Traction-separation Law Research Articles

Study on the Effect of Soft–Hard Material Interface Differences on Crack Deflection in Nacre-Inspired Brick-and-Mortar Structures

Nacre has excellent balanced strength and toughness. In this paper, the mechanical performance of the typical “brick-and-mortar” structure, including the stress–strain and strain at the interface as well as the stress in the bricks, was calculated by a simplified analytical model of the nacre. This paper proposes a new method to control the crack deflection based on the toughening mechanism of the nacre. The crack extension of the “brick-and-mortar” structure was simulated using cohesive elements based on the traction–separation law with elastic and softening stiffness as variables, and it was found that both stiffness could effectively control the crack extension. The strength and toughness of the models with different stiffness combinations were calculated and plotted as a function of elastic stiffness and softening stiffness, showing that elastic stiffness significantly affects strength and softening stiffness is a determinant of toughness.

A rate-dependent crack bridging model for dynamic fracture of CNT-reinforced polymers

Carbon nanotubes (CNTs) improve the fracture toughness of polymer-based matrix composites by bridging the crack growth path. This research presents a finite element (FE) rate-dependent crack bridging model of Mode-I dynamic crack growth in CNT-reinforced polymers accounting for rate of loading and rapid crack growth. Two distinct CNT bridging and matrix cracking damage mechanisms are taken into account in the fracture process zone (FPZ) accounting for the dissipation of fracture energy. A viscoelastic-viscoplastic material model is adapted for the matrix phase to capture the strain rate effects. The crack in the matrix phase is modeled using cohesive zone elements characterized by experimental data. A rate-dependent traction-separation law obtained from CNT pull-out simulation at relevant crack opening speeds is used to simulate the CNT bridging in the FPZ. Considering the given traction-separation law as a constitutive equation, the CNTs are replaced with non-linear spring elements to facilitate the FE simulation of crack bridging with numerous CNTs in the FPZ. The proposed rate-dependent FE model for crack bridging enables the study of the effect of key CNT factors such as length, orientation, waviness, volume fraction, and agglomeration on fracture energy dissipation at various crack speeds. The developed model can simultaneously consider the interactive effects of all CNT parameters which is useful for considering all processing-induced uncertainties in analyzing the effects of CNTs on the dynamic fracture toughness of nanocomposites.

Investigation of Low Velocity Impact Behavior of Aluminum Honeycomb Sandwich Structures with GFRP Face Sheets by Finite Element Method

The aim of this study is to examine the low velocity impact behavior of aluminum honeycomb sandwich structures with glass fiber reinforced plastic (GFRP) face sheets with the help of finite element method. In the study, low velocity impact tests were carried out in the LS DYNA finite element program to examine the effects of face sheets thickness, core number, wall thickness, impact location and impact velocity on maximum contact force, absorbed energy efficiency and damage mode. Progressive damage analysis based on the Hashin damage criterion and the combination of Cohesive Zone Model (CZM) and the bilinear traction-separation law was performed using the MAT-54 material model. At the end of the study, it was determined that the face sheets thickness in sandwich structures had a significant effect on the impact resistance up to a certain impact energy. It has been observed that as the impact velocity gradually increases, there is a decrease in the contact force after a certain threshold value. As the impactor velocity increases, the energy absorption efficiency also increases. It has been determined that the location of the impact is very effective on peak force and energy absorption efficiency. The effect of the number of core layers depends on the face sheets thickness. When the face sheets thickness was not damaged at first contact, the peak force value increased in parallel with the number of layers. It was determined that the dominant damage mode after impact was matrix damage. It has been observed that as the energy level of the impactor increases, damage also occurs on the back surfaces.

Assessing fracture behavior in Composite-Metal bonded joints under opening and sliding Modes: Insights from Experiments, CZM, and FEA

The fracture behavior of AA 7050-T6/CFRP adhesive joints was investigated under mode I and II loading. Digital Image Correlation (DIC) provided precise measurements of crack length and crack tip opening/shear displacement (CTOD/CTSD), while the Extended Global Method (EGM) was used to determine the Energy Release Rate (ERR) and resistance curves (R-curves) for each fracture mode. The direct method was applied to establish the traction-separation law (TSL) and bridging law. Based on observed failure mechanisms, a novel cohesive law with five linear components was proposed, with parameters derived from experimentally obtained TSL and bridging law. Experimental determination of cohesive zone lengths for both fracture modes was achieved using the DIC technique, which was then compared with analytical predictions. Finally, the five-linear and trapezoidal cohesive zone model (CZM) was used to simulate the mode I and mode II fracture processes, respectively, within a finite element framework.

Traction-separation law for glass/epoxy composite laminates under mixed mode I/II loading condition considering the effects of fiber bridging

This study analyzed the effects of fiber bridging on fracture behavior in glass/epoxy composite laminates under mixed mode I/II loading conditions and proposed new traction-separation laws (TSLs) for this loading condition. To this end, double cantilever beam (DCB), end notch flexure (ENF), and mixed mode I/II bending (MMB) tests were performed under mode I, mode II, and mixed mode I/II loading conditions. Also, finite element analysis (FEA) was employed to simulate these tests. Under mode I loading condition, the presence of fiber bridging increased fracture toughness significantly, which was modeled using a tri-linear TSL. In contrast, under mode II loading conditions, the effect of fiber bridging was negligible, and a bi-linear TSL was sufficient. On this basis, a novel TSL was proposed for mixed modes that considers the effect of fiber bridging under mode I loading conditions and neglects it under mode II loading conditions. This TSL was defined using a tri-linear TSL for mode I and a bi-linear TSL for mode II conditions, along with the B-K fracture criterion. In the bi-linear TSL, the point τb was defined corresponding to the fiber bridging strength (σb) of the tri-linear TSL, with the assumption that τb cannot exceed σb. To analyze the variation in the FEA results with respect to τb, three cases were defined: τb = 0.0001 σb, 0.5 σb, and σb, respectively. FEA results in the first case were observed to be consistent with load–displacement curves obtained from experimental results.

Concurrent experimental testing and computational micromechanical modeling of a UD NCF GFRP composite ply

The current research work presents a detailed and thoroughly validated computational micromechanical modeling methodology to study the damage initiation and propagation in a uni-directional (UD) glass fiber-reinforced non-crimp fabric (NCF) composite ply. Under the applied transverse tension and compression loads, the effect of various microscale material and geometrical parameters on the ply level stress–strain behavior is studied. To this end, along with the distinctly modeled individual microscale constituents of the UD NCF composite ply (axial fibers, backing fibers, and matrix), the generated RVE (Representative Volume Element) model consists of manufacturing-induced defects and variabilities such as voids as well as the backing fiber’s out-of-plane waviness. The fiber/matrix interface failure behavior in the generated RVE model is simulated using cohesive zone formulations that follow bi-linear traction-separation law. Whereas the hydrostatic pressure-dependent non-linear stress–strain response followed by the fracture of the epoxy matrix is captured using the linear Drucker-Prager plasticity model coupled with the stress triaxiality-based failure criterion. The backing fibers stress–strain and failure behavior is modeled using the linear elastic and isotropic material model in conjunction with the maximum stress criterion.The proposed numerical methodology is thoroughly validated both qualitatively and quantitatively by conducting detailed experiments on a neat epoxy as well as at the composites laminate level. Upon comparing the experimental and computational results, the observed knee or slope change in the bi-linear stress–strain response of the UD NCF composite ply under transverse tension is attributed to the loss of the load-carrying ability of the axial fiber bundle due to fiber/matrix interface debonding followed by the ply splitting. Under the application of transverse compression load, the composite ply failure behavior is governed by the formation of a dominant matrix plastic shear band in the axial fiber bundles, which is in turn triggered by the fiber/matrix interface failure. Under the applied loads in the matrix-dominated direction, the presented research work provides a detailed insight into the microscale damage initiation and propagation in a UD NCF composite ply and its consequent influence on the macroscale stress–strain response.

Mode II fracture behavior of glass fiber composite-steel bonded interface–experiments and CZM

The dominant failure mode was characterized as debonding in the novel non-welded wrapped composite joint made with GFRP composites wrapped around steel sections. Glass fiber composite-steel three-point end notched flexure (3ENF) and four-point end notched flexure (4ENF) specimens were utilized to experimentally investigate mode II fracture behavior of this composite-steel bonded interface. Two new methods were proposed with the help of digital image correlation (DIC) technique to quantify fracture data during the tests: 1) the “shear strain scaling method” to quantify the crack length a; 2) the asymptotic analysis method based on the longitudinal displacement distribution along the height of the specimen at the pre-crack tip to quantify the crack tip opening displacement (CTOD). To numerically simulate the mode II fracture behavior, a four-linear traction-separation law was proposed in the cohesive zone modeling (CZM) where the softening behavior with a plateau was defined by the authors between traditionally considered initiation and fiber bridging behavior. The experimental and numerical approaches were validated mutually through good matches between the test and FEA results. 3ENF test provided good insight into softening behavior while 4ENF contributed to quantification of fiber bridging. These findings contribute to a more comprehensive characterization and understanding of the ductile fracture behavior of bi-material bonded joints, especially in mode II failure scenarios.

Numerical Investigation of the Effects of Impactor Geometry on Impact Behavior of Sandwich Structures

The aim of this study is to examine the impact performance and damage behavior of sandwich composite structures with a core material of aluminum and a facesheet of glass fiber composites using the finite element method. In the study, the effects of impactor shape, impact velocity and number of core layers on peak force, absorbed energy efficiency, maximum displacement and damage deformation were examined. For low velocity impact simulation, progressive damage analysis was performed based on the Hashin damage criterion using the MAT 54 material model in the LS DYNA finite element program. While providing the connection between the core structure and its surfaces, a Cohesive Zone Model (CZM) based on the bilinear traction-separation law was created and examined. At the end of the study, it was determined that the shape of the impactor had a significant effect on impact resistance. Energy absorption efficiency may vary as impact energy changes. However, as the impact energy increases, the energy absorption efficiency increases. It was determined that the largest and dominant damage type for all three impactors was matrix damage.

Experimental and Simulation Study on Failure of Thermoplastic Carbon Fiber Composite Laminates under Low-Velocity Impact.

Numerous studies have demonstrated that under low-velocity, low-energy impact conditions, although the surface damage to fiber-reinforced composite laminates may be minimal, significant internal damage can occur. Consequently, a progressive damage finite element model was specifically developed for thermoplastic carbon fiber-reinforced composite laminates subjected to low-speed impact loads, with the objective of analyzing the damage behavior of laminates under impacts of varying energy levels. The model utilizes a three-dimensional Hashin criterion for predicting intralayer damage initiation, with cohesive elements based on bilinear traction-separation law for predicting interlaminar delamination initiation, and incorporates a damage constitutive model based on equivalent displacement to characterize fiber damage evolution, along with the B-K criterion for interlaminar damage evolution. The impact response of laminates at energy levels of 5 J, 10 J, 15 J, 20 J, and 25 J was analyzed through numerical simulation, drop-hammer experiments, and XCT non-destructive testing. The results indicated that the simulation outcomes closely correspond with the experimental findings, with both the predicted peak error and absorbed energy error maintained within a 5% margin, and the trends of the mechanical response curves aligning closely with the experimental data. The damage patterns predicted by the numerical simulations were consistent with the results obtained from XCT scans. The study additionally revealed that the impact damage of the laminates primarily stems from interlaminar delamination and intralayer tensile failure. Initial damage typically presents as internal delamination; hence, enhancing interlaminar bonding performance can significantly augment the overall load-bearing capacity of the laminate.

Joining and separating behavior of roughness interface in CF/PEEK nanocomposite

The rough contact plays an important role in the adhesion of carbon fiber/polymer matrix interface and interface modeling techniques are integral to quantify the effects of roughness factors on material properties. Taking the popular CF/PEEK materials as the object, an atomic method is proposed to construct CF/PEEK rough interfaces in this paper, which adopts a sinusoidal form to change the roughness regularly. Based on molecular dynamics (MD) simulations, CF/PEEK tensile separation experiment is processed and the response of the CF/PEEK interfaces with different roughness under mechanical loading are investigated. Based on the recorded CF/PEEK atomic force-displacement behavior, innovating roughness parameters, a traction separation law for the interface region is proposed. This study found the contact area between the two phases, which can be greatly improved through rough structures, determines the interfacial adhesion strength. In addition, this study observes interesting phenomena through the capturing atomic states, such as the polymer chains at the boundary between the two phases are greatly stretched.

A generalized phase-field cohesive zone model ([formula omitted]PF-CZM) for fracture

In this work a generalized phase-field cohesive zone model (μPF-CZM) is proposed within the framework of the unified phase-field theory for brittle and cohesive fracture. With the introduction of an extra dissipation function for the crack driving force, in addition to the geometric function for the phase-field regularization and the degradation function for the constitutive relation, theoretical and application scopes of the original PF-CZM are broadened greatly. These characteristic functions are analytically determined from the conditions for the length scale insensitivity and a non-shrinking crack band in a universal, optimal and rationalized manner, for almost any specific traction–separation law. In particular, with an optimal geometric function, the crack irreversibility can be considered without affecting the target traction–separation softening law. Not only concave softening behavior but also high-order cohesive traction, both being limitations of the previous works, can be properly dealt with. The global fracture responses are insensitive not only to the phase-field length scale but also to the traction order parameter, though the crack bandwidth might be affected by both. Despite the loss of variational consistency in general cases, the resulting μPF-CZM is still thermodynamically consistent. Moreover, the existing numerical implementation can be adopted straightforwardly with minor modifications. Representative numerical examples are presented to validate the proposed μPF-CZM and to demonstrate its capabilities in capturing brittle and cohesive fracture with general softening behavior. The insensitivity to both the phase-field length scale and the traction order parameter is also sufficiently verified.

Finite Element Analysis of Skin Deformation and Puncture for Microneedle Array Design.

The mechanics of microneedle insertion have thus far been studied in a limited manner. Previous work has focused on buckling and failure of microneedle devices, while providing little insight into skin deformation, puncture, and the final positioning of needle tips under full microneedle arrays. The current study aims to develop a numerical approach capable of evaluating deformation and puncture conditions for full microneedle array designs. The analysis included a series of finite element submodels used to calibrate the microneedle-epidermal interface for failure properties using traction-separation laws. The single needle model is validated using experimental data and imaging, including results from a customized nanoindentation procedure to measure loads and displacements during microneedle insertion. Upon validation, full microneedle arrays are implemented in a 3 D finite element model and a design framework is developed, allowing evaluation of different design variables (i.e. needle shape, material, spacing) with respect to outputs relevant to successful microneedle performance. Results from the model include skin deformation, force to puncture, penetration depth, and the punctured state at each microneedle tip. In addition to microneedle parameters, patient parameters such as subcutaneous tissue thickness are included to evaluate the sensitivity of different microneedle designs to expected patient and anatomical region variability.

Novel FGM-USDFLD approach in Graded Cohesive Zone Modeling (GCZM): Predicting debonding and crack propagation in composite-patched notched plates

This study uses a graded adhesive approach to investigate the efficacy of composite patch reinforcement on a notched aluminum plate. The methodology employs the volumetric fraction concept of Functionally Graded Materials (FGM) to develop a Graded Cohesive Zone Model (GCZM). A variable field, introduced through a Fortran-based USDFLD subroutine, adapts the formulation of this GCZM. Patch debonding is simulated via adhesive damage using the Cohesive Zone Model (CZM). At the same time, crack initiation and propagation within the plate are modeled using the Extended Finite Element Method (XFEM) implemented in ABAQUS finite element software. The adhesive behavior is characterized by a triangular traction-separation law, with the GCZM incorporating gradation in both shear and normal separation modes relative to the notch radius. The GCZM concept is compared against two non-graded cases, Araldite 420 and AV138 adhesives, with one case replicating a previous study. Three gradation concepts are explored: C-1, where the more resistant Araldite 420 is located at the notch; C-2, at the extremity; and C-3, where it is at both the notch and extremity. These configurations aim to homogenize load transfer to the composite reinforcement and elucidate how different GCZM concepts influence debonding between the plate and composite reinforcement. By implementing USDFLD, this work effectively demonstrates the impact of gradation concepts and volumetric fraction indices on the competition between debonding and crack initiation in the plate. The results provide valuable insights into optimizing adhesive properties for enhanced structural integrity in composite-reinforced metallic structures.

A new cohesive-based modelling of moisture-dependent mode II delamination of carbon/epoxy composites

The cohesive zone model (CZM) is widely employed for simulating delamination and debonding behaviour in engineering structures. However, the choice of CZM shape impacts the accuracy of simulation results. Therefore, the selection of a suitable Traction-Separation Law (TSL) with appropriate cohesive parameters is crucial. This study focuses on simulating the mode II delamination of unidirectional carbon/epoxy composites under varying moisture content levels (0%, 2.2%, 3.8%, and 5.3%) using the End Notched Flexure (ENF) test. Trapezoidal TSL (TTSL) with varying pseudo-plasticity parameter (Γ) was implemented and compared. A guideline was proposed in this study to aid in the selection of cohesive parameters, and a relationship between these parameters and moisture content was established. The results indicate that Γ = 0.99 yields a more accurate force-displacement response compared to Γ = 0. The estimated cohesive zone length falls within the range of 2.0–2.4 mm. During crack growth, the analysis reveals that, at the peak force, a region approximately 0.5–0.6 mm ahead of the crack tip undergoes total failure. Simultaneously, damage initiation occurs in the region 2.3–2.4 mm beyond the complete failure zone.

A new modified direct method for determining the mode I delamination traction-separation law

A new equation was developed for the crack-tip separation in the double cantilever beam (DCB) specimen, which has been standardised for mode I delamination of composites. The very simple closed-form equation is based on a pseudo-elastic beam model and on the effective crack concept. Moreover, it only requires the common load–displacement data up to crack initiation and easy to obtain elastic moduli. Strain-energy release rate versus crack-tip separation curves can then be differentiated for obtaining the tractions, as in the classical direct method. Numerical results for piecewise linear traction-separation laws (TSL) showed good accuracy of strain-energy release rate versus crack-tip separation curves predicted. Application to two carbon/epoxy materials gave very promising TSL results, including cohesive strengths similar to transverse tensile strengths and post-peak steep traction decreases.

Traction-separation law parameters for the description of age-related changes in the delamination strength of the human descending thoracic aorta.

Aortic dissection is a life-threatening disease that consists in the development of a tear in the wall of the aorta. The initial tear propagates as a discontinuity leading to separation within the aortic wall, which can result in the creation of a so-called false lumen. A fatal threat occurs if the rupture extends through the whole thickness of the aortic wall, as blood may then leak. It is generally accepted that the dissection, which can sometime extend along the entire length of the aorta, propagates via a delamination mechanism. The aim of the present paper is to provide experimentally validated parameters of a mathematical model for the description of the wall's cohesion. A model of the peeling experiment was built in Abaqus. The delamination interface was described by a piecewise linear traction-separation law. The bulk behavior of the aorta was assumed to be nonlinearly elastic, anisotropic, and incompressible. Our simulations resulted in estimates of the material parameters for the traction-separation law of the human descending thoracic aorta, which were obtained by minimizing the differences between the FEM predictions and the delamination force given by the regression of the peeling experiments. The results show that the stress at damage initiation, Tc, should be understood as an age-dependent quantity, and under the assumptions of our model this dependence can be expressed by linear regression as Tc = - 13.03·10-4·Age + 0.2485 if the crack front advances in the axial direction, and Tc = - 7.58·10-4·Age + 0.1897 if the crack front advances in the direction of the aortic circumference (Tc [MPa], Age [years]). Other model parameters were the stiffness K and the separation at failure, δf-δc (K = 0.5MPa/mm, δf-δc = 0.1mm). The material parameters provided by our study can be used in numerical simulations of the biomechanics of dissection propagation through the aorta especially when age-associated phenomena are studied.

Process simulation of laser shock-based disassembly of adhesively bonded composite/metallic structural parts: a numerical upscaling

ABSTRACT In previous works, both experimental and numerical investigations have shown the potential of the laser shock technique for disassembling adhesively bonded composite/metal coupons. This study extends this concept to upscale the method, focusing on the full disassembly of a foreign object damage (FOD) panel designed to replicate an aircraft engine fan blade. Utilizing LS-Dyna explicit FE software, the numerical simulation incorporates various material models: a progressive damage model for the 3D CFRP substrate, Johnson–Cook plasticity model combined with Grüneisen equation of state for the titanium layer, and a cohesive zone model with a bilinear traction separation law for the adhesive layer. Investigating the FOD panel’s inclined geometry, a preliminary analysis examines the impact of inclination angles on shock wave propagation and back face velocity, revealing minimal alterations. Initial simulations are conducted to determine double pulse delay times and evaluate spot location effects. Automation of the multi-step process simulation is achieved through a Python script. After approximately 30 shots, complete disassembly of the FOD strip is achieved, with observed damage primarily limited to matrix cracking in the composite substrate. Numerical findings support the efficacy of the double-shot laser shock method for disassembling adhesively bonded metallic/CFRP components, contingent upon appropriate experimental arrangements.

The Use of Bilinear Cohesive Zone Model to Study the Fracture of Mode I in Adhesive Joints

Adhesively bonded joints can be numericallysimulated using the Cohesive Zone Model (CZM) concepts.CZM are widely used for the strength prediction of adhesivejoints. The critical strain energy release rate and criticalinterface strength are the parameters which must be knownwhen cohesive elements in ABAQUS software are used. Theformulation of the cohesive finite elements is based on theCZM approach with the bilinear traction-separation law. Inthis work, the parameters of two industrial adhesivesHuntsman Araldite 2015 and resin LY3505/XB3405 forbonding of epoxy composites are identified. DoubleCantilever Beam (DCB) test data was used for theidentification. Finally, cohesive parameters are identifiedcomparing numerically simulated load-displacement curveswith experimental data retrieved from literature.Parametric study is performed to evaluate the variation ofinput parameters like initial stiffness, element size, peakstress and energy release rate ‘G’. From the numericalevaluation, it was noted that CZM simulation relies largelyon element size and peak cohesive strength.

A rate-dependent cohesive zone model for dynamic crack growth in carbon nanotube reinforced polymers

Carbon nanotubes (CNTs) enhance the fracture toughness of polymer-based matrix composites by dissipating the fracture energy through the pull-out deformation damage mechanism. The rate-dependent behavior of the matrix phase and the CNT/matrix interface affects the contribution of CNTs in enhancing the fracture toughness under dynamic loading and rapid crack growth. A continuum-based finite element (FE) model is utilized in this research to analyze the CNT pull-out damage mechanism. The influence of CNTs on the dynamic fracture behavior of polymer-based composites is studied taking into account the crack opening speed and loading rate effects. The matrix phase is treated as a viscoelastic-viscoplastic material and a new rate-dependent cohesive zone model (CZM) is proposed for modeling the behavior of interface between the CNTs and matrix. The rate-dependent traction-separation laws for the cohesive zone elements are established at different pull-out or crack opening speeds. The proposed rate-dependent FE model of pull-out mechanism facilitates the investigation of the effective factors of CNTs, including length, orientation, and waviness, on fracture energy dissipation at different pull-out speeds. Developed model is very suitable for very long CNTs where atomistic-based molecular dynamics and molecular mechanics methods are associated with difficulties and are more costly and time-consuming.

A quantitative description of the influence of plastic dissipation on crack growth behaviors

This paper has transferred the influence of plastic dissipation on the crack driving force into the crack growth resistance curve based on a displacement quantity defined at the current crack tip. Such a displacement is the crack-tip-opening displacement of the corresponding stationary crack for an elastic–plastic growing crack and represents the plastic wake height. Then, this displacement-based resistance curve provides a quantitative description of the plastic deformation influences during crack growth. This paper has three novel points: 1) the crack-tip-opening displacement for an imaginary stationary crack is divided into the separation displacement and the plastic wake height, in which the separation displacement is related to the crack driving force and the plastic wake height is correlated with the plastic influence term. 2) A unified constraint of the traction-separation law (TSL) for the cohesive zone is provided by the relation between separation displacement and the crack driving force, which can shed further light on how to choose a proper TSL. 3) According to the relation between the plastic wake height and the plastic dissipation term, the influence of plastic deformation on the crack driving force is found to be independent of initial crack length, specimen width and geometrical type as long as the crack tip plastic zone does not reach the outer boundary or merge with the plastic zone of the outer boundary.