite materials

Effects of defects on the mode-I interlaminar fracture behavior of composite materials are studied using computational fracture mechanics. Cohesive-zone Finite Element (FE) models of both the Interlaminar Tension (ILT) and Double Cantilever Beam (DCB) test configurations are simulated where randomly distributed defects are explicitly modeled on a critical fracture plane. The effective interlaminar tensile strength and the effective mode-I fracture energy are derived by matching the simulation results with appropriate homogenized models that do not consider the defects explicitly. The results from the computational parametric studies show that both the effective ILT strength and the effective mode-I fracture energy are quite sensitive to defects, scaling linearly with the defect area fraction on the critical fracture plane. The effects of defect size on the mode-I fracture behavior are also studied. It is shown that, for a fixed area fraction of the defects, the ILT strength is not sensitive to the defect size. On the other hand, the mode-I fracture propagation behavior is sensitive to the defect size especially when the defect size is greater than the fracture process-zone size of the delamination crack.

Experimental measurement of mode-I fracture toughness of dissimilar material joints with thermal residual stresses

The current study presents a novel test method to experimentally cancel out the thermal stresses in dissimilar material joints. For the commonly used double cantilever beam test the presence of thermal stresses results in a significant mode mixity at the crack tip, which varies with applied load even if the elastic properties of the adherends are similar. This is particularly a challenge for fibre reinforced plastics bonded to metals due to the large difference in thermal expansion coefficients. The presence of mode-II loading is likely to provide a higher fracture energy from experiments than if tested under pure mode-I loading, which can lead to non-conservative results when using standard test methods. To overcome this challenge a novel test method inspired by the mixed mode bending test is developed. It is shown that the thermal stresses can be cancelled by applying initial constant loads during testing, and that the fracture toughness under pure mode-I loading can be obtained under specific conditions. The test method is validated by carrying out virtual compliance calibration experiments using cohesive zone finite element modelling. As the test method relies solely on analytical calculations and can be used with standard test equipment, it is relatively simple to apply in practice.

Improve durability of plasma-splayed thermal barrier coatings by decreasing sintering-induced stiffening in ceramic coatings

In this study, a newly-tailored plasma-sprayed (PS) yttria-stabilized zirconia (YSZ) ceramic coating towards enhanced strain tolerance and sintering resistance was developed to improve the durability of TBCs. The thermal shock life was found to be markedly prolonged by more than four times. Failure mechanisms and sintering behavior of the newly-structured and conventional TBCs were systematically investigated through microstructural and mechanical analyses. Conventional TBCs suffered a premature spallation due to rapid sintering-induced stiffening of the ceramic top coat. In contrast, the new coating exhibits an enhanced sintering resistance whereby preserving a good strain tolerance over time. Specifically, its elastic modulus after thermal exposure remains comparable to the as-sprayed states. The effect of ceramic top coat stiffness on cracking behavior of TBCs was clarified by a corresponding cohesive zone finite element modeling. This study provides a new option for improving TBCs durability and the results could benefit the increased integrity of TBCs.

Fully coupled thermo-mechanical cohesive zone model with thermal softening: Application to nanocomposites

A computational framework is proposed for coupled thermo-mechanical analyses of interface separation and heat transport in carbon nanotubes (CNTs) enhanced composites. The numerical approach adopted is based on a newly developed cohesive zone finite element, with fully coupled interactions between load and heat transfer. The load transfer behavior is described by a damage (bilinear) model that can account for mixed-mode separation and for thermal degradation of the interface mechanical properties. The interface conductance consists of the conductance of connective bond, air and contact and is coupled to the cohesive zone damage and crack closure. The element is then used to numerically study the thermoelastic properties of nanocomposites. Due to the possibility of low interface conductance, composites containing higher volume fraction or better alignment of CNT may not have more favorable mechanical behaviors in thermo-mechanical loading. Contributions of connective, contact and air conductance on the heat transfer in the damaged cohesive zone are investigated. The proposed computational framework is an extension of mechanical only finite element analyses of the CNT-composites, providing an alternative to molecular dynamics in carrying out multiphysics simulation of CNT-composites with less computational cost. The present work provides valuable insight into understanding the interaction of the load and heat transfers in the CNT-composites, the evolution of interface conductance in the damaged interface and the effect of interface damage on the overall performance of the composite.

The study of fracture propagation in pre-acidized shale reservoir during the hydraulic fracturing

Due to the high stress difference, high breakdown pressure and undeveloped natural fracture, the pre-acidizing treatment is an effective method for deep shale reservoir hydraulic fracturing. However, the mechanism of complex fracture propagation in the acidized shale is unrevealed. The linear elastic mechanical theory cannot model the elastoplastic deformation of acidized shale and the changes of mechanical properties after acidizing. In this paper, the acidizing damage effect of the shale formation is studied by presenting a numerical model based on the cohesive zone finite element method which is capable for simulating complex fracture propagation. A constitutive model of acidized shale and an equivalent model for simulating the weak planes and natural fractures are embedded into the hydraulic fracturing model. The simulation results of a two-dimensional fracture intersection model considering acid damage effect show that it is more conducive for generation of complex fracture network. A three-dimensional multi-fracture propagation model considering weak planes and acid damage effect is established, and the effects of treatment parameters are analyzed. The simulation results show that the acid-damaged reservoirs are more likely to form complex fractures, which is consistent with the microseismic monitoring results. According to the modeling, the acid treatment could result in a more complex fracture geometry as well as a larger stimulated reservoir volume.

Recycled Stone/ABS particulate composite: Micromechanical finite element fracture analysis

New stone composite samples, fabricated using nano- to micro-sized recycled granite particles with irregular shapes and random distribution within a ABS matrix, demonstrate a highly nonlinear and complex fracture behavior. To model this behavior, a mixed mode cohesive zone finite element model is identified using the single-leg bending (SLB), in order to represent the granite particles-ABS interfacial debonding. An inverse methodology is then proposed to determine the parameters of the cohesive zone (CZM). A direct method based on J-integral approach is employed to determine the effective parameters of the traction-separation law. A two dimensional micromechanical extended finite element model (XFEM) of the composite is generated using X-ray micro-computed tomography (XMT) to mimic the actual shape of the particles. Finally, the identified cohesive model parameters have been employed to simulate the crack growth within the granite particulates/ABS composite. The comparison of the numerical and experimental results of the SLB test demonstrated the effectiveness of the proposed simulation framework.

Finite Element Modeling of Orthogonal Machining of Brittle Materials Using an Embedded Cohesive Element Mesh

Machining of brittle materials is common in the manufacturing industry, but few modeling techniques are available to predict materials’ behavior in response to the cutting tool. The paper presents a fracture-based finite element model, named embedded cohesive zone–finite element method (ECZ–FEM). In ECZ–FEM, a network of cohesive zone (CZ) elements are embedded in the material body with regular elements to capture multiple randomized cracks during a cutting process. The CZ element is defined by the fracture energy and a scaling factor to control material ductility and chip behavior. The model is validated by an experimental study in terms of chip formation and cutting force with two different brittle materials and depths of cut. The results show that ECZ–FEM can capture various chip forms, such as dusty debris, irregular chips, and unstable crack propagation seen in the experimental cases. For the cutting force, the model can predict the relative difference among the experimental cases, but the force value is higher by 30–50%. The ECZ–FEM has demonstrated the feasibility of brittle cutting simulation with some limitations applied.

Material Removal Simulation in Sawing Processes of Photovoltaic Silicon

The wafering of thin silicon substrates is done by wire sawing technology. In this work a numerical model for the investigation of microstructural mechanisms like cracking and damage evolution during the sawing process is presented. A three-dimensional finite element model representing the phase transformation properties of silicon is validated by loading curves from nano-indentation experiments. By using cohesive zone finite elements, the crack lengths as well as crack initiation depths can be quantified and compared with the experimental results in terms of the maximum depth of subsurface damage.

Uncertainty analysis of hydraulic fracture height containment in a layered formation

The prediction of hydraulic fracture height growth is of extreme interest in various engineering practices. To fully understand the dependence of the fracturing height in complex underground geological structures, it is crucial to develop theoretical and numerical hydraulic fracturing models to identify the key variables and their interactions to hydraulic fracture height containment. In this work, we adopt a three-dimensional hydro-mechanical coupling cohesive zone finite element model supported by logging data from a practical engineering project. A novel response surface method with Box–Behnken design is introduced to evaluate the statistical significance of tested variables and to forecast the optimal variable combinations for hydraulic fracture height. The key controlling variables are sorted according to their statistical significance from the analysis of variance, and only the minimum lateral stress ratios in mudstone layer and conglomerate layer are highly statistically significant. The minimum lateral in situ stress contrast is the predominant influence of fracture height containment regarding to their significant negative correlation, while the Young’s modulus contrast is probably not an important parameter in terms of direct control of fracture height. Upon optimization, 41 optimized variable combinations were achieved and could be served as references in regulating this engineering practice or even similar events.

3D patient-specific numerical modeling of the soft palate considering adhesion from the tongue

Collapse of the soft palate in the upper airway contributes to obstructive sleeping apnea (OSA). In this study, we investigate the influence of the adhesion from the tongue on the soft palate global response. This is achieved using a cohesive zone finite element approach. A traction-separation law is determined to describe the adhesion effect from the surface tension of the lining liquid between the soft palate and the tongue. According to pull-off experimental tests of human lining liquid from the oral surface of the soft palate, the corresponding cohesive properties, including the critical normal traction stress and the failure separation displacement, are obtained. The 3D patient-specific soft palate geometry is accounted for, based on one specific patient’s computed tomography (CT) images. The calculation results show that influence of the adhesion from the tongue surface on the global response of the soft palate depends on the length ratio between the cohesive length and the soft palate length. When the length of the cohesive zone is smaller than half of the soft palate length, the adhesion’s influence is negligible. When the adhesion length is larger than 70 percent of soft palate length, the adhesion force contributes to preventing the soft palate from collapsing towards to the pharynx wall, i.e. the closing pressure is more negative than in the no adhesion case. These results may provide useful information to the clinical treatment of OSA patients.

The impact of coal macrolithotype on hydraulic fracture initiation and propagation in coal seams

Macrolithotypes control the pore-fracture distribution heterogeneity in coal impacting stimulation via hydrofracturing and the coalbed methane (CBM) production. Given that it is affected by the discontinuities, hydraulic fracture geometry is complex in the vertical plane and is different from a simple fracture in a homogeneous reservoir. However, the initiation and propagation mechanism in the vertical plane is unclear. To clarify this, the cohesive zone finite element approach, with macrolithotype contributions included, was used to simulate and analyze the hydraulic fracture propagation. The experimental tests showed that, the bright and semi-bright coal usually have higher microfracture (cleat) density accompanied by the lower mechanical properties than that of the semi-dull and dull coals. The behavioral differences are likely to impact the geometry evolution of hydraulic fractures and which appears to vary when fracturing the different coal macrolithtypes. Thus, the cohesive zone finite element approach was used with two models to capture macrolithotype impacts. The result show that, when fracturing the dull coal (model 2), the overall propagation region rapidly displayed a simple plane in shape because of the less development of natural fractures. With the influence of the larger elastic modulus, the high-stress zone would be easy formed and suddenly release to generate pressure pulse when the hydraulic fracture penetrated the interface. As the hydraulic fracture initiates from the bright coal (model 1), the presence of the existing diverse cleat network contribute greatly to the increase of cracks number to form complex fractures. However, the opening of natural fractures will lead to the diversion of fracturing fluid, and the larger elastic modulus of the interlayer also plays a limiting role in the height of the hydraulic fracture. In addition, the monitoring of hydraulic fracture was carried out and shown that the height of the major fracture in model 1 was restricted and limited by the bright coal; and the height in model 2 is usually larger than the dull coal thickness, indicating that the hydraulic fracture has cut through the fracturing section (dull coal) and embedded into the upper and lower layers.