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.     

Numerical investigation on the failure phenomena of stiffened composite panels in post-buckling regime with discrete damages

The aim of this work is to investigate the final failure response of damaged composite stiffened panels in post buckling regime under compressive load, by using progressive failure analysis (PFA) methodology. The selected panel is characterized by T shaped stringers and it is representative of the upper skin panel, toward the wing tip, of the wing box of a typical regional aircraft. PFA methodology has been applied in order to predict in addition to the initiation of the local failure also its propagation up to the final collapse of the panel, in presence of local damage (barely visible impact damage, BVID) and in post-buckling regime. For this purpose, discrete damages have been considered in the skin of the panel. According to the indications contained in many guidelines finalized to the preliminary design of composite structures, a simplified design model of BVID has been considered in this work, in particular a hole 1/4 in. in diameter has been used to simulate this damage. The collapse load of the panel has been evaluated considering different locations of a single damage and also considering multi-damage maps (the latter are more representative of a real damage scenario). The results of PFA presented in this work illustrate the combined effect of the reduction of the panel stiffness and of the damage propagation, and the sensitivity of the buckling onset and of the residual strength of the panel with respect to different damage locations and damage density.     

Simulation of fatigue failure in composite axial compressor blades

Centrifugal forces are generated by a spinning impeller, of magnitudes that create large stresses. Aerodynamic forces are also imparted on an impeller blade, which varies with time and position. These two forces play different roles during compressor events. Damage accumulated from these events results in the fatigue failure of impeller material and structure. Therefore, it is important to design an impeller against dynamic and fatigue failure. The finite element method has been used in the study of impeller fracture mechanics and is regarded as an important tool in the design and analysis of material and structures.     

Fatigue life prediction of composite laminates by FEA simulation method

This paper is to simulate the fatigue damage evolution in composite laminates and predict fatigue life of the laminates with different lay-up sequences on the basis of the fatigue characteristics of longitudinal, transverse and in-plane shear directions by finite element analysis (FEA) method. In FEA model, considering the scatter of the material’s properties, each element was assigned with different material’s properties. The stress analysis was carried out in MSC Patran/Nastran, and a modified Hashin’s failure criterion was applied to predict the failure of the elements. A new stiffness degradation model was proposed and applied in the simulation and then a strength degradation model was deduced, which is coupled with the presented stiffness degradation model. The reduced or discounted elastic constants were determined based on the failure mechanism of the laminates and the restrictive conditions of orthotropic property. The fatigue behavior and fatigue life of six kinds of E-glass/epoxy composite laminates with different lay-up sequences were experimentally studied, and the S–N curves and stiffness degradation models in longitudinal, transverse and in-plane shear direction were obtained. These fatigue data were adopted in the simulation to simulate fatigue behavior and estimate life of the laminates. The simulation results, including the fatigue life predicted and the residual stiffness, were coincident with the experimental results well except for the quasi-isotropic laminate for the lack of consideration of the out-of-plane fatigue character in the simulation.     

Progressive crushing of fiber-reinforced composite structural components of a Formula One racing car

The present paper describes an experimental and numerical investigation on energy absorbers for Formula One side impact and steering column impact. The crash tests are performed measuring the load-shortening diagram and the energy absorbed by the structure. A finite element model is then developed using the non-linear, explicit dynamic code LS-DYNA. To set up the numerical model, tubes crushing testing are conducted to determine the material failure modes and to characterise them with LS-DYNA. The results presented in this study show that the composite structural components of the investigated Formula One racing car possess high value of specific absorbed energy and crash load efficiency around 1.1. The finite element simulations accurately predict the overall shape, magnitude and pulse duration in all the types of impact as well as the deformation and failure of the structures. Comparing the numerical data of the specific absorbed energy to the experimental results, the differences are around 10%.     

Prediction of the postbuckling response of composite airframe panels including ply failure

Future design scenarios aim to allow buckling in composite airframe panels. Reliable simulation procedures should be able to capture the postbuckling elastic as well as the inelastic response associated with damage. Damage in composite laminates in terms of ply failure may primarily occur as fiber fracture or matrix cracking. This paper presents a model which is able to capture both geometrical and material nonlinearity. It bases on the finite element formulation of a layered, iso-parametric, quadrilateral shell element which allows for an arbitrary reference surface as well as an arbitrary stacking sequence. Geometrical nonlinearity is accounted for by utilizing Green strains and second Piola–Kirchhoff stresses. Material nonlinearity is considered via a layerwise ideally brittle damage model. The model is applied to a buckling test of a stringer-stiffened composite airframe panel. The numerical results are compared with an experiment proving the applicability of the proposed concept.     

A meso-scale finite element model for simulating free-edge effect in carbon/epoxy textile composite

Textile composites are well known for their excellent through thickness properties and impact resistance. In this study, a representative unit cell model of a triaxial braided composite is developed based on the composite fiber volume ratio, specimen thickness and microscopic image analysis. A meso-scale finite element (FE) mesh is generated based on the detailed unit cell dimensions and fiber bundle geometry parameters. The fiber bundles are modeled as unidirectional fiber reinforced composites. A micromechanical finite element model was developed to predict the elastic and strength material properties of each unidirectional composite by imposing correct boundary conditions that can simulate the actual deformation within the braided composite. These details are then applied in the meso-mechanical finite element model for a 0°/+60°/−60° triaxially braided T700s/E862 carbon/epoxy composite. Model correlations are conducted by comparing numerical predicted and experimental measured axial tension and transverse tension response of a straight-sided, single-layer (one ply thick) coupon. By applying a periodic boundary condition in the loading direction, the meso model captures the local damage initiation and global failure behavior, as well as the periodic free-edge warping effect. The failure mechanisms are studied using the field damage initiation contours and local stress history. The influence of free-edge effect on the failure behaviors is investigated. The numerical study results reveal that this meso model is capable of predicting free-edge effect and allows identification of its impact on the composite response.     

Finite element formulation of a heat transfer problem for an axisymmetric composite structure

By using weighted residual method, the finite element formulation of a heat transfer problem for axisymmetric composite structures is established from the heat transfer differential equations expressed by heat fluid density. A few examples are included to indicate that the heat transfer anisotropy has an important effect on temperature field and to prove the accuracy and effectiveness of the finite element formulation.Aknowledgement Special thanks are due to the National Natural Science Foundation of China (No: 10272037) for supporting the present work.     

A computational model for failure analysis of fibre reinforced concrete with discrete treatment of fibres

Failure patterns and mechanical behaviour of high-performance fibre reinforced cementitious composites depend on the distribution of fibres within a specimen. In this contribution, we propose a novel computational approach to describe failure processes in fibre reinforced concrete. A discrete treatment of fibres enables us to study the influence of various fibre distributions on the mechanical properties of the material. To ensure numerical efficiency, fibres are not explicitly discretized but they are modelled by applying discrete forces to a background mesh. The background mesh represents the matrix while the discrete forces represent the interaction between fibres and matrix. These forces are assumed to be equal to fibre pull-out forces. With this approach experimental data or micro mechanical models, including detailed information about the fibre-matrix interface, can be directly incorporated into the model.     

Mixed-mode cohesive-zone models for fracture of an adhesively bonded polymer-matrix composite

As a direct extension of previous mode-I work on the adhesion of composite joints, this paper uses a cohesive-zone approach to model the mixed-mode fracture of adhesive joints made from a polymer-matrix composite. Mode-II cohesive-zone parameters were obtained using sandwich end-notch flexure specimens. These parameters were used directly with the previously determined mode-I parameters to predict the fracture and deformation of mixed-mode geometries. It was shown that numerical simulations provided quantitative predictions for these geometries, including predictions for both the strengths of the joints and for the failure mechanisms. In conjunction with the earlier work, these results demonstrate the use of cohesive-zone approaches for the design of adhesively bonded composite joints, and indicate approaches for determining the relevant material properties to describe mixed-mode fracture.     

Delamination prediction of composite filament wound vessel with metal liner under low velocity impact

Based on low velocity impact kinetic theory and corresponding damage criterion for the composite laminated structures, a 3-D incompatible, geometrically nonlinear finite element method was employed to investigate the impact mechanical behavior of the composite filament cylindrical vessel with metal liner with and without internal pressure and predict their damage distributions during and after impact. A modified Hertzian contact law was used to calculate the contact force between the impact body and impacted cylindrical vessel and a direct integral scheme-Newmark method was applied in time domain during impact analysis process. The damage styles and damage distributions of a typical vessel under different impact velocities are presented. From the numerical results, it is clear that the impact damage extent for composite filament wound vessel with internal pressure is more sever than that without internal pressure under low velocity impact case with same kinetic energy.     

A new damage model for composite laminates

Aircraft composite structures must have high stiffness and strength with low weight, which can guarantee the increase of the pay-load for airplanes without losing airworthiness. However, the mechanical behavior of composite laminates is very complex due the inherent anisotropy and heterogeneity. Many researchers have developed different failure progressive analyses and damage models in order to predict the complex failure mechanisms. This work presents a damage model and progressive failure analysis that requires simple experimental tests and that achieves good accuracy. Firstly, the paper explains damage initiation and propagation criteria and a procedure to identify the material parameters. In the second stage, the model was implemented as a UMAT (User Material Subroutine), which is linked to finite element software, ABAQUS™, in order to predict the composite structures behavior. Afterwards, some case studies, mainly off-axis coupons under tensile or compression loads, with different types of stacking sequence were analyzed using the proposed material model. Finally, the computational results were compared to the experimental results, verifying the capability of the damage model in order to predict the composite structure behavior.     

The effect of composite damage on fatigue life of the high pressure vessel for natural gas vehicles

In order to examine how the damages such as scratches, cuts and gouges on the composite materials have effects on the fatigue life of NGV vessels, several experiments on real vessels were conducted and finite element analyses were applied. The flaw depths of COPV used in the experiments were 1.5 mm, 2.0 mm, 3.0 mm, and 4.0 mm, while the flaw lengths were 50 mm, 100 mm, and 200 mm. A flaw tolerance test defined by ANSI/IAS NGV2-2000 was performed on 12 vessels using a combination of these flaw depths and lengths. In the finite element analyses, stress analyses were performed using a commercial FEM program after the 3-D modelling of liner, hoop and helical layers by using MSC.PATRAN™. The result of the tests and analyses demonstrated that the effect of the flaw damages on the fatigue life of high pressure vessel for natural gas vehicles increases when the flaw depth is more than 3.0 mm and the flaw length is more than 100 mm.     

The analysis of skin-to-stiffener debonding in composite aerospace structures

A comprehensive finite element (FE) analytical tool to predict the effect of defects and damage in composite structures was developed for rapid and accurate damage assessment. The structures under consideration were curved, T-stiffened, multi-rib, composite panels representative of those widely used in aerospace primary structures. The damage assessment focussed on skin-to-stiffener debonding, a common defect that can critically reduce the performance of composite structures with integral or secondary bonded stiffeners. The analytical tool was validated using experimental data obtained from the structural test of a large stiffened panel that contained an artificial skin-to-stiffener debond. Excellent agreement between FE analysis and test results was obtained. The onset of crack growth predictions also compared well with the test observation. Since the general damage tolerance philosophy in composite structures follows the “no-growth” principle, the critical parameters were established based the onset of crack growth determined using fracture mechanics calculations. Parametric studies were conducted using the analytical tool in order to understand the structural behaviour in the postbuckling range and to determine the critical parameters. Parameters considered included debond size, debond location, debond type, multiple debonds and laminate lay-up.     

Improved design methods for scarf repairs to highly strained composite aircraft structure

This paper presents an analytical method to optimise the profile of the scarf joint between dissimilar modulus adherends so that adhesive stresses are approximately uniform along the joint. The optimised scarf repair is expected to enhance joint strength and reduce the amount of material removal. Finite element analyses have been performed to both validate the optimal solution and to evaluate the use of low stiffness patch to repair carbon epoxy composites. In particular, the influence of patch lay-up on adhesive stresses has been investigated.     

Quasi-static crushing behaviour of hybrid and non-hybrid natural fibre composite solid cones

A comprehensive experimental investigation of the quasi-static axial crushing of hybrid and non-hybrid natural fibre/polyester composite solid cones between flat platens has been carried out. The composite solid cones were fabricated from two types of natural fibres namely oil palm fibre and coir fibre and different vertex angles varied from 0° to 60°. Typical load-deformation histories are presented and discussed. Crashworthiness parameters such as load carrying capacity; energy absorption capability and failure mechanism have been discussed. The results presented in this study will help us to understand the behaviour and characteristics of natural fibre composite as a filler material.     

Numerical method for optimizing design variables of carbon-fiber-reinforced epoxy composite coil springs

To successfully reduce a vehicle's weight by replacing steel with composite materials, it is essential to optimize the material parameters and design variables of the structure. In this study, we investigated numerical and experimental methods for determining the ply angles and wire diameters of carbon fiber/epoxy composite coil springs to attain a spring rate equal to that of an equivalent steel component. First, the shear modulus ratio for two materials was calculated as a function of the ply angles and compared with the experimental results. Then, by using the equation of the spring rate with respect to the shear modulus and design variables, normalized spring rates were obtained for specific ply angles and wire diameters. Finally, a finite element model for an optimal composite coil spring was constructed and analyzed to obtain the static spring rate, which was then compared with the experimental results.     

Fiber direction and stacking sequence design for bicycle frame made of carbon/epoxy composite laminate

According to the maximum stress theory and the results of strength-to-stress ratios, the fiber direction and stacking sequence design for the bicycle frame made of the carbon/epoxy composite laminates have been discussed in this paper. Three testing methods for the bicycle frame, i.e. torsional, frontal, and vertical loadings, are adopted in the analysis. From the finite element results, the stacking sequences [0/90/90/0]_s and [0/90/45/−45]_s are the good designs for the composite bicycle frames. On the contrary, the uni-directional laminates, i.e. [0/0/0/0]_s, [90/90/90/90]_s, [45/45/45/45]_s and [−45/−45/−45/−45]_s, are the bad designs. In addition, weak regions of failure occur at the fillets and connections of the frame, i.e. the stress concentration regions. All weak points occur at the inner or outer layer of the laminated composite tube. The 0°-ply and 90°-ply located on the inner and outer layer of the tube can effectively resist the higher stress at its location.     

Triple-scale failure estimation for a composite-reinforced structure based on integrated modeling approaches. Part 1: Microscopic scale analysis

The structural reliability of a composite component locally reinforced with a fibrous metal matrix composite is essentially affected by the micro-scale failures. The micro-scale failures such as fiber fracture or matrix damage are directly governed by the internal stress states such as mismatch thermal stress. A proper computational method is needed in order to obtain micro-scale stress data for arbitrary thermo-mechanical loads. In this work a computational scheme of microscale failure analysis is presented for a composite component. Micromechanics-based triple-scale FEM was developed using composite laminate element. The considered composite component was a plasma-facing component of fusion reactors consisting of a tungsten block and a composite cooling tube. The micro-scale stress and strain data were estimated for a fusion-relevant heat flux load. Ductile damage of the matrix was estimated by means of a damage indicator. It was shown that the risk of micro-scale composite failure was bounded below an acceptable level.     

Influence of post-buckling behaviour of composite stiffened panels on the damage criticality

In stiffened panels with defects, such as skin delaminations or stringer debonding, buckling may occur prior to the designed critical buckling load. Depending on the damage parameters, such defects may also affect the post-buckling behaviour and consequently the structural performance. An automated finite element (FE) modelling tool has been developed to predict the post-buckling behaviour of panels. It was coupled with a linear elastic fracture mechanics approach to determine damage criticality, based on the “no-growth” principle. The structural behaviour in the post-buckling range and its interaction with the damage parameters were analysed. Local buckling occurred as a result of localised stiffness reduction in the damage region. Global buckling occurred when sufficient in-plane strain was reached. The onset of local buckling was an important factor on stringer debonding criticality as the local buckling mode had an effect on the corresponding global buckling. In comparison, the onset of local buckling for the skin delamination was lower due to the thin sub-laminate separation. However, it was less influential on the damage criticality because the local buckling slowly dissipated in the far post-buckling range. It was found that the initiation of local buckling, and the interaction between the local and global buckling mode, would determine the damage criticality.