Cohesive Zone Law Research Articles

Numerical and experimental crack-tip cohesive zone laws with physics-informed neural networks

The cohesive zone law represents the constitutive traction versus separation response along the crack-tip process zone of a material, which bridges the microscopic fracture process to the macroscopic failure behavior. Elucidating the exact functional form of the cohesive zone law is a challenging inverse problem since it can only be inferred indirectly from the far-field in experiments. Here, we construct the full functional form of the cohesive traction and separation relationship along the fracture process zone from far-field stresses and displacements using a physics-informed neural network (PINN), which is constrained to satisfy the Maxwell-Betti's reciprocal theorem with a reciprocity gap to account for the plastically deforming background material. Our numerical studies simulating crack growth under small-scale yielding, mode I loading, show that the PINN is robust in inversely extracting the cohesive traction and separation distributions across a wide range of simulated cohesive zone shapes, even for those with sharp transitions in the traction-separation relationships. Using the far-field elastic strain and residual elastic strain measurements associated with a fatigue crack for a ZK60 magnesium alloy specimen from synchrotron X-ray diffraction experiments, we reconstruct the cohesive traction-separation relationship and observe distinct regimes corresponding to transitions in the micromechanical damage mechanisms.

Recurrent neural network (RNN) and long short-term memory neural network (LSTM) based data-driven methods for identifying cohesive zone law parameters of nickel-modified carbon nanotube reinforced sintered nano-silver adhesives

In this paper, we presented three neural network models including deep neural network (DNN), recurrent neural network (RNN), and long short-term memory neural network (LSTM), which are proposed to predict the cohesive zone parameter of sintered silver DCB joint with different contents of nickel modified carbon nanotube, thus reducing the complexity of CZM parameter acquisition for nanoparticle reinforced adhesive. The bilinear CZM model is used as the prediction target model for sintered silver joints with different contents of nickel-modified carbon nanotube filler, and data sets suitable for different networks are established through experimental and numerical simulation results. Three kinds of networks are trained based on the optimized hyperparameters obtained from the Bayesian hyperparameters tuning process. The results show that DNN, RNN, and LSTM frameworks can all predict CZM parameters of nanoparticle-reinforced sintered silver adhesive through load-displacement curves. Based on loss analysis and statistical indicator comparison after K-fold cross-validation, the RNN and LSTM models have better prediction accuracy and performance than the DNN model, and the accuracy of the LSTM model is further improved compared with the DNN model. RNN and LSTM models have high prediction accuracy and stronger recognition ability for the time series data, they can be used as suitable alternative models for inverse recognition of CZM parameters of nanoparticle-reinforced adhesives, and have broad application prospects.

Study on fracture failure behaviour of sapphire transparent window under ultra-high hydrostatic pressure

ABSTRACT Accurately predicting the fracture damage behaviour of light transmission windows is crucial in the design of deep-sea optoelectronic devices. This study proposes a simulation model based on the exponential cohesive zone law to predict the fracture failure of sapphire transparent windows (STW) under multi-dimensional load conditions. By utilising finite element simulation technology, the model accurately determine the fracture damage morphology and failure location of STW in different assembly structure schemes under a hydrostatic pressure of 127 MPa. These simulation results are then effectively validated through full sea depth pressure test experiments. Furthermore, by analyzing the simulation data, this study uncovers the internal mechanism of the fracture damage process of STW and presents a method to predict the fracture damage of STW. This research enhances the understanding of fracture behaviour in light transmission windows and offers valuable insights for the design and development of deep-sea optoelectronic devices.

Atomistic study of the properties and behavior under uniaxial tensile stress of some representative UO[formula omitted] grain boundaries

In irradiated polycrystalline uranium dioxide (UO2), the pressure generated at high temperature by the noble gases in the intergranular bubbles as well as the thermomechanical stresses due to temperature gradients cause the fracture of the grain boundaries. In this study, one analyzes through atomistic calculations of static and molecular dynamics type the properties of three UO2 grain boundaries and their behavior under uniaxial tensile loading up to fracture. In these atomistic simulations, the interactions between atoms are described using a many-body variable charge potential. Structural analysis, performed on the three grain boundary structures under uniaxial tensile stresses and over a wide temperature range, reveals no source of plasticity. This suggests a brittle behavior at fracture, in agreement with recent experimental studies carried out on micrometer size specimens containing grain boundaries. A method based on thermodynamic considerations is used to build normal cohesive zone laws for the UO2 grain boundaries using molecular dynamics simulation data. The cohesive zone laws will be employed in a future study in failure simulations at higher scales.

Investigation on Dynamic Impact Mechanism of Single Crystal Sapphire 3D Model Based on Cohesive Zone Law

AbstractBased on mesh reconstruction technology, a 3D solid model of single crystal sapphire (SCS) with global embedded cohesive element is established in this study. Using exponential cohesive zone law (CZL), the anisotropy of SCS can be effectively characterized by assigning the mechanical properties of matrix element and cohesive element. Taking the C‐plane SCS model as the research object, the whole process of dynamic evolution of cracks in the model under high‐speed surface impact and high concentrated stress impact is reproduced by finite element simulation technology. The simulation is compared with the experimental results from the aspects of crack initiation morphology, crack propagation path, sample fragmentation form, and mechanical response curve. The dynamic compressive strength reaches 1630.3 MPa with the impact velocity of 30 m s–1 in surface impact type. The initial maximum loading force reaches 320 N when the impact velocity is 8.35 m s–1 in the indentation impact type. In addition, by combining the simulation results, this study clarifies the mechanism of strain rate effect exhibited by SCS from the perspective of stress–strain data and crack evolution characteristics. Therefore, the model established in this study can effectively reflect the mechanical behavior of SCS under impact load.

Nonlocal modeling of crack-interface interaction in a composite system

The mechanical response and the fracture phenomena in a composite system not only depend on the elastic and fracture properties of individual constituents but also on additional parameters such as fiber alignment, fiber volume fraction, interface properties and laminate layup. Fiber alignment is one such parameter that governs the design of the composite according to the purpose required. In the present work, a nonlocal approach combined with a cohesive zone model is proposed and implemented in finite element framework. The proposed model can capture different failure phenomena in a matrix- fiber system. The influence of various properties of fiber, matrix, and the fiber-matrix interface on the mechanical response of the composite system is studied. An exponential coupled cohesive zone law is considered for modeling fiber-matrix interface. Smeared representation of crack and interface are considered in the analysis. The results are validated with numerical simulations present in the literature.

Phase-field regularised cohesive zone model for interface modelling

A discrete interface is represented as a smeared interface in the framework of phase field regularisation. Due to the numerical challenge when imposing boundary conditions we prescribe the phase field in the domain using analytical solutions. We obtain the displacement and the strain from the variational form of the energy functional, but also in the framework of the regularised extended finite element method. Indeed, both approaches result in identical forms, validating the rigour of the method. We have examined different forms of the phase field model and conclude that models with a compact support are more appropriate for modelling interfaces. The method combines advantages of discrete and smeared approaches. Compared to discrete interface models, the method holds similar properties as the extended finite element method (XFEM): no need to treat cracks as geometric discontinuities and avoiding mesh refinement around crack tips. Different from the XFEM, however, the method does not introduce enrichment functions to describe cracks. An advantage compared to the phase field method is that this method directly employs the cohesive zone law from the discrete model, which is physically relevant. The accuracy of the approach for cohesive interface modelling is demonstrated by several numerical examples, including a bar, an L-shaped specimen, and a fibre embedded in an epoxy matrix.

Cohesive Zone Interpretations of Phase-Field Fracture Models

Abstract Unlike micromechanics failure models that have a well-defined crack path, phase-field fracture models are capable of predicting the crack path in arbitrary geometries and dimensions by utilizing a diffuse representation of cracks. However, such models rely on the calibration of a fracture energy (Gc) and a regularization length-scale (lc) parameter, which do not have a strong micromechanical basis. Here, we construct the equivalent crack-tip cohesive zone laws representing a phase-field fracture model, to elucidate the effects of Gc and lc on the fracture resistance and crack growth mechanics under mode I K-field loading. Our results show that the cohesive zone law scales with increasing Gc while maintaining the same functional form. In contrast, increasing lc broadens the process zone and results in a flattened traction-separation profile with a decreased but sustained peak cohesive traction over longer separation distances. While Gc quantitatively captures the fracture initiation toughness, increasing Gc coupled with decreasing lc contributes to a rising fracture resistance curve and a higher steady-state toughness—both these effects cumulate in an evolving cohesive zone law with crack progression. We discuss the relationship between these phase-field parameters and process zone characteristics in the material.

Mechanical Characterisation and Cohesive Law Calibration for a Nitrocellulose Based–Cyclotetramethylene Tetranitramine (HMX) Polymer Bonded Explosive

BackgroundMechanical characterisation of polymer bonded explosives (PBXs) is crucial for their safe handling during storage and transportation. At temperatures higher than the binder's glass transition temperature, fracture is caused predominantly by interface debonding between the binder and explosive crystals. Interfacial friction between debonded crystals can lead to accidental detonation of the PBX material, even under a very small external load. Cohesive zone laws can describe this interfacial debonding.ObjectiveThis study aims to experimentally calibrate the interfacial cohesive zone parameters of a nitrocellulose based–cyclotetramethylene tetranitramine (HMX) PBX, a particulate composite with an 88% volume fraction of crystals.MethodsCompact tension fracture tests, coupled with Digital Image Correlation (DIC) were used to capture the strain fields around the crack tip. The experimental data were used in conjunction with an extended Mori–Tanaka method considering the effect of interfacial debonding.ResultsThe cohesive zone parameters were successfully calibrated and were found to be crosshead rate independent. The values of the critical traction {sigma }_{int}^{max} and interfacial energy release rate, {gamma }_{if}, dropped significantly with increasing temperature. The experimental method followed in this study is generic, and it can be employed to extract the cohesive zone parameters characterising the interface behaviour between the filler and matrix in other particulate filled, polymer composite materials.ConclusionsCohesive zone properties can be experimentally determined to provide inputs in micromechanical simulations linking the microstructure of the PBX composite to its macroscopic response as well as enabling the estimation of hot spot formation at debonded crystal interfaces.

Mode II cohesive zone law of porous sintered silver joints with nickel coated multiwall carbon nanotube additive under ENF test

Various contents of nickel coated carbon nanotube added sintered silver joints are fabricated through mechanical alloying. An analytical method is presented to compute the fracture energy of ENF tests incorporating shearing effect and thickness effect, which shows better accuracy compared with traditional method, which are closer to the solutions of compliance based beam method. Mode II fracture energy, mode II fracture toughness and mode II cohesive zone model for different contents of nickel coated carbon nanotube added sintered silver joints are presented based on the data extraction of the ENF tests. With the increase of adhesive layer thickness, the fracture energy and the mode II fracture toughness improve. However, thickness effect is less significant but not negligible comparing with the strengthening effect on the improvement of fracture toughness, which is caused by adding nickel coated multiwall carbon nanotubes. The relation between mode II fracture toughness and porosity is also discussed. For most of the conditions, the mode II fracture toughness is higher than mode I fracture toughness regardless of additive content due to the crack deflection, crack bridging and pull-out mechanisms during the crack propagation except for those high content of additive whose fracture energy is reduced because of aggregation effect.

Fracture characterisation of bone-cement bonded joints under mode I loading

Over the years, many techniques have been developed for the stabilisation of bone fractures. The study of the adhesion of bone-to-bone cement is an important step towards the development of new immobilization systems. Although bone cement has been used for more than fifty years, very few studies have been performed regarding the evaluation of fracture properties. In this work, numerical and experimental investigations were conducted to evaluate the strain energy release rate under mode I loading in a bone-cement bonded joint, using the Double Cantilever Beam (DCB) test. Cohesive zone laws were also measured combining the finite element method with non-linear elastic fracture mechanics. This has been made in a cortical bone bonded joint with polymethylmethacrylate (PMMA). Consistent results have been obtained regarding fracture toughness in a widely used bone-to-bone cement joint in many biomedical applications.

An inverse method to reconstruct crack-tip cohesive zone laws for fatigue by numerical field projection

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loadings, but the functional form of such phenomenological models does not have a strong micromechanical basis. While numerical techniques have been developed to extract the crack-tip cohesive zone law for monotonic fracture from experimental strain information, elucidating the unloading-reloading hysteresis representing accumulated and irreversible damage under fatigue cycling is still challenging. Here, we introduce a novel field projection method (FPM) to reconstruct the cohesive zone laws for steady-state fatigue crack growth from elastic strain field information at various loading and unloading stages within a single steady-state fatigue cycle. The method is based on the Maxwell-Betti’s reciprocal theorem, which considers the material response to be linear elastic during loading and unloading, albeit with a reciprocity gap to account for the inhomogeneous residual elastic strain accumulated at the end of each fatigue cycle. Through numerical experiments, we demonstrate that this FPM is capable of accurately extracting the crack-tip cohesive tractions and separations, along with the elusive unloading-reloading hysteresis, which constitute the cohesive zone law for fatigue crack growth. We discuss the errors and uncertainties associated with this inverse approach.

Atomic mixed-mode cohesive-zone dual constitutive laws of impurity-embrittled grain boundaries in polycrystalline solids via nanoscale field projection method

Atomic-scale mixed-mode intergranular fracture, featured by non-local non-linear discrete atomic debonding processes near a crack tip along a grain boundary (GB), is modeled with a cohesive zone in a continuum scale controlled by cohesive-zone dual constitutive relations, a balanced traction-separation relationship, i.e., a conventional cohesive-zone law (CZL), and an unbalanced traction (UT)-centerline displacement (CD) relationship. In order to bridge two different scales, we developed a nanoscale field projection method (nano-FPM) based on atomic-scale interaction J and M integrals, for which asymptotic anisotropic elastic fields near an interfacial crack with balanced and unbalanced crack-face tractions are used as probing fields of the CZL and UT-CD relationship, respectively. Cracking phenomena along a GB in nickel with segregated sulfur impurity atoms under mixed-mode loadings are simulated with molecular dynamics. Embrittlement by sulfur impurity atoms is quantitatively estimated with the mixed-mode CZL of the GBs in nickel via the nano-FPM developed in this study. UT-CD relationship, a special feature of atomic fracture, representing the micromechanical change of surface stress between GB and cracked surfaces, is also obtained by the nano-FPM. New functional relationships for CZL, UT-CD relationship, and decohesion potential obtained by the nano-FPM are proposed to facilitate the implementation of them into mesoscale or continuum-scale analysis on mixed-mode intergranular fracture.

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.

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.

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.

Численная оценка кинетических параметров докритического роста трещин в конструкционных клеевых соединениях при длительном статическом нагружении с использованием модели когезионной зоны и экспериментальных данных

The article proposes a numerical method for modeling and calculating the kinetics of subcritical crack growth and creating kinetic G-V diagrams for structural adhesive joints under prolonged static loading. The load was set by the global subcritical crack opening according to mode I. Modeling and calculations were carried out using a cohesive zone model implanted into the finite element method in the ANSYS software package. The parameters of the cohesive zone law and the kinetics of subcritical crack growth were experimentally determined for samples in the form of a double cantilever beam made of aluminum alloy plates glued with industrial grade epoxy glue. Comparison of the calculated and experimental data showed a good correlation.

Atomistic Simulation-Based Cohesive Zone Law of Hydrogenated Grain Boundaries of Graphene

The impact of hydrogenation on the fracture toughness and strength of grain boundaries in graphene are studied. Molecular dynamics (MD) modeling are used to extract the traction–separation laws of ...

Two-scale porosity effects on cohesive crack growth in a ductile media

Microstructures with two distinct size-scales of voids are commonplace in additively-manufactured metals. The smaller-scale voids nucleate from inclusions within the metal, while the larger-scale voids originate from unsintered powder particles. In this work, we study the interaction between these two size-scales of voids ahead of a crack, and the influence on the ductile fracture process. We adopt a finite element model of a centerline crack subjected to small-scale yielding conditions. The diffuse process zone ahead of the crack is modeled by several rows of void-containing cell elements governed by a Gurson porous material relation. Results show that the larger-scale voids near the initial crack tip generally reduces the fracture toughness by facilitating void coalescence with the crack-tip to form a single contiguous damage zone. However, strategic placements of these larger-scale voids within the active plastic zone of the crack-tip can promote crack-tip shielding, leading to diffused damage in the form of multiple unconnected damage zones, and ultimately, a several-fold improvement in toughness. We quantify the fracture behavior, as a function of the relative size and proportion of larger-scale voids in the diffuse process zone, by reconstructing the equivalent crack-tip cohesive zone laws in an elasto-plastic medium via nonlinear field projection. We demonstrate that the cohesive strength, cohesive energy, as well as the functional form of the cohesive zone law, are strongly dependent on the dual void size-scales, which introduces a size-effect into the homogenized traction-separation relationship.

Quantitative investigations on multi-layer interface debonding behaviors for sisal fiber reinforced composites using acoustic emission and finite element method

Complete interfacial performances of sisal fiber (a typical plant fiber) reinforced composites (SFRCs) during the single fiber pull-out experiments were investigated experimentally with numerical simulation in the present study. The single SFRCs were found to present three-interface failure. The failure behaviors of the three interfaces were characterized by in-situ acoustic emission technique and identified as interfacial failure between technical fiber and matrix, that between elementary fibers and that between micro-fibrils of cell walls using microscope observation. Statistical analysis was employed to evaluate pull-out probability of technical fiber, elementary fibers and micro-fibrils. The embedded fiber length was concluded to dominate the failure modes of SFRCs. To further gain insight in the complete failure processes and mechanisms of the multi-layer SFRCs, a triple-interface finite element model was developed based on the cohesive zone law. Quantitative comparisons of applied stress between numerical predictions and experimental results surmised that the triple-interface model could accurately describe the multi-stage pull-out behaviors of the single SFRCs.