Cohesive Zone Law Research Articles

A chemo-mechanical grain boundary model and its application to understand the damage of Li-ion battery materials

Although the unique mechanical and transport features of grain boundaries (GBs) in polycrystalline ion conductors have been recognized, the understanding of the chemo-mechanical interplay and its impact is insufficient. We present a coupled GB model which includes both the damage-dependent across-grain transport and a mechanical cohesive zone law. 3D simulations on LiNixMnyCozO2 demonstrate that the chemical process and the mechanical degradation go hand-in-hand: the enhanced intergranular chemical inhomogeneity challenges the GB mechanical strength, while the GB damage influences or even blocks the across-grain transport. Results explain well the experimentally observed features including chemical hot spots and surface layer delamination.

Shear band multiplication induced strong strain delocalization and high tensile ductility in amorphous thin films by metallic substrates

Metallic glass usually ruptures at a small strain by forming single dominant shear band under tension at room temperature. Experiments have shown that multiple shear bands can be induced in metallic glass film by a ductile metallic substrate, and the ductility of the film can be elevated significantly. However, the mechanism behind remains unsolved. Here we established a computational model to investigate the effect of a Ni substrate on the deformation of a Ni-P amorphous film. The shear band evolution in the film was described by a free volume-based constitutive theory, while the deformation of the Ni substrate was simulated by a dislocation density-based model. The film/substrate interface was modeled by a cohesive zone law. In the simulations, the shear band evolution and the stress in the film can be measured directly, which is difficult to achieve in experiments. Our simulations show that multiple shear bands have been formed in the substrate-supported metallic glass film if the film thickness hf is less than 10 µm. The thinner the film is, the more the shear bands the film has. The number of shear bands can reach as high as 16 as hf is refined down to 2.5 µm. The generation of the multiple shear bands alleviated the strong strain-softening as observed in free standing film, as clearly shown in the stress-strain response of the thin film in the film/substrate system. The suppressed strain-softening induces significantly enhanced tensile ductility in the amorphous film. The tensile ductility of the 2.5 µm-thick film on the Ni substrate can reach as high as 13.3%, which is much higher than that of the corresponding freestanding film, i.e., 3.1%. The proposed computational model has been validated by the coincident stress-strain responses between simulations and experiments. The findings revealed that the enhanced tensile ductility originates from the shear band multiplication-induced strain delocalization in the amorphous film due to the constraint of the metallic substrate.

A Chemo-Mechanical Grain Boundary Model and Its Application to Understand the Damage of Li-Ion Battery Materials

Although the unique mechanical and transport features of grain boundary (GB) in polycrystalline ion conductors have been recognized, the study on the chemo-mechanical interplay and its impact is insufficient. We present a coupled GB model, which includes both the damage-dependent across-grain transport and the mechanical cohesive zone law. 3D simulations on LiNixMnyCozO2 demonstrate that the chemical process and the mechanical degradation go hand-in-hand: the enhanced intergranular chemical inhomogeneity challenges the GB mechanical strength, while the GB damage influences or even blocks the across grain transport. Results explain well the experimentally observed features including chemical hot spots and surface layer delamination.

Formulation of a mixed-mode multilinear cohesive zone law in an interface finite element for modelling delamination with R-curve effects

A constitutive model for an interface finite element is proposed to enable simulation of delamination in composite materials with R-curve effects. The constitutive model is formulated in the framework of cohesive zone modelling (CZM). In essence, a multilinear CZ law with an arbitrary number of line segments is developed. The CZ law seeks to enable constitutive modelling of failure mechanisms on multiple scales within the fracture process zone and reduce conventional a priori assumptions regarding the shape of the CZ law. The CZ law relies on damage mechanics, an equivalent one-dimensional formulation, and criteria for mode interactions to simulate delamination under mixed-mode loading. Special emphasis is put on the derivation of interpolation formulas and a constitutive tangent stiffness tensor for the multilinear formulation. The constitutive model is implemented in the commercial FE program ANSYS Mechanical, for implicit finite element analysis (FEA), using user-programmable features. The implementation is verified through single interface element numerical studies, and its applicability is demonstrated by simulating an experiment of quasi-static delamination showing large-scale fiber bridging in pure mode I DCB glass-fiber epoxy specimens. Experimental measurements and simulation outputs using the novel cohesive element is compared to those of the conventional bi- and trilinear CZ laws.

Delamination mechanism maps for coatings/substrates system subjected to adhesive contact loads

Previous delamination mechanism maps for coatings/substrates system cannot predict the critical conditions for delamination nucleation under adhesive contact loads, because the effects of surface adhesion on delamination are not considered. In this paper, the finite element simulation of a rigid sphere in adhesive contact with an elastic coating on an elastic-plastic substrate is undertaken to clarify interface crack initiation and growth, in which the surface adhesion of the indenter/coating contact system is modeled by nonlinear spring elements with a force-displacement relationship derived from a Lennard-Jones potential, and the coating/substrate interface is represented by an irreversible cohesive zone law. By conducting parametric studies, delamination mechanism maps considering surface adhesion are constructed. It is found that increasing the adhesion work will initiate delamination nucleation, and the critical indentation depth increases with increasing the interfacial cohesive energy in the presence of the surface adhesion. For relatively stronger adhesion, the higher the coating elastic modulus or the coating thickness is, the greater the critical indentation depth becomes. However, for relatively weaker adhesion, increasing the coating elastic modulus will decrease the critical indentation depth, and increasing the coating thickness will increase the critical indentation depth for lower indentation depths, but an opposite trend occurs for higher indentation depths.

A weak penalty formulation remedying traction oscillations in interface elements

A frequently used approach to modeling of fracture along predefined paths (e.g. grain boundaries in metals) is to use intrinsic interface elements. Despite their popularity, it is well known that the use of such elements in combination with a stiff cohesive zone model may result in traction oscillations. A common strategy to alleviate this problem is to employ reduced Lobatto integration along the cohesive surface. Even though such reduced integration has been demonstrated to work well for some cases, the present work shows that there are situations where the use of this integration method results in severe traction oscillations. More precisely, it is shown that intrinsic interface elements (with full or reduced integration) share stability properties with an equivalent mixed formulation, and hence oscillations result from the violation of the inf–sup (LBB) condition for the mixed formulation. As a remedy for these oscillations, the interface elements are modified using a weak penalty formulation, based on a traction approximation fulfilling the inf–sup condition. Using this method, oscillation free results can be obtained without modifying the cohesive zone law or introducing additional unknowns. These oscillation free results are demonstrated by several numerical examples, including straight, curved and intersecting cracks.

Closed-form solutions for cohesive zone modeling of delamination toughness tests

Closed-form solutions for cohesive zone modeling within the framework of classical lamination theory (CLT), for the popular mode I double cantilever beam (DCB) test, the mode II end notched flexure (ENF) test and mixed-mode I/II bending (MMB) test are provided in this paper. Zero-thickness virtual multi-linear traction–separation laws are introduced to simulate the cohesive interactions between potential crack surfaces. The problem is formulated by solution forms corresponding to each segment of the cohesive laws and using appropriate boundary and continuity conditions. Detailed algorithms for each case are provided to clearly show the influence of the cohesive zone law on the ensuing crack growth. The superposition method used for mixed-mode growth in the MMB test for homogenous material or mid-plane symmetric laminates is proved both theoretically and numerically. Comprehensive parametric studies are performed on the crack growth response and the process zone length, revealing their relations to the delamination length, cohesive parameters, the shape of the traction–separation laws and the mode mixity. With applicability to general multilayered structures, and the capability to incorporate arbitrary, piecewise linear cohesive constitutive laws, the closed-form solutions can serve as a tool to determine the accuracy of numerical solutions used in conjunction with finite element simulations.

The Deformation Mechanisms in Process of Crack Propagation for Alpha Titanium with Compounding Microdefects

The multiscale analysis method based on traction-separation law (TSL) and cohesive zone law was used to describe the cross-scale defective process of alpha titanium (α-Ti) material with compounding microdefects in this paper. First, the properties of T-S curve and the reasonable range of T-S area relative to the length of defects were discussed. Next, based on the conclusions above, the molecule dynamics analysis of three models ofα-Ti with compounding microdefects was conducted and cross-scaly simulated. The phenomenon, principles, and mechanisms of different compound microscale defects propagation ofα-Ti were observed and explained at atomic scale, and the effects of different microdefects on macrofracture parameters of materials were studied.

A meso-scale approach to modelling stable dynamic crack propagation in glass under rate-dependent loading

This paper presents a meso-scale approach to dynamic crack propagation, which incorporates a phenomenological rate-dependant cohesive zone law into the eXtended Finite Element Method for crack representation (XCZM). This approach is applied to a Double Cantilever Beam made of glass, for which an analytical solution and well-known experimental data are available. A comparison of model predictions with experimental observations shows that the proposed approach is capable of reproducing all essential features of dynamic cracking of glass, lending support to the method applicability to other classes of brittle and quasi-brittle materials.

Discrete dislocation modeling of stress corrosion cracking in an iron

Abstract Material strengthening and embrittlement are controlled by interactions between dislocations and hydrogen that alter the observed deformation mechanisms. In this work, we used an energetics approach to differentiate two fundamental stress corrosion mechanisms in iron, namely, hydrogen-enhanced localized plasticity and hydrogen-enhanced decohesion. Considering the small-scale yielding condition, we use a discrete dislocation framework with line dislocations to simulate the crack-tip plastic behavior. The crack growth was modeled using the change in surface energies (cohesive zone laws) due to hydrogen segregation. The changes in the surface energies as a function of hydrogen concentration are computed using atomistic simulations. Results indicate that, when hydrogen concentrations are low, crack growth occurs by alternating mechanisms of cleavage and slip. However, as the hydrogen concentrations increased above some critical value, the crack grows predominately by the cleavage-based decohesion process.

Predicting deformation-induced polymer–steel interface roughening and failure

Abstract A novel integrated framework is presented for the prediction of deformation-induced interface roughening and failure in polymer-coated steels. Crystal plasticity is employed to predict the change in steel surface roughness in-situ. The steel substrate is coated with a thin polymer layer and the polymer–steel interface is modeled using an exponential cohesive zone law. Uniaxial tensile simulations are performed and the results show that the predicted roughness increases with the applied deformation. The local changes in the steel surface profile result in initiation and growth of local interface failure. Furthermore, a compression simulation shows that the roughening rate of the steel is increased compared to tension, with an increase in the predicted interface damage as a result. The presented framework thus allows for a detailed numerical study of the initiation and growth of interface damage in polymer-coated steels during applied deformation. The incorporation of the crystal plasticity model to predict the changes in the steel surface profile complements the cumbersome measurements of detailed experimental displacement fields that accompany deformation-induced roughening and thus enables the analysis of deformation processes where measuring the steel surface profile is difficult if not impossible, e.g. industrial forming processes such as deep-drawing.

Multiscale modeling of functionalized interface effects on the effective elastic material properties of CNT–polyethylene nanocomposites

The effects of functionalization of the interface between carbon nanotubes (CNTs) and the polymer matrix on the macroscale elastic mechanical material properties have been investigated using a multiscale model. Molecular dynamic (MD) simulations are used to investigate the influence of functionalization on the nanoscale load transfer ability of the interface between the CNT and the polymer matrix material in CNT–polyethylene (PE) nanocomposites. Graphene–polymer interface models with variable numbers of functional groups grafted between the graphene sheet and the polymer chains are adopted to represent the interface between the CNTs and the polymer matrix. Normal mode and sliding mode separations are performed using MD simulations in order to characterize the load transfer of the functionalized graphene–polymer interface in terms of force-separation responses. The influence of the functionalization density on the load transfer at the interface is studied parametrically. Two force field potentials, the consistent valence force field (CVFF) and adaptive intermolecular reactive empirical bond order (AIREBO) potential, are used to simulate the interactions between the atoms in the polymer matrix and the functional groups. An energy based bond breaking criteria is introduced into the CVFF potential such that both potentials allow for bond breaking. Comparison of the two potentials is conducted by comparing the MD simulation results where it is found that two potentials give different force-separation responses, but that in both cases, there is significant increase in load transfer capability and toughness of the interface with increasing degree of functionalization of the interface. With cohesive zone laws derived from MD results, a finite element implementation of the cohesive zone models is used to calculate the effective elastic mechanical properties of the CNT–PE nanocomposites in order to study the influence of functionalization at the nanoscale on their macroscale mechanical performance.

Low‐cycle fatigue delamination initiation and propagation in fibre metal laminates

AbstractThe aim of this paper is to develop an elastic–plastic‐damage constitutive law and a tool for simulation of delamination initiation and propagation in fibre metal laminates (FMLs) under low‐cycle fatigue loading regime. In the previous studies, the significance of plasticity in delamination growth and modelling of FMLs was not considered. Hence, cohesive zone law that combines the damage evolution with plasticity is developed. The new fatigue damage model is implemented as user‐written subroutines that links with ansys based on the cohesive finite element method. The cohesive zone model constitutive law has been verified by modelling of the delaminated adhesively bonded aluminium joint under normal and shear loadings and compared with the available results in the literature. The developed procedure and tool have been used for the analyses of DCB and ENF specimens under uniform and variable loadings. The obtained results for progressive damage and delamination and stress–strain curves are discussed in this paper.

Shear fatigue of the bonded and frictional interface under constant normal pre-stress

Fatigue damage in the idealised bonded interfaces under constant normal pre-stress is studied by scanning electron microscopy and it is found to involve several microstructurally small cracks with different lengths and orientations. Evolution of fatigue damage in the adhesive occurs as the small cracks grow, coalesce and interact with each other. The theory related to these phenomena is not yet established. Therefore, a phenomenological model of fatigue damage is proposed based on the experimentally-measured compliance of the modified napkin ring specimen. The cohesive zone law describing the quasi-static fracture of the interface is re-formulated to include the effect of fatigue damage.

Multiscale modeling of concrete and of the FRP–concrete interface

Cracking and failure processes in concrete members as well as debonding mechanisms between concrete surfaces and fiber-reinforced polymer composites used for structural strengthening are often modeled through macroscopic empirically-based cohesive zone models. This approach presents a number of limitations, as macroscopic laws spatially homogenize complex damage and failure processes taking place at the lower scales. This paper proposes a multiscale approach for concrete and for the determination of mixed-mode cohesive zone models for the composite–concrete interface based on mesomechanical analysis. The mesomechanical model includes the explicit description of the heterogeneous material geometry close to the interfacial zone, as well as a continuum damage description for both the cement matrix and the matrix-aggregate interfacial transition zone. Macroscopic mixed-mode cohesive zone laws are then obtained through a numerical homogenization procedure. The choice of the representative volume element is discussed and the cohesive behavior under mode-I, mode-II and loading conditions with different degrees of mode mixity is analyzed. Comparisons with available experimental and analytical results are also performed.

Creep–rupture model of aluminum alloys: Cohesive zone approach

In this article, a creep–rupture model of aluminum alloys is developed using a time-dependent cohesive zone law. For long-term creep rupture, a time jump strategy is used in a cohesive zone law. Stress–rupture scatter of aluminum alloy 4032-T6 is fitted with a power law form. Then, change in the slope of a stress-rupture line is identified on a log–log scale. Implicit finite element analysis is employed with a model containing a cohesive zone. Stress–rupture curves at various given temperatures are calculated and compared with experimental ones. Results show that a proposed method allows predicting creep–rupture life of aluminum alloys.

Fretting fatigue simulation for aluminium alloy using cohesive zone law approach

Abstract This paper describes high-cycle fretting fatigue modelling for 7050-T7451 aluminium alloy using a cohesive zone law. For the sake of crack generation arising from cyclic bending, a bilinear, cycle-dependent cohesive zone law is used including stiffness degradation and reduction of fracture energy with respect to fatigue cycles. The reduction rate of fracture energy is determined with experimental data. Implicit analysis is employed with commercial finite element software. Additionally, bending fretting experiments are performed with unnotched specimens and flat-and-rounded pads. Imposed stress amplitude (S)–number of cycles to failure (N) curves are determined after fretting fatigue tests. Direct comparison between simulation and experimental S–N curves is performed; maximum error is found to be 20% at the 5×104th cycle. It is demonstrated that a proposed method allows simulating fretting fatigue and predicting fretting life of aluminium alloys.

Time-dependent adhesion of a polydimethylsiloxane (PDMS) elastomer film to a flat indenter tip characterized using a cohesive-zone law

The work of adhesion between a polydimethylsiloxane (PDMS) elastomer film and a flat diamond tip was measured by instrumented indentation. The results showed that the apparent work of adhesion between the tip and the PDMS film increases with increasing dwell time and retreating velocity; on the other hand, the indentation depth has no significant effect on adhesion. The indentation experiment was analysed with viscoelastic finite element simulations with rate-dependent cohesive elements, from which the time evolution of adhesion was quantitatively implemented into a rate-dependent cohesive-zone law.

Development of a Fatigue Model for Low Alloy Steels Using a Cycle-Dependent Cohesive Zone Law

A fatigue model for SAE 4130 steels is developed using a cycle-dependent cohesive zone law. Reduction of fracture energy and degradation of stiffness are considered to describe failure resistance after certain number of cycles. The reduction rate of fracture energy is determined with experimental stress ( S)- number of cycles to failure ( N) scatter found in the literature. Three-dimensional finite element models containing a cohesive zone are generated with commercial software (ABAQUS). Calculated fatigue lives at different stress ratios are in good agreement with experimental ones. In addition, fatigue behavior of hardened SAE 4130 steels is predicted with that of normalized material.

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.