Numerical stress and crack initiation analysis of the compressor blades after foreign object damage subjected to high-cycle fatigue

This paper presents results of the complex stress and crack initiation analysis of the PZL-10 W turbo-engine compressor blade subjected to high cycle fatigue (HCF). A nonlinear finite element method was utilized to determine the stress state of the blade during the first mode of transverse vibration. In this analysis, the numerical models without defects and also with V-notches were defined. The quality of the numerical solution was checked by the convergence analysis. Obtained results were next used as an input data into crack initiation (ε–N) analyzes performed for the load time history equivalent to one cycle of the transverse vibration. In the fatigue analysis the different methods such as: Neuber elastic–plastic strain correction, linear damage summation and Palmgreen–Miner rule were utilized. As a result of ε–N analysis, the number of load cycles to the first fatigue crack appearing in the compressor blades was obtained. Moreover, the influence of the blade vibration amplitude on the number of cycles to the crack initiation was analyzed. Values of the fatigue properties of the blade material according to Baumel–Seeger and Muralidharan methods were calculated. The influence of both the notch radius and values of the UTS of the blade material on the fatigue behavior of the structure was also considered. In the last part of work, the finite element results were compared with the results of an experimental vibration HCF tests performed for the compressor blades.     

Characterization of fatigue damage in long fiber epoxy composite laminates

A study of damage characterization of a GFRC laminate is presented here. Forty fatigue tests were executed and S–N curves traced. Two parameters were chosen to monitor damage evolution during each test: stiffness and dissipated energy per cycle. Moreover, the presence of three zones in graphs of processed data can be observed and it is evident that the most important structural transformations take place only in the very final part of life. Adopting a continuum mechanics approach, the degradation through the whole life in composite is evaluated and it is shown that the two parameters are strictly related to damage state of composite material. A method for predicting the remaining life in a GFRC is here proposed.     

A micro-mechanics damage approach for fatigue of composite materials

A new model for fatigue damage evolution of polymer matrix composites (PMC) is presented. The model is based on a combination of an orthotropic damage model and an isotropic fatigue evolution model. The orthotropic damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. This approach facilitates the determination of model parameters since the orthotropic damage model parameters can be determined from available data from quasi-static-loading tests. Then, limited amount of fatigue data is needed to adjust the fatigue evolution model. The combination of these two models provides a compromise between efficiency and accuracy. Decomposition of the state variables down to the constituent scale is accomplished by micro-mechanics. Phenomenological damage evolution models are then postulated for each constituent and for the micro-structural interaction among them. Model parameters are determined from available experimental data. Comparison between model predictions and additional experimental data is presented.     

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.     

Impact damage tolerance of laminated composite helicopter blades

The paper is concerned with the study of the damage resistance of laminated composite helicopter blades subjected to impact loading. Dynamic stress intensity factors are determined for composite laminate and separate layers using combined theoretical and experimental approach. The effect of the projectile size on the damage tolerance of composite blade is investigated and tolerable sizes of the defects are estimated.     

A numerical approach for predicting the failure locus of fiber reinforced composites under combined transverse compression and axial tension

A computational model based on the finite element method is presented for the estimation of strength of a fiber-reinforced lamina subjected to a combination of the transverse compression and axial tension. A complex damage mechanism including fiber breakage, fiber/matrix debonding and matrix plastic deformation is reproduced in the proposed model by using appropriate constitutive equations. The numerical simulation of mechanical response of the unidirectional lamina under biaxial loading is used to obtained the failure locus. Subsequently, the model is verified against an analytical solution and experimental data. It was found that the numerical calculations agree better with experimental results than analytical predictions.     

Evaluation of static and fatigue strength of long fiber GRP composite material considering moisture effects

The paper presents results of a partial experimental programme of evaluation of static mechanical and fatigue properties of long glass-fiber reinforced polymer composite material with a multiaxial orientation of glass fibers to be used for a manufacture of the flywheel hub disc, the main component of the storage unit accumulating kinetic energy of a vehicle during braking for further use during acceleration. Though humidity is not supposed to be an issue in operation of the unit, an experimental programme evaluating the material static strength and durability under combination of static load with vibration component was carried out to complete the overall general material characterisation. Study of an effect of absorbed moisture was a part of the experimental work. Water absorption was a long-term process, without saturation even after several months. Degradation of strength and fatigue properties due to the absorbed distilled water was confirmed for this material. The material sensitivity on vibration component of the load, even with quite low amplitude of 10% of the static load was ascertained. Damage accumulation and continuous stiffness reduction during fatigue tests, which rate was connected with final durability, was an important phenomenon.     

Damage indices for failure of concrete beams under fatigue

In this study, an analytical method is proposed to correlate local damage variables such as relative crack depth and crack tip opening displacement with a newly defined global damage index for a concrete beam under fatigue loading. This global damage index may be used to assess the response of a degraded concrete beam under service loading. The damage is assumed to appear in the form of a major crack that propagates under constant amplitude fatigue loading. The progressive cracking phenomenon is modeled within a finite element framework using a crack beam element, which takes into account the compliance variation due to discrete cracking within the member. The flexural stiffness degradation of the member is computed based on an Eigen analysis of the global stiffness matrix. It is seen that the degree of flexural stiffness degradation due to discrete cracking is the same for geometrically similar specimens when the relative crack depth is used as a local damage parameter. Further, in order to improve the accuracy of the response prediction using the above global damage index, another global damage parameter is defined based on the nature of applied loading.     

A fatigue damage model of composite materials

The mechanical properties of composite materials degrade progressively with the increasing of the number of cyclic loadings. Based on the stiffness degradation rule of composites, a phenomenological fatigue damage model is presented in this paper, which contains two material parameters. They are proportional to the fatigue life of materials and inversely proportional to the fatigue loading level. Thirteen sets of experimental data of composite stiffness degradation were employed to verify the presented model, and the statistical results showed that this model is capable of describing the damage evolution of composite materials. The characteristics of damage development and accumulation of composite materials subjected to variable loading were studied in this paper. Four sets of two-level loading experimental data were cited to verify the damage model, and the results showed that the predicted life is in good agreement with the experimental ones.     

Investigations on fretting fatigue in aircraft engine compressor blade

An investigation of several cracked blade tangs in the military aircraft engine compressor was conducted to identify the root cause of the failure. These cracks were found during the scheduled maintenance with fluorescent penetration inspection. The engine compressor blade made of Ti–6Al–4V is attached to compressor rotor by means of inserting retaining pin through rotor and blade tang. By analyzing the fracture surface of the failed blade tang, it is found that the crack in the blade tang was initiated by fretting fatigue and propagated under low cycle fatigue. Stress analysis of the blade using a non-linear finite element method is coincident with the results of fractography. The clearance between retaining pin and tang hole caused small amplitude of sliding motion leading to fretting wear during engine operation. Consequently, the damaged area due to fretting wear acts as a stress raiser inside tang hole and contributes to accelerate fretting fatigue.     

Effect of delamination failure in crashworthiness analysis of hybrid composite box structures

In the present paper the effects of delamination failure of hybrid composite box structures on their crashworthy behaviour will be studied and also their performance will be compared with non-hybrid ones. The combination of twill-weave and unidirectional CFRP composite materials are used to laminate the composite boxes. Delamination study in Mode-I and Mode-II with the same lay-ups was carried out to investigate the effect of delamination crack growth on energy absorption of hybrid composite box structures. The end-loaded split (ELS) and double-cantilever beam (DCB) standard test methods were chosen for delamination studies. In all hybrid composite boxes the lamina bending crushing mode was observed. Regarding the delamination study of hybrid DCB and ELS the variation of the specific energy absorption (SEA) versus summation of G_IC and G_IIC were plotted to combine the effect of Mode-I and Mode-II interlaminar fracture toughness on the SEA. From this relationship it was found the hybrid laminate designs which showed higher fracture toughness in Mode-I and Mode-II delamination tests, will absorb more energy as a hybrid composite box in crushing process. The crushing process of hybrid composite boxes was also simulated by finite element software LS-DYNA and the results were verified with the relevant experimental result.     

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.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Variational-asymptotic modeling of the thermoelastic behavior of composite beams

This paper deals with steady state thermoelastic problems in composite beam structure by using variational-asymptotic method. First, the original three-dimensional heat conduction problem is reduced to be a two-dimensional thermal cross-sectional analysis along with an optional one-dimensional heat conduction analysis. The one-dimensional heat conduction analysis exists only if the temperature is not prescribed at any point of the cross-section along the span except the end surfaces. Then we reduce the one-way coupled, three-dimensional thermoelasticity problem into a two-dimensional, one-way coupled thermoelastic cross-sectional analysis and a one-dimensional, one-way coupled, thermoelastic beam analysis. The present theory is implemented into the computer program, variational-asymptotic beam sectional analysis (VABS). Several examples are studied using the present theory and the results from VABS are compared with available analytical solutions and the three-dimensional analysis using the commercial finite element package ANSYS.     

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.     

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 analysis of intralaminar failure mechanisms in composite structures. Part II: Applications

A three-dimensional continuum damage mechanics-based material model was implemented in an implicit Finite Element code to simulate the progressive intralaminar degradation of fibre reinforced laminates based on ply failure mechanisms. This paper presents some structural applications of the progressive failure model implemented. The focus is on the non-linear response of the shear failure mode and its interaction with other failure modes. Structural applications of the damage model show that the proposed model is able to reproduce failure loads and patterns observed experimentally.     

Evaluation of the residual strength degradation in composite laminates under fatigue loading

Residual strength degradation in graphite/epoxy composite laminates is evaluated and a model proposed relating the residual strength to the applied fatigue cycles and the maximum applied stress. Based on this model, the statistical distribution of the residual strength is derived and compared with available experimental data. Good agreement is observed between the proposed model and experimental results.     

Thermal fatigue analysis of solar panel structure for micro-satellite applications

Thermal fatigue analysis based on 2D finite difference and 3D finite element methods is carried out to study the performance of solar panel structure during micro-satellite life time. Solar panel primary structure consists of honeycomb structure and composite laminates. The 2D finite difference (I-DEAS) model yields predictions of the temperature profile during one orbit. Then, 3D finite element analysis (ANSYS) is applied to predict thermal fatigue damage of solar panel structure. Meshing the whole structure with 2D multi-layer shell elements with sandwich option is not efficient, as it misses thermal response of the honeycomb structure. So we applied a mixed approach between 3D solid and 2D shell elements to model the solar panel structure without the sandwich option.     

Numerical analysis of intralaminar failure mechanisms in composite structures. Part I: FE implementation

This paper presents a three-dimensional continuum damage mechanics-based material model which was implemented in an implicit finite element code to simulate the progressive intralaminar degradation of fibre reinforced laminates. The damage model is based on ply failure mechanisms and uses seven damage variables assigned to tensile, compressive and shear damage at a ply level. Non-linear behaviour and irreversibility were taken into account and modelled. Some issues on the numerical implementation of the damage model are discussed and solutions proposed. Applications of the methodology are presented in Part II [1].