Traction-separation Law Research Articles

Cohesive Behaviors of Hydrogel Under Large-Scale Bridging

Abstract It has been recently revealed that large-scale bridging mechanism can be invoked to drastically improve the debonding resistance of hydrogel adhesion, but the optimization of the improvement remains elusive. Aiming at shedding light on the optimization, the present article investigates the cohesive behaviors of hydrogel under the condition of large-scale bridging in 90-deg peel. A quasi-static model is established based on the principle of minimum potential energy, with the traction-separation law determined from experiments. The model is proved reliable in predicting the force-displacement response and the backing profile up to the peak peel force. Further theoretical analyses indicate that, within the range of interest, the peak peel force decreases with the extended length, increases with the Young’s modulus of backing, increases, and then plateaus with the adhesion length and the thickness and bending stiffness of backing. In addition, the vertical displacement at peak peel force escalates with the extended length, remains mostly constant with varying adhesion length, declines with the Young’s modulus of backing, and declines and then stabilizes with increasing thickness and bending stiffness of backing. These theoretical insights may help tailor the material properties and geometric parameters for on-demand design of hydrogel adhesion and other soft adhesives for biomedicine and engineering.

A two-scale strategy for the modeling of hook and loop fasteners

Hook-and-loop-like joints have been widely used in many engineering applications and even observed in nature. The demand for computational models to predict the behavior of fasteners is increasing as they will be key for reducing design process time and manufacturing costs. Here, we develop a bottom-up two-scale modeling strategy, which enables us to capture the mechanical performance of a hook-and-loop fastener at both micro- and macroscales. In particular, we employ a two-scale homogenization approach capable of predicting the mechanical behavior of the hook-and-loop fastener. The model starts with a micromechanical model of a hook-and-loop fastener which considers the detailed geometry of the individual building blocks of the hook-and-loop fastener and their statistical geometrical variability through a so-called Representative Hook and Loop Element (RHLE) computational domain. The second scale considers the homogenization of the micromechanical model into a Detachment Process Zone (DPZ) which reveals an emerging length scale. The resulting effective traction-separation law concept is then employed at the macroscale with a Double Cantilever Beam (DCB) test using a macroscale model, which is then validated with experiments. The results suggest that the two-scale model strategy is able to predict the mechanical behavior of hook-and-loop fastener and to capture the main deformation and dissipative mechanisms at the relevant length scales.

Membrane mode enhanced cohesive zone element

PurposeIn certain cases, traction–separation laws do not reflect the behaviour sufficiently so that thin volumetric elements, Internal Thickness Extrapolation formulations, bulk material projections or various other approaches are applied. All of them have disadvantages in the formulation or practical application.Design/methodology/approachDamage within thin layers is often modelled using at cohesive zone elements (CZE). The constitutive behaviour of cohesive zone elements is usually described by traction–seperation laws (TSLs) that consider the (traction separation) relation in normal opening and tangential shearing direction. Here, the deformation (separation) as well as the reaction (traction) are vectorial quantities.FindingsIn this contribution, a CZE is presented that includes damage from membrane modes.Originality/valueMembrane mode-related damaging effects that can be seen in physical tests that could not be simulated with standard CZEs are well captured by membrane mode–enhanced cohesive zone elements.

Fracture Behaviour of Real Coarse Aggregate Distributed Concrete under Uniaxial Compressive Load Based on Cohesive Zone Model.

Two-dimensional meso-scale finite element models with real aggregates are developed using images obtained by digital image processing to simulate crack propagation processes in concrete under uniaxial compression loading. The finite element model is regarded as a three-phase composite material composed of aggregate, mortar matrix and interface transition zone (ITZ). Cohesive elements with traction–separation laws are used to simulate complex nonlinear fracture. During the experiment, digital image correlation (DIC) was used to obtain the deformation and cracks of the specimens at different loading stages. The concept of strain ratio is proposed to describe the effectiveness of simulation. Results show that the numerical strain ratio curve and stress–strain curves are both in good agreement with experimental data. The consistency between the cracks obtained by simulation and those obtained by DIC shows the good performance of cohesive elements as well as the effectiveness of simulation. In summary, the model is able to provide accurate predictions of the whole fracture process in concrete under uniaxial compression loading.

Experimental and numerical analyses of temperature effect on glare panels under quasi-static perforation

The purpose of this work is to experimentally and numerically analyse the quasi-static perforation of fibre metal laminates (FML) at elevated temperatures. Quasi-static experimental tests were conducted on the FML panels at temperatures of 30, 70 and 110 °C. Explicit nonlinear code LS-DYNA was then employed to develop the finite element model of the FML with Johnson-Cook material model for the aluminium, Chang-Chang material model for the GFRP and cohesive zone model with bilinear traction separation law for the epoxy adhesive. The majority of energy dissipation is contributed by aluminium plastic deformation, with a small fraction by adhesive delamination and GFRP fibre breakage and matrix cracking. A higher temperature degrades the cohesive and GFRP material by a larger degree compared to aluminium. The FE modelling methodology proposed herein provides the means to simulate, predict and analyse the quasi-static perforation of FMLs with consideration of temperature effects.

Fatigue crack propagation within Al-Cu-Mg single crystals based on crystal plasticity and XFEM combined with cohesive zone model

A method combining crystal plasticity (CP), the eXtended Finite Element Method (XFEM), and cohesive zone model (CZM) with traction separation law is developed for an Al-Cu-Mg alloy to predict the effect of grain orientation on fatigue crack propagation (FCP) during stage ΙΙ within a single crystal. The simulation results show that of all the orientations, Goss grain possesses the largest fatigue crack deflection, then followed by Cube orientation. Comparatively, Brass, Copper, S and Random grains have relatively small crack deflection angles. Besides, it is found that Goss grain with the largest fatigue crack deflection possesses the lowest FCP rate as compared with other orientations. The results of simulations are consistent with previous experimental observations. This indicates that this coupled CP XFEM CZM simulation method is capable of well predicting the effect of grain orientation on FCP during fatigue stage ΙΙ of Al-Cu-Mg single crystal.

Three-dimensional mechanical behavior of composite with fibre-matrix delamination through homogenization of micro-structure

Delamination is a crucial failure mode of fibre composites and layered materials in general. Delamination, or interfacial failure, leads to loss of stiffness and load-carrying capacity and, ultimately, to failure of the structure. Modeling fibre composites and delamination can be challenging due to the complex architecture of the material. One approach is through homogenization where the heterogeneous material is transformed into a homogeneous one with equivalent mechanical behavior. In this work, a three-dimensional homogenization of a fibre composite is developed. The fibre and matrix materials are allowed to have nonlinear constitutive relations. A traction-separation law is implemented between the fibre and the matrix promoting separation between them on a micro-level. This permits the homogenization to include delamination in its structural response. The new model is compared with existing models from the literature and a finite element model. A satisfying agreement is reported.

An X–FEM Technique for Modeling the FRP Strengthening of Concrete Arches with a Plastic–Damage Model; Numerical and Experimental Investigations

In this paper, an enriched–FEM method is presented based on the X-FEM technique by applying a damage–plasticity model to investigate the effect of FRP strengthening on the concrete arch. In this manner, the damage strain is lumped into the crack interface while the elastic and plastic strains are employed within the bulk volume of element. The damage stress–strain relation is converted to the traction separation law using an acoustic tensor. The interface between the FRP and concrete is modeled using a cohesive fracture model. The X-FEM technique is applied where the FE mesh is not necessary to be conformed to the fracture geometry, so the regular mesh is utilized independent of the position of the fracture. The accuracy of the proposed plastic-damage model is investigated under the monotonic tension, compression, and cyclic tension loading. Furthermore, the accuracy of the cohesive fracture model is investigated using the experimental data reported for the debonding test. In order to verify the accuracy of the proposed computational algorithm, the numerical results are compared with those of experimental data obtained from two tests conducted on reinforced concrete arches strengthened with FRP. Finally, a parametric study is performed by evaluating the effects of high to span ratio, longitudinal reinforcement ratio, and strengthening method.

Grain size dependence of cracking performance in polycrystalline NiTi alloys

Nickle-titanium (NiTi) alloys are widely considered as one of the most intelligent materials with great commercial values. This study focuses on investigating the grain size (GS) effect on crack propagation of polycrystalline NiTi alloys through molecular dynamics (MD) simulations combined with cohesive zone model (CZM). The GS distribution is statistically achieved by electron backscatter diffraction experiment, while the Voronoi tessellation is applied to characterize the microstructures. MD modeling is conducted to determine the traction-separation (T-S) law of CZM. The plastic behavior and phase transition are examined as well. Subsequently, the characteristic parameters extracted from the T-S law are embedded into the cohesive elements along grain boundaries, and then the intergranular fracture of NiTi alloys with various grain sizes are reproduced by conducting finite element simulations. Interestingly, an unexpected subcritical crack growth (SCG) is found during the simulations, and its mechanism is explored at the atomic scale. Moreover, the critical stress intensity factor (KIC) of compact tension specimens with average grain size from 17 to 45 µm is predicted. It is discoverable that the SCG duration and KIC increase as the grains become coarsened. Besides, the internal toughening mechanism of GS is probed from the aspects of stress-induced martensitic transformation and crack-path configuration. A comparison between numerical results and published experimental data demonstrates that this hybrid method could be used to successfully simulate the crack growth behavior.

Determination of fracture energy (mode I) in the inverse fiber metal laminates using experimental–numerical approach

Fiber metal laminates (FML) are hybrid materials consisting of metal and composite layers. They have great mechanical and fatigue properties. However, interface between metal and composite layers can be critical for their final properties. In this paper, process of determination of some fracture parameters of this interface in unusual FML material is described. Experimental tests following ASTM norm were conducted using Double Cantilever Beam (DCB). However, due to asymmetry, fracture energy cannot be obtained directly from the force–displacement curve. Finite element method simulations were carried out using cohesive elements and cohesive surfaces approach. The cohesive behavior of interface layers were modelled using traction separation law. Key properties of this law were obtained—maximal traction and fracture energy. In this particular case cohesive approach was better in reflecting experimental results. Determined values can be used in later research tasks (like modelling big structures containing this material) as material properties. The presented approach can be used successfully to obtain fracture energy in cases of materials for which standard approach is insufficient.

Hydrogen-Assisted Brittle Fracture Behavior of Low Alloy 30CrMo Steel Based on the Combination of Experimental and Numerical Analyses.

Compact-tension (CT) specimens made of low alloy 30CrMo steels were hydrogen-charged, and then subjected to the fracture toughness test. The experimental results revealed that the higher crack propagation and the lower crack growth resistance (CTOD-R curve) are significantly noticeable with increasing hydrogen embrittlement (HE) indexes. Moreover, the transition in the microstructural fracture mechanism from ductile (microvoid coalescence (MVC)) without hydrogen to a mixed quasi-cleavage (QC) fracture and QC + intergranular (IG) fracture with hydrogen was observed. The hydrogen-enhanced decohesion (HEDE) mechanism was characterized as the dominant HE mechanism. According to the experimental testing, the coupled problem of stress field and hydrogen diffusion field with cohesive zone stress analysis was employed to simulate hydrogen-assisted brittle fracture behavior by using ABAQUS software. The trapezoidal traction-separation law (TSL) was adopted, and the initial TSL parameters from the best fit to the load-displacement and J-integral experimental curves without hydrogen were calibrated for the critical separation of 0.0393 mm and the cohesive strength of 2100 MPa. The HEDE was implemented through hydrogen influence in the TSL, and to estimate the initial hydrogen concentration based on matching numerical and experimental load-line displacement curves with hydrogen. The simulation results show that the general trend of the computational CTOD-R curves corresponding to initial hydrogen concentration is almost the same as that obtained from the experimental data but in full agreement, the computational CTOD values being slightly higher. Comparative analysis of numerical and experimental results shows that the coupled model can provide design and prediction to calculate hydrogen-assisted fracture behavior prior to extensive laboratory testing, provided that the material properties and properly calibrated TSL parameters are known.

Fracture predictions based on a coupled chemo-mechanical model with strain gradient plasticity theory for film electrodes of Li-ion batteries

High-capacity electrodes in Li-ion batteries inevitably undergo a large volume deformation originating from high diffusion-induced stresses during charging and discharging processes. In this paper, we firstly develop a new elastoplastic model for describing diffusion-induced deformation in the framework of high-density dislocation defects generated due to the migration of Li atoms. Then, we analyze the film size effect, diffusion-induced stress, plastic yielding, and hardening of electrode materials based on the evolutions of Li concentration by a strategy combining the strain gradient plasticity theory and finite element simulations. Finally, according to the traction-separation law, interface damage and debonding are characterized in the active film materials (with a thickness of 150, 200, and 250 nm, respectively) on a rigid substrate.

Understanding Nanoscale Topology–Adhesion Relationships Via Support Vector Regression

AbstractAdhesion is an important property related to interfacial failure and is crucial in nanofabrication, nanodevices, and biomedicine. Nanoscale roughness significantly reduces the adhesion predicted by classical mechanical models. To quantify the adhesion, an intrinsic traction–separation relation is required. Previous investigations establish traction separation laws with pre‐assumed forms and use statistical topological parameters to summarize details of roughness. Here, support vector regression (SVR) is performed on nanoscale topology–adhesion correlated atomic force microscopy (AFM) data to establish a data‐driven traction–separation relation. Instead of using statistical parameters, full details of the roughness are used as input features. Over 200 000 topological data sets are analyzed and an accurate prediction of adhesion with R2 more than 0.98 is achieved. More importantly, a traction–separation relation is derived from an SVR‐based machine learning process, followed by validation via finite element analysis. This work presents an AFM–SVR integrated approach to characterize nanoscale adhesion that can be generalized for different materials and interfaces.

Numerical simulation of fracturing behavior of reinforced concrete structures using independent cover method

In this paper, a simple approach based on the independent cover method is presented for failure analysis of reinforced concrete structures. Capability of complex fracture representation and simplicity in numerical implementation are main features of this approach. The intrinsic cohesive zone model (CZM) is used for characterizing quasi-brittle fracture initiation and propagation behavior. In the independent cover method, the fictitious thin layer connecting neighboring independent covers naturally defines an initial elastic stiffness required for intrinsic CZM. According to the defined traction-separation law in CZM, a damage factor is introduced to the fictitious thin layer to represent material deterioration. Furthermore, the fictitious thin layer technique is used for concrete-discrete reinforcement coupling including rigid bond and slip bond. The applicability of the present method is verified by a model experiment for analyzing the failure behavior of a damaged rectangular sewer culvert. Good agreements regarding key structural responses and failure pattern between numerical and experimental results are observed.

Phase-field modelling of cohesive fracture

In phase-field models the damage evolution problem is considered as a minimisation problem of a Griffith-like energy functional, governed by the principles of irreversibility, stability and energy balance. Herein, we consider phase-field models characterised by different degradation and energy dissipation functions. With a proper choice for the characteristic functions in phase-field models, it is possible to reproduce cohesive fracture in a one-dimensional setting. We consider a one-dimensional bar with stress softening, which exhibits homogeneous deformations provided that the length of the bar length is below a state-dependent critical value. Otherwise, the bar will lose stability and show a localised response. It appears that the phase-field method can partially reproduce the response of a cohesive zone model, for instance the traction–separation law, but not all aspects of the model, like the dissipated energy. For a one-dimensional problem, the crack nucleation load varies smoothly from that predicted by a strength criterion to that of a toughness criterion for different lengths of the bar. We have compared the one-dimensional results with the numerical solutions in a two-dimensional setting, which yielded a very good agreement.

A computational framework for energy absorption and damage assessment of laminated composites under ballistic impact and new insights into target parameters

In this research, by means of advanced methods within the framework of the FE method, an effective modeling approach is proposed to simulate the ballistic perforation behaviors of multi-directional woven composite panels. Within that scope, constitutive models for intraply and interfacial or interply damage mechanisms are formulated and implemented into ABAQUS/Explicit FE code. The constitutive law of ply-level damage model incorporates the nonlinear material response, degradation of material properties, progressive failure and the element deletion scheme. The interfaces between the individual plies are modeled using a cohesive surface method, and the behaviors of interply degradation and failure are described using a traction-separation law. Besides, the material responses with large nonlinearity due to fiber rupture, matrix cracking, plasticity effects due to micro-matrix cracking under shear loading, and interface delamination are accounted for by appropriate material degradation models. The proposed developments are first validated against the available experimental and analytical results. Next, the ballistic impact simulations of woven composite targets are carried out in a two-phase research. The first phase analyzes the ballistic impact behavior and ballistic performance of the composite laminates in terms of residual velocity and energy absorbing capacity. The second phase involves the investigation of the impact characteristics and failure mechanisms of the composite materials. More specifically, the key perforation mechanisms and associated impact damage extents and patterns with respect to projectile velocity are investigated for the composite panels. We further perform parametric analysis in order to understand the influence of a certain number of parameters on the laminate ballistic impact response. These parameters are categorized based on materials such as fiber type material, interface systems, and geometry such as stacking sequences and support conditions. Numerical results reveal that the ballistic impact performance depends significantly on the cohesive material properties, the stacking sequence, and the woven fabric material, whereas less contribution of support conditions to the ballistic perforation characteristic is noticed.

Comparative study of failure models for prediction of mixed-mode failure characteristics in composite adhesively bonded joint with brittle/Quai-brittle adhesive using finite element analysis

In the paper, detailed numerical comparisons are considered for the mixed-mode failure characteristics of different composite adhesively bonded joints with brittle/quasi-brittle adhesive using following failure models: cohesive zone model (CZM), virtual crack closure technology (VCCT), mixed-mode continuum damage model (MCDM) and finite fracture mechanics (FFM). Detailed numerical comparisons contain the stress and energy, and crack propagation near a crack tip with mode mixity when the adhesively bonded joint made of unidirectional carbon fiber reinforced composite adherend (SEAL® Texipreg HS 160 RM) and brittle adhesive AV138 is subjected to the mixed-mode load. The traction-separation law assumes the bilinear cohesive law to model the brittle/quasi-brittle adhesive and the quadratic stress criterion and B-K energy failure criterion are used. Also, an alternative numerical formulation of FFM is considered for the prediction of failure characteristics in the composite single lap joint. Moreover, the sensitivity analysis is performed to account the effect of parameters in the coupled FFM criteria, using four parameters. Next, predicted failure loads are compared with results in previous references for various types of adhesively bonded joints such as double lap joint (DLJ), scarf joint and single-L joint. Finally, the effect of constraint due to adherend bending is analyzed with varying the adhesive thickness, leading to more accurate prediction of failure load.

Interaction of anisotropic crack phase field with interface cohesive zone model for fiber reinforced composites

A new phase field model considering the interfacial damage for different configurations of a fiber reinforced composite is proposed and formulated. Crack and non local interface are considered to be diffused. A coupled traction separation law based on a potential function is adopted to represent the behavior of the interface. Anisotropy is introduced into the elastic equilibrium by considering the distinct contributions of fiber and matrix in different modes. The present model captures the predominant failure phenomena in a composite such as matrix failure, delamination by considering the role of fiber orientation, interface fracture properties and configuration of lamina. The proposed formulation is extended to a fiber reinforced composite lamina consisting of two fiber families oriented in different directions. Parametric studies are conducted to understand the effect of anisotropy parameter, length scales, fracture properties of fiber, matrix and interface on crack propagation and mechanical response of the whole system. Numerical examples are performed to validate the proposed model, understand the anisotropic crack growth for unidirectional and woven fiber reinforced composites, study the interaction of anisotropic crack with composite-composite interface and metal-composite interface.

Coupling between cohesive element method and node‐to‐segment contact algorithm: Implementation and application

AbstractIn materials, the evolution of crack surfaces is intimately linked with the self‐contact occurring between them. The developed contact forces not only mitigate the effect of stress concentration at crack tip but also contribute significantly to the transfer of shear and normal stresses. In this article, we present a numerical framework to study the simultaneous process of fracture and self‐contact between fracturing surfaces. The widely used approach, where contact constraints are enforced with the cohesive element traction separation law, is demonstrated to fail for relative displacements greater than the characteristic mesh length. A hybrid approach is proposed, which couples a node‐to‐segment contact algorithm with extrinsic cohesive elements. Thus, the fracture process is modeled with cohesive elements, whereas the contact and the friction constraints are enforced through a penalty‐based method. This hybrid cohesive‐contact approach is shown to alleviate any mesh topology limitations, making it a reliable and physically based numerical model for studying crack propagation along rough surfaces.

Investigation of cracking behaviors in divertor armor-blocks under cyclic loading

Optimal design of materials and configurations is necessary to assure intended functions of divertor module against nuclear fusion plasma. Relevant activities performed not only diverse numerical analyses of armor-blocks and structures but also material property tests of specimens and limited experiments of mock-ups under harsh environments. As recent studies reported remarkable cracks in the tungsten-armored multiple-block subjected to cyclic loading, this research is intended to investigate cracking behaviors and to establish a promising numerical approach for engineering application. First of all, three sets of traction-separation law(TSL) parameters for a tungsten material were assumed based on reference data under a severe heat flux of 20 MW/m2. Extended finite element analyses were carried out mainly for the mock-up that consists of five blocks to determine a proper set of TSL parameters by comparing with experimental observation. Subsequently, parametric analyses were conducted to examine further realistic situations by changing the number of blocks and joining restraints. As results of analyses, crack propagation directions and amounts as well as initiation locations were predicted in the simulated blocks. Different cracking behaviors were also evaluated in relation to the number of applied cycles followed by a discussion of key findings from the thermal fatigue and failure assessment standpoint.