Numerical study of the structural behaviour of impacted composite laminates subjected to compression load

Composite materials allow all the benefits which a high specific strength involves, in a design process their application involves many critical problems. Currently, these problems, such as environmental conditions, notch sensitivity, damaging under low velocity impacts, are taken into account by means of the application of conservative design safety factors regarding the ultimate tensile strength. In order to try to reduce these safety factors, this work aimed to study and to understand the impact damage growing mechanisms due to compression loads. To this purpose, compression tests have been experimentally performed on composite panels, which have been previously subjected to low velocity impact phenomena, considering impact energies of 6 J, 10 J and 13 J respectively. Moreover, numerical model able to simulate Low Velocity Impacts (LVI) and Compression After Impacts (CAI) onto CFRP panels is proposed. A single explicit finite element analysis has been carried out by using the Abaqus^® finite element code; the need to build a numerical model, which allows simulation in only one analysis both LVI and CAI steps, depends on the difficulty to import the impact damage distribution into a separate compression analysis. In fact, in only one analysis the compression step can occur directly onto the impacted plate, which allows to consider the effective impact damage distribution as the starting configuration for quasi static analysis under operating loads.     

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.     

Analytical and experimental studies on the low-velocity impact response and damage of composite laminates under in-plane loads with structural damping effects

In this paper, low-velocity impact response and damage of composite laminates under in-plane loads are analytically and experimentally investigated. The authors recently proposed a modified displacement field of plate theory, considering the effect of initially loaded in-plane strain, and used a finite element program to analyze the structural behavior of the composite laminate. In this study, the program is upgraded to account for the structural damping effect of the laminate. A pendulum type impact test system and an in-plane loading fixture are constructed for the experimental study. The analytical and experimental impact behaviors are compared at different impact energy levels for cases with an initial in-plane tensile load and a compressive load, as well as cases without the initial in-plane load. The results show good correspondence between the analytical and experimental impact force histories. The effect of the initial in-plane load reduces for higher impact energies. The numerical estimation of the damaged area is in good agreement with the results from C-scanning experiments.     

The low velocity impact response of foam-based sandwich panels

This paper describes the results of a combined experimental/numerical study to investigate the perforation resistance of sandwich structures. The impact response of plain foam samples and their associated sandwich panels was characterised by determining the energy required to perforate the panels. The dynamic response of the panels was predicted using the finite element analysis package ABAQUS/Explicit. The experimental arrangement, as well as the FE model were also used to investigate, for the first time, the effect of oblique loading on sandwich structures and also to study the impact response of sandwich panels on an aqueous support.     

A damage evolution study of E-glass/epoxy composite under low velocity impact

To predict the behavior of composites in case of low velocity impact, various material models are available in the literature. Damage evolves exponentially or linearly with strain in these models. These models are using either characteristic length ‘L_c’ or material exponent parameters, ’m’ to solve the problem of strain localization. A method to relate these parameter to each other is suggested here. The choice of material exponent, ‘m’ for a particular mesh size is also discussed. Low velocity impact simulations for E-glass/epoxy composite are performed using continuum damage mechanics based material model and compared with the experiments. The damage observed through the light projected area on the laminate, contact forces and displacement plots with respect to time were studied and compared with finite element analysis results to demonstrate the effectiveness of the model. Digital Image Correlation (DIC) technique is used for experimentation to obtain displacement on the surface of the plate.     

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.     

Failure analysis of fiber-reinforced composite laminates subjected to biaxial loads

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are carried out to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.     

Adaptive multi-scale modeling of high velocity impact on composite panels

A computationally efficient adaptive multi-scale methodology for modeling composites under high rates of loading is proposed. The physically based model relies on micromechanical properties of the constituents only. The adaptive algorithm switches between two different constitutive laws. Initially, the material response is calculated based on effective linear-elastic, orthotropic material properties at the ply scale which are calculated using the rule of mixtures. A modified Hashin–Rotem criterion is then used to identify the switch to a more accurate micromechanical analysis based on the generalized method of cells (GMC). The methodology is verified by simulating tensile tests on laminates with different stacking sequences. Finally the model validated against experimental data for high-velocity impact on quasi-isotropic composite targets taken from the literature in order to illustrate the efficiency and accuracy of the proposed methodology.     

Multiscale analysis of damage progression in newly designed UACS laminates

In this paper, the damage progression in laminates fabricated by unidirectionally arrayed chopped strands (UACS) with newly designed slit distribution patterns under tension is simulated based on a multiscale analysis. The multiscale analysis includes a homogenization analysis and a multiscale damage progression analysis of a microscopic region and a macroscopic region. The elastic constants of the laminas used in the macroscopic region are calculated by the homogenization analysis. The silt distribution patterns are exactly modeled in the microscopic region. Cohesive interface element and maximum stress criterion are employed for the simulation of the progression of delamination and other failure modes in the laminates, respectively.     

Experimental and numerical investigations of low velocity impact on functionally graded circular plates

This paper addresses low-velocity impact behaviour of functionally graded clamped circular plates. An experimental work was carried out to investigate the impact behaviour of FG circular plates which is composed of ceramic (SiC) and metal (Al) phases varying through the plate thickness by using a drop-weight impact test system. The influence of the compositional gradient exponent and impactor velocity on the contact forces and absorbed energies was concentrated on the tests. The explicit finite element method, in which a volume fraction based elastic–plastic model (the TTO model) was implemented for the functionally graded materials, was used to simulate their drop-weight impact tests. Effective material properties at any point inside FGM plates were determined using Mori–Tanaka scheme. The experimental and numerical results indicated that the compositional gradient exponent and impactor velocity more effective on the elasto-plastic response of the FG circular plates to a low-velocity impact loading. The comparison at the theoretical and experimental results showed that the use of the TTO model in modelling the elasto-plastic behaviour of FG circular plates results in increasing deviations between the numerical and experimental contact forces for ceramic-rich compositions whereas it becomes more successful for metal-rich compositions.     

A quasi-static indentation test to elucidate the sequence of damage events in low velocity impacts on composite laminates

Any attempt to achieve composite laminates with improved damage tolerance to low velocity impacts must depart from the understanding of the sequence of damage mechanisms taking place. To this purpose, a series of quasi-static indentation experiments was conducted on AS4D/TC350 carbon/epoxy specimens. The induced damage at different indenter displacements was characterized using electron microscopy and C-scan, while the residual indentation profiles were captured with a 3D surface roughness machine. The indentation depth was shown to have relaxed after the test, reaching a steady value after 14 days. For the conditions explored, the relaxation was not dependent on the damage extent. The results showed that matrix cracking is in fact the crucial damage mechanism as it is responsible for the first sudden loss of load capacity and triggers the progressive growth of delaminations.     

Behaviour of multiple composite plates subjected to ballistic impact

An experimental and numerical investigation has been carried out to study the behavior of single and multiple laminated panels subjected to ballistic impact. A pressurized air gun is used to shoot the impactor, which can attain sufficient velocity to penetrate all the laminates in a multiple laminated panel. The incidental and residual velocity of the impactor is measured to estimate the energy absorption in the impact process. The commercially available code ABAQUS has been used for the numerical simulation where the impactor has been modeled as a rigid body and the laminates have been modeled with a simple shell element. A user material model based on a continuum damage mechanics concept for failure mechanism of laminated composites has been implemented. Experimental tests showed that the numerical model could satisfactorily predict the energy absorption. Most interestingly, it has clearly demonstrated a feasible phenomenon behind counterintuitive experimental results for the multiple laminated panels.     

Transverse impact damage and energy absorption of 3-D multi-structured knitted composite

Knitted composites have higher failure deformation and energy absorption capacity under impact than other textile structural composites because of the yarn loop structures in knitted performs. Here we report the transverse impact behavior of a new kind of 3-D multi-structured knitted composite both in experimental and finite element simulation. The knitted composite is composed of two knitted fabrics: biaxial warp knitted fabric and interlock knitted fabric. The transverse impact behaviors of the 3-D knitted composite were tested with a modified split Hopkinson pressure bar (SHPB) apparatus. The load–displacement curves and damage morphologies were obtained to analyze the energy absorptions and impact damage mechanisms of the composite under different impact velocities. A unit-cell model based on the microstructure of the 3-D knitted composite was established to determine the composite deformation and damage when the composite impacted by a hemisphere-ended steel rod. Incorporated with the unit-cell model, a elasto-plastic constitute equation of the 3-D knitted composite and the critical damage area (CDA) failure theory of composites have been implemented as a vectorized user defined material law (VUMAT) for ABAQUS/Explicit. The load–displacement curves, impact deformations and damages obtained from FEM are compared with those in experimental. The good agreements of the comparisons prove the validity of the unit-cell model and user-defined subroutine VUMAT. This manifests the applicability of the VUMAT to characterization and design of the 3-D multi-structured knitted composite structures under other impulsive loading conditions.     

Predicting evolution of ply cracks in composite laminates subjected to biaxial loading

An energy-based model is developed to predict the evolution of sub-critical matrix crack density in symmetric multidirectional composite laminates for the case of multiaxial loading. A finite element-based numerical scheme is also developed to evaluate the critical strain energy release rate, G_Ic, associated with matrix micro-cracking, a parameter that previously required fitting with experimental data. Furthermore, the prediction scheme is improved to account for the statistical variation of G_Ic within the material volume by using a two-parameter Weibull distribution. The variation of G_Ic with increasing crack density is also accounted for based on reported experimental evidence. The simulated results for carbon/epoxy and glass/epoxy cross-ply laminates demonstrate the ability of the improved model to predict the evolution of multidirectional ply cracking. By integrating this damage evolution model with the synergistic damage mechanics approach for stiffness degradation, the stress-strain response of the studied laminates is predicted. Finally, biaxial stress envelopes for ply crack initiation and pre-determined stiffness degradation levels are predicted to serve as representative examples of stiffness-based design and failure criterion.     

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.     

Investigation of the response to low velocity impact and quasi-static indentation loading of particle-toughened carbon-fibre composite materials

This work investigates damage caused by low velocity impact and quasi-static indentation loading in four different particle-toughened composite systems, and one untoughened system. For impact tests, a range of energies were used between 25 and 50 J. For QSI, coupons were interrupted at increasing loading point displacement levels from 2 to 5 mm to allow for monitoring of damage initiation and propagation. In both loading cases, non-destructive inspection techniques were used, consisting of ultrasonic C-scan and X-ray micro-focus computed tomography. These techniques are complemented with instrumentation to capture force–displacement data, whereby load-drops are associated with observed damage modes. Key results from this work highlight particular issues regarding strain-rate sensitivity of delamination development and an earlier onset of fibre fracture associated with particle-toughened systems. These issues, in addition to observations on the role of micro-scale events on damage morphology, are discussed with a focus on material development and material testing practices.     

Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach

The subject of this paper is numerical prediction of bird strike induced damage in real aeronautical structures using highly detailed finite element models and modern numerical approaches. Due to the complexity of today’s aeronautical structures, numerical damage prediction methods have to be able to take into account various failure and degradation models of different materials. A continuum damage mechanics approach has been employed to simulate failure initiation and damage evolution in unidirectional composite laminates. Hashin’s failure initiation criteria have been employed in order to be able to distinct between four ply failure modes. The problem of soft body impacts has been tackled by applying the Coupled Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. This improvement in impactor deformation modelling resulted in a more realistic behaviour of bird material during impact. Numerical geometrical and material nonlinear transient dynamic analyses have been performed using Abaqus/Explicit. The main focus of the work presented in this paper is the application of the damage prediction procedure in damage assessment of bird impact on a typical large airliner inboard flap structure. Due to the high cost of gas-gun testing of aircraft components, experimental testing on the real flap structure could not have been performed. In order to evaluate the accuracy of the presented method, the bird and composite damage model have been validated against experimental data available in the literature.     

Two-dimensional strain-based interactive failure theory for multidirectional composite laminates

A 2-D strain-based interactive failure theory is developed to predict the final failure of composite laminates subjected to multi-axial in-plane loading. The stiffness degradation of a laminate during loading is examined based on the individual failure modes of the maximum strain failure theory, and a piecewise linear incremental approach is employed to describe the nonlinear mechanical behavior of the laminate. In addition, an out-of-plane failure mode normal to the laminate is also investigated to more accurately predict the failure of multidirectional laminates. The theoretical results of the failure model presented are compared with the experimental data provided by the World-Wide Failure Exercise, and the accuracy of the model’s predictive capabilities is investigated.     

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.