Layerwise modeling of progressive damage in fiber-reinforced composite laminates

This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C ⁰ continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C ⁰ continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.     

Damage response of stitched cross-ply laminates under impact loadings

The impact response of stitched graphite/epoxy laminates was examined with the aim of evaluating the efficiency of stitching as a reinforcing mechanism able to improve the delamination resistance of laminates. The investigation, which focussed on two classes of cross-ply stacking sequences ([0₃/90₃]_s and [0/90]_3s), showed that the role of stitches in controlling damage progression of laminates and their capability to reduce the impact sensitivity of specimens are greatly dependent on the impact behaviour of base (unstitched) laminates. In [0₃/90₃]_s laminates, in particular, stitching is able to reduce damage area, on condition that the impact energy is higher than a threshold level and delaminations are sufficiently developed. In [0/90]_3s laminates, on the other hand, stress concentration regions generated by the stitching process appear to promote the initiation and propagation of fibre fractures, thereby inducing a decrease in the penetration resistance of the laminate.     

Modelling low-speed drop-weight impact on composite laminates

The impact responses of typical laminates are investigated numerically in this research. Delamination responses among plies and fibre and/or matrix damage responses within plies are simulated to understand the behaviours of laminates under different impaction conditions. Damage resistance of a laminate is highly dependent upon several factors including geometry, thickness, stiffness, mass, and impact energies (impact velocities), which are here considered by the finite element (FE) method. Three groups of composite laminates are simulated and the numerical results in general are in good agreement with corresponding experiments. Models containing different stacking sequences and impact energies are built to study their influence on impact responses and demonstrate that clustered (or nearly clustered) plies in the laminate can effectively reduce the degree of interface damage. Models containing different indenters and plate shapes are also built to systematically study their influence on the low-speed drop-weight behaviour of composite laminates. Suggestions are proposed for designing impact tests for particular purposes.     

Numerical modelling of perforation failure in fibre metal laminates subjected to low velocity impact loading

Low velocity impact tests have been conducted on fibre metal laminates (FMLs). The resulting load–displacement traces and deformation/failure modes were then used to validate a series of numerical models. Here, finite element (FE) models were developed to simulate the impact response of the 2/1, 3/2 and 4/3 FMLs, focussing, in particular on the perforation threshold and the associated failure mechanisms. The effect of target size, projectile size and striking location on the perforation behaviour of the FMLs was considered. Good agreement was obtained in terms of the load–displacement traces, as well as the deformation and failure modes.     

Irreversibly absorbed energy and damage in GFRP laminates impacted at low velocity

The scope of this paper was to establish a correlation between the damage occurring in a composite as a consequence of low-velocity impact and the energy dissipated during the impact phenomenon. To this aim, instrumented impact tests were carried out on glass fabric/epoxy laminates of three different thicknesses, using different energy levels. The irreversibly absorbed energy was obtained from the force–displacement curves provided by the impact machine. To assess damage progression as a function of impact energy, ply-by-ply delamination and fibre breakages revealed by destructive tests were measured. A previous model, based on energy balance considerations, was applied to interpret the experimental results, together with an original method of data reduction, allowing for the isolation of the maximum energy portion due to indentation and vibrational effects. From the results obtained, the contribution of fibre breakage and matrix damage to the irreversibly absorbed energy is comparable at low impact energies; with increasing initial energy levels, delamination becomes predominant in determining energy dissipation. However, the critical energy-release rate required to propagate delamination, as calculated from impact data, is considerably higher than the typical values deriving from Mode II delamination tests performed under laboratory conditions.     

Low velocity impact modeling in composite laminates capturing permanent indentation

This paper deals with impact damage and permanent indentation modeling. A numerical model has been elaborated in order to simulate the different impact damage types developing during low velocity/low energy impact. The three current damage types: matrix cracking, fiber failure and delamination, are simulated. Inter-laminar damage, i.e. interface delamination, is conventionally simulated using interface elements based on fracture mechanics. Intra-laminar damage, i.e. matrix cracks, is simulated using interface elements based on failure criterion. Fiber failure is simulated using degradation in the volume elements. The originality of this model is to simulate permanent indentation after impact with a “plastic-like” model introduced in the matrix cracking elements. This model type is based on experimental observations showing matrix cracking debris which block crack closure. Lastly, experimental validation is performed, which demonstrates the model’s satisfactory relevance in simulating impact damage. This acceptable match between experiment and modeling confirms the interest of the novel approach proposed in this paper to describe the physics behind permanent indentation.     

Predicting low velocity impact damage and Compression-After-Impact (CAI) behaviour of composite laminates

Low-velocity impact damage can drastically reduce the residual strength of a composite structure even when the damage is barely visible. The ability to computationally predict the extent of damage and compression-after-impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant time and cost penalties. A high-fidelity three-dimensional composite damage model, to predict both low-velocity impact damage and CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The intralaminar damage model component accounts for physically-based tensile and compressive failure mechanisms, of the fibres and matrix, when subjected to a three-dimensional stress state. Cohesive behaviour was employed to model the interlaminar failure between plies with a bi-linear traction–separation law for capturing damage onset and subsequent damage evolution. The virtual tests, set up in ABAQUS/Explicit, were executed in three steps, one to capture the impact damage, the second to stabilize the specimen by imposing new boundary conditions required for compression testing, and the third to predict the CAI strength. The observed intralaminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing without the need of model calibration which is often required with other damage models.     

Damage sequence in thin-ply composite laminates under out-of-plane loading

The study of the damage sequence in polymer-based composite laminates during an impact event is a difficult issue. The problem can be more complex when the plies are thin. In this paper, quasi-static indentation tests were conducted on thin-ply laminates to understand qualitatively the damage mechanisms and their sequence during low-velocity impact loading. TeXtreme® plain weave plies were used with two different thicknesses, 0.08 mm and 0.16 mm (referenced as ultra-thin-ply and thin-ply, respectively), and tested under different load levels. Load–displacement curves were analyzed and the extent of damage was inspected using optical microscopy and ultrasonic technique. The results showed that the damage onset occurs earlier in thin-ply laminates. The damage onset in thin-ply laminates is matrix cracking which induces delaminations, whereas for ultra-thin-ply laminates is due to delaminations which are induced by shear forces and small amount of matrix cracking. Moreover, the fiber breakage appears earlier in ultra-thin-ply laminates.     

Experimental investigation of impact on composite laminates with protective layers

This paper presents an experimental study of low energy impacts on composite plates covered with a protective layer. In service, composite materials are subjected to low energy impacts. Such impacts can generate damage in the material that results in significant reduction in material strength. In order to reduce the damage severity, one solution is to add a mechanical protection on composite structures. The protection layer is made up of a low density energy absorbent material (hollow spheres) of a certain thickness and a thin layer of composite laminate (Kevlar). Energy absorption ability of these protective layers can be deduced from the load/displacement impact curves. First, two configurations of protection are tested on an aluminium plate in order to identify their performance against impact, then the same are tested on composite plates. Test results from force–displacement curves and C-scan control are compared and discussed and finally a comparison of impact on composite plates with and without protection is made for different configurations.     

Progressive damage analysis and testing of composite laminates with fiber waves

In this work, the Progressive Damage Analysis (PDA) of composite laminates with waves was developed, experimentally validated, and discussed. PDA using Continuum Damage Modeling (CDM) and Discrete Damage Modeling (DDM) was conducted. In CDM, the material continuum constitutive properties are updated to incorporate the influence of progressive damage. In DDM, the actual damage is modeled, consistent with the progressive damage model analysis and observations. A commercial finite element code ABAQUS was used for all of the analysis with specialty user subroutines for the CDM and DDM. The laminate wave parameters (wavelength and amplitude) were determined from a statistical analysis of as-manufactured laminates from failed composite wind turbine blades. Laminates with waves under tension and compression loading were considered to create a benchmark set of tests for laminates and waves, and to provide an unambiguous comparison between CDM and DDM for this type of defect. Both methods (CDM and DDM) are compared and contrasted with experimental data. It is important to note that no assumed damage (such as a crack or other discontinuity) was necessary for the analysis. The failure mode and progressive damage is a consequence of the analysis. Correlations are found with each, and the pros and cons are evaluated and discussed. Better correlations were found with DDM, but accounting for nonlinear shear in the stress–strain response using CDM in the analysis provided numerical stability and the best experimental/analytical correlations.     

A numerical study on the impact resistance of composite shells using an energy based failure model

This paper presents a numerical study on the impact resistance of composite shells laminates using an energy based failure model. The damage model formulation is based on a methodology that combines stress based, continuum damage mechanics (CDM) and fracture mechanics approaches within a unified procedure by using a smeared cracking formulation. The damage model has been implemented as a user-defined material model in ABAQUS FE code within shell elements. Experimental results obtained from previous works were used to validate the damage model. Finite element models were developed in order to investigate the pressure and curvature effects on the impact response of laminated composite shells.     

Damage analysis of thin 3D-woven SiC/SiC composite under low velocity impact loading

Thin 3D-woven SiC_f/SiC samples were subjected to low velocity impact tests at room temperature. For this purpose, hemispherical impactors and circular supports of various diameters were used. The extent of damage was evaluated with the help of optical microscopy. Formation of micro-cracks initiating from the indented site is observed. The predominant internal damages (fiber bundle and matrix cracking) remain localized beneath the impactor. This is confirmed by thermography analysis and post-impact tensile tests. The diameter of the damaged zone can be related to the energy absorbed by the specimen during the impact event.     

Simulation of drop-weight impact and compression after impact tests on composite laminates

This paper presents finite element simulations of two standardized and sequential tests performed in polymer–matrix composite laminates reinforced by unidirectional fibers: the drop-weight impact test and the compression after impact test. These tests are performed on laboratory coupons, which are monolithic, flat, rectangular composite plates with conventional stacking sequences. The impact and the compression after impact tests are simulated using constitutive material models formulated in the context of continuum damage mechanics. The material models account for both ply failure mechanisms and delamination. Comparisons with experimental data are performed in order to assess the accuracy of the predictions.     

Damage detection of surface cracks in composite laminates using modal analysis and strain energy method

This paper presents an approach to detect surface cracks in various composite laminates. Carbon/epoxy composite AS4/PEEK was used to fabricate laminated plates, [0]₁₆, [90]₁₆, [(0/90)₄]_S and [±45/0/90]_2S. Surface crack damage was created on one side of the plate using a laser cutting machine. Modal analysis was performed to obtain the mode shapes from both experimental and finite element analysis results. The mode shapes were then used to calculate strain energy using the differential quadrature method (DQM). Consequently, the strain energies of laminated plates before and after damaged were used to define a damage index which successfully identified the surface crack location.     

Modelling damage evolution in composite laminates subjected to low velocity impact

In this paper, the impact damage of composite laminates in the form of intra- and inter-laminar cracking was modelled using stress-based criteria for damage initiation, and fracture mechanics techniques to capture its evolution. The nonlinear shear behaviour of the composite was described by the Soutis shear stress–strain semi-empirical formula. The finite element (FE) method was employed to simulate the behaviour of the composite under low velocity impact. Interface cohesive elements were inserted between plies with appropriate mixed-mode damage laws to model delamination. The damage model was implemented in the FE code (Abaqus/Explicit) by a user-defined material subroutine (VUMAT). Numerical results in general gave a good agreement when compared to experimentally obtained curves of impact force and absorbed energy versus time. The various damage mechanisms introduced during the impact event were observed by non-destructive technique (NDT) X-ray radiography and were successfully captured numerically by the proposed damage evolution model.     

Damage mechanisms and failure modes in cross-ply laminates under monotonic tensile loading: The influence of fiber sizing

In this study, the effect of fiber-matrix interphase on the damage modes and failure mechanisms in (0, 90₃), cross-ply graphite-toughened epoxy laminates is investigated. Two material systems (designated as 810 A and 810 O) with the same fiber and same matrix, but with different fiber sizings, were used to study the effect of the interphase. The system designated as 810 A contained an unreacted Bisphenol-A (epoxy) sizing, while a thermoplastic polyvinylpyrrolidone (PVP) sizing was used in the 810 O system. Damage accumulation in the cross-ply laminates under monotonic tensile loading was monitored using edge replication, x-ray radiography, acoustic emission, optical and scanning electron microscopy. Results indicate that the fiber-matrix bond strength is lower in the 810 O system compared to the 810 A system. Transverse matrix cracking initiates at a significantly lower stress level in the 810 O laminate. The 810 O laminates also exhibit longitudinal splitting, while the stronger bonding suppress this damage mode in the 810 A laminates. Numerous local delamination occur on the 0/90 interface at the intersection of 0 and 90 degree ply cracks, in the 810 O laminates. These are absent in the 810 A laminates. The failure modes are also different in the two material systems used in this study. The 810 A laminate exhibits a brittle failure, controlled by the local stress concentration effects near broken fibers. In the 810 O laminates, the presence of longitudinal splits result in the reduction of stress concentration effects near fibe fractures. This results in a global strain controlled failure in the 810 O system. It is concluded that the presence of different fiber sizings result in different damage modes and failure mechanisms in the cross-ply laminates used in this study.Research Associate, Research Assistant, Alexander Giacco Professor and Professor respectively.     

An efficient approach for damage quantification in quasi-isotropic composite laminates under low speed impact

An efficient method to determine the type, size, and location of damage in impacted quasi-isotropic composite laminates is presented. The method uses the peak force during impact obtained from energy balance, a Hertzian contact formulation and energy minimization to determine the complete state of stress in the laminate. Comparisons of the analytical predictions to limiting cases of infinite thickness plates or to detailed finite element models for finite thickness plates shows the predicted stresses to be in excellent agreement with other methods. The stresses are then modified to account for the creation of damage and used in out-of-plane and in-plane failure criteria to predict delamination sizes, matrix failure and fiber failure. The predicted damage states are then compared to published test results for two different materials, eight different stacking sequences, and a range of impact energies from 5 to 50 J. Very good agreement of the predicted damage sizes with the experimentally measured values is observed for a wide range of energy levels but, for two laminates, the discrepancies are significant. Possible improvements of the method are discussed briefly. This method is very promising and can be used in preliminary design allowing extensive trade studies and, eventually, layup optimization. It can also form the beginning of an efficient methodology to predict compression after impact strength of quasi-isotropic laminates.     

A progressive failure model for mesh-size-independent FE analysis of composite laminates subject to low-velocity impact damage

An original, ply-level, computationally efficient, three-dimensional (3D) composite damage model is presented in this paper, which is applicable to predicting the low velocity impact response of unidirectional (UD) PMC laminates. The proposed model is implemented into the Finite Element (FE) code ABAQUS/Explicit for one-integration point solid elements and validated against low velocity impact experimental results.     

Low-velocity impact of pressurised pipelines

Experimental tests are reported on steel pipelines which have been struck by a relatively large rigid wedge-shaped mass travelling up to 10.4 m/s. A pipeline is supported across a span, is fully clamped at both ends and is struck at the mid-span and at the one-quarter span positions. Most of the pipelines are pressurised with a nitrogen gas. The initial impact energy produces large inelastic ductile deformations of the pipeline and, in some cases, failure.     

The finite element analysis of composite laminates and shell structures subjected to low velocity impact

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection. The impact response of the structure is proportional to the impactor velocity.