Bilinear Cohesive Model Research Articles

A New Procedure for Mode I Fracture Characterization of Cement‐Based Materials

AbstractFracture characterization under mode I loading of a cement‐based material using the single‐edge‐notched beam loaded in tree‐point‐bending was performed. A new method based on beam theory and crack equivalent concept is proposed to evaluate the Resistance‐curve, which is essential to determine fracture toughness with accuracy. The method considers the existence of a stress relief region in the vicinity of the crack, dispensing crack length monitoring during experiments. A numerical validation was performed by finite element analysis considering a bilinear cohesive damage model. Experimental tests were performed in order to validate the numerical procedure. Digital image correlation technique was used to measure the specimen displacement with accuracy and without interference. Excellent agreement between numerical and experimental load–displacement curves was obtained, which validates the procedure.

Experimental and numerical investigation of fracture behavior of asphalt mixture under direct shear loading

Experiments and heterogeneous simulations are combined to investigate cracking behavior of sheared asphalt mixture. A series of direct shear tests are performed at different temperatures with a self-manufactured direct shear test setup, and then a heterogeneous fracture modeling approach based on the random aggregate generation and packing algorithm and the bilinear cohesive crack model is utilized to simulate shear fracture processes. Two kinds of fracture, the single crack type for −20 and −10°C, and the double crack type for 0 and 5°C, are observed. Some internal mechanisms are analyzed based on numerical simulations.

Bio-inspired composite structures subjected to underwater impulsive loading

Designing lightweight high-performance materials that can sustain high impulsive loadings is of great interest to marine and civil applications. When designing tough, strong new materials from relatively weak components, mimicking structures from nature can be a highly promising strategy, as illustrated by nacre from red abalone shells. One of nacre’s most impressive features is its ability to laterally spread damage and dissipate energy over millimetre length scales at crack tips and other defects. In this work, a composite panel is redesigned to mimic nacre’s microstructure. The bio-inspired composite panel and the original composite structure, which have identical areal mass, are subjected to an underwater impulsive loading scenario. Their performances are compared numerically in terms of damage and deflection. A finite element fluid–structure interaction model is developed to capture the water impact on E-glass/vinylester composite facets and to provide insights into the deformation modes and failure mechanisms. Damage and degradation in individual unidirectional composite laminas are simulated using Hashin’s composite damage model. The delamination between laminas is modelled by a bilinear cohesive model. Results interpreted from this numerical study will be used as guidance for the future manufacturing and experimental characterisation of bio-inspired composite structures.

Effect of temperature on the shear strength of aluminium single lap bonded joints for high temperature applications

An experimental and numerical investigation into the shear strength behaviour of adhesive single lap joints (SLJs) was carried out in order to understand the effect of temperature on the joint strength. The adherend material used for the experimental tests was an aluminium alloy in the form of thin sheets, and the adhesive used was a high-strength high temperature epoxy. Tensile tests as a function of temperature were performed and numerical predictions based on the use of a bilinear cohesive damage model were obtained. It is shown that at temperatures below Tg, the lap shear strength of SLJs increased, while at temperatures above Tg, a drastic drop in the lap shear strength was observed. Comparison between the experimental and numerical maximum loads representing the strength of the joints shows a reasonably good agreement.

Crack equivalent based method applied to wood fracture characterization using the single edge notched-three point bending test

In this work the single edge notched-three point bending test applied to wood fracture characterization in mode I is analysed. A new data reduction scheme founded on the equivalent linear elastic fracture mechanics with remarkable advantages relatively to classical methods is proposed. The method is based on the beam theory accounting for a triangular stress relief region and on the crack equivalent concept. It does not require crack monitoring during its propagation and provides a complete R-curve which is fundamental for a clear identification of the fracture energy. The model was validated numerically by means of a bilinear cohesive damage model which allows the simulation of damage initiation and growth. The size of the stress relief region in the neighbouring crack zone was estimated and a consistent value was found relatively to the one achieved by other authors.

Numerical modelling of fracture of particulate composites using SPH method

Simplicity of mesh generation and robustness against mesh entanglement during large deformations are key attractive features of particle based methods. These features can be exploited in number of engineering problems where traditional techniques suffer due to aforementioned limitations. Numerical modelling of particulate composites is one of such ideal engineering applications where particle based methods can be effectively used due to their simplicity and robustness. Complicated geometrical configurations of particulate composites obtained from techniques such as scanning electron microscopy (SEM) can be easily converted to particle based mesh without loosing much information. This enables more accurate analysis of the chosen composite materials. Therefore, a smooth particle hydrodynamics (SPH) based numerical technique is developed here to investigate the mechanical properties and evolution of debonding process in particulate composites. To perform the numerical study, a Lagrangian corrected SPH (CSPH) method is presented together with an appropriate numerical model for treating material interface discontinuity within the particulate composites. The material interface discontinuity is enforced using an innovative method which combines penalty formulation with a bilinear interface cohesive model for SPH method. The proposed SPH methodology is used in a number of numerical examples involving composite materials and related interface problems. The effect of penalty value on the interface model and of the smoothing length of the SPH method are also analysed during these simulations. The results illustrate the effectiveness, robustness and potential of the developed methodology. It is concluded that the proposed numerical techniques can be easily and effectively applied to simulate multi-phase composites with various interface conditions and, can provide useful information regarding the inherent mechanism of damage evolution and fracture of particulate or fibre reinforced composites.

Debonding analysis of FRP–concrete interface between two balanced adjacent flexural cracks in plated beams

A cohesive interface modeling approach to debonding analysis of adhesively bonded interface between two balanced adjacent flexural cracks in conventional material (e.g., concrete or wood) beams strengthened with externally bonded FRP plates is presented. Both the strengthened beam and strengthening FRP are modeled as two linearly elastic Euler–Bernoulli beams bonded together through a thin adhesive layer. A bi-linear cohesive model, which is commonly used in the literature, is adopted to characterize the stress-deformation relationship of the FRP–concrete interface. Completely different from the single-lap or double-shear pull models in which only the axial pull force is considered, the present model takes the couple moment and transverse shear forces in both the substrates into account to study the second type of intermediate crack-induced debonding (IC debonding) along the interface. The whole debonding process of the FRP–concrete interface is discussed in detail, and closed-form solutions of bond slip, interface shear stress, and axial force of FRP in different stages are obtained. A rotational spring model is introduced at locations of the two adjacent flexural cracks to model the local flexibility of the cracked concrete beam, with which the relationship between the local bond slip and externally applied load is established and the real bond failure process of the FRP-plated concrete beam with the increasing of the externally applied load is revealed. Parametric studies are further conducted to investigate the effect of the thickness of adhesive layer on the bond behavior of FRP–concrete interface. The present closed-form solution and analysis on the local bond slip versus applied load relationship for the second type of IC debonding along the interface shed light on the bond failure process of structures externally strengthened with FRP composite plates and can be used effectively and efficiently to predict ductility and ultimate load of FRP-strengthened structures.

Numerical fracture analysis on the specimen size dependency of asphalt concrete using a cohesive softening model

Cracking in asphalt concrete is one of the major causes of structural and functional deterioration of pavement systems. Various experimental and numerical approaches with typical specimen size have been applied to analyze the fracture mechanism of asphalt concrete but the specimen size dependency on the fracture has an important role. Herein, the clustered discrete element method (DEM) approach was applied into the investigation of size effect on fracturing of asphalt concrete based on a disk-shaped compact tension (DC(T)) test. A bilinear cohesive softening model was implemented into the DEM framework to enable simulation of crack initiation and propagation in asphalt concrete. The laboratory tests were conducted for specimen sizes of asphalt concrete varying from 100 to 450 mm. Micromechanical fracture modeling approach was also applied to investigate the heterogeneous fracture behaviors for different specimen sizes. Image processing procedure was conducted to determine the microstructure of asphalt specimen and to project it into the numerical mesh. The specimen size dependency of asphalt concrete was captured by the developed experimental fracture test and the clustered DEM fracture model was able to accurately predict the size-dependent fracture behavior when considering viscoelasticity and heterogeneity.

A densification model for powder materials under cold isostatic pressing—Effect of adhesion and friction of rubber molds

The effect of adhesion and friction of a rubber mold on powder compacts was studied during unloading under cold isostatic pressing. The densification model by Lee and Kim was used for compaction of powder, based on the yield function of the Cap model and volumetric strain evolution. The bilinear cohesive model was used to study a detaching process and stress distributions at the interface between the mold and the compact. We also studied the failure of the powder compact during unloading under cold isostatic pressing due to friction at the interface, and compared experimental data with finite element results.

低速衝撃荷重下におけるCFRP擬似等方性板の損傷進展予測

In this paper, to understand the mechanism of delamination propagation in low-velocity impact problems, a weight-drop test is performed for quasi-isotropic composite plates of 32 plies. Due to the high computational cost, up to date, there have been almost no computational effects for simulating the damage propagations in quasi-isotropic composite laminates of 32 plies. This low-velocity impact problem is further numerically modeled and the damage propagation is simulated. A stress-based criterion is adopted for modeling various in-plane damages, such as transverse matrix cracking. A bi-linear cohesive interface model is employed for interface damages, such as delaminations. Moreover, to remove the numerical instability in simulations when using the traditional cohesive model, we propose a new technique, i.e., adaptive cohesive model. The effectiveness of this cohesive model is investigated using a DCB example. Then, it is applied to the low-velocity impact problem of quasi-isotropic composite laminates of 32 plies. The validity of the proposed numerical methodology is verified by comparing the numerical results with the experimental results.

Semi-Analytical Finite Element Method for Bilinear Cohesive Crack Model in Mode I Crack Propagation

Based on the Hamiltonian theory and method of elasticity, a ring and a circular hyper-analytical-elements are constructed and formulated. The hyper-analytical-elements give a precise description of the displacement and stress fields in the vicinity of crack tip for the bilinear cohesive crack model. The new analytical element can be implemented into finite element method program systems to solve crack propagation problems for plane structures with arbitrary shapes and loads. Numerical results for typical problems show that the method is simple, efficient and accurate.

Stable numerical simulations of propagations of complex damages in composite structures under transverse loads

In this paper, to deal with complex damage propagations in various composite structures under quasi-static transverse loads, a numerical simulation methodology based on the three-dimensional (3D) finite element method (FEM) is proposed. In this numerical model, two categories of damage patterns existing in composite structures under transverse loads are tackled independently. First, a kind of stress-based criteria is adopted to deal with the first category, which includes various in-plane damages, such as fiber breakage, transverse matrix cracking, matrix crushing, etc. Second, a bi-linear cohesive interface model is employed to deal with the second category, i.e., interface damages, such as delaminations. Also, to overcome the numerical instability problem when using the cohesive model, a simple and useful technique is proposed. In this technique, the move-limit in the cohesive zone is built up to restrict the displacement increments of nodes in the cohesive zone of laminates after delaminations occurred. The effectiveness of this method is illustrated using a DCB example and its characteristic is discussed in detail. This numerical model is further applied to various composite structures, such as 2D laminated plates and 3D laminated shells under transverse loads. The results of the numerical simulations are compared with the experimental results and good agreements are observed. The obtained information is helpful for understanding the propagation mechanisms of various damages in composite structures.

横荷重下におけるFRP積層構造の損傷進展予測

In this paper, to deal with the complex damage propagations in various composite structures under quasi-static transverse loads, a numerical simulation methodology based on the three-dimensional (3D) finite element method is proposed. In this numerical model, two categories of damage patterns existing in composite structures under transverse loads are tackled independently. First, a stress-based criterion is adopted to deal with the first category, i.e. various in-plane damages, such as fiber breakage, transverse matrix cracking etc. Second, a bi-linear cohesive interface model is employed to deal with the second category, i.e., interface damages, such as delaminations. Also, to remove the numerical instability when using the cohesive model, we propose a simple and useful technique, where the move-limit in the cohesive zone is built up to restrict the displacement increments of nodes in the cohesive zone after the occurring of delaminations. This numerical model is further applied to various composite structures, such as 2D laminated plates and 3D laminated shells under the transverse loads. A lot of information is provided for understanding the propagation mechanisms of various damages in composite structures.

コヒーシブ要素を用いた層間はく離シミュレーションにおける数値安定化

In this paper, we propose a very useful and simple technique to stabilize the finite element simulations of delamination propagation in composite laminates when using cohesive interface model of comparatively coarse meshes. In this method, the move limit in the cohesive zone is built up to restrict the displacements of upper and lower layers of laminates. A forward Lagrange multiplier method, which is employed to enforce these constraint conditions, is realized in the explicit time integration scheme. The size of the move limit is theoretically discussed. Furthermore, a damping technique for avoiding the numerical instability put forward by other researchers is modified for the explicit time integration scheme and bi-linear cohesive model for composites. The characteristics of these two techniques are examined. Moreover, a DCB problem is employed to illustrate the validity of the present method.

Cohesive modeling of dynamic fracture in functionally graded materials

The dynamic fracture of functionally graded materials (FGMs) is modeled using an explicit cohesive volumetric finite element scheme that incorporates spatially varying constitutive and failure properties. The cohesive element response is described by a rate-independent bilinear cohesive failure model between the cohesive traction acting along the cohesive zone and the associated crack opening displacement. A detailed convergence analysis is conducted to quantify the effect of the material gradient on the ability of the numerical scheme to capture elastodynamic wave propagation. To validate the numerical scheme, we simulate dynamic fracture experiments performed on model FGM compact tension specimens made of a polyester resin with varying amounts of plasticizer. The cohesive finite element scheme is then used in a parametric study of mode I dynamic failure of a Ti/TiB FGM, with special emphasis on the effect of the material gradient on the initiation, propagation and arrest of the crack.

Bounds for element size in a variable stiffness cohesive finite element model

AbstractThe cohesive finite element method (CFEM) allows explicit modelling of fracture processes. One form of CFEM models integrates cohesive surfaces along all finite element boundaries, facilitating the explicit resolution of arbitrary fracture paths and fracture patterns. This framework also permits explicit account of arbitrary microstructures with multiple length scales, allowing the effects of material heterogeneity, phase morphology, phase size and phase distribution to be quantified. However, use of this form of CFEM with cohesive traction–separation laws with finite initial stiffness imposes two competing requirements on the finite element size. On one hand, an upper bound is needed to ensure that fields within crack‐tip cohesive zones are accurately described. On the other hand, a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand. Both issues are analysed in this paper within the context of fracture in multi‐phase composite microstructures and a variable stiffness bilinear cohesive model. The resulting criterion for solution convergence is given for meshes with uniform, cross‐triangle elements. A series of calculations is carried out to illustrate the issues discussed and to verify the criterion given. These simulations concern dynamic crack growth in an Al2O3 ceramic and in an Al2O3/TiB2 ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour. Copyright © 2004 John Wiley & Sons, Ltd.

Choice of standard fracture test for concrete and its statistical evaluation

The main characteristics of the cohesive (or fictitious) crack model, which is now generally accepted as the best simple fracture model for concrete, are (aside from tensile strength) the fracture energies GF and Gf corresponding to the areas under the complete softening stress-separation curve and under the initial tangent of this curve. Although these are two independent fracture characteristics which both should be measured, the basic (level I) standard test is supposed to measure only one. First, it is argued that the level I test should measure Gf , for statistical reasons and because of relevance to prediction of maximum loads of structures. Second, various methods for measuring Gf (or the corresponding fracture toughness), including the size effect method, the Jenq- Shah method (TPFM), and the Guinea et al. method, are discussed. The last is clearly the most robust and optimal because: (1) it is based on the exact solution of the bilinear cohesive crack model and (2) necessitates nothing more than measurement of the maximum loads of notched specimens of one size, supplemented by tensile strength mea- surements. Since the identification of material fracture parameters from test data involves two random variables, f � t (tensile strength) and Gf , statistical regression should be applied. But regression is not feasible in the original Guinea et al.'s method. The present study proposes an improved version of Guinea et al.'s method which reduces the statistical problem to linear regression thanks to exploiting the systematic trend of size effect. This is made possible by noting that, according to the cohesive (or fictitious) crack model, the zero-size limit σN0 of nominal strength σN of a notched specimen is independent of Ff and thus can be easily calculated from the measured f � t . Then, the values of σN0 obtained from the measured f � t values, together with the measured σN -values of notched specimens, are used in statistical regression based on the exact size effect curve calculated in advance from the cohesive crack model for the chosen specimen geometry. This has several advantages: (1) the linear regression is the most robust statistical approach; (2) the difficult question of statistical correlation between measured f � t and the nominal strength of notched specimens is bypassed, by virtue of knowing the size effect trend; (3) the resulting coefficient of variation of mean Gf is very different and much more realistic than in the original version; (4) the coefficient of variation of the deviations of individual data from the regression line is very different from the coefficient of variation of individual notched test data and represents a much more realistic measure of scatter; and (5) possible accuracy improvements through the testing of notched specimens with different notch lengths and the same size, or notched specimens of different sizes, are in the regression setting straightforward. For engineering purposes where high accuracy is not needed, the simplest approach is the previously proposed zero-brittleness method, which can be regarded as a simplification of Guinea et al.' method. Finally, the errors of TPFM due to random variability of unloading-reloading properties from one concrete to another are quantitatively estimated.