Cohesive Law Research Articles

Simulation of Mode I Interlaminar Damage of a GFRP Composite Using Cohesive Laws in the Framework of the Equivalent LEFM R-Curve and an Optimised Algorithm.

This paper is focused on mode I delimitation of a unidirectional glass fibre reinforced polymer (GFRP) composite. The aim is to propose an accurate and simple characterisation of three cohesive zone models (CZM)—bilinear, trilinear, and potential—from the measurement of the load-displacement curve during a double cantilever beam experimental test. For that, a framework based on the equivalent linear elastic fracture mechanics (LEFM) R-curve is here proposed, which has never before been developed for a bilinear and a potential CZM. Besides, in order to validate this strategy, an optimisation algorithm for solving an inverse problem is also implemented. It is shown that the parameters’ identification using the equivalent LEFM R-curve enables the same accuracy but reduces 72% the numerical efforts respect to a “blind fitting” (i.e., the optimisation algorithm). Therefore, even if optimisation techniques become popular at present due to their easy numerical implementation, strategies founded on physical models are still better solutions especially when evaluating the objective function is expensive as in mechanical problems.

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.

Endowing explicit cohesive laws to the phase-field fracture theory

One of the fundamental but unsolved problems in the phase-field theory is how to obtain the energy density expression based on an arbitrary cohesive law. In this paper, we propose a phase-field model with the energy density determined by the cohesive law with an arbitrary form, which builds a rigorous link between the phase-field theory and the cohesive zone theory. Using the proposed method, the energy density in the phase-field model for any cohesive law can be determined from a unified formula. As examples, we derive the explicit energy density expressions for the linear, exponential, polynomial, and Cornelissen cohesive laws. Five numerical examples are presented to show the effectiveness of the proposed method, including a uniaxial tension test for mode-I failure, a uniaxial compression test for mode-II failure, a mixed-mode fracture test, the mode-I failure in a wedge splitting test, and the mixed-mode failure of an L-shaped panel. In the first three numerical examples, the predicted mode-I, mode-II and mixed-mode cohesive laws are extracted and compared with the target analytical cohesive laws. Excellent agreements are observed. In the last two numerical examples, the predicted global responses and the crack paths are in good agreement with the experimental results.

A new cohesive law for the simulation of crack propagation under cyclic loading. Application to steel- and concrete-FRP bonded interface

This paper presents a new cohesive law for modelling interfaces under mixed-mode cyclic loading. The formulation is based on the definition of a free energy function which governs the interface behaviour under monotonic loading, which is then extended to cyclic-driven decohesion through the introduction of a scalar damage variable, whose evolution in time is governed by a phenomenological rate equation. The cohesive model is formulated for a mixed-mode problem and then it is applied for the simulation of debonding phenomena occurring at the interface under a pure a shear stress state. Experimental results available in literature, related to single-lap shear tests, performed on both concrete and steel specimens reinforced by fibre reinforced composite (FRP), are used to validate the proposed model and to show its effectiveness to simulate very closely the observed experimental behaviour.

Molecular Dynamics-Based Cohesive Law for Epoxy–Graphene Interfaces

Molecular dynamics simulations are used to obtain mode I and mode II fracture energies and cohesive laws for bulk epoxy and interfaces formed between epoxy and single-layer graphene (SLG), multilayer graphene (MLG), and multilayer graphene oxide (MLGO). The elastic moduli and ultimate tensile and shear strengths of epoxy–graphene interfaces are calculated from uniaxial tension and simple shear loadings. The results show that Young’s modulus and the ultimate tensile strength increase relative to bulk epoxy, whereas the shear modulus and ultimate shear strength are reduced. Failure of epoxy–graphene interfaces in tension occurs due to the formation of voids in the epoxy. Failure in shear is due to tangential slipping at the interface. Under mixed-mode conditions, the shear modulus and shear strength decrease with increasing tensile load. The critical energy release rate $$G_{\text{c}}$$ for the studied epoxy–SLG/MLG/MLGO systems is obtained using a continuum fracture mechanics approach and is found to be significantly lower than for bulk epoxy. All of the results are combined to define mode I and II cohesive laws for bulk epoxy and epoxy–SLG/MLG/MLGO interfaces that can be used in theoretical models and numerical methods, such as finite elements, that employ cohesive zones.

An Experimental and Computational Study on the Low Velocity Impact-Induced Damage of a Highly Anisotropic Laminated Composite Panel

Abstract The low velocity impact (LVI)-induced damage of a highly anisotropic laminate [0/90/0/909]s has been studied experimentally and numerically. The purpose of the analyses of this laminate is that this stacking sequence resembles a sandwich composite panel, in the sense that the [0/90/0] outer layers serve as the “face sheet” while the inner 18 plies of 90 deg layers serve as the “core.” The LVI-induced damage pattern of this laminate is unique and referred to as the “kidney” shape. The “kidney” shape damage is caused by a strong interaction between matrix transverse cracking and delamination, hence is challenging to be computationally captured. The enhanced Schapery theory (EST) model has been improved with the capability to model material inelasticity, as well as a novel mixed-mode cohesive law, to tackle this problem. EST with inelasticity (EST-InELA) is shown to be able to predict load responses and damage morphology accurately and efficiently. The aim of this paper is to provide a challenging LVI case to examine and calibrate computational models.

Dynamic interfacial crack propagation and kinking in sandwich panels

The dynamic interfacial crack propagation and crack kinking phenomena in sandwich panels are studied. The paper derives an analytical approach based on the Extended High-Order Sandwich Panel Theory (EHSAPT) and a cohesive interface modeling. The mathematical modeling of the panel makes a distinction between the face sheets and the core. The core is further divided into two bodies aiming to allow the nucleation of a shear crack in the core or the kinking of a core-face sheet crack into the core. The panel therefore includes four layers that are interconnected through three interfaces. The First-Order Shear Deformation Theory (FSDT) is adopted for the two face sheets and the EHSAPT is applied to the two core layers. Translational, rotational, and high order inertial effects are considered in all components. A geometrical nonlinear behavior with linear elastic laws is adopted for the face sheets while the core layers use linear kinematic relations and linear constitutive laws. The interfaces use nonlinear cohesive laws to model the dynamic nucleation, propagation, and kinking of cracks. The dynamic model is used for a numerical study of sandwich panels subjected to three point bending and end shortening loading conditions. The study explores the coupling of the crack propagation with the dynamic response. A comparison of the dynamic results with their static counterparts further explains the physical response of the sandwich panel and the dynamic characteristics of its failure mechanism.

Molecular dynamics simulation of enhanced interfacial cohesive behavior of Ni-coated MWCNT/Mg composites

ABSTRACT Debonding processes of different Ni-coated MWCNT/Mg interface models were studied by molecular dynamics simulations, and the stress–displacement relationships of different interface models were obtained by fitting a modified exponential cohesive zone law for interface. In addition, the debonding behaviors of Ni-coated and uncoated MWCNT/Mg interface were compared. The results show that CNT wall numbers and inner diameters as well as interface orientations have significant effects on the Ni-coated and uncoated MWCNT/Mg interface cohesive-zone model parameters. Compared with the above two kinds of uncoated MWCNT/Mg interface models, the average values of the peak stress and the work of separation for the Ni-coated MWCNT/Mg interface models are both increased significantly, showing that the addition of a Ni-modified coating on the surface of MWCNTs can effectively enhance the adhesion capacity of the MWCNT/Mg interface.

A rate-dependent cohesive zone model with the effects of interfacial viscoelasticity and progressive damage

A generalized rate-dependent cohesive zone model for describing the interfacial viscoelasticity and progressive damage of mode I fracture is presented. The proposed model has efficiently extended the traditional bi-linear cohesive traction-separation law to remove the assumptions that some of the rate-dependent parameters such as elastic stiffness, initial separation and strength, critical separation are constant at different loading speeds. Furthermore, the rate-dependency of the damage evolution, which is observed in experiments but largely neglected in the previous models, is established to describe the rate-dependent fracture process linked with the generalized traction-separation law, and an equivalent generalized Maxwell model (GMM), based on the Kohlrausch-William-Watts function with significant fewer material parameters required as input, is proposed to describe the time and history dependent stress–strain relationship of the viscoelastic interface material. The proposed model is validated by the simulations of the DCB tests with both the SBR/NR rubber interface and Polyurethane interface.

A multi-state progressive cohesive law for the prediction of unstable propagation and arrest of Mode-I delamination cracks in composite laminates

In this paper, a finite element simulation study was performed on the dynamic crack propagation and arrest in double cantilever beam (DCB) specimens with interleaves. The expressions of crack initiation toughness, propagation toughness, arrest toughness, and kinetic energy during unstable crack propagation were theoretically derived based on the energy balance principle. The dynamic fracture toughness parameters were calibrated based on the DCB test results. For the simulations, a multi-state progressive cohesive law (MP-CL) suitable for quasi-static analysis was proposed, and the MP-CL parameters were introduced into the finite element model using the USDFLD subroutine in the ABAQUS software. The unstable crack stick–slip propagation behavior of the DCB specimens was successfully simulated, revealing the complex mechanical characteristics, such as the load–displacement response, kinetic and fracture energy, and crack propagation velocity, during unstable crack propagation. The simulation results were quite consistent with the experimental results, validating the correctness and effectiveness of the proposed model.

Identification of the interfacial cohesive law parameters of FRP strips externally bonded to concrete using machine learning techniques

A machine learning-based artificial neural network (ANN) approach is developed to automatically identify the interfacial cohesive parameters between fiber-reinforced polymers (FRPs) and concrete. A refined finite element (FE) model employing a cohesive zone model is established to simulate the interfacial Mode-II fracture. According to the database of load–displacement responses generated from the FE model, the trained ANN model can accurately and concurrently identify the cohesive law parameters. Moreover, based on a finite set of training data, the proposed approach shows high accuracy for the cases whose interfacial properties fall within the gap in or outside of the training dataset.

Onset of sliding across scales: How the contact topography impacts frictional strength

When two solids start rubbing together, frictional sliding initiates in the wake of slip fronts propagating along their surfaces in contact. This macroscopic rupture dynamics can be successfully mapped on the elastodynamics of a moving shear crack. However, this analogy breaks down during the nucleation process, which develops at the scale of surface asperities where microcontacts form. Recent atomistic simulations revealed how a characteristic junction size selects if the failure of microcontact junctions either arises by brittle fracture or by ductile yielding. This work aims at bridging these two complementary descriptions of the onset of frictional slip existing at different scales. We first present how the microcontacts failure observed in atomistic simulations can be conveniently "coarse-grained" using an equivalent cohesive law. Taking advantage of a scalable parallel implementation of the cohesive element method, we study how the different failure mechanisms of the microcontact asperities interplay with the nucleation and propagation of macroscopic slip fronts along the interface. Notably, large simulations reveal how the failure mechanism prevailing in the rupture of the microcontacts (brittle versus ductile) significantly impacts the nucleation of frictional sliding and, thereby, the interface frictional strength. This work paves the way for a unified description of frictional interfaces connecting the recent advances independently made at the micro- and macroscopic scales.

Interaction between interfacial damage and crack propagation in quasi-brittle materials

A thermodynamically consistent phase field formulation for modeling the interactions between interfacial damage and bulk brittle fracture is presented. A regularization scheme is considered for both the interface and the crack phase field. A coupled exponential cohesive zone law is adopted to model the interface which has the contributions of both normal and tangential displacement jump components. A novel nonlocal approach is devised to evaluate the smoothened values of jump at the regularized interface using element-specific geometric information. Such a description of the interface allows a more realistic mechanical response of any composite system in terms of accurately representing failure modes such as matrix/bulk cracking, deflection and or branching of crack at interface, through thickness penetration at interface, and delamination. The possibility of these would depend on modulus mismatch, inclination of the interface, length of the interface and relative fracture toughness of the interface to the bulk. Several numerical examples are solved to validate the performance of the proposed model by peel test, crack interaction with an inclined interface, crack at a bimaterial interface, and stiff-soft interface crack interaction.

Finite element modeling of mode I fatigue delamination growth in composites under large-scale fiber bridging

In this study, the Turon et al. and Kawashita-Hallett fatigue damage models are extended with a trilinear cohesive law to simulate mode I fatigue delamination in the composites undergoing large-scale fiber bridging. The trilinear cohesive zone model (CZM) is constructed by superposition of two bilinear CZMs. In order to implement the developed models, a user defined element (UEL) subroutine is prepared in the Abaqus software and finite element analyses are conducted based on the envelope loading technique to simulate the 3D double cantilever beam (DCB) specimens under high-cycle fatigue loading. The finite element models are assessed through the experimental data from the literature and also five available fatigue damage models based on the bilinear CZM. It is concluded that the trilinear CZMs has more accuracy than the bilinear ones in prediction of fatigue delamination with fiber bridging effects. A parametric study is performed on the two extended models and sensitivity of models to the fitting parameters and quasi-static CZM parameters are comprehensively investigated.

Determining cohesive parameters for modeling interfacial fracture in dissimilar-metal friction stir welded joints

Predicting the structural performance of a joint requires mechanical characterization of the joint interface. Use of the cohesive-zone model (CZM) is an effective approach for implementing fractures, seams, and joints in the structures. The CZM requires a cohesive constitutive law, which, in the context of a welded joint, relates the traction at the interface to the separation displacement of the two surfaces. Typical configurations for fracture testing to obtain the parameters for a cohesive law involve assumptions including large weld areas and undisturbed substrate, making those techniques unsuitable for friction stir welded joints. This paper presents an approach of experimentation combined with finite element modeling to determine the cohesive law parameters to mechanically characterize the interface obtained in friction stir welded joints.

Modelling delaminations using adaptive cohesive segments with rotations in dynamic explicit analysis

Multiple delamination planes can form when a composite structure is subjected to out-of-plane stresses during static over-loading or impact loading. Numerical modelling of such events is often prohibitively expensive because large numbers of cracks can co-exist and interact, and fracture models usually affect the time step size in explicit solutions. Here a new method called Adaptive Mesh Segmentation is proposed, which introduces segmentation ‘on-the-fly’ in meshes of quadratic finite elements with six degrees of freedom per node, without any intervention from the user and without any reductions in time step size for solution stability. A novel cohesive formulation with rotational degrees of freedom is introduced which increases the resolution of the numerical cohesive zone and allows the use of relatively coarse meshes. Once a critical stress criterion is met, new degrees of freedom are added at element boundaries to model strong discontinuities. A new moment–damage relationship is proposed to link the discontinuity in rotational degrees of freedom with the cohesive zone law which is translational by definition. A method for initiating cohesive tractions and moments with minimal disturbances to the surrounding stress field is also presented. Finally, the model is applied in the analysis of composite delamination benchmarks using relatively coarse meshes and modest model sizes. Considerable improvements in accuracy are observed when compared to conventional methods.

Mode II cohesive law extrapolation procedure of composite bonded joints

A novel extrapolation procedure to predict the mode II cohesive laws of adhesive joints is presented. At first, a recently proposed compliance based experimental method to extract mode II Cohesive Laws is extended to the eccentric end-notched flexure test EENF and generalized including the effect of the bond line thickness and to this end, improved expressions for the compliance, J-Integral and shear displacement at the crack tip are derived.Assuming that every effect associated to the damage is included in the equivalent crack length, new expressions related to the Compliance (C0), J- Integral (J0) and crack tip shear displacement (Δ0) are defined and invariant relations between J0-Δ0 and Δ0- C0 are elicited for a given material system and test configuration.Finally, an extrapolation procedure is presented, based on the J0-Δ0 and Δ0- C0 calibrated curves, which enables to estimate the cohesive laws for a wide range of adhesive to adherend ratio of a given material system by processing only the load –displacement curve.

Direct Evaluation of Mixed Mode I+II Cohesive Laws of Wood by Coupling MMB Test with DIC.

Governing cohesive laws in mixed mode I+II loading of Pinus pinaster Ait. are directly identified by coupling the mixed mode bending test with full-field displacements measured at the crack tip by Digital Image Correlation (DIC). A sequence of mixed mode ratios is studied. The proposed data reduction relies on: (i) the compliance-based beam method for evaluating strain energy release rate; (ii) the local measurement of displacements to compute the crack tip opening displacement; and (iii) an uncoupled approach for the reconstruction of the cohesive laws and its mode I and mode II components. Quantitative parameters are extracted from the set of cohesive laws components in function of the global phase angle. Linear functions were adjusted to reflect the observed trends and the pure modes (I and II) fracture parameters were estimated by extrapolation. Results show that the obtained assessments agree with previous experimental measurements addressing pure modes (I and II) loadings on this wood species, which reveals the appropriateness of the proposed methodology to evaluate the cohesive law under mixed mode loading and its components.

Study of the Bond Capacity of FRCM- and SRG-Masonry Joints

Fiber-reinforced cementitious matrix (FRCM) and steel-reinforced grout (SRG) have been increasingly applied as externally bonded reinforcement to masonry members in the last few years. Unlike fiber-reinforced polymer (FRP), FRCM and SRG have good performance when exposed to (relatively) high temperature and good compatibility with inorganic substrates, and they can be applied to wet surfaces and at (reasonably) low temperatures. Although numerous studies investigated the mechanical properties and bond performance of various FRCM and SRG, new composites have been developed recently, and their performance still needs to be assessed. In this study, the bond behavior of three FRCM composites and one SRG composite applied to a masonry substrate is investigated. Sixteen single-lap direct shear tests (four tests for each composite) are performed. The FRCM studied comprised one layer of carbon, PBO (polyparaphenylene benzobisoxazole), or alkali-resistant (AR)-glass bidirectional textile embedded within two cement-based matrices. The SRG composite comprised one layer of a unidirectional stainless-steel cord textile embedded within a lime-based matrix. The results show a peculiar bond behavior and failure mode for each composite. Based on these results, the behavior of the carbon and PBO FRCM is modeled solving the bond differential equation with a trilinear cohesive material law (CML).

Cohesive zone analysis of cylindrical ice adhesion: Determining whether interfacial toughness or strength controls fracture

Ice accretion remains an unsolved challenge in many industrial and residential applications. The iced area can vary from ~1 cm2 to many square meters depending on the situation, and this directly affects the ice debonding mechanism. The fracture of short interfaces is controlled by interfacial shear strength, whereas interfacial toughness dominates the fracture of longer interfaces. The transition from strength-controlled to toughness-controlled fracture occurs at a critical interfacial length. Here we study the fracture mechanics and debonding of ice from several polymeric materials evaluated by the common Zero-Degree Cone Test (ZDCT). Cohesive zone analyses assuming Dugdale-type and linear cohesive laws are performed in cylindrical coordinates. For most materials, the calculated critical length is smaller than the actual interfacial length previously used in the ZDCT, indicating that ice detachment was controlled by interfacial toughness. Good agreement was observed between the values of interfacial toughness calculated in the present study and those reported in the literature. From the data, lower bounds for the ice adhesion strengths are estimated based on the actual length of ice. Our analysis indicates that the prior fracture stresses measured using the ZDCT were not the material's ice adhesion strength, but rather the asymptotic detachment load per interfacial area. Overall, the zero-degree cone test should not be used to measure the ice adhesion strength with its prior or current dimensions, but is an excellent tool for characterizing the interfacial toughness between ice and a material.