## Fachbereich Maschinenbau und Verfahrenstechnik

### Filtern

#### Erscheinungsjahr

- 2007 (10) (entfernen)

#### Dokumenttyp

- Dissertation (9)
- Habilitation (1)

#### Sprache

- Englisch (10) (entfernen)

#### Schlagworte

- Nichtlineare Finite-Elemente-Methode (2)
- continuum mechanics (2)
- Anisotropie (1)
- Biomechanik (1)
- Composites (1)
- Damage (1)
- Diskontinuität (1)
- Elastoplasticity (1)
- Elastoplastizität (1)
- Festkörper (1)

- Investigations of sewn preform characteristics and quality aspects for the manufacturing of fiber reinforced polymer composites (2007)
- Sewn net-shape preform based composite manufacturing technology is widely accepted in combination with liquid composite molding technologies for the manufacturing of fiber reinforced polymer composites. The development of threedimensional dry fibrous reinforcement structures containing desired fiber orientation and volume fraction before the resin infusion is based on the predefined preforming processes. Various preform manufacturing aspects influence the overall composite manufacturing processes. Sewing technology used for the preform manufacturing has number of challenges to overcome which includes consistency in preform quality, composite quality, and composite mechanical properties. Experimental studies are undertaken to investigate the influence of various sewing parameters on the preform manufacturing processes, preform quality, and the fiber reinforced polymer composite quality and properties. Sewing thread, sewing machine parameters, shortcomings of sewing process, and remedies are explained according to their importance during preforming and liquid composite molding. The stitches and fiber free zone in the form of ellipse that are generated in the thickness direction were investigated by evaluating the laminate micrographs. Correlation between ellipse formation phenomenon, sewing thread, and sewing machine parameters is established. A statistical tool, analysis of variance, was used to emphasize the major preform processing factors influencing the preform imperfections. For assessing the preform quality, the observations of sewing thread requirements for preform and structural sewing were well documented during the experimental studies and explained according to their significance in the composite processing. Furthermore, selection criteria for sewing thread according to end application are discussed in detail. Investigations on polyester sewing thread as a high speed preform manufacturing element are also performed. Applicability of polyester sewing thread for the preform sewing and challenges to be overcome for its extensive utilization in the composite components are explained. Apart from this, influence of physical structure of sewing thread on the laminate quality and properties are explained and relationship between them is discussed in brief. Furthermore, challenges caused due to applied spin-finishes and sizing and remedies for the same are discussed. Sewing threads made of high performance fibers that are available in the market, e.g., carbon, glass, and Zylon are studied for effect of thread material on through-thethickness laminate properties. Threads made up of carbon or glass fibers are very rigid and produces number of defects, which is a major cause of concern. Optimized sewing procedure has been implemented to minimize the in-plane and through-thethickness imperfections and to improve mechanical properties and surface characteristics of composite laminate. Preform sewing process and final ready to impregnate preforms were analyzed for quality appearance. The sewing defects and their influence on composite structure are monitored. Preform compressibility before and after the sewing operations are intensively studied and correlation with sewing parameters is developed. Influence of sewing process parameters on the warpage and change in preform area weight are also explained in detail. Results of analytical experiments can help to improve further exploitation of sewn preforms for composite manufacturing and overall preform and laminate quality.

- Characterization, Modeling and Prediction of the Creep Resistance of Polymer Nanocomposites (2007)
- The broad engineering applications of polymers and composites have become the state of the art due to their numerous advantages over metals and alloys, such as lightweight, easy processing and manufacturing, as well as acceptable mechanical properties. However, a general deficiency of thermoplastics is their relatively poor creep resistance, impairing service durability and safety, which is a significant barrier to further their potential applications. In recent years, polymer nanocomposites have been increasingly focused as a novel field in materials science. There are still many scientific questions concerning these materials leading to the optimal property combinations. The major task of the current work is to study the improved creep resistance of thermoplastics filled with various nanoparticles and multi-walled carbon nanotubes. A systematic study of three different nanocomposite systems by means of experimental observation and modeling and prediction was carried out. In the first part, a nanoparticle/PA system was prepared to undergo creep tests under different stress levels (20, 30, 40 MPa) at various temperatures (23, 50, 80 °C). The aim was to understand the effect of different nanoparticles on creep performance. 1 vol. % of 300 nm and 21 nm TiO2 nanoparticles and nanoclay was considered. Surface modified 21 nm TiO2 particles were also investigated. Static tensile tests were conducted at those temperatures accordingly. It was found that creep resistance was significantly enhanced to different degrees by the nanoparticles, without sacrificing static tensile properties. Creep was characterized by isochronous stress-strain curves, creep rate, and creep compliance under different temperatures and stress levels. Orientational hardening, as well as thermally and stress activated processes were briefly introduced to further understanding of the creep mechanisms of these nanocomposites. The second material system was PP filled with 1 vol. % 300 nm and 21 nm TiO2 nanoparticles, which was used to obtain more information about the effect of particle size on creep behavior based on another matrix material with much lower Tg. It was found especially that small nanoparticles could significantly improve creep resistance. Additionally, creep lifetime under high stress levels was noticeably extended by smaller nanoparticles. The improvement in creep resistance was attributed to a very dense network formed by the small particles that effectively restricted the mobility of polymer chains. Changes in the spherulite morphology and crystallinity in specimens before and after creep tests confirmed this explanation. In the third material system, the objective was to explore the creep behavior of PP reinforced with multi-walled carbon nanotubes. Short and long aspect ratio nanotubes with 1 vol. % were used. It was found that nanotubes markedly improved the creep resistance of the matrix, with reduced creep deformation and rate. In addition, the creep lifetime of the composites was dramatically extended by 1,000 % at elevated temperatures. This enhancement contributed to efficient load transfer between carbon nanotubes and surrounding polymer chains. Finally, a modeling analysis and prediction of long-term creep behaviors presented a comprehensive understanding of creep in the materials studied here. Both the Burgers model and Findley power law were applied to satisfactorily simulate the experimental data. The parameter analysis based on Burgers model provided an explanation of structure-to-property relationships. Due to their intrinsic difference, the power law was more capable of predicting long-term behaviors than Burgers model. The time-temperature-stress superposition principle was adopted to predict long-term creep performance based on the short-term experimental data, to make it possible to forecast the future performance of materials.

- Fracture of Nanoparticle Filled Polymer Composites (2007)
- In recent years, nanofiller-reinforced polymer composites have attracted considerable interest from numerous researchers, since they can offer unique mechanical, electrical, optical and thermal properties compared to the conventional polymer composites filled with micron-sized particles or short fibers. With this background, the main objective of the present work was to investigate the various mechanical properties of polymer matrices filled with different inorganic rigid nanofillers, including SiOB2B, TiOB2B, AlB2BOB3B and multi-walled carbon nanotubes (MWNT). Further, special attention was paid to the fracture behaviours of the polymer nanocomposites. The polymer matrices used in this work contained two types of epoxy resin (cycloaliphatic and bisphenol-F) and two types of thermoplastic polymer (polyamide 66 and isotactic polypropylene). The epoxy-based nanocomposites (filled with nano-SiOB2B) were formed in situ by a special sol-gel technique supplied by nanoresins AG. Excellent nanoparticle dispersion was achieved even at rather high particle loading. The almost homogeneously distributed nanoparticles can improve the elastic modulus and fracture toughness (characterized by KBICB and GBICB) simultaneously. According to dynamic mechanical and thermal analysis (DMTA), the nanosilica particles in epoxy resins possessed considerable "effective volume fraction" in comparison with their actual volume fraction, due to the presence of the interphase. Moreover, AFM and high-resolution SEM observations also suggested that the nanosilica particles were coated with a polymer layer and therefore a core-shell structure of particle-matrix was expected. Furthermore, based on SEM fractography, several toughening mechanisms were considered to be responsible for the improvement in toughness, which included crack deflection, crack pinning/bowing and plastic deformation of matrix induced by nanoparticles. The PA66 or iPP-based nanocomposites were fabricated by a conventional meltextrusion technique. Here, the nanofiller content was set constant as 1 vol.%. Relatively good particle dispersion was found, though some small aggregates still existed. The elastic modulus of both PA66 and iPP was moderately improved after incorporation of the nanofillers. The fracture behaviours of these materials were characterized by an essential work fracture (EWF) approach. In the case of PA66 system, the EWF experiments were carried out over a broad temperature range (23~120 °C). It was found that the EWF parameters exhibited high temperature dependence. At most testing temperatures, a small amount of nanoparticles could produce obvious toughening effects at the cost of reduction in plastic deformation of the matrix. In light of SEM fractographs and crack opening tip (COD) analysis, the crack blunting induced by nanoparticles might be the major source of this toughening. The fracture behaviours of PP filled with MWNTs were investigated over a broad temperature range (-196~80 °C) in terms of notched impact resistance. It was found that MWNTs could enhance the notched impact resistance of PP matrix significantly once the testing temperature was higher than the glass transition temperature (TBgB) of neat PP. At the relevant temperature range, the longer the MWNTs, the better was the impact resistance. SEM observation revealed three failure modes of nanotubes: nanotube bridging, debonding/pullout and fracture. All of them would contribute to impact toughness to a degree. Moreover, the nanotube fracture was considered as the major failure mode. In addition, the smaller spherulites induced by the nanotubes would also benefit toughness.

- Theory and numerics of non-classical thermo-hyperelasticity (2007)
- Thermoelasticity represents the fusion of the fields of heat conduction and elasticity in solids and is usually characterized by a twofold coupling. Thermally induced stresses can be determined as well as temperature changes caused by deformations. Studying the mutual influence is subject of thermoelasticity. Usually, heat conduction in solids is based on Fourier’s law which describes a diffusive process. It predicts unnatural infinite transmission speed for parts of local heat pulses. At room temperature, for example, these parts are strongly damped. Thus, in these cases most engineering applications are described satisfactorily by the classical theory. However, in some situations the predictions according to Fourier’s law fail miserable. One of these situations occurs at temperatures near absolute zero, where the phenomenon of second sound1 was discovered in the 20th century. Consequently, non-classical theories experienced great research interest during the recent decades. Throughout this thesis, the expression “non-classical” refers to the fact that the constitutive equation of the heat flux is not based on Fourier’s law. Fourier’s classical theory hypothesizes that the heat flux is proportional to the temperature gradient. A new thermoelastic theory, on the one hand, needs to be consistent with classical thermoelastodynamics and, on the other hand, needs to describe second sound accurately. Hence, during the second half of the last century the traditional parabolic heat equation was replaced by a hyperbolic one. Its coupling with elasticity leads to non-classical thermomechanics which allows the modeling of second sound, provides a passage to the classical theory and additionally overcomes the paradox of infinite wave speed. Although much effort is put into non-classical theories, the thermoelastodynamic community has not yet agreed on one approach and a systematic research is going on worldwide.Computational methods play an important role for solving thermoelastic problems in engineering sciences. Usually this is due to the complex structure of the equations at hand. This thesis aims at establishing a basic theory and numerical treatment of non-classical thermoelasticity (rather than dealing with special cases). The finite element method is already widely accepted in the field of structural solid mechanics and enjoys a growing significance in thermal analyses. This approach resorts to a finite element method in space as well as in time.

- Computational Modeling of Biomechanical Phenomena - Remodeling, Growth and Reorientation (2007)
- The main concern of this contribution is the computational modeling of biomechanically relevant phenomena. To minimize resource requirements, living biomaterials commonly adapt to changing demands. One way to do so is the optimization of mass. For the modeling of biomaterials with changing mass, we distinguish between two different approaches: the coupling of mass changes and deformations at the constitutive level and at the kinematic level. Mass change at the constitutive level is typically realized by weighting the free energy function with respect to the density field, as experimentally motivated by Carter and Hayes [1977] and computationally realized by Harrigan and Hamilton [1992]. Such an ansatz enables the simulation of changes in density while the overall volume remains unaffected. In this contribution we call this effect remodeling. Although in principle applicable for small and large strains, this approach is typically adopted for hard tissues, e.g. bone, which usually undergo small strain deformations. Remodeling in anisotropic materials is realized by choosing an appropriate anisotropic free energy function. <br> Within the kinematic coupling, a changing mass is characterized through a multiplicative decomposition of the deformation gradient into a growth part and an elastic part, as first introduced in the context of plasticity by Lee [1969]. In this formulation, which we will refer to as growth in the following, mass changes are attributed to changes in volume while the material density remains constant. This approach has classically been applied to model soft tissues undergoing large strains, e.g. the arterial wall. The first contribution including this ansatz is the work by Rodriguez, Hoger and McCulloch [1994]. To model anisotropic growth, an appropriate anisotropic growth deformation tensor has to be formulated. In this contribution we restrict ourselves to transversely isotropic growth, i.e., growth characterized by one preferred direction. On that account, we define a transversely isotropic growth deformation tensor determined by two variables, namely the stretch ratios parallel and perpendicular to the characteristic direction. <br> Another method of material optimization is the adaption of the inner structure f a material to its loading conditions. In anisotropic materials this can be realized by a suitable orientation of the material directions. For example, the trabeculae in the human femur head are oriented such that they can carry the daily loads with an optimum mass. Such a behavior can also be observed in soft tissues. For instance, the fibers of muscles and the collagen fibers in the arterial wall are oriented along the loading directions to carry a maximum of mechanical load. If the overall loading conditions change, for instance during a balloon angioplasty or a stent implantation, the material orientation readapts, which we call reorientation. The anisotropy type in biomaterials is often characterized by fiber reinforcement. A particular subclass of tissues, which includes muscles, tendons and ligaments, is featured by one family of fibers. More complex microstructures, such as arterial walls, show two fiber families, which do not necessarily have to be perpendicular. Within this contribution we confine ourselves to the first case, i.e., transversely isotropic materials indicated by one characteristic direction. The reorientation of the fiber direction in biomaterials is commonly smooth and continuous. For transverse isotropy it can be described by a rotation of the characteristic direction. Analogous to the theory of shells, we additionally exclude drilling rotations, see also Menzel [2006]. However, the driving force for these reorientation processes is still under discussion. Mathematical considerations promote strain driven reorientations. As discussed, for instance, in Vianello [1996], the free energy reaches a critical state for coaxial stresses and strains. For transverse isotropy, it can be shown that this can be achieved if the characteristic direction is aligned with a principal strain direction. From a biological point of view, depending on the kind of material (i.e. bone, muscle tissue, cartilage tissue, etc.), both strains and stresses can be suggested as stimuli for reorientation. Thus, whithin this contribution both approaches are investigated. <br> In contrast to previous works, in which remodeling, growth and reorientation are discussed separately, the present work provides a framework comprising all of the three mentioned effects at once. This admits a direct comparison how and on which level the individual phenomenon is introduced into the material model, and which influence it has on the material behavior. For a uniform description of the phenomenological quantities an internal variable approach is chosen. Moreover, we particularly focus on the algorithmic implementation of the three effects, each on its own, into a finite element framework. The nonlinear equations on the local and the global level are solved by means of the Newton-Raphson scheme. Accordingly, the local update of the internal variables and the global update of the deformation field are consistently linearized yielding the corresponding tangent moduli. For an efficient implementation into a finite element code, unitized update algorithms are given. The fundamental characteristics of the effects are illustrated by means of some representative numerical simulations. Due to the unified framework, combinations of the individual effects are straightforward.

- Frontiers in Inelastic Continuum Mechanics (2007)
- The main goal of this work is to examine various aspects of `inelastic continuum mechanics': first, fundamental aspects of a general finite deformation theory based on a multiplicative decomposition of the deformation gradient with special emphasis on the incompatibility of the so-called intermediate configuration are discussed in detail. Moreover, various balance of linear momentum representations together with the corresponding volume forces are derived in a configurational mechanics context. Subsequent chapters are consequently based on these elaborations so that the applied multiplicative decomposition generally serves as a fundamental modelling concept in this work; after generalised strain measures are introduced, a kinematic hardening model coupled with anisotropic damage, a substructure evolution framework as well as two different growth and remodelling formulations for biological tissues are presented.

- Generalized Parameter Identification for Finite Viscoelasticity (2007)
- Elastomeric and other rubber-like materials are often simultaneously exposed to short- and long-time loads within engineering applications. When aiming at establishing a general simulation tool for viscoelastic media over these different time scales, a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account. In this work an algorithm for the identification of material parameters for large strain viscoelasticity is presented. Thereby, data of multiple experiments are considered. Based on this method the experimental loading intervals for long-time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short- and long-time loads without separating the parameters due to these different time scales. The employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium. The identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and FEM simulations at given (measured) force loads. Within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi-analytical sensitivity analysis is calculated. Representative numerical examples are referred to measured data for different polyurethanes. In order to show the general applicability of the identification method for multiple tests, in the last part of this work the parameter identification for small strain plasticity is presented. Thereby three similar test programs on three specimen of the aluminum alloy AlSi9Cu3 are analyzed, and the parameter sets for the respective individual identifications, and for the combination of all tests in one identification, is compared.

- Thermo-Mechanical Modelling of Solids and Interfaces -Theory, Numerics and Applications (2007)
- In the present work the modelling and numerical treatment of discontinuities in thermo-mechanical solids is investigated and applied to diverse physical problems. From this topic a structure for this work results, which considers the formulation of thermo-mechanical processes in continua in the first part and which forms the mechanical and thermodynamical framework for the description of discontinuities and interfaces, that is performed in the second part. The representation of the modelling of solid materials bases on the detailed derivation of geometrically nonlinear kinematics, that yields different strain and stress measures for the material and spatial configuration. Accordingly, this results in different formulations of the mechanical and thermodynamical balance equations. On these foundations we firstly derive by means of the concepts of the plasticity theory an elasto-plastic prototype-model, that is extended subsequently. In the centre of interest is the formulation of damage models in consideration of rate-dependent material behaviour. In the next step follows the extension of the isothermal material models to thermo-mechanically coupled problems, whereby also the special case of adiabatic processes is discussed. Within the representation of the different constitutive laws, the importance is attached to their modular structure. Moreover, a detailed discussion of the isothermal and the thermo-mechanically coupled problem with respect to their numerical treatment is performed. For this purpose the weak forms with respect to the different configurations and the corresponding linearizations are derived and discretized. The derived material models are highlighted by numerical examples and also proved with respect to plausibility. In order to take discontinuities into account appropriate kinematics are introduced and the mechanical and thermodynamical balance equations have to be modified correspondingly. The numerical description is accomplished by so-called interface-elements, which are based on an adequate discretization. In this context two application fields are distinguished. On the one side the interface elements provide a tool for the description of postcritical processes in the framework of localization problems, which include material separation and therefore they are appropriate for the description of cutting processes. Here in turn one has to make the difference between the domain-dependent and the domain-independent formulation, which mainly differ in the definition of the interfacial strain measure. On the other side material properties are attached to the interfaces whereas the spatial extension is neglectable. A typical application of this type of discontinuities can be found in the scope of the modelling of composites, for instance. In both applications the corresponding thermo-mechanical formulations are derived. Finally, the different interface formulations are highlighted by some numerical examples and they are also proved with respect to plausibility.