Experimental study on delamination migration in composite laminates

The transition of delamination growth between different ply interfaces in composite tape laminates, known as migration, was investigated experimentally. The test method used promotes delamination growth initially along a 0/θ ply interface, which eventually migrates to a neighbouring θ/0 ply interface. Specimens with θ = 60° and 75° were tested. Migration occurs in two main stages: (1) the initial 0/θ interface delamination turns, transforming into intraply cracks that grow through the θ plies; this process occurs at multiple locations across the width of a specimen, (2) one or more of these cracks growing through the θ plies reaches and turns into the θ/0 ply interface, where it continues to grow as a delamination. A correlation was established between these experimental observations and the shear stress sign at the delamination front, obtained by finite element analyses.Overall, the experiments provide insight into the key mechanisms that govern delamination growth and migration.     

XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.     

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.     

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%.     

Experimental and numerical studies of initial cracking in CFRP cross-ply laminates

This work is concerned with the conditions for formation of the first (initial) cracks in composite laminates with cutouts or ply drop-offs subjected to in-plane loading. We study here the crack formation on the free edge of CFRP cross-ply laminates experimentally and by numerical stress and failure analysis. The free-edge surface strains are measured by the digital image correlation (DIC) technique. The numerical analysis consists of a two-scale approach, where the macro-level analysis is performed with a three-dimensional finite-element method (3D FEM) and the micro-level analysis uses a periodic unit-cell (PUC) in the transverse plies. The constitutive assumption made for the macro-level analysis is an orthotropic linear thermo-elastic solid for the unidirectional plies with a thin isotropic viscoplastic layer between the longitudinal and transverse plies. In the PUC, the fibers are assumed linear elastic, while the matrix is modeled as an elastic–viscoplastic solid. Crack formation is assumed to occur in the matrix by the dilatation induced brittle failure mechanism for which the dilatation energy density criterion is used.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

Effective stiffness concept in bending modeling of laminates with damage in surface 90-layers

Simple approach based on Classical Laminate Theory (CLT) and effective stiffness of damaged layer is suggested for bending stiffness determination of laminate with intralaminar cracks in surface 90-layers and delaminations initiated from intralaminar cracks. The effective stiffness of a layer with damage is back-calculated comparing the in-plane stiffness of a symmetric reference cross-ply laminate with and without damage. The in-plane stiffness of the damaged reference cross-ply laminate was calculated in two ways: (1) using FEM model of representative volume element (RVE) and (2) using the analytical GLOB-LOC model. The obtained effective stiffness of a layer at varying crack density and delamination length was used to calculate the A, B and D matrices in the unsymmetrically damaged laminate. The applicability of the effective stiffness in CLT to solve bending problems was validated analyzing bending of the damaged laminate in 4-point bending test which was also simulated with 3-D FEM.     

Characterization and evolution of matrix and interface related damage in [0/90]S laminates under tension. Part I: Numerical predictions

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical method that assumes a Generalized Plane Strain (GPS) state. A 2D Boundary Element Method (BEM) model is generated to investigate the two types of damage progression in a [0/90]_S laminate: transverse cracks in the 90° lamina and delamination between both laminae. The model permits the contact between the surfaces of the cracks. The study is carried out in terms of the dependence of the Energy Release Rates (ERR) of the two types of crack on their respective lengths. A special emphasis is put on the mechanisms of the joining of the two aforementioned types of crack, including the study of the distribution of the stresses along the interface between the two plies when the transverse crack is approaching this interface.     

A numerical investigation into the size effect in the transverse crack tension test for mode II delamination

In experimental studies, a size effect has been measured for the fracture energy in the transverse crack tension test. This paper presents a numerical investigation into the cause of this size effect. A finite element model has been developed that includes delamination, friction and shear nonlinearity. After calibration of the model, the size effect was reproduced well. It is shown that shear nonlinearity and friction separately contribute to the measured size effect and that significant amplification of the size effect takes place because of their interaction. As a consequence of their interaction, the unstable crack growth that was observed for the thicker specimens in the experiments is also present in the model results.     

Tensile failure of laminates containing an embedded wrinkle; numerical and experimental study

The failure of a quasi-isotropic composite laminate containing an embedded out-of-plane fibre wrinkle defect was investigated under tension loading. Laboratory test specimens with controlled severity of fibre waviness were manufactured. Along with recording load–displacement data, high resolution camera images were taken at regular intervals which monitored the initiation and interaction of different damage mechanisms during test. Three-dimensional FE models were built following the geometry of actual test specimens. The information obtained from the tests was used to develop user material subroutines, implemented in Abaqus/Explicit as continuum damage and cohesive zone models for intra- and inter-ply failure respectively. The results of the simulations showed very good correlation with test observations in terms of failure load, location of damage initiation and interaction between different damage mechanisms for a range of waviness cases tested.     

Cryogenic delamination growth in woven glass/epoxy composite laminates under mixed-mode I/II fatigue loading

This paper investigates the fatigue delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode I/II conditions at cryogenic temperatures. Fatigue delamination tests were performed with the mixed-mode bending (MMB) test apparatus at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), in order to obtain the delamination growth rate as a function of the range of the energy release rate, and the dependence of the delamination growth behavior on the temperature and the mixed-mode ratio of mode I and mode II was examined. The energy release rate was evaluated using three-dimensional finite element analysis. The fractographic examinations by scanning electron microscopy (SEM) were also carried out to assess the mixed-mode fatigue delamination growth mechanisms in the woven GFRP laminates at cryogenic temperatures.     

Characterization of crack propagation in mode I delamination of multidirectional CFRP laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) invalidating the tests. In an earlier numerical study [9], we reported that this problem could be eliminated by choosing the appropriate bending stiffness of the beam arms.     

Effects of temperature on impact damages in CFRP composite laminates

In this paper, the effect of temperature variations (low and high temperatures) was studied experimentally on impact damage to CFRP laminates. The composite laminates used in this experiment were CF/EPOXY orthotropic laminated plates with lay-up [0₆/90₆]_s and [0₄/90₄]_s, and CF/PEEK orthotropic laminated plates with a lay-up of [0₆/90₆]_s. A steel ball launched by the air gun was used to generate the CFRP laminate impact damage. For impact-damaged specimens, nondestructive evaluation (NDE), such as a scanning acoustic microscopy (SAM) was performed on the delamination-damaged samples to characterize damage growth at different temperatures.

Therefore, this study was undertaken to experimentally determine the interrelations between impact energy and impact damage (i.e. the delamination area and matrix) of CFRP laminates (CF/EPOXY and CF/PEEK) subjected to foreign object damages (FOD) at low and high temperatures.     

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.     

Composite delamination modelling using a multi-layered solid element

This paper focuses on the latest development of a solid hexahedron element for composite delamination analysis. The 8-node solid is derived from a 20-node hexahedron. It is transformed into two physical independent 4-node shell elements according to the propagation of delamination process within the element.     

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.     

Health monitoring of cross-ply laminates: Modelling the correlation between damage evolution and electrical resistance change

In this work an analytical solution is developed to accurately predict the stiffness reduction in conductive cross-ply laminates, caused by matrix cracking in the transverse layers, as a function of the electrical resistance change of the laminate itself.To this end a closed form solution is initially developed with the aim to link the density of transverse cracks to the electric resistance of the cross-ply laminate. Such an expression is later used within a further model which allows the stiffness degradation associated to a given crack density to be estimated.The accuracy of the proposed model is verified by comparison with a bulk of FE analyses.     

Interpreting the stress ratio effect on delamination growth in composite laminates using the concept of fatigue fracture toughness

This paper provides a study on fatigue delamination growth in composite laminates using energy principles. Experimental data has been obtained from fatigue tests conducted on Double Cantilever Beam (DCB) specimens at various stress ratios. A concept of fatigue fracture toughness is proposed to interpret the stress ratio effect in crack growth. The fatigue fracture toughness is demonstrated to be interface configuration independent but significantly stress ratio dependent. An explanation for this phenomenon is given using SEM fractography. Fracture surface roughness is observed to be similar in different interfaces at the same stress ratio. But it is obviously more rough for high stress ratio in comparison with that for low stress ratio, causing the fatigue resistance increase. Therefore, the stress ratio effect in fatigue crack growth can be physically explained by a difference in resistance to crack growth.