Mixed-mode Delamination Research Articles

Stress based fracture criteria for mixed-mode I/II delamination of unidirectional composite laminates

Mixed mode delamination is prone to occur in composite laminates subjected to complicated loading. In current study, the modified maximum principal stress (M-MPS) criterion and the modified maximum shear stress (M-MSS) criterion considering the effect of mode ratio on the critical distance are developed to predict the mixed mode delamination of unidirectional laminates. The accuracy of the proposed fracture criteria is validated by the comparison of the predicted fracture locus curve with extensive experimental data available in the literatures, a higher correlation is observed between the predicted results and the experimental data. Finally, comprehensive discussion on the capability of the proposed M-MPS and M-MSS criteria is conducted, a dimensionless parameter named fracture index composed of the difference of elastic properties and the difference of pure mode fracture toughness is proposed to reveal the fracture mechanisms of the unidirectional composites.

Failure analysis of curved interface in pultruded fiber-reinforced polymer laminations using phase-field approach

Pultruded fiber-reinforced polymer (FRP) composites frequently encounter fabric misalignment perpendicular to the pultrusion direction, resulting in the formation of a curved interface. For predicting delamination in pultruded fabric with curved interfaces, the phase field model is employed in the commercial software ABAQUS® through the UMAT and HETVAL subroutines. In this study, the Mode-I, Mode-II, and mixed-Mode delamination behavior are successfully simulated to validate the efficiency of the proposed phase field method. A parametric study is conducted to investigate the impact of mesh size and phase field length on the simulation results. The recommended mesh size and interface length of the phase-field model are given. Finally, the validated phase-field model is used to predict the delamination behavior exposed to Mode-I, Mode-II, and mixed-Mode loading for the curved interface. The results indicate that specimens with a curved interface exhibit greater bearing capacity compared to those with a planar interface.

Phase field approach to predict mixed-mode delamination and delamination migration in composites

In this work, we present a mixed-mode phase field approach to model delamination progression and its migration. The proposed model includes the volumetric and deviatoric effects that occur during the mixed-mode delamination and migration. The volumetric–deviatoric split is combined with a power law criterion of delamination to capture the mixed-mode effects. An anisotropic tensor is used in the crack surface density function for capturing the anisotropic fracture. Two history parameters are introduced to ensure the irreversibility of the damage field throughout the evolution process of delamination and to consider the maximum value of the strain energy. A staggered approach is implemented for solving the equilibrium and evolution equations. The algorithm enables to obtain stable numerical solutions with faster convergence. Several examples of mode I and mode II as per standard tests have been incorporated to demonstrate the working of the proposed method. The numerical examples are validated by comparison with experimental results from the literature. It is observed that the proposed model can predict crack paths and angles closer to the experimental results. Examples of multiple delamination and delamination migration are also studied to understand the kinking in the delamination scenario. It is observed that the delamination migration is governed by the ratio of notch length a to the distance of the load from the edge L, and by the stress state in front of the crack tip. In the case of laminates with multiple interphases, the event of delamination impinging and kinking at interphase depends on the fracture toughness ratio of the bulk and the interphase. The example of the single-edge notched composite lamina and open-hole tension test with different fiber orientations has been validated with the literature and experiments.

A fragile points method with a numerical-flux-based interface debonding model to simulate the delamination migration in composite laminates

Predicting damage in composite laminates is essential for a better utilization of the material, but it is challenging especially when the inter- and intra-ply damages are coupled. In this paper, a Fragile Points Method (FPM) with a numerical-flux-based interface debonding model is proposed to simulate the laminates’ damage. The FPM is a novel meshless method using the discontinuous Galerkin weak formulations and the point-based discontinuous polynomial trial functions. In this work, an orthotropic interface debonding model has been developed based on the numerical fluxes to simulate the mixed-mode inter- and intra-ply damage. For any interior interface in an FPM model, the interface damage is triggered when the damage criterion is satisfied and the interface is separated when the fracture energy is reached. Due to the discontinuous characteristics of the FPM, the inter- and intra-ply damage modes are introduced explicitly, and thus the coupling between them can be naturally captured. In this paper, the proposed FPM is verified by four benchmark examples for Mode I, Mode II and Mixed Mode delamination. Then the proposed method is applied to simulate the delamination migration, used as an example for the inter- and intra-ply damage. The FPM results show that this method is able to provide reliable prediction on the load–displacement curves as well as the damage and crack patterns, and the mechanism governing the delamination migration is also discussed based on the FPM results.

Digital image correlation technique for failure and crack propagation of fibre-reinforced polymer composites – A review

Digital image correlation (DIC) is a powerful technique for determining material deformation and damage and currently is viewed as a potential method to study failure and crack propagation in advanced composite materials. Case studies in concrete, epoxy adhesives, and carbon/epoxy laminates demonstrate the effectiveness of the DIC technique in visualizing crack propagation. This review highlights the applications, challenges, and implementation of the DIC technique in the failure and crack propagation of fibre-reinforced polymer (FRP) composites. The important factors such as field of view, speckle pattern, and algorithm choice are discussed while emphasizing the need for careful selection and calibration. The review concludes by highlighting the significance of crack propagation studies for composite behaviour and the role of DIC in calibrating and validating models of composite failure analysis. Future research directions include investigating mixed-mode delamination, improving calibration procedures, assessing DIC accuracy for large deformations, and comparing different DIC algorithms, which are discussed.

A comprehensive experimental investigation of the rate-dependent interlaminar delamination behaviour of CFRP composites

The paper presents a systematic experimental study of the interlaminar delamination behaviour of a carbon composite subjected to Mode I, Mode II and Mixed-mode delamination at both quasi-static (QS) and high-rate (HR) conditions, which were conducted on a screw-driven test machine and in-house Hopkinson bar systems, respectively. A methodology integrating digital image correlation and the compliance-based beam theory was employed to circumvent the challenges in measuring the loads at HR tests and maintain good consistency during the data analysis of all delamination tests. The results demonstrated a positive rate-dependent delamination behaviour, with the HR Mode I, Mode II and Mixed-mode fracture toughness properties being 1.56, 1.66 and 1.60 times their QS counterparts, respectively. The cause of such a dependency was revealed following a detailed fractographic analysis, which highlighted that the observed dependency was associated with the transition of the predominant failure mechanisms in the QS and HR conditions.

Delamination behaviors of an epoxy-impregnated REBCO pancake coil during a quench

For the epoxy-impregnated high-temperature superconducting (HTS) REBa2Cu3O7-x (REBCO) magnets, the quench cannot be still avoided in the operation, which may induce the mechanical damage of the magnets and even burning out. In this research, an electromagnetic-thermo-mechanical coupling model is proposed to explore the delamination mechanisms of an epoxy-impregnated REBCO pancake coil during a quench, and thereinto, a cohesive zone model (CZM) based on the mixed-mode traction-separation law is used to simulate the onset and growth of the delamination. The numerical results indicate that the delamination of the coil is mainly concentrated in the quenching turns. The reason is that localized high-temperature gradients are generated in these turns due to the large temperature increase during a quench, and thus the accumulated stress induced by the thermal mismatch stress locally leads to the cracking of the interface between the superconducting layer and Hastelloy substrate. Meanwhile, the delamination onset of the coil is predicted by mixed-mode delamination according to the quadratic failure criterion, and the delamination propagation is mainly determined by shear stress. Up to now, the delamination mechanisms of the epoxy-impregnated pancake coil during a quench are clarified in detail, which is different from those during cooling down. To further understand the delamination behaviors of the epoxy-impregnated pancake coil during a quench, the effects of the location and height of the heater, and the thickness of the epoxy resin on the interface delamination failure are discussed in the paper.

Modeling Large-Surface Impact-Induced Damage in Iteratively Characterized Filament-Wound Composite Pipes: A Numerical and Experimental Investigation

With the widespread use of fiber reinforced polymer (FRP) composite pipes, their susceptibility to impact damage remains a significant cause of concern. This work investigates the structural response and damage propagation of glass-fiber reinforced epoxy (GRE) pipes under large-surface low-velocity impacts. A series of drop-weight impact tests of varying heights is conducted and compared to numerical finite element (FE) simulations. Then, plies are individually modeled and assigned with properties obtained from the authors’ earlier work. Utilizing composite failure theories and mixed-mode delamination theories, the simulated structural responses including the load–displacement, strain–displacement response and damage propagation are compared and validated with the experimental results. It was found that the structural response is well predicted at higher drop heights and there is a significant change in damage type and propagation with increasing drop heights. The proposed approach builds on the authors’ earlier work and provides a modeling approach for the prediction of structural response, inter- and intra-laminar damage with just pipe level properties.

Continuum damage analysis of delamination in composite laminates using a stress-based layerwise plate model

This contribution addresses the modelling of delamination in a stress-based layerwise plate model. Such models benefit from a good representation of the local 3D stress field, especially inter-laminar stresses which are natural generalized stress unknowns arising in their derivation. We extend their construction to situations involving onset and propagation of interfacial delamination. We propose a variational formulation relying on a continuous damage description of the opening and sliding interfacial degradation processes using two damage variables. A mixed-mode delamination propagation criterion can be obtained through proper coupling between both variables. Finally, the model predictions are validated against classical delamination tests in pure and mixed modes.

Displacement rate effects on mixed-mode I/II delamination of laminated carbon/epoxy composites

Mixed-mode delamination is one of the common failures of composites which has not been studied under low-impact loading. This paper studies the influence of displacement rate on mixed-mode I/II delamination of unidirectional carbon/epoxy composites. Single leg bending test is performed at displacement rates of 1, 10, 100, and 500 mm/min. Experimental results reveal that the mixed-mode I/II fracture toughness is invariant with the displacement rate. In addition, scanning electron micrographs shows that shear cusps are more obvious at 1, 10, and 100 mm/min. At 500 mm/min, significant matrix debris is noticed. Furthermore, the proposed three-dimensional rate-dependent fracture criterion is found to well predict the fracture toughness. Numerical simulation using cohesive zone model suggests that the lower numerical peak load is due to lower damage dissipated energy. In addition, the theoretical and numerical traction-separation responses show significant differences, which is also reflected in the numerical phase angle. This implies that the local mixed-mode ratio is not constant throughout the simulation process.

Mixed Cohesive Zone Modeling of Interface Debonding between Propellant and Insulation

High-quality interface between propellant and insulation is the strict requirement difficult to quantify in solid rocket motor. In this study, the mixed mode delamination process of propellant and insulation interface is considered in double cantilever sandwich beam (DCSB) and single lap-joint (SLJ) test. The PPR cohesive zone model (CZM) and bilinear CZM in ABAQUS are introduced in this mixed fracture progress. In order to implement the PPR model in ABAQUS, user subroutine user element (UEL) is programmed for the novel CZM. Two simple pure mode I and mode II fracture problems are designed to check the accuracy of the UEL, and the result of verification is excellent. DCSB and SLJ test and their corresponding results are used again in the same inverse analysis with the two typical effective displacement-based and potential-based CZM. Base on the results, a series discussion and some conclusions are made. The debonding progress of the propellant and insulation interface in DCSB and SLJ test are mixed mode. The PPR CZM is prior in simulation than the bilinear CZM in ABAQUS because the PPR CZM is much more flexible with changeable traction-separation shape. The real normal and tangential displacement at damage initiation shows the unreasonable change in bilinear CZM in ABAQUS under mixed mode fracture. The PPR CZM and bilinear CZM in ABAQUS are all thickness-dependent model. The real initial stiffness and the critical displacement in the bilinear CZM and the real maximum traction in PPR model are dependent on the thickness of cohesive element. The different thickness dependence of the two model is caused by the implementation method.

Mixed-mode delamination in laminate plate with crack

This paper deals with numerical modelling of laminate composite plate delamination that consists of unidirectional fiber reinforced layers. The delamination may be a fundamental problem in design of composite structures. The first-order shear laminate plate theory and fracture and contact mechanics were adopted for the methodology. The sublaminate modelling and delamination modelling are described by the help of finite element analysis. The displacements, reaction forces in springs and energy release rate along the lamination front are computed in modelling of interface. The numerical results are presented for problems with delamination of the mixed mode by using of 2D finite element analysis in the commercial ANSYS software. Copyright © 2018 VBRI Press.

Simulating delamination in composite laminates involving large scale fiber bridging based on the mixed-mode three-linear cohesive zone model

A three-linear cohesive zone model (CZM) superposed by two bilinear laws for modelling mixed-mode delamination with the effect of large scale fiber bridging is proposed in this study. The parameters in the formulation can be obtained from pure mode delamination tests or selected by reliable guidelines, making the CZM easy to be implemented in the finite element model. A novel method to determine the bridging strength by applying varied values in the different regions of the prearranged delamination path is developed. The division of the region is based on the concept of the length of the fracture process zone (FPZ). Simulations of mode I delamination in unidirectional and multidirectional composite laminates and mixed-mode I/II delamination in multidirectional laminate are performed in the finite element analysis software. Good agreement between the predicted load–displacement responses and the corresponding experimental results are achieved by adopting the established CZM and the bridging strength determination method, validating their efficiency in predicting the delamination behaviors under both pure mode and mixed-mode loadings.

Experimental and numerical study on the compressive behaviour of partially accessible concrete columns strengthened by a layer of high-performance concrete

In this paper, a novel reinforcement system for partially accessible concrete columns is studied experimentally and numerically. This technique involves the application of a layer of high-performance mortar only on one side of the existing concrete columns with built-in shear connectors that, together with the concrete-mortar interface, transfer the load between the two components. In the experimental campaign, three different fibre-reinforced high-performance mortars have been used for the reinforcement of a concrete column. The influence of the thickness and the material of the reinforcement layer on the increase of the bearing capacity of the columns have been assessed. In addition, a novel finite-element formulation for a multi-layer beam allowing for plastic deformation (and failure) of the layers and mixed-mode delamination between them is proposed to model the reinforced columns. The model has been capable of simulating the complex structural behaviour of the experimental testing with low computational burden and robust solution procedure, allowing to conclude that the amount of the interlayer relative displacements strongly influences the effectiveness of the reinforcement technique.

A hysteresis cohesive approach for predicting mixed-mode delamination onset of composite laminates under cyclic loading: Part II, numerical and experimental analyses

Delamination onset of composite laminates is investigated under cyclic loading by numerical simulation and fatigue experiments. Firstly, laminated composites in the form of double cantilever beam (DCB) testing specimens are fabricated. Two different manufacturing methods including hand layup and vacuum infusion process are used for fabricated three different lay-up configurations. All specimens are subjected to cyclic loading under displacement control conditions. The variations of compliance versus number of cycles are monitored and recorded during the performed fatigue tests. Then, the developed novel approach in the companion article (Part I) is implemented in this article and numerical simulation is performed to predict the onset of fatigue-induced delamination for the same investigated testing specimens. Results show a good agreement with experimental data. It is observed that the proposed model is able to capture the interfacial degradation by employing a damage evolution law in the onset stage of delamination.

A hysteresis cohesive approach for predicting mixed-mode delamination onset of composite laminates under cyclic loading: Part I, model development

A new approach is proposed to predict onset of fatigue-induced delamination in composite laminates under cyclic loading by progressive interface degradation. Based on the hysteresis cohesive zone approach, a new damage parameter is defined to construct an irreversible cohesive zone model. Residual displacement jump is introduced and used along with mixed-mode bilinear traction-separation law parameters for calculating the damage parameter. Fatigue-induced delamination onset is then predicted by proposing a damage criterion. 3-D Finite Element (FE) formulation is developed with proper elements for plies and also proper elements for the interface. Cyclic loading is also simulated mimicked by the MIN-MAX method. The current research is conducted in two parts as Part I and Part II. While this article focuses on the theoretical framework of the developed modeling, the numerical implementation of the modeling and also a comparison of the outputs with experimental observations will be presented in the companion paper as Part II.

On the delamination of polyvinyl butyral laminated glass: Identification of fracture properties from numerical modelling

This work investigates the delamination behaviour of polyvinyl butyral (PVB) laminated glass under quasi-static loading based on a cohesive zone model (CZM) with an isotropic bilinear traction - separation (T – δ) law. It presents a 2D model of a through-cracked tensile (TCT) test within an implicit finite element framework of the commercial software ANSYS. Test results from literature are used to calibrate the adhesion properties of the PVB-glass interface in a numerical cohesive zone approach. The previous TCT tests were performed at a loading rate of 6 mm/min and a temperature of approx. 22 °C. Three different PVB adhesion grades, i.e., BG R10 (low), BG R15 (medium) and BG R20 (high) are considered. Given the uncertainty in the identification of adhesion parameters, including interfacial fracture energy, cohesive strength and stiffness, a parametric analysis is conducted quantifying the influences of model parameters on the simulation results. The study allows for decoupling of individual parameters in the calibration. Then, interfacial fracture energies and cohesive strengths of the PVB-laminated glass are calibrated by matching the force – displacement curves of the numerical simulations with those from the TCT experiments. One representative case was chosen for each adhesion grade. We obtain interfacial fracture energies of 425 J/m2, 650 J/m2 and 1000 J/m2 for BG R10, BG R15 and BG R20 PVBs, respectively, while the corresponding cohesive strengths are 3 MPa, 5 MPa and 10 MPa, respectively. Moreover, based on numerical simulation results, the conversion of energy during the delamination process is extracted and discussed. The mixed-mode delamination mechanism is investigated by calculating the mode I and mode II energy release rates with respect to different PVB thicknesses and adhesion. The results show that the proportion of the mode I energy release rate is around 30%∼40% of the total energy release rate at the stable delamination stage and increases with PVB thickness. The presented study contributes to the adhesion properties of various types of PVB interlayers reported in open literatures and proposes a methodology for the unique identification of adhesion properties.

Application of scaled boundary finite element method for delamination analysis of composite laminates using cohesive zone modelling

In this paper, the scaled boundary finite element method (SBFEM) is evaluated for two-dimensional delamination analysis of composite laminates. The delamination phenomenon was studied using cohesive zone modelling (CZM). A bi-linear (triangular) traction-separation law was used to describe the interface behaviour, which was modelled using zero-thickness interface elements. Local arc-length solution technique was used to solve the non-linearity due to the interface behaviour. In this research, pure Mode I and Mode II as well as mixed mode delamination studies have been conducted using the SBFEM formulation. A variety of numerical experiments were performed. Good agreement was observed between the SBFEM simulation and the available numerical and experimental results in the open literature. A comparison between the SBFEM and other traditional methods shows that the presented formulation can solve the same physical problem with a reduction in the computational cost by more than half. The study highlights the advantages of SBFEM over other methods for modelling delamination in composite laminates using CZM.

Numerical study of interface cracking in composite structures using a novel geometrically nonlinear Linear Elastic Brittle Interface Model: Mixed-mode fracture conditions and application to structured interfaces

Interface cracking is one of the most prominent failure modes in fibre reinforced polymer (FRP) composites. Recent trends in high-tech applications of FRP composites exploit the limits of the load bearing capacity, generally encompassing the development of notable nonlinear effects from geometrical and material signatures. In this investigation, we present a comprehensive assessment of the new Linear Elastic Brittle Interface Model (LEBIM) in geometrically nonlinear applications undergoing mixed-mode fracture conditions. This interface model for triggering fracture events is formulated through the advocation of continuum-like assumptions (for initial non-zero interface thickness) and allows the incorporation of the potential role of in-plane deformation effects. The performance of the present interface model is demonstrated through the simulation of specimens with mixed-mode delamination, with special attention to its application in samples equipped with structured interfaces. Predictions exhibit an excellent agreement with experimental data, validating the proposed methodology.

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.