Cohesive Finite Element Research Articles

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.

On the tensile resistance of UHPC at impact

Ultra-High Performance Concrete (UHPC) is a new class of concrete which shows high strength and durability. In this paper experimental investigations on the dynamic properties of a low-silica UHPC are presented. By means of Hopkinson Pressure Bar experiments the dynamic elastic modulus and the tensile resistance of the material are determined. Additional numerical fracture simulations, based on a cohesive finite element technique, confirm the measured data and illustrate the possibilities to obtain predictive simulations.

Modelling the fracture behaviour of thermal barrier coatings containing healing particles

The performance of a self-healing Thermal Barrier Coating (TBC) containing dispersed healing particles depends crucially on the mismatch in thermomechanical properties between the healing particles and the TBC matrix. The present work systematically investigates this phenomenon based on numerical simulations using cohesive element-based finite element analysis. The effect of the mismatch in Coefficient of Thermal Expansion (CTE) and fracture strength between the healing particles and the matrix on the fracture characteristics is quantified in detail. Unit cell-based analyses are conducted on a representative self-healing TBC system under a thermal loading step typically experienced by TBC systems in jet turbines. Two different simulation setups are considered within the TBC unit cell namely (i) a single pair of healing particles and (ii) a randomly distributed array of healing particles. The results of the simulations are reported in terms of the fracture pattern, crack initiation temperature and crack length for various CTE mismatch ratios. Correlations are established between the results obtained from the two simulation setups essentially revealing the effect of spatial distribution and proximity of healing particles on the fracture pattern. The results obtained from the analyses can be utilised to achieve a robust design of a self-healing TBC system.

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.

Local Monte Carlo Method for Fatigue Analysis of Coarse-Grained Metals with a Nanograined Surface Layer

The fatigue resistance of coarse-grained (CG) metals can be greatly improved by introducing a nanograined surface layer. In this study, the Weibull distribution is used to characterize the spatially-random fracture properties of specimens under axial fatigue. For the cylindrical solid specimen, the heterogeneity of element sizes may lead to unfavorable size effects in fatigue damage initiation and evolution process. To alleviate the size effects, a three-dimensional cohesive finite element method combined with a local Monte Carlo simulation is proposed to analyze fatigue damage evolution of solid metallic specimens. The numerical results for the fatigue life and end displacement of CG specimens are consistent with the experimental data. It is shown that for the specimens after surface mechanical attrition treatment, damage initiates from the subsurface and then extends to the exterior surface, yielding an improvement in the fatigue life. Good agreement is found between the numerical results for the fatigue life of the specimens with the nanograined layer and experimental data, demonstrating the efficacy and accuracy of the proposed method.

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.

Insights on rock fracture from digital imaging and numerical modeling

Rock fracture and the induced displacement field are investigated through physical and numerical experiments. A Berea sandstone specimen with a central notch was tested in three-point bending. Digital image correlation (DIC) was used to obtain the displacement patterns as the fracture initiated and propagated. The DIC results clearly show the development of a damage zone and displacement discontinuity along the center line of the beam at peak load. It is suggested that a traction-free or cohesionless crack may exist before the unstable growth, a condition normally ruled out in the literature based on numerical modeling within the frame work of a cohesive zone finite element analysis. In this note, the displacement profiles determined from DIC are compared with those from numerical simulations using (i) nonlinear finite element and (ii) bonded particle models. It is shown that the bonded particle model is capable of reproducing the physical displacement field with better accuracy compared to that from the finite element model with softening. Furthermore, as supported by experiments and bonded particle simulations, it appears that a cohesionless crack can develop at peak load, an observation that is not confirmed by the nonlinear finite element analysis.

Material heterogeneity, microstructure, and microcracks demonstrate differential influence on crack initiation and propagation in cortical bone.

The recent studies have shown that long-term bisphosphonate use may result in a number of mechanical alterations in the bone tissue including a reduction in compositional heterogeneity and an increase in microcrack density. There are limited number of experimental and computational studies in the literature that evaluated how these modifications affect crack initiation and propagation in cortical bone. Therefore, in this study, the entire crack growth process including initiation and propagation was simulated at the microscale by using the cohesive extended finite element method. Models with homogeneous and heterogeneous material properties (represented at the microscale capturing the variability in material property values and their distribution) as well as different microcrack density and microstructure were compared. The results showed that initiation fracture resistance was higher in models with homogeneous material properties compared to heterogeneous ones, whereas an opposite trend was observed in propagation fracture resistance. The increase in material heterogeneity level up to 10 different material property sets increased the propagation fracture resistance beyond which a decrease was observed while still remaining higher than the homogeneous material distribution. The simulation results also showed that the total osteonal area influenced crack propagation and the local osteonal area near the initial crack affected the crack initiation behavior. In addition, the initiation fracture resistance was higher in models representing bisphosphonate treated bone (low material heterogeneity, high microcrack density) compared to untreated bone models (high material heterogeneity, low microcrack density), whereas an opposite trend was observed at later stages of crack growth. In summary, the results demonstrated that tissue material heterogeneity, microstructure, and microcrack density influenced crack initiation and propagation differently. The findings also elucidate how possible modifications in material heterogeneity and microcrack density due to bisphosphonate treatment may influence the initiation and propagation fracture resistance of cortical bone.

Numerical Investigation of Grouting of Rock Mass with Fracture Propagation Using Cohesive Finite Elements

Numerical Investigation of Grouting of Rock Mass with Fracture Propagation Using Cohesive Finite Elements

Determination of fracture strength and fracture energy of (metallo-) ceramics by a wedge loading methodology and corresponding cohesive zone-based finite element analysis

A wedge loaded testing methodology to determine the fracture energy and strength of (semi-) brittle (metallo-)ceramics is presented. The methodology combines a tailored specimen geometry and a comprehensive finite element analysis based on cohesive zone modelling. The use of a simulation-based approach to extract both fracture strength and energy from experimental data avoids the inherent inaccuracies found in closed-form expressions that rely on a priori assumptions about the deformation field. Results from wedge splitting tests on Ti3SiC2 and Ti2AlC (MAX phase) materials are used to illustrate the procedure. The simulation-based approach is further validated by comparing the fracture strength and fracture energies predicted by the proposed method and those indicated by a conventional four-point bending fracture toughness test (ASTM standard). The new protocol offers the possibility to measure not only the fracture properties of brittle material in its pristine state but also in the healed state.

Axial-torsional high-cycle fatigue of both coarse-grained and nanostructured metals: A 3D cohesive finite element model with uncertainty characteristics

In this study the combined axial–torsional fatigue life and damage evolution of both coarse-grained (CG) and nanostructured metals are modeled by a 3D cohesive finite element method with uncertainty characteristics. To account for the random nature of metal fatigue, we combine the Monte Carlo simulation with the three-parameter Weibull statistical distribution function. For both CG and nanostructured metals, we find that the axial load levels have greater effects than random fields on the amplitude of specimen rotation. Compared with the CG metals, the nanostructured metals are found to exhibit an improved fatigue resistance, for the reason that their damage process initiates from the subsurface beneath the nanograined layer and then extends to the exterior surface. Good agreements between the numerical results and experimental data are also observed. It shows the applicability of the 3D cohesive finite element method for the analysis of damage evolution and prediction of fatigue life in these two classes of metals.

Experimental and numerical investigation on the bond strength of self-sensing composite joints

Laboratory experiments demonstrate that a novel carbon nanotube (CNT)-based sensing layer embedded in the bondline of an adhesively bonded structural joint can detect and monitor deformation and damage progression of the adhesive layer. In this study, experimental and numerical investigations were performed to identify any effect of an embedded CNT-based sensing layer on the bond strength of that joint. To evaluate the mechanical behavior of such a bondline configuration, two sets of single-lap specimens, with and without sensing layer, were prepared and tested to determine the bond strengths of the respective types. Two-dimensional digital image correlation (2D DIC) was utilized to estimate the load-displacement response of the test specimens. Three-dimensional cohesive surface finite element models of the test specimens, with and without the sensing layer, were created and validated using the experimental measurements. It is shown that the embedded CNT-based sensing layer does not influence the bond strength of the single-lap joint.

Multiscale cohesive zone modeling and simulation of high-speed impact, penetration, and fragmentation

In this work, a multiscale cohesive zone model (MCZM) is developed to simulate the high-speed penetration induced dynamic fracture process such as fragmentation in crystalline solids. This model describes bulk material as a local quasi-continuum medium which follows the Cauchy–Born rule while cohesive zone element is governed by an interface depletion potential, such that the cohesive zone constitutive descriptions are genetically consistent with that of bulk element. This multiscale method proved to be effective in describing material inhomogeneities and it is constructed and implemented in a cohesive finite element Galerkin weak formulation. Numerical simulations of high-speed penetration with different shape of penetrators, i.e., square, circle and parabola nose penetrators are performed. Results show that the proposed MCZM can successfully capture spall fracture, the penetration process and different characteristics of fragmentation under different shape of penetrators.

Cohesive finite element modeling of the delamination of HTPB binder and HMX crystals under tensile loading

Accurately modeling the mechanical behavior of the polymer binders and the degradation of interfaces between binder and crystal is important to science-based understanding of the macro-scale response of polymer bonded explosives. The paper presents a description of relatively a simple bi-crystal HMX-HTPB specimen and associated tensile loading experiment including computed tomography imaging, the pertinent constitutive theory, and details of numerical simulations used to infer the behavior of the material during the delamination process. Within this work, mechanical testing and direct numerical simulation of this relatively simple bi-crystal system enabled reasonable isolation of binder-crystal interface delamination, in which the effects of the complicated thermomechanical response of explosive crystals were minimized. Cohesive finite element modeling of the degradation and delamination of the interface between a modified HTPB binder and HMX crystals was used to reproduce observed results from tensile loading experiments on bi-crystal specimens. Several comparisons are made with experimental measurements in order to identify appropriate constitutive behavior of the binder and appropriate parameters for the cohesive traction-separation behavior of the crystal-binder interface.This research demonstrates the utility of directly modeling the delamination between binder and crystal within crystal-binder-crystal tensile specimen towards characterizing the behavior of these interfaces in a manner amenable to larger scale simulation of polycrystalline PBX materials. One critical aspect of this approach is micro computed tomography imaging conducted during the experiments, which enabled comparison of delamination patterns between the direct numerical simulation and actual specimen. In addition to optimizing the cohesive interface parameters, one important finding from this investigation is that understanding and representing the strain-hardening plasticity of HTPB binder is important within the context of using a cohesive traction-separation model for the delamination of a crystal-binder system.

Data-driven simulation for fast prediction of pull-up process in bottom-up stereo-lithography

Cohesive finite element simulation is a mechanics-based computational approach that can be used to model the pull-up process in bottom-up stereo-lithography (SLA) system to significantly increase the reliability and through-put of the bottom-up SLA process. This modeling relates the pull-up velocity and separation of the fabricated part during the pull-up process. However, finite element (FE) simulation of the pull-up process for the individual part is computationally very expensive, time-consuming, and not amenable to online monitoring. This paper outlines a computationally efficient data-driven scheme to predict the separation stress distribution in bottom-up SLA process. The proposed scheme relies on 2D shape context descriptor, neural network (NN), and a limited number of offline FE simulations. Towards this end, FE models and results for the cross-section of n-fold symmetric shapes form our databases. The 2D shape context descriptor represents different shapes through log-polar histograms in our database. A backpropagation (BP) neural network is trained using the log-polar histograms of the geometric shapes as inputs and the FE simulated stress distributions as outputs. The trained NN can then be used to predict the separation stress distribution of a new shape. The results demonstrate that the proposed data-driven method can drastically reduce computational costs and apply to any general databases. The comparison between the predicted results by the data-driven approach and the simulated FE results on new shapes verify the validity of the proposed method.

Effect of interface chemistry and strain rate on particle-matrix delamination in an energetic material

In this work, interface mechanical strength of a set of Hydroxyl-terminated polybutadiene (HTPB)-Ammonium Perchlorate (AP) interfaces is characterized using dynamic microscale impact experiments at strain rates up to 100 s−1. The experiments were conducted on the interfaces with varying amount of binding agent Tepanol with an impacter of radius 1 µm. Measurements of strain rates and plastic-residual depths were correlated to obtain the interface level strains and stresses. A power law viscoplastic constitutive model was fitted to the stress–strain-strain rate data in order to predict rate dependent constitutive behaviors of interfaces, particle, and matrix. An in-situ mechanical Raman spectroscopy (MRS) setup was used to analyze the effect of binding agent on interface level stress variation at different temperatures. The MRS setup is also used to obtain cohesive fracture separation properties in the analyzed samples including interface delamination strength and interface fracture energy. The measured cohesive fracture parameters capture the effect of interface chemistry variation. The cohesive parameters and the viscoplastic model obtained from the experiment were implemented in a cohesive finite element scheme to simulate dynamic crack propagation as well as delamination in model energetic material samples. Results quantify influence of the rate of loading and interface binding agent variation on rate dependent fracture. Results show that the time at which the interface delamination starts increases linearly with the increase in cohesive strength and decreases exponentially with an increase in loading rate.

Investigation on tensile deformation behavior of compacted graphite iron based on cohesive damage model

Compacted graphite iron (CGI) is a typical engineering material with double phases, of which graphite morphology largely determines its mechanical performances. Although microstructural effects have been widely investigated, quantitative relations between mechanical properties and microstructures are still limited. In this study, a micro-scale damage cohesive finite element model (CFEM) was reconstructed and identified based on the tensile properties and damage characteristics of CGI, and then the effects of graphite including distribution, size, volume fraction and morphology on tensile behaviors were investigated. The agreement of yield strength and fracture mechanism between experimental and simulation results shows that the developed methods, combining the digital image-based technique (DIT) and CFEM, can be used to simulate CGI effectively. Furthermore, the quantitative relations between yield strength and microstructures were established. It is found that graphite distribution and volume fraction affect the yield strength much more compared with graphite size and morphology. Specifically, interesting results were found that yield strength does not monotonically change with volume fraction and aspect ratio of graphite, but reaches a maximum value under an optimal graphite size, which is in contrast to the traditional results. The established quantitative relations between microstructures and tensile properties of cast alloys can be utilized to design and manufacture the metallic composite with optimal mechanical properties.

A Cohesive Zone Model for the Stamping Process Encountered During Three-Dimensional Printing of Fiber-Reinforced Soft Composites

Fiber-reinforced soft composites (FrSCs) are seeing increasing use in applications involving soft actuators, four-dimensional printing, biomimetic composites, and embedded sensing. The three-dimensional (3D) printing of FrSCs is a layer-by-layer material deposition process that alternates between inkjet deposition of an ultraviolet (UV) curable polymer layer and the stamping of electrospun fibers onto the layer, to build the final part. While this process has been proven for complex 3D geometries, it suffers from poor fiber transfer efficiencies (FTEs) that affect the eventual fiber content in the printed part. In order to address this issue, it is critical to first understand the mechanics of the fiber transfer process. To this end, the objective of this paper is to develop a cohesive zone-based finite element model that captures the competition between the “fiber–carrier substrate” adhesion and the “fiber–polymer matrix” adhesion, encountered during the stamping process used for 3D printing FrSCs. The cohesive zone model (CZM) parameters are first calibrated using independent microscale fiber peeling experiments involving both the thin-film aluminum carrier substrate and the UV curable polymer matrix. The predictions of the calibrated model are then validated using fiber transfer experiments. The model parametric studies suggest the use of a roller-based stamping unit design to improve the FTE of the FrSC 3D printing process. Preliminary experiments confirm that for a 0.5 in diameter roller, this new design can increase the FTE to ∼97%, which is a substantial increase from the 55% efficiency value seen for the original flat-plate stamping platen design. The model has broader applications for the transfer-printing of soft material constructs at the submicron scale.

Evaluation of a proposed model for concrete at mesoscopic scale

Abstract This work deals with numerical modeling of mechanical behavior in quasi-brittle materials, such as concrete. For this propose, a two-dimensional meso-scale model based on RVE existence is presented. The material is considered as a three-phase material consisting of interface zone (ITZ), matrix and inclusions - each constituent modeled by an independent constitutive model. The Representative Volume Element (RVE) consists of inclusions idealized as circular shapes symmetrically and non-symmetrically placed into the specimen. The interface zone is modeled by means of cohesive contact finite elements. The inclusion is modeled as linear elastic and matrix region is considered as elastoplastic material. Our main goal here is to show a computational homogenization-based approach as an alternative to complex macroscopic constitutive models for the mechanical behavior of the brittle materials using a finite element procedure within a purely kinematical multi-scale framework. Besides, the fundamental importance of the representing dissipative phenomena in the interface zone to model the complex microstructural responses of materials like concrete is focused in this work. A set of numerical examples, involving the microcracking processes, is provided in order to illustrate the performance of the proposed modeling.

Multiscale Analysis of Structures Composed of Metal Matrix Composites Considering Phase Debonding

Multiscale analyses considering the stretching problem in plates composed of metal matrix composites (MMC) have been performed using a coupled BEM/FEM model, where the boundary element method (BEM) and the finite element method (FEM) models, respectively, the macrocontinuum and the material microstructure, denoted as representative volume element (RVE). The RVE matrix zone behavior is governed by the von Mises elasto-plastic model while elastic inclusions have been incorporated to the matrix to improve the material mechanical properties. To simulate the microcracks evolution at the interface zone surrounding the inclusions, a modified cohesive fracture model has been adopted, where the interface zone is modeled by means of cohesive contact finite elements to capture the effects of phase debonding. Thus, this paper investigates how this phase debonding affects the microstructure mechanical behavior and consequently affects the macrostructure response in a multiscale analysis. For that, initially, only RVEs subjected to a generic strain are analyzed. Then, multiscale analyses of plates have been performed being each macro point represented by a RVE where the macro-strain must be imposed to solve its equilibrium problem and obtain the macroscopic constitutive response given by the homogenized values of stress and constitutive tensor fields over the RVE.