Στα πλαίσια της παρούσας διατριβής προσεγγίστηκε το πρόβλημα της κρούσης των σύνθετων υλικών μέσω μιας συνολικής μεθοδολογίας. Ο όρος συνολική μπορεί να χαρακτηρίσει την παρούσα εργασία της διατριβής γιατί η αναλυτική και αριθμητική υλοποίηση του προβλήματος που παρουσιάσθηκε επιλύει πολλά παράπλευρα προβλήματα. Η επίλυση του προβλήματος της κρούσης χαμηλής ταχύτητας σε σύνθετα υλικά κινήθηκε σε τέσσερις φάσεις. Σε πρώτη φάση αναπτύχθηκε το κύριο εργαλείο με το οποίο εξελίσσεται η διαδικασία μοντελοποίησης του προβλήματος. Η κατάστρωση του μοντέλου επίλυσης φυσικών συχνοτήτων και η αριθμητική επίλυση αυτού δίνει εκτιμήσεις για την ακρίβεια της μεθόδου Ritz με τη χρήση των αποδεκτών συναρτήσεων p-Ritz. Η μέθοδος Ritz επιτρέπει την πλήρη μοντελοποίηση του πολύστρωτου λαμβάνοντας υπόψη και τους καμπτικούς όρους σύζευξης κάτι που μέχρι στιγμής δεν έχει παρουσιαστεί στη βιβλιογραφία. Κατά τη δεύτερη φάση και μετά την τεκμηρίωση της πρώτης φάσης και τον έλεγχο της ακρίβειας των υπολογισμών των φυσικών συχνοτήτων, διατυπώθηκε το δυναμικό πρόβλημα. Η ακρίβεια των υπολογισμών ήταν εξαιρετική και σε ικανοποιητική σύγκλιση με τα αποτελέσματα του κώδικα πεπερασμένων στοιχείων LSDYNA3D. Παράλληλα αποδείχτηκε ότι το δυναμικό μοντέλο, επιλύει το δυναμικό φαινόμενο για όλα τα σχήματα και τους συνδυασμούς συνοριακών συνθηκών. Σε εξέλιξη των ανωτέρω έγινε η διατύπωση του συζευγμένου προβλήματος της κρούσης και επιλύθηκε για διάφορα υλικά και συνοριακές συνθήκες που αποτελούν μοντέλα υποδείγματα στη διεθνή βιβλιογραφία. Η ικανότητα πρόβλεψης των μοντέλων χαρακτηρίζεται ιδιαίτερα ικανοποιητική ενώ παρουσιάστηκε ο τρόπος εισαγωγής μη γραμμικών νόμων επαφής, στο συζευγμένο σύστημα διαφορικών εξισώσεων. Με σκοπό τον πλήρη χαρακτηρισμό του φαινομένου αλλά και τη μείωση των παραμέτρων που χαρακτηρίζουν το πρόβλημα σε μια προσπάθεια χαρακτηρισμού των κύριων παραμέτρων που διέπουν την κρούση παρουσιάζεται ο τρόπος υπολογισμού των αδιάστατων ομάδων που περιγράφουν την κρούση. Στα πλαίσια αυτής της ανάλυσης υπολογίστηκε το Νομογράφημα Κρουστικής Απόκρισης. Το Νομογράφημα Κρουστικής Απόκρισης μπορεί να χρησιμοποιηθεί στην οργάνωση πειραμάτων χαρακτηρισμού της κρουστικής αντοχής πολύστρωτων διατάξεων. Για την επίλυση του κύριου προβλήματος προτάθηκε μια διαδικασία ιεραρχικής αντιμετώπισης του προβλήματος. Για να καθοριστεί η κρουστική απόκριση του πολύστρωτου η διάταξη υποβάλλεται σε δυναμικό και στατικό χαρακτηρισμό με τη χρήση αριθμητικών μοντέλων που βασίζονται στη μέθοδο Ritz. Υλοποιήθηκε μια μέθοδος που δύναται να επιλύει διάφορες γεωμετρίες σε ποικιλία συνοριακών συνθηκών. Στη βιβλιογραφία μέχρι στιγμής έχουν παρουσιαστεί μοντέλα για παραλληλόγραμμες πλάκες, ειδικώς ορθότροπες και σε συνοριακές συνθήκες απλής έδρασης. Υλοποιήθηκαν προγράμματα σε Fortran που επιλύουν στατικά και δυναμικά προβλήματα σε καμπτικά φορτία και για ποικίλους συνδυασμούς συνοριακών συνθηκών. Υλοποιήθηκε το συζευγμένο πρόβλημα της κρούσης πολύστρωτης διάταξης από σφαίρα (διεισδυτή) σε χαμηλές ταχύτητες Έγινε σύγκριση ελαστοπλαστικών μη γραμμικών μοντέλων επαφής με γραμμικά μοντέλα επαφής. Με τη χρήση της θεωρίας αδιαστατοποίησης καθορίστηκαν οι αδιάστατες ομάδες που διέπουν το πρόβλημα της κρούσης και δημιουργήθηκε το Νομογράφημα Κρουστικής Απόκρισης. Αποδείχτηκε ότι το Νομογράφημα Κρουστικής Απόκρισης ισχύει για οιαδήποτε συμμετρική πολύστρωτη διάταξη σε όποια συνοριακή συνθήκη και αν είναι και οιοδήποτε σχήμα πλάκας. Αποδείχτηκε ότι το Νομογράφημα Κρουστικής Απόκρισης μπορεί να χρησιμοποιηθεί ως χάρτης αντοχής και ανοχής σε κρούση με τη χρήση της αδιάστατου Κατωφλιού Δύναμης για Διαστρωματική Αποκόλληση. / Low-velocity impact in composite laminates is a destructive loading condition since it leads to significant internal damage, no detectable by visual inspection. Numerous researchers have made significant efforts to model the impact response of composite plates and facilitate the analysis and design for impact resistance, using simple linear spring-mass models or a combination of continuum mechanics models and contact laws. Many investigators have used simple engineering structures beams, plates and shells to demonstrate the impact response of composite structures. The basic concept for modelling the impact of an object to a target was proposed by Timoshenko (1913). He introduced the procedure where the description of the interaction between the impactor and the structure (Euler beam) was implemented using the Hertzian contact law. This approach was further extended in isotropic plates and shells. Lee, 1940; Greszcuk, 1982; Lee et al., 1983 and Shivakumar et al, 1985, proposed simple models of the low-velocity impact problem. Although many important contributions exist in the bibliography for the characterization of the impact response of laminated plates, analytical solutions are considered to be very few. Most of the models proposed are for analyzing specially orthotropic plates subjected to a local dominated impact. In addition, these models do not take into account the shear coupling terms of the bending stiffness matrix, e.g. D16 and D26. Sun and Chattopadhyay (1975), Dobyns (1981), and Ramkumar and Chen (1983) employed the first order shear deformation theory developed by Whitney and Pagano (1970), and used it in conjunction with the Hertzian contact law or plasticity contact law for characterizing the impact of laminated composite plates. In their analysis they have studied the impact response of a simply supported orthotropic plate subjected to central impact using the lamination theory that includes transverse shear deformations. It is evident that the contact force history must be computed as part of the solution of the dynamic response problem solving the nonlinear integral equation. Christoforou and Swanson (1991) and Carvalho (1996), obtained an analytical solution of the impact problem using the Laplace transform technique. Qian and Swanson (1990) obtained analytical solutions by linearising the contact deformation law and compared this with a Rayleigh-Ritz approach with numerical integration in time. The three dimensional finite element method with an explicit formulation where also used in the dynamic analysis of laminated plates subjected to low velocity impact. Moreover, many researchers have proposed simple models for characterizing the impact phenomenon. Shivakumar et.al. (1985) developed a simple model to predict the impact force and the duration of the impact phenomenon on composite plates. The composite plates were modeled as three springs while their stiffness was calculated by the plate properties and the contact parameters. Other researchers instead of a classical Hertzian law used the statical indentation law presented by Yang and Sun (1982) and Tan and Sun (1985). The non Hertzian Contact impact was considered for combining the overall deformation of the structure to the local deformation in the contact area and was used to predict the impact response of transversely isotropic beams and plates. In general, it is impossible to obtain the exact solution for an impact problem except by ignoring the local contact deformation or pre-assuming the contact force. The first step for understanding the problem is to predict the force applied by the projectile on the structure during impact. In order to characterize the contact force history, the model should account for the motion of the target, the effective stiffness of the projectile The present work deals with the development of a numerical scheme for the calculation of the dynamic response of any type of laminated composite plates subjected to any type (and/or combination) of boundary conditions under low-velocity impact. Using the p-version Ritz polynomials any shape that can be represented in Cartesian coordinates can be formulated. The governing second order differential equations are derived and allow furnishing solutions with a variety of boundary conditions along the edges of the plate shape represented in Cartesian coordinates. Statically determined non-linear contact laws, for loading and unloading conditions, are coupled with the partial differential equations governing the dynamic response of the composite plate. These nonlinear governing equations of the contact-impact problem are decoupled according to the second order terms by the method of principal transformation and then solved numerically. The dynamic response of fully clamped cross-ply and a variation of simply support and fixed boundary conditions for angle ply and cross ply composite laminates was investigated. Rectangular, circular and elliptical plates where analysed using the developed numetrical scheme. A total analysis method is used in order to check the efficiency of the results. Starting from the homogeneous formulation of the structure the eigenfrequencies and eigenshapes were calculated for all material and boundary conditions cases. Using the “transformation of the principal” method all cases were subjected in force and pressure pulses in order to check the efficiency of the dynamic solver developed. The efficiency of the present method was investigated comparing the respective results with well-known benchmark problems, experimental results and FEM analysis using MSC-NASTRAN and LSDYNA 3D codes. Following this exhaustive analysis, the coupled contact-impact problem was formulated and numerous contact schemes were applied to the problem. For the impact problem the type of the response is intimately related to the contact stiffness, impact energy, ply thickness and orientation, geometrical configuration and boundary conditions, as well as the orthotropic material properties and the longitudinal, transverse and interlaminar strength both in compression and in tension. Three types of dynamic responses were found to exist, local, global and transitional. All types are categorised and analysed. Using Buckingham Theorem the numerous parameters of the dynamic contact-impact problem were grouped to non-dimensional groups in order to provide a flexible analysis scheme for theoretical and experimental evaluation of the low velocity impact problem. A general normalised graph for characterising the impact response of structures was constructed. The numerous advantages for analysing impact phenomena using the normalised curve developed were presented. Moreover its use for predicting composite material damage area on low velocity impact conditions was presented.

The objective of this study was to investigate the low velocity impact behavior of both monolithic and laminated aluminum alloy plates. For this purpose, a drop-weight test unit was used. The test unit included the free fall and impact of an 8 kg hammer with an 8 mm punching rod from 0.5 m to 4 m. The relationship between the change in static mechanical properties (hardness, ultimate tensile strength, yield strength, strain hardening rate) and low velocity impact behavior of monolithic aluminum plates were investigated. Tested material was AA 2024, heat treatable aluminum alloy, which was artificially aged to obtain a wide range of mechanical properties. In the second stage of the study, the relationship between the low velocity impact behavior of laminated plates was compared with that of monolithic aluminum plates at identical areal densities. For this purpose, a series of AA 2024 thin plates were combined with different types of adhesives (epoxy, polyurethane or tape). Finally, fracture surface of the samples and microstructure at the deformation zone were examined with both scanning electron microscope and optical microscope. It is found that the ballistic limit velocities of AA 2024 plates increase with increase in hardness, yield strength and ultimate tensile strength. It is also found that a linear relation exists between the ballistic limit velocity and strain hardening rate or hardness. When the low velocity impact behaviors of laminated and monolithic targets were compared, it was seen that monolithic targets have a higher ballistic limit velocity values for from the 2.5 to 10 mm thick targets. It was also observed that adhesives are not so effective to strengthen the low velocity impact performance. On the other hand, with increasing Charpy impact energy, penetration and perforation behaviors are getting worse in 10 to 30 joules energy range. Different types of failure mechanisms involving, plugging, dishing, stretching and bending were determined. For high strength and thick plates plugging type deformation was leaded. In contrast, for thinner and weaker targets bending, stretching and dishing type failures were dominating. For laminated targets also dishing type failure was determined.

Afin de mieux comprendre et de mieux quantifier la formation des dommages d'impact et leurs conséquences sur la tenue de la structure composite, le recours à la simulation numérique semble être un complément indispensable pour enrichir les campagnes expérimentales. Cette thèse a pour objectif la mise au point d'un modèle d'impact pour la simulation numérique par éléments finis dynamique implicite, capable de prévoir les dommages induits.La première étape du travail a consisté à élaborer un modèle s'appuyant sur le modèle de comportement du pli « Onera Progressive Failure Model » (OPFM) et sur le modèle bilinéaire de zones cohésives proposé par Alfano et Crisfield, puis d'évaluer la sensibilité aux différentes composantes des lois de comportement de la réponse à un impact et des dommages prévus. Des essais d'impact et d'indentation sur des plaques stratifiées en carbone/époxy ont ensuite été réalisés, analysés et enfin confrontés aux résultats numériques, afin d'évaluer les performances à l'impact du modèle OPFM et ses limites.Ces travaux permettent d'aboutir à trois principales conclusions. Premièrement, l'usage de modèles de zones cohésives semble nécessaire pour prévoir la chute de force caractéristique de l'impact sur stratifiés. Deuxièmement, la prise en compte des contraintes hors plan, notamment les cisaillements, est indispensable pour prévoir correctement l'endommagement d'impact. Enfin, si le modèle OPFM est capable de prévoir qualitativement les dommages d'impact, l'absence de caractère adoucissant ou de viscoplasticité semble cependant limiter leur prévision quantitative. / In order to improve the understanding and the quantification of the impact damage formation and of their consequences on the composite structure behavior, numerical simulation seems to be a necessary complement to experiments. This thesis aims at designing an impact model suited for a dynamic implicit finite element numerical simulation, able to predict the induced damages.The first step of the work consisted in building an impact model using the ply behavior law “Onera Progressive Failure Model” (OPFM) and the bilinear cohesive law defined by Alfano and Crisfield, then in evaluating the impact response and the predicted damage sensitivity to the different parameters of the behavior laws. Impact and indentation tests on carbon/epoxy laminate plates have then been performed, analyzed and compared with the numerical results, in order to evaluate the impact performance of OPFM and its limits.This work points out three key results. First, the use of cohesive zone models seems necessary to predict the typical load drop. Secondly, the out-of-plane constraints, especially the shearing, must be taken into account to correctly predict impact damages. Finally, even if the OPFM model is able to qualitatively predict impact damages, the lack of softening or viscoplasticity seems to limit their quantitative prediction.

No description available.

Transparent laminates are widely used for body armor, goggles, windows and windshields. Improved understanding of their deformations under impact loading and of energy dissipation mechanisms is needed for minimizing their weight. This requires verified and robust computational algorithms and validated mathematical models of the problem. Here we have developed a mathematical model for analyzing the impact response of transparent laminates made of polymeric materials and implemented it in the finite element software LS-DYNA. Materials considered are polymethylmethacrylate (PMMA), polycarbonate (PC) and adhesives. The PMMA and the PC are modeled as elasto-thermo-visco-plastic and adhesives as viscoelastic. Their failure criteria are stated and simulated by the element deletion technique. Values of material parameters of the PMMA and the PC are taken from the literature, and those of adhesives determined from their test data. Constitutive equations are implemented as user-defined subroutines in LS-DYNA which are verified by comparing numerical and analytical solutions of several initial-boundary-value problems. Delamination at interfaces is simulated by using a bilinear traction separation law and the cohesive zone model. We present mathematical and computational models in chapter one and validate them by comparing their predictions with test findings for impacts of monolithic and laminated plates. The principal source of energy dissipation of impacted PMMA/adhesive/PC laminates is plastic deformations of the PC. In chapter two we analyze impact resistance of doubly curved monolithic PC panels and delineate the effect of curvature on the energy dissipated. It is found that the improved performance of curved panels is due to the decrease in the magnitude of stresses near the center of impact. In chapter three we propose constitutive relations for finite deformations of adhesives and find values of material parameters by considering test data for five portions of cyclic loading. Even though these values give different amounts of energy dissipated in the adhesive, their effect on the computed impact response of PMMA/adhesive/PC laminates is found to be minimal. In chapter four we conduct sensitivity analysis to identify critical parameters that significantly affect the energy dissipated. The genetic algorithm is used to optimally design a transparent laminate in chapter five. / Ph. D.

This master thesis focuses on modelling and simulation of impact tests of composite panels. Simulations and analysis were made by using Finite Element Method in software MSC Patran and Dytran. The first part of the thesis deals with describing the properties of composite panels during impact testing and other cases of impacts on composite structures. Next part deals with the used models and results from Dytran. These results are compared with experimental data from real low-velocity impact tests. Part of the thesis is devoted to impact on panels with the stacking sequences which is supposed to be used for design of air duct for airplane Aero L-39NG.

This thesis documents the findings of a three year experimental investigation into the impact damage resistance and damage tolerance of composite honeycomb sandwich panels. The primary area of work focuses on the performance of sandwich panels under quasi-static and low-velocity impact loading with hemispherical and flat-ended indenters. The damage resistance is characterised in terms of damage mechanisms and energy absorption. The effects of varying the skin and core materials, skin thickness, core density, panel boundary conditions and indenter shape on the transverse strength and energy absorption of a sandwich panel have been examined. Damage mechanisms are found to include delamination of the impacted skin, core crushing, limited skin-core de bonding and top skin fibre fracture at high loads. In terms of panel construction the skin thickness is found to dominate the panel strength and energy absorption with core density having a lesser influence. Of the external factors considered the indenter noseshape has the largest effect on both failure load and associated damage area. An overview of existing analytical prediction methods is also included and the most significant theories applied and compared with the experimental results from this study. The secondary area of work expands the understanding obtained from the damage resistance study and assesses the ability of a sandwich panel to withstand in-plane compressive loading after sustaining low-velocity impact damage. The importance of the core material is investigated by comparing the compression-after-impact strength of both monolithic carbon-fibre laminates and sandwich panels with either an aluminium or nomex honeycomb core. The in-plane compressive strength of an 8 ply skinned honeycomb sandwich panel is found to be double that of a 16 ply monolithic laminate, with the type of honeycomb also influencing the compressive failure mechanisms and residual compressive strength. It is concluded that under in-plane loading the stabilising effect of the core opposes the de-stabilising effect of any impact damage.

With the development of the design and manufacture technology, composite materials are widely used in the aeronautical industry. But, one of the main concerns which affects the application of composites is foreign object impact. The damages induced by the Low Velocity Impact (LVI), which can significantly reduce the strength of the structures, can’t be easily inspected routinely. The so-called Barely Visible Impact Damages (BVID) due to LVI typically includes interlaminar delamination, matrix cracks and fibre fracture at the back face. Previous researches have shown that the results of LVI test are similar to that of the Quasi-Static Load (QSL) test. The initiation and propagation of delamination can be detected more easily in the QSL test and the displacement and reaction force of the impactor can be controlled and measured much more accurately. Moreover, it is easier to model QSL tests than dynamic impacts. To investigate the impact damage induced by LVI, a Finite Element (FE) model employing cohesive elements was used. At the same time, the ply clustering effect, when several plies of the same orientation were stack together, was modelled in the FE model in terms of damage resistance and damage size. A bilinear traction-separation law was introduced in the cohesive elements employed to simulate the initiation and propagation of the impact damage and delamination. Firstly, a 2D FE model of the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) specimens were built using the commercial FEM software ABAQUS. The results have shown that the cohesive elements can be used to simulate mode I and mode II delamination sufficiently and correctly. Secondly, an FE model of a composite plate under QSL but without simulating damage was built using the continuum shell elements. Agreement between the FEA results with published test results is good enough to validate the capability of continuum shell elements and cohesive elements in modelling the composite laminate under the transverse load condition (QSL). Thirdly, an FE model containing discrete interface delamination and matrix cracks at the back face of the composite plate was built by pre-setting the cohesive failure elements at potential damage locations according to the experimental observation. A cross-ply laminate was modelled first where fewer interfaces could be delaminated. Good agreement was found in terms of the delamination area and impactor’s displacement-force curve. Finally, the effect of ply clustering on impact damage resistance was studied using Quasi-Isotropic (QI) layup laminates. Because of the limited time available for calculation, the simulation was only partly completed for the quasi-isotropic laminates (L2 configuration) which have more delaminated interfaces. The results showed that cohesive elements obeying the bilinear traction-separation law were capable of predicting the reaction force in quasi-isotropic laminates. However, discrepancies with the test results in terms of delamination area were observed for quasi-isotropic laminates. These discrepancies are mainly attributed to the simplification of matrix cracks simulation and compressive load at the interface in the thickness direction which is not taken into account.

This thesis reports on a design study, conducted for an advanced composite helmet shell for helicopter pilots. The helmet shell is expected to provide a level of protection against low velocity impacts with its weight criteria. Therefore, ergonomy, light weight, and the ability to withstand low velocity impact became the main issues for this study. For this purpose, an experimental program has been developed including low velocity impact tests on specimens. The drop height, drop weight, specimen stacking sequences and size were constant parameters. Test specimens were produced using the plate size of 220x220 mm having different thicknesses. Specimen materials were aramid, carbon, and a hybrid form of these two. Thus, the parameters of the study were specimen thickness and the material types. The impact tests are carried out on a specially designed test rig. The design decisions are made in accordance with the results of the experiments. In compliance with the lightweight and manufacturing criteria, the hybrid specimen was selected helmet shell. For the purpose of ergonomy a geometric design was also conducted from headfrom sizes of Turkish Army by using 3D design software. After specifying the composite material, manufactured helmet shell was tested in another test rig according to the ANSI Z90.1.1992. For the requirement of the acceleration level 300g, the helmet shell design was found to be successful at seven different and critical impact points.

No description available.