Cohesive Parameters Research Articles

Application of the FDEM Based on the CZM in Simulating Three-Point Bending Test of Frozen Soil

The combined finite–discrete element method (FDEM) based on the cohesive zone model (the CZM) achieves cracking simulation by inserting cohesive elements between solid elements. In this study, three-point bending fracture tests of frozen soil were simulated by using the FDEM based on the CZM. Firstly, the sensitivity of the cohesive model parameters was analyzed. Secondly, through a series of simulations of the three-point bending test of frozen soil, it was found that the model with reasonable values of the CZM parameters had a good adaptability to the three-point bending cracking test of frozen soil, as the model not only reflects the load-displacement curve, but also has good correspondence with the fracture pattern compared with the test. Finally, the relationship between the CZM parameters and the specimens’ temperature under two loading rates of 1 mm/min and 0.1 mm/min was analyzed, and it was found that the CZM parameters had a good linear relationship with the specimens’ temperature. This paper is expected to provide a new possibility for the numerical simulation of frozen soil cracking.

Multiscale modeling for dynamic compressive behavior of polymer bonded explosives

The impact damage behavior of polymer bonded explosives (PBXs) is critical to ensure the safety of explosive systems. PBX 1314 (60 wt% RDX, 16 wt% aluminum, and 24 wt% HTPB) is a popular propellant owing to its characteristics of high energy density and low sensitivity. In this study, the compressive damage evolution rules and the strain rate effect of PBX 1314 were investigated by using a multiscale method. To acquire damage evolution data during loading, a finite element model based on real crystal morphology, with a cohesive zone model (CZM) for describing the damage, was developed. A novel hybrid/inverse optimization strategy was developed to calibrate the cohesive parameters of PBX 1314, and the accuracy of the parameters was verified basis experimental results. Using an as-developed bilinear model, the shift of damage pattern with the variation of strain rate was observed, and the nonlinearity of the stress–strain curve was presented at the mesoscale. The crack parameters and distribution of damaged elements in each mesoscopic component were acquired to quantitively characterize the strain rate dependence of PBX 1314, and the mechanism of crack propagation and the shift of damage mode under various strain rates was illustrated. The findings of this study provide insights for understanding the nonlinearity of macroscopic mechanical behavior and the influence of strain rate on the mesoscopic damage mode of PBXs with high binder content.

Probabilistic Analysis of Strip Footings Using the Subset Simulation Approach and the Influence of Spatial Variability of Two Clay Layers

Abstract This article studies the probabilistic analysis at the ultimate limit state (ULS) of a strip footing resting on a purely cohesive soil composed of two layers with spatial variability of the upper or lower layer and treats the simultaneous effect of the variability of the two layers on the probability of failure Pf value using the subset simulation approach. The results are examined by comparing the Pf values obtained with the Pf value corresponding to the reference case of two homogenous clay layers. In general, the subset simulation approach is used in cases of uncertain parameters modeled by random variables. But in this paper, it is employed with uncertain parameters modeled by random fields because the spatial variability of soil properties strongly affects the behavior of geotechnical structures and causes a significant change in the variability of their responses. The soil cohesion parameter is modelled as a non-Gaussian (log-normal) anisotropic random field using a square exponential autocorrelation function by the optimal linear expansion estimation (EOLE) and the deterministic model is based on numerical simulations using the finite difference software FLAC3D.

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto‐Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

AbstractWe present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2‐D planar rate‐and‐state fault with off‐fault visco‐plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co‐evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off‐fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off‐fault bulk even at higher angles of maximum compression. This produces damage patterns that deviate from the traditional off‐fault fan‐like distribution observed in dynamic rupture simulations and emphasizes the significance of long‐term deformation in interpreting observations.

Influence of natural fractures on hydraulic fracture propagation behaviour

The propagation behaviour of hydraulic fractures is affected by natural fractures in unconventional reservoirs and determines the effect of reservoir reconstruction to a certain extent. Using the splitting mode of mesh nodes and zero-thickness cohesive elements, we established a hydraulic fracture random propagation method. The KGD model and Blanton’s experiment were used to verify the reliability of this method, and the cohesive element parameters of the natural shale core were obtained using three-point bending and digital image correlation methods. Finally, the model was used to simulate the propagation behaviour of hydraulic fractures in natural fracture–developed formations. The results show that even if the hydraulic fracture does not come into contact with the natural fracture, the natural fracture will open, accompanied by the shear slip of the natural fracture surface. The propagation of hydraulic fractures generates a stress shadow effect, causing an increase in the local formation pore pressure and minimum horizontal stress. When the horizontal stress difference was more than 2 MPa, the hydraulic fracture expanded along the direction of the maximum horizontal stress, and the fracture morphology was simple. A formation with a high elastic modulus and high injection rate can contribute to increasing the hydraulic fracture complexity. Hydraulic fracture propagation can be captured using natural fractures. Simultaneously, owing to the stress shadow effect, the stress state at the tip of the hydraulic fractures may change from tensile stress to compressive stress, eventually leading to the stop propagation of hydraulic fractures and the formation of asymmetric hydraulic fractures. The research results are helpful for improving the understanding of the geometric shape of the propagation behaviour of hydraulic fractures in natural fractures that develop formations.

Direct measurement and verification of cohesive zone model parameters for basalt/PProds using the transverse tensile test and virtual double cantilever beam test

AbstractTo further our understanding of failure in thermoplastic‐based composite rods, the mode I‐governed cohesive zone model parameter of a basalt fiber reinforced polypropylene composite rod is evaluated. The relations between stress and strain, the maximum normal traction and final separation displacement are examined using a transverse tensile test method. The measured traction is verified by three‐dimensional finite element analysis of rod‐shaped double cantilever beam specimens. The numerical results show the close relation between the crack length and cube root of compliance, and yields a representative value of the mode I‐governed critical fracture energy.

Study on micro crack propagation mechanism of ferrite–pearlite gas transmission pipeline steel with lamellar structure

The deformation and failure characteristics of pipeline steel depend on its atomic structure and microstructure. Based on the serial multi-scale analysis technology, the ferrite/cementite (α-Fe/Fe3C) lamellar atomic structure with Bagaryatskii orientation relationship is established. In order to obtain the experimental sample of the lowest energy state, The step-by-step relaxation method of conjugate gradient energy minimization and constant temperature and constant pressure relaxation under NPT conditions is carried out, and the energy state and atomic structure of the relaxed samples are analyzed. For the models of different cementite terminal plane structures, the tension displacement curves on the propagation path of mode I central through crack are extracted respectively, combined with the bilinear cohesion zone model, The cohesion parameters at the atomic scale are successfully transferred from bottom to top to the macro and micro scales. By simulating the reaction force and displacement response law at the loading point, the critical fracture toughness of each terminal interface of ferrite–pearlite pipeline steel at different scales is calculated, which provides a reliable path for exploring the micro mechanism of macro cracking behavior of pipeline steel.

Determination of cohesive zone model parameters for tape delamination based on tests and finite element simulations

Determination of cohesive zone model parameters for tape delamination based on tests and finite element simulations

Mesoscale modeling and failure mechanism of concrete considering pore structures and actual aggregate shapes

This contribution focuses on the modeling and failure mechanism of concrete which is constituted by aggregates, mortar matrix, interfacial transition zones (ITZs) and pore structures. Firstly, actual geometrical shapes of aggregates were obtained by laser scanning technique. Secondly, a random aggregate placement algorithm and a pore structure generation algorithm were proposed to generate 2D concrete models which could realistically reflect the highly heterogenous meso-structure of concrete. Then, zero-thickness cohesive elements with traction - separation laws were embedded in the finite elements to simulate the complex fracture process and nonlinear mechanical characteristics. Finally, uniaxial compression simulations were carried out, and the effect of porosity and aggregate volume content on carrying capacity, elastic modulus and fracture process of concrete were investigated and compared with similar experimental results. The parametric study for cohesive elements is also conducted. Results showed that porosity and aggregate content have a significant influence on the mechanical properties of concrete, the mesoscale model is capable of simulating the failure process and mechanical behavior of concrete. The effect of each cohesive element parameter is clearly identified.

Mechanical Characterisation and Cohesive Law Calibration for a Nitrocellulose Based–Cyclotetramethylene Tetranitramine (HMX) Polymer Bonded Explosive

BackgroundMechanical characterisation of polymer bonded explosives (PBXs) is crucial for their safe handling during storage and transportation. At temperatures higher than the binder's glass transition temperature, fracture is caused predominantly by interface debonding between the binder and explosive crystals. Interfacial friction between debonded crystals can lead to accidental detonation of the PBX material, even under a very small external load. Cohesive zone laws can describe this interfacial debonding.ObjectiveThis study aims to experimentally calibrate the interfacial cohesive zone parameters of a nitrocellulose based–cyclotetramethylene tetranitramine (HMX) PBX, a particulate composite with an 88% volume fraction of crystals.MethodsCompact tension fracture tests, coupled with Digital Image Correlation (DIC) were used to capture the strain fields around the crack tip. The experimental data were used in conjunction with an extended Mori–Tanaka method considering the effect of interfacial debonding.ResultsThe cohesive zone parameters were successfully calibrated and were found to be crosshead rate independent. The values of the critical traction {sigma }_{int}^{max} and interfacial energy release rate, {gamma }_{if}, dropped significantly with increasing temperature. The experimental method followed in this study is generic, and it can be employed to extract the cohesive zone parameters characterising the interface behaviour between the filler and matrix in other particulate filled, polymer composite materials.ConclusionsCohesive zone properties can be experimentally determined to provide inputs in micromechanical simulations linking the microstructure of the PBX composite to its macroscopic response as well as enabling the estimation of hot spot formation at debonded crystal interfaces.

Determination of cohesive parameters for fibre-reinforced composite interfaces based on finite element analysis and machine learning

This paper proposed a method for determining the cohesive parameters of fibre-reinforced composite interfaces based on finite element analysis (FEA) and machine learning. 3D FEA models with different boundary conditions and 2D FEA models were created to simulate the process of microdroplet tests, and to compare their maximum reaction forces and the time costs. The proper FEA model that is accurate and efficient was adopted to establish the data set of machine learning. Machine learning based on the FEA data set was divided into two steps: feature selection and kernel ridge regression (KRR) prediction. Feature selection was carried out to confirm the validity of the features, to obtain the optimal parameter of KRR prediction and to quantitatively illustrate the effect of the cohesive parameters on the maximum reaction force. Interfacial shear strength (IFSS) and interfacial fracture toughness (IFFT) of a poly ( p-phenylene benzobisoxazole) (PBO) fibre-reinforced epoxy composite were successfully predicted by the KRR method without extra mechanical theories or assumptions.

Multi-scale modeling method for polycrystalline materials considering grain boundary misorientation angle

Grain boundaries (GBs) are microstructures in polycrystalline materials, which influence the mechanical properties of materials significantly. Simulation is an indispensable means to study GBs due to its high flexibility. However, the existing GB simulation models mostly focus on a single simulation scale, lack the consideration of the grain boundary misorientation angle (GBMA) characteristic and fail to describe the coupled elastic–plastic damage behavior between grains and GBs accurately. To describe the influence mechanism of GB on the mechanical behavior of materials accurately, a GBMA-considered multi-scale modeling method for polycrystalline materials is proposed in this paper. The method is based on molecular dynamics (MD), the crystal plasticity finite element method and the cohesive zone model, which considers the GBMA information at grain and atomic scales comprehensively. Firstly, a GB geometric model containing GBMA characteristic is generated at grain scale through EBSD information. Then the GB cohesive parameters are obtained at the atomic scale by MD simulation. Finally, some experiments are performed for verification, which indicates the high accuracy of the proposed method. Furthermore, three models with the same geometric shape and different grain orientation and GBMA are established to study the influence of GBMA on the mechanical properties of polycrystalline materials.

Learning from Global Sensitivity Analysis about identification of adhesion properties between an elastoplastic film and a rigid substrate

When peeling an elastoplastic film from rigid substrates, the work of separation (WOS) lumps the fracture energy of adhesion, i.e., the work of adhesion (WOA), and the dissipation from other sources, such as plastic deformation. This lumping poses a challenge for measuring the WOA of elastoplastic films to rigid substrates. A remedy would be to identify properties by matching numerical predictions with experimental measurements. Distinguishing the most informative metrics from the data produced by a peeling test is of initial significance in constructing the objective function to guarantee the efficiency and accuracy of that inverse identification. To evaluate the sensitivity of various experimental data/objective functions to the classical cohesive parameters characterizing adhesion, a model-based global sensitivity analysis is performed using Sobol’s approach. We combine a finite element model and a theoretical model to replicate the process of peeling an elastoplastic film under 90∘, including loading and unloading. The metrics, i.e., the plateau peeling force, the peeling arm profile, and the residual curvature after release are formulated as the cost functions and then are assessed. It is found that the peeling force, as a direct indicator of WOS, shows the most significant sensitivity to the fracture energy Gc, and the maximum curvature of the peeling arm is the most sensitive metric to the critical traction tc. Among the considered metrics to quantify the profile similarity of peeling arm, Fréchet distance is the most relevant for incorporation in the objective function for inverse identification purposes, considering sensitivity, accessibility, and tolerance to measurement error. The results also highlight the effect of film’s thickness on energy dissipation and on the sensitivity of metrics. For the peeling scenario with specified input properties, plastic dissipation increases with increasing film thickness, mainly because of the enhancement of the peeling film’s moment-bearing capacity. The increasing thickness enhances the sensitivity to Gc of peeling arm profile and the residual curvature while reducing their sensitivity to tc; minimal effect on peeling force is apparent. A tailored objective function incorporating the peeling force and the Fréchet distance is proposed, the effectiveness of which has been demonstrated by a FEMU identification of the adhesive properties between an annealed copper film and a rigid substrate.

Transient creep‐fatigue crack growth in creep‐brittle materials: Application to Alloy 718

AbstractThis study presents incremental finite element computations of creep‐fatigue crack growth in Alloy 718 at in air. Alloy 718 is representative of creep‐brittle materials, in which viscoplastic deformation is restricted near the tip of a growing crack. The computations predict crack growth using a unique combination of an irreversible cohesive zone formulation and a strain gradient viscoplastic material model based on the Kocks–Mecking formulation. Cohesive zone damage parameters are estimated using sustained loading and constant‐amplitude cyclic loading experiments. Computations of crack extension under three different waveforms containing overloads all predict post‐overload retardation. The amount of retardation depends strongly on the overload ratio, consistent with experiments in the literature using similar waveforms. Analysis of the crack‐tip fields demonstrates retardation is associated with unloading in the highly deformed material near the advancing crack tip. Dynamic recovery and geometrically necessary dislocations are shown to significantly influence post‐overload crack extension.

Implementation of a probabilistic machine learning strategy for failure predictions of adhesively bonded joints using cohesive zone modeling

Adhesive bonding as an assembly procedure in aviation products is very efficient from both weight and recurring cost points of view. However, even with strict inspections, process control, and quality assurance protocols, it is difficult to evaluate and predict joint strength and performance. To manage this risk, regulators require determination of the maximum allowed disbond size as part of bonded joint design. This study proposes a methodology for determination of the bond-line strength characteristics based on a comprehensive test data from 88 Mixed Mode Bending (MMB) specimens. The Cohesive Zone Model (CZM) was employed to simulate disbond propagation, and nearly 2000 finite element simulations were conducted with a wide range of failure parameters. Combined experimental and numerical data was analyzed using the Gaussian Process Regression (GPR) machine learning algorithm to obtain the optimized CZM failure parameters. Statistical analysis was conducted to determine safety factors and B-Basis cohesive zone failure parameters, ensuring sufficient reliability of the failure predictions. The proposed failure parameters were validated by means of several benchmark problems, including single bonded lap joints and a bonded scarf joint, showing very good agreement with the test data.

Finite Element Modeling of FHWA-Accelerated Loading Facility Test Sections With Fatigue Damage Using a Nonlinear Viscoelastic Cohesive Zone Integrated With Gaussian Damage Evolution

This study presents a computational fracture modeling approach for predicting highly nonlinear viscoelastic cracking, such as fatigue damage, in asphalt mixtures and pavements. The modeling approach is presented and validated against field performance data from the FHWA-Accelerated Loading Facility (ALF) performance test sections. To that end, five mixtures differing either in the type of binder used or the amount of reclaimed asphalt pavement and reclaimed asphalt shingles were selected to assess their linear viscoelastic behavior, fracture properties, and field performance. A nonlinear viscoelastic cohesive zone fracture model was used along with a Gaussian distribution damage evolution to characterize the mixture fracture properties through a numerical-experimental calibration process. Individual mixture characteristics were then used as inputs to analyze the ALF pavement structure, and the fatigue response was predicted and compared with the field performance data for model validation. Although there are several model limitations to improve, the good agreement in performance rank order among test lanes demonstrates the capability and validity of the modeling approach. This implies that the computational modeling approach attempted in this study could potentially be used to analyze and design pavements in a mechanistic manner. This could be done with just a few laboratory tests for mixture properties such as viscoelastic dynamic modulus and cohesive zone fracture parameters.

Influence of the DCB/Wedge beam kinematics on the identification of the cohesive parameters of interfaces

DCB and Wedge tests are widely used in experimental fracture mechanics in order to identify fracture properties of materials or assembled parts, like toughness. In order to extract data from those experiments, it is very common to model the sample as two adhesive beams with a crack growing in between as an external loading is applied. This study is devoted to investigating the influence of two types of beam kinematics on the identification of the cohesive zone parameters of interfaces. A critical comparison between beam models based on an Euler–Bernoulli or a Timoshenko beam kinematics is carried out in the case of the DCB and Wedge loaded DCB tests. The size of the process zone extent is used as a parameter to evaluate the difference between the two models predictions. Euler–Bernoulli kinematics neglects the effect of shear stress on the beam’s deflection whereas Timoshenko kinematics accounts for it. The aim of the present work is to evaluate the validity of each kinematics, both used in the literature, especially when the process zone length becomes comparable to the specimen’s height. In both frameworks, an analytical prediction is presented and compared over a wide range of cohesive zone parameters and beam geometries, using a non-dimensional representation. Our results show that when we compare both kinematics in term of the fracture process zone, the relative error varies from a few percent to more than 1000%, depending on the specimen’s geometry, properties and the loading conditions. In addition, for many cases, no Euler–Bernoulli kinematics can fit the Timoshenko kinematics, especially around the fracture process zone. The cases for which Timoshenko and Euler–Bernoulli kinematics yield similar results are highlighted. The model and the results of the study can be used as a guideline for users in order to determine which model is required in order to get an accurate determination of the cohesive parameters in their particular system of interest.

Mechanical Behavior of the Alkali-Treated Ichu Fiber-Cementitious Matrix Interface Through Experimental Tests, Numerical, and Analytical Models

ABSTRACT The interaction properties between natural fiber and matrix play an important role in the mechanical performance of composite materials. The adhesion properties and the mechanical interaction between an Ichu fiber (Stipa obtusa) treated with sodium hydroxide and a cementitious matrix were studied by conducting experimental, numerical, and analytical pull-out tests. Through the experimental tests, the force–displacement curve for a fiber length embedded 5 mm deep in the cementitious matrix, maximum force, cohesive parameters, and the type of interface failure were determined. The results were used to calibrate the numerical and analytical models for different lengths of fiber (3, 5, 7, 9, and 11 mm) embedded in the cementitious matrix. The numerical model was implemented in the finite element software Abaqus CAE, and the analytical formulation considered the fiber embedded in a half-space continuous medium. From the experimental test, the force–displacement curve, interfacial shear strength of 0.124 MPa, and the softening type slip were obtained, despite obtaining the hardening-type slip in certain tests. The numerical and analytical results of the load–displacement curve closely approximate the experimental results. This study provides a numerical and analytical model to simulate the alkali-treated Ichu fiber–cementitous matrix interface.

The solubility of helium in lead–lithium eutectic alloy

• The He solubility value needed to evaluate helium saturation conditions and bubble nucleation in nuclear fusion liquid metal blankets. • He solubility values in lead and lead–lithium eutectic proposed by using semi-empiric correlations sustained on cohesion models and historic data for Li, Na, K and Hg. • Satisfactory soundness of semi-empirical correlation based on Kumaŕs cohesion model to approach available historic measurements. • New experimental approaches needed to confirm the low values obtained. The helium production rates in liquid metals (Pb-Li eutectic alloy, LLE and others) Blanket Breeders (BB) are nearly mol-to-mol linked to tritium and intimately associated with the compulsory requirement of high tritium self-sufficiency of next fusion reactors. When LLE is oversaturated and the helium solubility limit is exceeded, helium atoms can nucleate in the form of bubbles. The presence of helium bubbles within LLE channels could have severe impact on the diverse BB designs, in particular on tritium transport permeation and its recovery. Even though He is an inert gas assumed to be insoluble, the helium Henry’s constant ( K H ) in a liquid metal is not zero. The very low K H and difficulties to measure it has historically driven to the absence of basic data. A semi-empirical correlation is proposed providing the helium solubility (i.e.: the helium Henry’s constant) based on Kumar’s cohesion model using the available thermo-physical experimental solubility data for lithium, sodium, potassium, mercury. The proposed expression for eutectic lead–lithium is: K H at . fr . Pa - 1 = 5.99 · 10 - 4 exp ( - 1.16 · δ k ) exp - 54.23 / RT , being K H the Henry’s constant; T [K], R [8.314 10 -3 kJ mol −1 K −1 ] and δ k the Kumar’s cohesive parameter. From a δ k justified value of 18.2 MPa 1/2 in LLE the values for K H range from 1.14·10 -17 to 1.35·10 -15 at.fr.Pa −1 for temperatures between 350 and 870C. The helium solubility should integrate the lead–lithium eutectic nuclear material database for fusion systems design.

Cyclic cohesive zone model damage parameter acquisition for fatigue crack growth considering crack closure effect

This paper presents a method to obtain damage parameters for cyclic cohesive zone model based on the crack closure experiments. The damage evolution is modified by introducing equivalent separation to quantify the nonuniform damage distribution along the crack path. The damage parameters acquisition is realized with digital image correlation analysis, where the effect of crack closure is accordingly elaborated. An adaptive cycle jump technique is established based on the damage rate, aiming to reduce the computational cost. Compared with the experimental data, the proposed model exhibits the capability in predicting fatigue crack growth rate.