Traction-separation Curve Research Articles

Evaluation of Corrosion and Its Impact on the Mechanical Performance of Al-Steel Joints.

Aluminum-steel joints are increasingly used in the automotive industry to meet the requirements for energy saving and emission reduction. Among various joining technologies, self-pierce riveting (SPR) and resistance spot welding (RSW) are two well-established technologies for fabricating dissimilar joints with stable and high mechanical performance. However, corrosion will occur in these joints inevitably due to different electrochemical properties, which can degrade the surface quality and the mechanical performance, such as strength. This paper presents a method of understanding the corrosion mechanisms in joining aluminum and steel. For this understanding, a hybrid method combining experimental observations, mechanical properties identification, and analytical approaches was used to assess the evolution of the impact of corrosion on the joining performance, such as traction separation curves. The study was conducted on common combinations used in the vehicles, e.g., a 1.2 mm thickness aluminum alloy (AA 6022) and 2.0 mm thickness hot deep galvanized steel (HDG HSLA 340) joined by SPR and RSW. After the fabrication of these joints, accelerated cyclic corrosion tests of up to 104 cycles were performed, which reproduced the environmental conditions to which a vehicle was exposed. By investigating the microstructural evolution within the joints, the corrosion mechanisms of SPR and RSW joints were revealed, including the initiation and propagation. Moreover, the intrinsic impact of the corrosion on the mechanical performance, including the strength, axial stiffness, and crashworthiness, was analyzed by performing a lap-shear test. It showed that as corrosion proceeds, the fracture modes and mechanical performance are affected significantly.

Molecular dynamics simulation-based study to analyse the properties of entrapped water between gold and graphene 2D interfaces.

Heterostructures based on graphene and other 2D materials have received significant attention in recent years. However, it is challenging to fabricate them with an ultra-clean interface due to unwanted foreign molecules, which usually get introduced during their transfer to a desired substrate. Clean nanofabrication is critical for the utilization of these materials in 2D nanoelectronics devices and circuits, and therefore, it is important to understand the influence of the "non-ideal" interface. Inspired by the wet-transfer process of the CVD-grown graphene, herein, we present an atomistic simulation of the graphene-Au interface, where water molecules often get trapped during the transfer process. By using molecular dynamics (MD) simulations, we investigated the structural variations of the trapped water and the traction-separation curve derived from the graphene-Au interface at 300 K. We observed the formation of an ice-like structure with square-ice patterns when the thickness of the water film was <5 Å. This could cause undesirable strain in the graphene layer and hence affect the performance of devices developed from it. We also observed that at higher thicknesses the water film is predominantly present in the liquid state. The traction separation curve showed that the adhesion of graphene is better in the presence of an ice-like structure. This study explains the behaviour of water confined at the nanoscale region and advances our understanding of the graphene-Au interface in 2D nanoelectronics devices and circuits.

Flexural performance of reinforced concrete beams strengthened with FRP-reinforced geopolymer matrix: Numerical validation and parametric study

This study investigates the flexural performance of reinforced concrete (RC) beams strengthened by FRP-reinforced geopolymer matrix (FRGM) through a comprehensive numerical analysis. A two-dimensional (2D) finite element (FE) model is developed to simulate the behavior of the FRGM-strengthened RC beams, including the failure modes, load-deflection curves, and interfacial slips. The settings of the FE model, such as material properties, boundary conditions and interfacial bond properties between the FRGM and RC beams, are firstly validated by comparing the predicted results with the existing experimental data from previous publication. Subsequently, a parametric analysis involving 200 specimens is conducted to evaluate the effects of FRGM thickness, sectional area, location and type of the FRP rebar. The results indicate that the uniaxial compressive behaviors of geopolymer mortar and interfacial properties can be accurately described by the parabolic curve and bilinear traction-separation curve, respectively. The failure mode and load-carrying capacity of the specimens are primarily influenced by the axial strength of the reinforced FRP rebar. Additionally, the interfacial slip distributions transform from an inverse tangential shape to a sawtooth shape depending on the cracking pattern of the specimen.

Multi scale simulation of crack propagation in polycrystalline SiC

Silicon carbide (SiC) is considered one of the most promising emerging materials in the fields of refractory materials and semiconductors. In this paper, a multi-scale numerical simulation method is proposed to investigate crack propagation in SiC at different scales, using a combination of cohesive zone model and molecular dynamics (MD). The microstructure of the material is represented by Voronoi subdivision, and bilinear treatment is applied at the grain boundaries. Firstly, MD models with different microscopic defects were established to obtain the corresponding traction separation curves. Then, the element parameters, obtained by fitting the traction separation law, were inserted into the cohesive elements located at the grain boundary and within the grain. Finally, the finite element models were simulated by the failure criterion. The fracture toughness of the material is predicted, and the influence of microscopic defects and grain distribution on macroscopic fracture toughness is explored. The results indicate that the grain distribution and the type of micro defect have an impact on the crack growth path and macro fracture toughness. The simulation results are consistent with published experimental results, which demonstrates the viability of employing this multi-scale analysis method for examining and replicating the micro-, meso-, and macro-scale crack propagation characteristics of SiC.

Application of ABAQUS Flow-Solid coupling model to evaluate sealing capability of sandstone formation interface based on the cracking behavior of cohesive force units

Estimating the sealing property of the cementing interface is vital for judging the quality of well cementing construction. The main methods currently used to evaluate the sealing property of the cementing interface (hydraulic cementing strength method and shear cementing strength method) are susceptible to the effects of specimen geometric regularity, interfacial cementing condition, and shear damage pressure source, and the measurement results are not stable, making it difficult to use them as effective methods to evaluate the real cementing interface sealing performance. In this paper, based on the cracking behavior of cohesive units, a method to evaluate the sealing performance of the cementing interface by simulating the cracking process of fluid breaking through the cementing interface in ABAQUSTM FEA software was investigated. The research process includes two parts: first, using a self-designed holding stretching device after eliminating the errors caused by non-interface displacement in the conventional stretching method by repeated stretching and subtraction. The real interfacial traction-separation curve and formation cohesion unit parameters were obtained. Secondly, the cohesive unit parameters obtained in the first step were input into ABAQUSTM FEA software to build a fluid–solid coupling model to simulate the cracking process in the interface region when the fluid breaks through the cementing interface, in which obtaining the solid interface cracking sealing pressure and evaluating its sealing performance are finished. And the accuracy and feasibility of this method were verified by a homemade physical sealing model of the cementing interface. In addition, the factors affecting the fluid pressure at the breakthrough of the cemented interface were investigated in this paper, and it was concluded that changing the elastic modulus of sandstone and cement sheath had a more significant effect on the fluid pressure at the breakthrough of the cemented interface than their Poisson's ratios. Furthermore, the results of this paper also indicate that when the permeability of cement sheath and sandstone is in the range of 0.001 mD–10 mD, the fluid pressure at the time of breaking the cemented interface decreases as the permeability of cement sheath and sandstone increases, and beyond this interval, the effect of the sudden change in permeability of cement sheath and sandstone on the fluid pressure at the time of breaking the cemented interface is no longer obvious.

Multiscale investigation on bitumen-aggregate interfacial debonding using molecular dynamics and finite element method

Adhesive failure between bitumen and aggregates is the primary cause of cracking in asphalt mixtures and pavement moisture damage. The resulting pavement distress poses a significant challenge to the service durability of the road infrastructure. Previous studies have validated that aggregate mineralogy has a significant influence on the adhesion properties between bitumen and aggregates; however, there is still a lack of a mechanistic understanding of the influence of the mineral constitution and distribution on the interfacial debonding behavior. This study aims to fill this knowledge gap by proposing a multiscale approach based on molecular dynamics (MD) simulations and the finite element method (FEM). First, the MD method was employed to extract the traction-separation curve of the interface between bitumen and minerals at a molecular scale. The obtained traction-separation relationship was then utilized as the input parameter for the zero-thickness cohesive element in the microscale bitumen-aggregate finite element model. The combined simulation results indicate that quartz with bitumen has the best cracking resistance at the molecular scale, followed by albite, mica, pyroxene, and anorthite. Among the three selected aggregates, the greywacke aggregate exhibited the best cracking resistance at the microscale level. Moreover, the distribution microstructure of the minerals was found to affect the cracking path of the bitumen-aggregate interface, and the bitumen-mica interface elements at the junction area with quartz have a late debonding. The proposed research method spearheads the prediction of multiscale bitumen-aggregate interfacial behavior by considering the aggregate mineralogical heterogeneity.

Atomistic study on crystal orientation-dependent crack propagation and resultant microstructure anisotropy in NiTi alloys

The primary objective of this study was to explore the crystal orientation-dependent fracture mechanism of nickel–titanium (NiTi) alloys by using molecular dynamics simulations. We discovered that the stress concentration ahead of the crack tip induced the formation of martensite with a herringbone twin or mixed HCP/OTHER atom morphology, while reverse martensite transformation occurred behind the crack tip due to stress relaxation. Interestingly, typical brittle fracture by cleaving along the high-energy domain boundary, quasi-brittle fracture as a result of the transformation-induced plasticity, as well as ductile fracture caused by a combination of phase transition, stacking fault, and atomic slip were observed in the samples with (1¯00) [010], (110) [11¯0], and (1¯1¯2) [111] crack orientations, respectively. The findings demonstrated that the crack growth behavior in each orientation was closely correlated to the microstructure evolution around the crack tip. Moreover, the relationship between the traction force and separation was achieved from the fracture process zone near the crack surface. The reported orientation dependency of the traction–separation curves was decisively driven by the anisotropy of cracking characteristics and microstructure morphologies. The results of this work offer comprehensive insights into the importance of crystal orientations on the atomic-scale fracture performance of NiTi alloys.

A novel cohesive zone model for predicting the interface bonding behaviours of the ballastless track of high-speed railway

The interface damage is one of the main concerns for high-speed railway ballastless track structures during its whole service life, as it would affect the reliability of track structures or even cause the high-speed train accident. In this paper, various existing cohesive zone models (CZMs) were identified and compared regarding the performance in modeling the interface behaviors of ballastless track structures. The results show that the existing CZMs cannot accurately represent the nonlinear relationship of the ascending and descending sections in the interface traction-separation curve concurrently. Therefore, a new CZM was proposed in this study, and the feasibility of the proposed model was examined by the experimental results. It indicates that the proposed model can reasonably describe the nonlinear behaviors of the ascending and descending sections in the traction-separation curve by introducing exponential coefficients. The proposed CZM also exhibits higher accuracy in predicting the normal and tangential cracking behaviors of the interlayer interface of the ballastless track structures in comparison with the existing models, with the coefficients of determination (R2) in the fitting results all above 0.85. As a result, this model can be used for the analysis of the interface behaviours of ballastless track structures.

Effects of interatomic potential on fracture behaviour in single- and bicrystalline tungsten

In the present work, we have evaluated the performance of different embedded atom method (EAM) and second-nearest neighbour modified embedded atom method (2NN-MEAM) potentials based on their predictive capabilities for modelling fracture in single- and bicrystalline tungsten. As part of the study, a new 2NN-MEAM was fitted with emphasis on reproducing surface, unstable stacking fault and twinning energies as derived from density functional theory (DFT) modelling. The investigation showed a systematic underestimation of surface energies by most EAM potentials, and a significant variation in unstable stacking and twinning fault energies. Moreover, the EAM potentials in general lack the ability to reproduce the DFT traction–separation (TS) curves. The shorter interaction length and higher peak stress of the EAM TS curves compared to the 2NN-MEAM and DFT TS curves result in one order of magnitude higher lattice trapping than for cracks studied with 2NN-MEAM. These differences in lattice trapping can lead to significant qualitative differences in the fracture behaviour. Overall, the new 2NN-MEAM potential best reproduced fracture-relevant material properties and its results were consistent with fracture experiments. Finally, the results of fracture simulations were compared with analytical predictions based on Griffith and Rice theories, for which emerging discrepancies were discussed.

Three-dimensional modeling of fracture in quasi-brittle materials using plasticity and cohesive finite elements

This paper presents a three-dimensional discrete approach based on the use of interface cohesive elements with zero thickness to model the crack formation and propagation in quasi-brittle materials. The interface constitutive model incorporates concepts of nonlinear fracture mechanics and plasticity. A Coulomb-based surface is used as yield function, and an exponential traction–separation curve as softening law. The model features a non-associated flow rule with an implicit integration scheme and is able to simulate the propagation of single and multiple cracks in mode I and mixed-mode. The proposed model was tested through extension and shear paths and applied in the simulation of experimental tests in concrete specimens available in the literature. Also, a study on the effect of the use of different bulk elements was performed. Numerical results, including peak loads and load-CMOD curves showing softening behavior, are in good agreement with the experimental data.

On the Temperature Dependent Mechanical Response of Dynamically-loaded Shear-dominated Adhesive Structures

A mode II mechanical characterisation of the adhesive joints is performed testing shear lap joint specimens in a Split Hopkinson Tensile Bar (SHTB), equipped with a temperature chamber. The experimentallyobtained traction-separation curves were used to develop a Cohesive Zone Model (CZM) capable of representing the strain-rate and temperaturedependent mechanical response of the adhesive joints. To validate the model, End Notch Flexure (ENF) multi-material specimens made from titanium and carbon fibre reinforced polymer composite laminates were tested at different temperatures using a Split Hopkinson Pressure Bar setup with an in-house made temperature chamber. The finite element (FE) simulations of such tests employing the developed CZM showed the model’s ability to accurately predict the adhesive joints’ failure as well as to understand the failure sequence of multi-material adhesive joint combinations.

Atomistic-scale modeling of nano-clay-filled shape memory polymers

Shape memory polymers (SMPs) have been defined as materials that can recover an early programmed shape after subjecting to an external stimulus. The epoxy/clay nano-composites are developed as a mix of shape recovery behavior and improved thermomechanical properties. The epoxy/clay interface zone plays a big role in material failure. The existence of multiple material phases, as well as multiple interaction forces that interact phases with each other, make the interface zone very complicated to study and simulate. Furthermore, such a tiny size zone is very hard to characterize using the conventional experiment types of equipment. Therefore, the Molecular Dynamics method (MD) has come to light as an effective simulation method to study the atomistic scale dynamic material phenomena. In this work, the MD method is employed to evaluate the thermomechanical performance of the epoxy/clay nano-composites at the atomistic scale level. The estimated elastic parameters confirmed the improvement of the thermomechanical properties of the epoxy/clay nano-composites. Furthermore, the transition temperature and the thermal expansion coefficient are included inside the MD simulation for both the pure epoxy polymer and epoxy/clay nano-composites. The computed above-mentioned parameters are in fairly good agreement with the experimental observations that make these calculated parameters generally appropriate for use at a higher length scale level model. In addition, the response of the epoxy/clay interface zone under mechanical load was also investigated for different silicate layer orientations, namely, 0°, 20°, 45°, 70°, and 90° aligned to the external uniaxial load. The main cohesive parameters like cohesive stiffness, cohesive strength, and maximum separation are derived numerically for every silicate layer orientation. The resulting traction-separation curves of the interface zone provided a deep understanding of the material failure initiation. Moreover, the cohesive zone model parameters are estimated and parameterized in equations with the silicate layer orientations to use in a multiscale modeling framework.

Atomistic investigation of functionalized polyethylene-alumina interfacial strength and tensile behaviour

We study the adhesion and tensile behaviour of bi-layer interfaces comprising polyethylene, doped with carbonyl and hydroxyl functional groups emanating from ozone treatment, and α-Al2O3 by means of density functional theory and classical atomistic modelling. The results show that the deformations are localized within the polymer and comprise chain slip, disentanglement and detachment from the substrate, where only the latter is notably affected by the doping. The binding energies and excess forces associated with the detachment of functional groups from the alumina substrate are of the order of 1.7 eV and 1 nN, respectively, for both types. Although such forces do not affect the maximum peak stress notably, they give rise to spikes in the traction-separation curves following the fibril formation and promote increased total work of fracture.

Application of cohesive zone model to large scale circumferential through-wall and 360° surface cracked pipes under static and dynamic loadings

This paper presents ductile fracture simulation of full-scale cracked pipe for nuclear piping materials using the cohesive zone model (CZM). The main objective of this study is to investigate the applicability of CZM to predict ductile fracture of cracked pipes with various crack shapes and under quasi-static/dynamic loadings. The transferability of the traction-separation (T-S) curve from a small-scale specimen to a full-scale pipe is demonstrated by simulating small- and full-scale tests. T-S curves are calibrated by comparing experimental data of compact tension specimens with finite element analysis results. The calibrated T-S curves are utilized to predict the fracture behavior of cracked pipes. Three types of full-scale pipe tests are considered: pipe with circumferential through-wall crack under quasi-static/dynamic loadings, and with 360° internal surface crack under quasi-static loading. Computational results using the calibrated T-S curves show a good agreement with experimental data, demonstrating the transferability of the T-S curves from small-scale specimen.

Molecular Dynamics-Based Cohesive Zone Model for Mg/Mg17Al12 Interface

The fracture of the Mg/Mg17Al12 interface was investigated by molecular dynamics simulations. The interface crack extends in a brittle manner without noticeable plasticity. The distributions of normal stress and separation along the interface were examined to render a quantitative picture of the fracture process. A normal traction–separation curve was extracted from simulation and compared with three cohesive zone models, i.e., cubic polynomial cohesive zone model, exponential cohesive zone model, and bilinear cohesive zone model. The exponential cohesive zone model exhibits the best agreement with simulation results, followed by the bilinear cohesive zone model.

Atomistic simulation of interfacial properties and damage mechanism in graphene nanoplatelet/epoxy composites

This study provides a comprehensive investigation on the effect of epoxy crosslinking density and number of graphene layers on the interfacial mechanical behavior of graphene/epoxy nanocomposites. In particular, the graphene layers are detached in the normal and sliding directions within the framework of steered molecular dynamics, and the traction-separation curves are extracted for the whole separation process. The damage mechanism is also studied by analyzing the evolution of the local number density during pull-out tests. For better results interpretation, the variation of the interaction and adhesion energies, the number of pulled-out epoxy chains, and the distribution of crosslinked and uncrosslinked species are also investigated and discussed. Based on the results obtained, the crosslinking density has a significant effect on the interfacial properties between graphene and epoxy, especially in the normal mode. The damage behavior is also determined as the function of the epoxy crosslinking density so that at low crosslinking densities, the damage occurs in the polymer near the graphene, while the failure takes place in the interphase for higher crosslinking degrees. Increasing the number of graphene layers leads to a weaker interfacial strength, except for the double-layered graphene systems which have the highest traction peak among all samples.

Experimental and numerical investigation of the mixed mode delamination of monolithic laminates exhibiting severe fiber bridging

A recently developed cohesive zone traction-separation formulation for mode I facesheet to core disbonding, which includes the effects of fiber bridging in a novel way, is extended to account for mode II and mixed mode delamination. The pure mode I and mode II behavior of the model is calibrated based on traction separation curves which are extracted from Double Cantilever Beam (DCB) and End Notched Flexure (ENF) experiments utilizing the J integral. An existing mixed mode framework, which requires no further parameters, is used to predict the load displacement curves of Mixed ode Bending (MMB) tests. Very close agreement between numerical predictions and experimental results is observed for all demonstrated mixed mode ratios.

Cohesive zone representation of interfacial fracture in aluminum-silicon bimaterials

Interfacial fracture in three aluminum-silicon bimaterials with different crystal orientations under tensile loading was investigated by molecular dynamics simulations. Interface crack propagates in a brittle manner regardless of crystal orientation. The overall distribution of normal stress and separation along the interface is consistent with conventional continuum fracture mechanics. Normal traction-separation curves were extracted from simulation results and compared with three cohesive zone models. Crystal orientation shows negligible effect on the trend of normal traction-separation curves. From the perspective of the trend of the normal traction-separation curves, the exponential cohesive zone model exhibits the closest match with simulation results. When it comes to fracture toughness, the bilinear cohesive zone model has the best agreement with simulation results.

Identification of traction-separation curves for self-adhesive polymeric films based on non-linear theory of beams and digital images of T-peeling

In this paper, to investigate the influence of variation in some parameters such as adhesive material and thickness, on the adhesive behavior of the self-adhesive polyethylene films, experiments and evaluation procedures were established and utilized. The evaluation model was provided based on the inverse problem of identifying the traction-separation behavior of self-adhesive polymeric films from their deformation configuration during T-peel test (Nase, 2016). Towards this goal, the traction-separation diagrams were extracted from the results of T-peel tests for five different self-adhesive polyethylene films. The peel test procedure was recorded with a microscopic camera, in order to extract the digital images of the deformed shape of the films within the delamination zone. The deformed lines were approximated by polynomial series based on the least square method. The traction-separation curve for each picture was calculated by inserting the polynomial equations in the mechanical evaluation models, based on the Complementary Energy Approach. The obtained traction-separation curves for each material provide several properties, can represent a clear comparison of how each parameter can influence the adhesive properties and delamination behavior. The evaluation procedure can be followed by the graphical abstract of Fig. 1.

Study on micro-scale properties of cohesive zone in shale

Cohesive fracture model is well known for obtaining a concise interpretation on the underlying mechanism of failure in the near-crack-tip field, especially in concrete and rock materials. In this study, the micro-scale properties of the cohesive zone in brittle shale are investigated. Micro-scale measuring method is designed to capture the crack opening displacement. A small apparatus is developed to induce the ongoing subcritical crack within double-cantilever-beam specimen in environmental scanning electron microscope, by which successive in-situ images of crack propagation are acquired. Micro-scale crack opening displacement of Mode I fracture is either directly measured or measured by digital image correlation method. By comparing experimental results and analytical solutions of micro-scale crack opening displacement, the fitting of cohesive zone models is performed. Based on numerous observations of results, the concept of cohesive-zone-model unit is introduced to provide a better understanding of the essence of cohesive stress. The mechanical properties of cohesive-zone-model unit is simulated using a two-dimensional particle flow code. The simulation results conform to the fitting results. Taking both the fitting and the simulation results into consideration, the traction-separation curve based on cubic polynomial law provides the best interpretation of the micro-mechanical properties of cohesive zone in shale. The introduction of cohesive-zone-model unit gives a better interpretation on the essence of cohesive stress in brittle material with small-scale flaws.