Finite element simulation of delamination growth in composite materials using LS-DYNA

In this paper, a modified adaptive cohesive element is presented. The new elements are developed and implemented in LS-DYNA, as a user defined material subroutine (UMAT), to stabilize the finite element simulations of delamination propagation in composite laminates under transverse loads. In this model, a pre-softening zone is proposed ahead of the existing softening zone. In this pre-softening zone, the initial stiffness and the interface strength are gradually decreased. The onset displacement corresponding to the onset damage is not changed in the proposed model. In addition, the critical energy release rate of the materials is kept constant. Moreover, the constitutive equation of the new cohesive model is developed to be dependent on the opening velocity of the displacement jump. The traction based model includes a cohesive zone viscosity parameter (η) to vary the degree of rate dependence and to adjust the maximum traction. The numerical simulation results of DCB in Mode-I is presented to illustrate the validity of the new model. It is shown that the proposed model brings stable simulations, overcoming the numerical instability and can be widely used in quasi-static, dynamic and impact problems.     

Quasi-static and dynamic fracture behavior of composite sandwich beams with a viscoelastic interface crack

Fracture analysis of sandwich beams with a viscoelastic interface crack under quasi-static and dynamic loading has been studied. Firstly, a three-parameter standard solid material model was employed to describe the viscoelasticity of the adhesive layer. And a novel interfacial fracture analysis model called three material media model was established, in which an interface crack was inserted in the viscoelastic layer. Secondly, a finite element procedure based on Rice J-integral and Kishimoto J-integral theories was used to analyze quasi-static and dynamic interface fracture behavior of the sandwich beam, respectively. Finally, the influence of viscoelastic adhesive layer on the quasi-static J-integral was discussed. In addition, comparison of quasi-static Rice J-integral with Kishimoto J-integral under various loading rates was carried out. The numerical results show that the oscillating characteristic of dynamic J-integral is more evident with shorter loading rise time.     

An enhanced FEM model for particle size dependent flow strengthening and interface damage in particle reinforced metal matrix composites

By incorporating the dislocation punched zone model, the Taylor-based nonlocal theory of plasticity, and the cohesive zone model into the axisymmetric unit cell model, an enhanced FEM model is proposed in this paper to investigate the particle size dependent flow strengthening and interface damage in the particle reinforced metal matrix composites. The dislocation punched zone around a particle in the composite matrix is defined to consider the effect of geometrically necessary dislocations developed through a mismatch in the coefficients of the thermal expansion. The Taylor-based nonlocal theory of plasticity is applied to account for the effect of plastic strain gradient which produces geometrically necessary dislocations due to the geometrical mismatch between the matrix and the particle. The cohesive zone model is used to consider the effect of interfacial debonding. Lloyd’s experimental data are used to verify this enhanced FEM model. In order to demonstrate flow strengthening mechanisms of the present model, we present the computational results of other different models and evaluate the strengthening effects of those models by comparison. Finally, the limitations of present model are pointed out for further development.     

Predicting mode-II delamination suppression in z-pinned laminates

A finite element model for predicting delamination resistance of z-pin reinforced laminates under the mode-II load condition is presented. End notched flexure specimen is simulated using a cohesive zone model. The main difference of this approach to previously published cohesive zone models is that the individual bridging force exerted by z-pin is governed by a specific traction-separation law derived from a unit-cell model of single pin failure process, which is independent of the fracture toughness of the unreinforced laminate. Therefore, two separate traction-separation laws are employed; one represents unreinforced laminate properties and the other for the enhanced delamination toughness owing to the pin bridging action. This approach can account for the so-called large scale bridging effect and avoid using concentrated pin forces in numerical models, thus removing the mesh-size dependency and permitting more accurate and reliable computational solutions.     

Modelling the simulation of impact induced damage onset and evolution in composites

This paper presents two modelling strategies for the simulation of low velocity impact induced damage onset and evolution in composite plates. Both the strategies use a global–local technique to refine the mesh in the impact zone in order to increase the accuracy in predicting the impact phenomena without affecting the computational cost. Cohesive elements are used to simulate the inter-lamina damage behaviour (delaminations) and Hashin’s failure criteria are adopted to predict the intra-lamina failure mechanisms. The two modelling strategies differ in terms of input parameters for the inter-lamina and intra-lamina damage evolution laws and in terms of modelling solutions in the impacted area. Comparisons between numerical and experimental results on composite plates subjected to different impact energies, according to the ASTM D7136 requirements, have been used to assess the peculiarities and the fields of application for the two proposed modelling strategies. Both the strategies have been tested by adopting the finite element code ABAQUS®. The different approaches to set the parameters of cohesive elements’ constitutive laws and Hashin’s criteria and the different choices made in quantifying the dependence of failure criteria on the finite elements’ average size have been taken into account.     

A novel approach based on ALE and delamination fracture mechanics for multilayered composite beams

A novel approach able to predict debonding or fracture phenomena in multilayered composite beams is proposed. The structural model is based on the first-order shear deformable laminated beam theory and moving mesh strategy developed in the framework of Arbitrary Lagrangian–Eulerian (ALE) formulation. The former is utilized to evaluate fracture parameters by using a multilayer approach, in which a low number of interface elements are introduced along the thickness, whereas the latter is utilized to reproduce crack tip motion due to the crack extension produced by moving boundaries. The model is able to avoid computational complexities introduced by an explicit crack representation in bi-dimensional structures, in which typically high computational efforts are expected for handling moving boundaries. To this aim, a moving mesh strategy is proposed for the first time in the context of beam modeling based on a multilayered configuration. Such an approach, essentially based on ALE formulation, is able to reproduce interfacial crack paths by using a low number of computational elements. The numerical method is proposed in the framework of the finite element formulation for a quasi-static or dynamic evolution of the crack tip front. In order to investigate the accuracy and to validate the proposed methodology, comparisons with experimental data and existing formulations available from the literature are developed. Moreover, a parametric study in the framework of dynamic fracture is developed to investigate the capability of the proposed model to reproduce more complex loading cases.     

Multi-scale fracture modeling of asphalt composite structures

A multi-scale model for predicting the fracture evolution of multi-phase solid materials in layered composite structures subject to monotonic loading is presented. The objective of such a model is to develop the capability to predict various fracture mechanisms of layered structure considering realistic microstructures of particle-reinforced composites. The meso-scale fracture model developed herein is firstly verified with experimental test results to determine proper materials parameters and to consider the independency of fracture tests. Essential ingredients within the context of the models are an image processing technique for obtaining microstructures of composites and cohesive softening models for representing fracture behavior of multi-phase composites. The multi-scale fracture model shows potential capabilities for predicting various fracture mechanisms and for characterizing the fracture process zone in layered composite structures.     

A cohesive zone model for predicting delamination suppression in z-pinned laminates

This paper presents a cohesive zone model based finite element analysis of delamination resistance of z-pin reinforced double cantilever beam (DCB). The main difference between this and existing cohesive zone models is that each z-pin bridging force is governed by a traction-separation law derived from a meso-mechanical model of the pin pullout process, which is independent of the fracture toughness of unreinforced laminate. Therefore, two different traction-separation laws are used: one representing the toughness of unreinforced laminate and the other the enhanced delamination toughness owing to the pin bridging action. This approach can account for the large scale bridging effect and avoid using concentrated pin forces, thus removing the mesh dependency and permitting more accurate analysis solution. Computations were performed using a simplified unit strip model. Predicted delamination growth and load vs. displacement relation are in excellent agreement with the prediction by a complete model, and both models are in good agreement with test measured load vs. displacement relation. For a pinned DCB specimen, the unit strip model can reduce the computing time by 85%.     

Computational modeling of mixed-mode fatigue crack growth using extended finite element methods

The extended finite element method (XFEM) combined with a cyclic cohesive zone model (CCZM) is discussed and implemented for analysis of fatigue crack propagation under mixed-mode loading conditions. Fatigue damage in elastic-plastic materials is described by a damage evolution equation in the cohesive zone model. Both the computational implementation and the CCZM are investigated based on the modified boundary layer formulation under mixed-mode loading conditions. Computational results confirm that the maximum principal stress criterion gives accurate predictions of crack direction in comparison with known experiments. Further popular multi-axial fatigue criteria are compared and discussed. Computations show that the Findley criterion agrees with tensile stress dominant failure and deviates from experiments for shear failure. Furthermore, the crack propagation rate under mixed mode loading has been investigated systematically. It is confirmed that the CCZM can agree with experiments.     

Potential-based constitutive models for cohesive interfaces: Theory,implementation and examples

Cohesive interfaces appear in many materials or structures, e.g. composites or adhesive bonds. Originally introduced to model crack tips in fracture mechanics, cohesive zone models are used to describe the constitutive behavior of cohesive interfaces since the early 1990s. In the present contribution, the concept of generalized standard materials (GSM) is transferred from the modeling of bulk behavior to cohesive zones. The potential-based framework obtained hereby is referred to as standard dissipative cohesive zones (SD-CZ). Within this framework, an irreversible interface model is developed for the one-dimensional case and subsequently extended to three-dimensional transverse isotropy. While the potential structure of the constitutive law may be required for certain applications, it also brings benefits with regard to the numerical implementation. To the best knowledge of the authors, this is the first approach to interface modeling in a GSM-like framework, where dissipative effects like damage and softening are considered as well as normal-tangential coupling for mixed-mode decohesion. Comparisons to experimental data and existing cohesive zone models outline the capabilities of the approach.     

Assessment of debond simulation and cohesive zone length in a bonded composite joint

Finite element methods combined with cohesive elements were used to simulate progressive failure behaviour in a bonded double cantilever beam configuration. The introduced cohesive zone was represented by three cases. Responses of both global load–displacement and local cohesive traction–separation were investigated. An unexpected finding was that the overall cohesive traction stiffness was much less than the assumed input value. In addition, the local nodal separation moment was identified. Consequently, correct cohesive zone lengths were obtained using the extracted traction profile along the cohesive zone path at this moment. Information of the global load–displacement profile, traction stiffness, and cohesive zone length induced by the three zone cases was explored. Moreover, the study can explain why very small cohesive zone lengths are generated numerically, as compared to theoretical solutions. Recommendations on the application of the numerical model with cohesive elements to practical experimental analysis were suggested.     

A boundary integral method for a dynamic, transient mode I crack problem with viscoelastic cohesive zone

We consider the problem of the dynamic, transient propagation of a semi-infinite, mode I crack in an infinite elastic body with a nonlinear, viscoelastic cohesize zone. Our problem formulation includes boundary conditions that preclude crack face interpenetration, in contrast to the usual mode I boundary conditions that assume all unloaded crack faces are stress-free. The nonlinear viscoelastic cohesive zone behavior is motivated by dynamic fracture in brittle polymers in which crack propagation is preceeded by significant crazing in a thin region surrounding the crack tip. We present a combined analytical/numerical solution method that involves reducing the problem to a Dirichlet-to-Neumann map along the crack face plane, resulting in a differo-integral equation relating the displacement and stress along the crack faces and within the cohesive zone.     

Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model

This paper presents a model for predicting damage evolution in heterogeneous viscoelastic solids under dynamic/impact loading. Some theoretical developments associated with the model have been previously reported. These are reviewed briefly, with the main focus of this paper on new developments and applications. A two-way coupled multiscale approach is employed and damage is considered in the form of multiple cracks evolving in the local (micro) scale. The objective of such a model is to develop the ability to consider energy dissipation due to both bulk dissipation and the development of multiple cracks occurring on multiple length and time scales. While predictions of these events may seem extraordinarily costly and complex, there are multiple structural applications where effective models would save considerable expense. In some applications, such as protective devices, viscoelastic materials may be preferred because of the considerable amount of energy dissipated in the bulk as well as in the fracture process. In such applications, experimentally based design methodologies are extremely costly, therefore suggesting the need for improved models. In this paper, the authors focus on the application of the newly developed multiscale model to the solution of some example problems involving dynamic and impact loading of viscoelastic heterogeneous materials with growing cracks at the local scale.     

Dynamic micromechanical modeling of textile composite strength under impact and multi-axial loading

Micromechanical finite element modeling has been employed to define the failure behavior of S2 glass/BMI textile composite materials under impact loading. Dynamic explicit analysis of a representative volume element (RVE) has been performed to explore dynamic behavior and failure modes including strain rate effects, damage localization, and impedance mismatch effects. For accurate reflection of strain rate effects, differences between an applied nominal strain rate across a representative volume element (RVE) and the true realized local strain rates in regions of failure are investigated. To this end, contour plots of strain rate, as well as classical stress contours, are developed during progressive failure. Using a previously developed cohesive element failure model, interfacial failure between tow and matrix phases is considered, as well as classical failure modes such as fiber breakage and matrix microcracking. In-plane compressive and tensile loading have been investigated, including multi-axial loading cases. Highly refined meshes have been employed to ensure convergence and accuracy in such load cases which exhibit large stress gradients across the textile RVE. The effect of strain rate and phase interfacial strength have been included to develop macro-level material failure envelopes for a 2D plain weave and 3D orthogonal microgeometry.     

Experimental and numerical study of compression after impact of sandwich structures with metallic skins

A finite element model is proposed to determine the residual print of sandwich structures with Nomex honeycomb core and metallic skins indented by a spherical indenter and to simulate its behavior when this indented structure is subjected to lateral compressive loading (known as CAI/ Compression after impact). The particularities of this model rely on representing the honeycomb with a grid of non-linear springs which its behavior law calibrated from uniform compression test. This simple model, after integrating the cycle behavior law of honeycomb, allows predicting the geometry of residual print with a good precision. This model is then developed to propose a complete computation from indentation, residual print geometry to lateral compressive loading after indentation (CAI). This model also allows predicting numerically the residual strength of structure in CAI and the elliptical evolution of residual print geometry during CAI loading. A good correlation with test results is obtained except for the very small residual print depth.     

Experimental testing and phenomenological modelling of the fragmentation process of braided carbon/epoxy composite tubes under axial and oblique impact

A new simulation technique is presented for the phenomenological modelling of stable fragmentation in fibre reinforced composite structures under dynamic compressive loading. An explicit crash code is used for implementation of a hybrid modelling technique, in which two distinct material models act simultaneously. The first model is implemented in a multi-layered shell element and uses a unidirectional composites fracture criterion to predict potential ply fracture mechanisms on a macroscopic scale. This model is, however, unable to represent the complex localised fracture mechanisms that occur on a meso (sub-ply) scale under compression fragmentation loading. Therefore, a second constitutive model is added to capture the energy absorbing process within the fragmentation zone, utilising an Energy Absorbing Contact (EAC) formulation between the composite structure and the impacting body. The essential benefits of the procedure are that it requires minimal input data that can be obtained from simple fragmentation tests, and that the procedure is computationally efficient enabling application to large scale industrial structures. The EAC theory is discussed, together with the required material model parameters. A series of dynamic axial and oblique impact tests and simulations of cylindrical continuous carbon fibre reinforced composite tubes have been performed to validate the approach. Furthermore, the application to more complex load cases including combinations of fragmentation and global structural fracture have also shown a good correlation with test results.