Academic literature on the topic 'Multi-filament yarn'

A new spinning method was presented to spin three-axial stainless steel filament wrapped yarn by modified ring-spinning, where the stainless steel filament was set as the core yarn and the nylon filament for decoration wrapping the stainless steel filament in the fields of the fabric for Shielding application. A set of process parameters was obtained by the ring spinning frame improvement and spinning process optimization, which realized to spin nylon filament wrapped stainless steel filament yarn. Moreover, the structure, and tensile mechanical properties were measured on the wrapped yarns. The results show that the process can spin stainless steel wire wrapped yarn and acquire the excellent performance of the yarn.

This paper reports a comparative experimental study of single jersey knitted fabrics made from a novel bio-based and degradable polylactide acid/poly (hydroxybutyrate-co-hydroxyvalerate) (PLA/PHBV) multi-filament yarn, together with polylactide acid , Cupro, polyethylene terephthalate (PET) and polyamide 6 (PA 6) multi-filament yarns. Their structures, mechanical, thermal and surface properties and performances as well as anti-bacterial behavior are measured and compared. It has been found that the polylactide acid/poly (hydroxybutyrate-co-hydroxyvalerate) (PLA/PHBV) filament yarn has adequate thermal and mechanical properties for normal textile and coloration/finishing processes. The Young's modulus of polylactide acid/poly (hydroxybutyrate-co-hydroxyvalerate) (PLA/PHBV) multi-filament yarn is the lowest among all the candidates investigated except for polyamide 6 (PA 6). The dyed polylactide acid/poly (hydroxybutyrate-co-hydroxyvalerate) (PLA/PHBV) fabric has the highest softness rating among all the fabrics. Single jersey knitted fabrics from the polylactide acid/poly (hydroxybutyrate-co-hydroxyvalerate) (PLA/PHBV) filament yarn have a bursting strength, extension and recovery that satisfy the industrial requirement. In addition, after fully relaxation, the dyed polylactide acid/poly (hydroxybutyrate-co-hydroxyvalerate) (PLA/PHBV) knitted fabrics exhibit an outstanding pilling resistance, favorable snagging property, as well as good air permeability, Qmax and smoother surface. Finally, this study has led to a discovery of excellent anti-bacterial performance of 100% polylactide acid/poly (hydroxybutyrate-co-hydroxyvalerate) (PLA/PHBV) fabrics against staphylococcus aureus, klebsiella pneumoniae, candida albicans according to AATCC100-2012.

The work is devoted to the study of the geometric parameters of a knitted loop. It has been found that the optimal model is a loop model detailed at the yarn level, which considers the change in the cross-sectional shape and sets the properties of the porous material in accordance with the internal porosity of the yarn. A mathematical description of the coordinates of the characteristic points of the loop and an algorithm for calculating the coordinates of the control vertices of the second order spline, which determine the configuration of the yarn axes in the loop, are presented in this work. To create 3D models, Autodesk AutoCAD software and Structura 3D software, developed in the AutoLisp programming language, were used. The simulation of the air flow process was carried out in the Autodesk CFD Simulation environment. For the experimental investigation, plane knits from 44 tex × 3 linear density ultra-high molecular weight polyethylene yarns were produced, and their air permeability was tested according to Standard DSTU ISO 9237:2003. The results obtained during the laboratory experiment and simulation differed by less than 5%.

Sixty five cocoons were selected to combine with fine denier polyester filaments, and flat treatment was made for the composition on a multi-component composite textured yarn homemade device to produce silk/ synthetic fiber composite flat filament. Then this flat multi-filaments was used as weft to develop zonal silk composite flat multi-filaments fabric. According to the testing of the glossiness and bulkiness, the results show that the glossiness of flat multi-filaments fabric was better than 8% of that of the ordinary fabric, and the fluffiness was also comparatively better than that of the ordinary fabric.

In order to study the wearability of multi-component blended fabrics, there are 9 kinds of fabrics which belong to A, B and C three series were woven. They were blended with different proportions e.g. PTT, PLA, Cooldry, triangular shaped polyester yarn, cotton, hemp, viscose, conductive filament, and so on. Anti-pilling property, crease recovery, drapability, moisture transmission and air permeability of the fabrics were tested and analyzed. From the test results, following conclusions can be gotten. 1) The anti-pilling property is good for fabrics with tighter weave construction; 2) The crease recovery is good for fabrics with smaller weft density; 3) The moisture permeability is good for fabrics with smaller tightness; 4) The crease resistance, drapability, moisture permeability and air permeability of the fabrics can be improved by looser weave construction and smaller binding point.

Continuous multi-filament boron nitride fibers have been prepared on a large scale using the melt drawn technique from a low-cost boracic acid. Boracic acid was heated to obtain the molten boric oxide in a melting tank. Molten boric oxide was melt spun in a conventional manner through an 200-tip bushing to produce a continuous multifilament yarn consisting of 200 filaments of boric oxide. Boric oxide fibers were nitrided in an ammonia and were annealed in an inert atmosphere while simultaneously subjecting the fibers to sufficient longitudinal tension as to at least prevent longitudinal shrinkage of the fibers. The resulting fibers, consisting essentially of boron nitride, were less than about 8 μm in diameter and greater than 500 m in length. It indicated that the boron nitride fibers has a sound mechanical function with tensile strength of 1.40 GPa. The continuous boron nitride fibers of high-performance were especially suitable for reinforcing plastic, ceramic or metal matrices in the preparation of fiber reinforced composites.

The scope of the presented master thesis was the experimental study of multi-filament yarns made of AR-glass and used for textile-reinforced concrete. The behavior under the tensile loading was investigated by laboratory tests. A high number of yarn specimens (over 300) of six different lengths (from 1 cm to 74 cm) was tested to obtain statistically significant data which were subsequently corrected and statistically processed. The numerical model of the multi-filament bundle was studied and applied for prediction of the yarn performance and for later results interpretation. The model of n parallel filaments describes the behavior of a bundle with varying parameters representing different sources of disorder of the response and provides the qualitative information about the influence of their randomization on the overall bundle response. The aim of the carried experiment was to validate the model presumptions and to identify the model parameters to fit the real load-displacement curves. Unfortunately, due to unsuccessful correction of measured displacements devalued by additional non-linear contribution of the unstiff experiment device the load-displacement diagrams were not applicable to model parameters identification. The statistical evaluation was carried only for the maximal load values and the effect of the specimen size (length) on its strength was demonstrated. The size effect curve did not exclude the existence of spatial correlation of material mechanical properties modifying the classical statistical Weibull theory.

The paper presents a meso-scopic modeling framework for the simulation of three-phase composite consisting of a brittle cementitious matrix and reinforcing AR-glass yarns impregnated with epoxy resin. The construction of the model is closely related to the experimental program covering both the meso-scale test (yarn tensile test and double sided pull-out test) and the macro-scale test in the form of tensile test on the textile reinforced concrete specimen. The predictions obtained using the model are validated using a-posteriori performed experiments.

Cette recherche porte sur les fils multifilamentaires de verre utilisés pour renforcer les matériaux à base de ciment. Elle est focalisée sur les interactions mécaniques de ce type de fils, constitués d'un assemblage de milliers de filaments micrométriques, avec un micro-béton et sur le rôle spécifique de l'imprégnation du fil par cette matrice cimentaire. Trois pré-conditionnements des fils ont été employés lors de la fabrication des éprouvettes afin de moduler les conditions d'imprégnation par la matrice cimentaire. L'imprégnation de 5 fils multi-filamentaires par la matrice cimentaire a été caractérisée et les paramètres d'imprégnation ont été définis en s'appuyant sur des observations MEB, ainsi que des essais de porosimétrie au mercure et des essais spécifiques d'écoulement le long du fil enrobé. Des essais classiques d'arrachement de type pull-out ont été utilisés pour la caractérisation mécanique. L'analyse des liens entre les propriétés mécaniques et les paramètres d'imprégnation ont permis de mieux comprendre les micro-mécanismes d'interaction filaments / matrice cimentaire et d'expliquer le comportement macroscopique à l'arrachement
This research deals with multi-filaments glass yarns used as reinforcement of cement based materials. It focuses on the mechanical interactions of these yarns, made of thousands of micrometric filaments, with a micro-concrete and on the specific part of the impregnation of the yarn by the cementitious matrix. Modulated impregnation conditions of the yarns were obtained by using three different manufacturing processes for the samples preparation. The impregnation of 5 multi-filament yarns by the cementitious matrix has been characterized and physical parameters of impregnation were determined using SEM investigations, mercury intrusion porosity measurements and specific tests of flow all along the embedded yarn. Classical pull-out tests have been used for the mechanical characterisation. The study of the links between the mechanical properties and the physical parameters of impregnation allowed accessing a better understanding of the filaments / cementitious matrix interaction micro-mechanisms, and explaining the macroscopic pull-out behaviour

Zur Charakterisierung der Mikrostruktur wurde die Geometrie des Verbundes aus REM-Aufnahmen ausgewertet, sowie die Verbundwirkung einzelner Filamente aus Filament-Pull-Out-Versuchen abgeleitet. Die gewonnenen Parameter bilden die Grundlage für die Modellierung von Garnauszugs- und Rissüberbrückungsmodellen. Unabhängig davon wurde ein Filament-Matrix-Verbund-Gesetz simuliert. Die Übereinstimmungen zwischen der Simulation und der experimentellen Untersuchung des Ausziehverhaltens werden in dem Artikel diskutiert
The microstructure is characterized by analysing the bond geometrically and experimentally. The data to evaluate these two ways are from SEMimages and filament-pull-out-tests. Based on these data yarn-pull-out-models and crack-bridging-models are calculated. In addition a filament-matrix-bond-law is simulated independently. The correlation between the simulation and the experimental analysis of the pull-out behaviour is discussed in this paper

Zur Untersuchung der Schädigungs- und Versagensmechanismen eines in Beton eingebetteten Multifilamentgarns im Auszugversuch wurde die Schallemissionsanalyse zur Identifizierung und Lokalisierung von Filamentbrüchen eingesetzt. Im ersten Schritt wurden dazu die Schall emittierenden Ursachen (Filamentriss, Filamentablösung und Mikroriss im Beton) für eine Differenzierung charakterisiert. Es wurden Versuche zur Erzeugung von isolierten Signalen durchgeführt, welche mit Hilfe der Signal- und Frequenzanalyse untersucht wurden. Bei dem durchgeführten Garnauszugversuch konnte eine hohe Lokalisierungsgenauigkeit der Filamentbrüche erzielt werden. Der Schädigungsverlauf des Garns während des Auszugversuchs konnte detailliert untersucht werden.

Ces dernières années, les matériaux composites à matrices minérales ont suscité un grand intérêt dans le domaine du génie civil, en raison de leurs multiples avantages tels que la grande résistance en traction, le comportement pseudo-ductile, la facilité de mise en oeuvre, la nontoxicité et la compatibilité aux substrats. Toutefois, l’efficacité de ces composites est souvent limitée du fait de la faible adhérence du renfort avec la matrice. Cela est du à la faible pénétration des particules de la matrice entre les filaments internes du fil, ce qui entraine une rupture prématurée du matériau. Ce travail a pour but d’améliorer l’adhérence fil-matrice par pré-imprégnation du renfort, afin d’optimiser le comportement mécanique des composites. Deux méthodes de pré-imprégnation ont été utilisées : pré-imprégnation classique par voie humide et pré-imprégnation par voie sèche. Cette dernière se base sur l’application d’un champ électrostatique alternatif permettant la pénétration de la poudre au sein du renfort. La première méthode a déjà été utilisée dans la littérature et a permis d’améliorer les propriétés mécaniques du composite. Cependant, son utilisation reste limitée aux éléments préfabriqués simples contrairement à la deuxième méthode qui peut être appliquée pour réaliser des éléments de construction de grande taille, ou bien pour le renforcement et la réparation des structures in situ. La présente étude s’appuie sur une analyse multi-échelles permettant d’aborder le problème d’adhérence à l’échelle d’interface (fil-matrice) et à l’échelle du composite (fil-matrice et textile-matrice). Tout d’abord, des essais d’arrachement ont été conduits sur des fils de verre enrobés dans une matrice ettringitique. Huit configurations ont été étudiées afin d’évaluer l’effet du processus de pré-imprégnation et le type des matériaux de pré-imprégnation à sec. Il en sort que le comportement d’arrachement est amélioré par pré-imprégnation du fil par voie humide et sèche mais, précisons que par voie sèche, l’amélioration est significative seulement dans le cas d’utilisation de poudre de particules très fines. Une modélisation numérique de l’essai d’arrachement a été également réalisée afin d’identifier les propriétés d’interface fil-matrice. En se basant sur ces résultats, une étude expérimentale et numérique du comportement en traction des composites fil-matrice a été ensuite réalisée. Cinq configurations ont été retenues, après avoir écarté les prétraitements de fil ayant eu un effet néfaste sur l’adhérence fil-matrice. Il s’est avéré que les deux procédés contribuent à une augmentation significative des propriétés mécaniques du composite. De plus, un modèle numérique 3D a été développé pour simuler l’essai de traction d’un composite sec et pré-imprégné. Il a permis d’une part de prédire le comportement global du matériau et d’autre part d’apporter une meilleure compréhension de ce comportement grâce à l’analyse des états de déformation et de contrainte au niveau du fil, de la matrice et de l’interface. Enfin, une comparaison de l’effet des deux procédés de pré-imprégnation a été établie à l’échelle du composite textile-matrice au moyen d’essais de traction et d’analyse de corrélation d’image. Cinq différents types de tissu de verre unidirectionnel ont été utilisés. La pré-imprégnation par voie sèche a démontré la plus forte amélioration des performances du composite quel que soit le grammage du tissu, contrairement à la pré-imprégnation par voie humide qui trouve sa limite quand le textile devient dense
In recent years, mineral matrix composites have gained great interest in the field of civil engineering, thanks to their multiple advantages such as high tensile strength, pseudo-ductile behavior, ease of implementation, non-toxicity and substrate compatibility. However, the efficiency of these composites is often limited because of the low adhesion of the reinforcement to the matrix. This is due to the low penetrability of matrix particles into the space between the inner filaments of the yarn, which leads to premature failure of the material. The purpose of this work is to improve the yarn-matrix adhesion by pre-impregnating the reinforcement in order to optimize the mechanical behavior of composites. Two pre-impregnation methods were used : conventional pre-impregnation in a wet manner and pre-impregnation in a dry manner. This last is based on an alternating electrostatic field used to impregnate yarns with powder. The first method has already been used in the literature and has improved the mechanical properties of the composite. However, it is suited only for the manufacturing of simple prefabricated elements, unlike the second method, which can be applied for the construction of large elements, or for strengthening or repairing structures in site. This study is based on a multi-scale analysis to investigate the bond problem at the interface scale (yarn-matrix) and at the composite scale (yarn-matrix and textile-matrix). First, pull-out tests were conducted on glass yarns embedded in an ettringitic matrix. Eight configurations were studied to evaluate the effect of the pre-impregnation process and the type of dry pre-impregnation powders. It results that the pull-out behavior is improved by pre-impregnating the yarn in wet and dry manner but, it should be noted that in dry process, the improvement is significant only when using very fine particle powders. A numerical modeling of the pull-out test was also carried out in order to identify the yarn-matrix interface properties. Based on these results, an experimental and numerical study of the tensile behavior of yarn-matrix composites was then carried out. Five configurations were selected, after excluding the yarn pre-treatments that had a negative effect on the yarn-matrix bond. It was found that both processes contribute to a significant increase in the mechanical properties of the composite. In addition, a 3D numerical model has been developed to simulate the tensile test of a dry and pre-impregnated composite. It allowed on the one hand to predict the global behavior of the material and on the other hand to provide a better understanding of this behavior by analyzing the deformation and stress states at the level of the yarn, the matrix and the interface. Finally, a comparison of the effect of the two pre-impregnation processes was established at the textile-matrix composite scale by means of tensile tests and image correlation analysis. Five different types of unidirectional glass fabric were used. The dry pre-impregnation has shown the best improvement in composite performance regardless of fabric density, unlike the wet pre-impregnation, which has its limits when the textile becomes dense

This experimental study focuses on the links that exist between the mechanical pull-out behaviour of multi-filament yarns embedded in concrete and the impregnation of the yarn by the concrete. To this aim, 5 glass yarns have been embedded in concrete (AR and E glass yarns from assembled or direct roving). A pre-treatment was applied to the yarn before the casting, and was chosen in the following three: wetting, drying or pre-impregnation with a cement slurry. By this way, 15 yarn / pre-treatment combinations were obtained that generate 15 conditions of impregnation of the yarn by the cementitious matrix. In each case, the mechanical properties were determined from a classical pull-out test and the yarns impregnation properties were characterized by two dedicated tests: yarns porosity measurements and along yarn water flow measurements. By studying the relationship between the mechanical behaviour and the physical properties of the impregnated yarns, it is shown that the pre- and post-peak behaviour are mainly connected to the flow rate measured during the water flow measurements, which suggest a specific influence of the connected pores parallel to the filaments and of the penetration depth of the matrix into the yarn. The postpeak and the residual behaviour are moreover linked to the yarn pore volume associated to the disorder induced in the filaments assembly by the penetration of the matrix. The overall result of this work is a contribution to the understanding of the relationship between the impregnation of the yarns and the pull-out behaviour.

In the present work, the load-bearing behaviour of Textile Reinforced Concrete (TRC), which is a composite of a fine-grained concrete matrix and a reinforcement of high-performance fibres processed to textiles, exposed to uniaxial tensile loading was investigated based on numerical simulations. The investigations are focussed on reinforcement of multi-filament yarns of alkali-resistant glass. When embedded in concrete, these yarns are not entirely penetrated with cementitious matrix, which leads associated with the heterogeneity of the concrete and the yarns to a complex load-bearing and failure behaviour of the composite. The main objective of the work was the theoretical investigation of effects in the load-bearing behaviour of TRC, which cannot be explained solely by available experimental results. Therefore, a model was developed, which can describe the tensile behaviour of TRC in different experimental test setups with a unified approach. Neglecting effects resulting from Poisson’s effect, a one-dimensional model implemented within the framework of the Finite Element Method was established. Nevertheless, the model takes also transverse effects into account by a subdivision of the reinforcement yarns into so-called segments. The model incorporates two types of finite elements: bar and bond elements. In longitudinal direction, the bar elements are arranged in series to represent the load-bearing behaviour of matrix or reinforcement. In transverse direction these bar element chains are connected with bond elements. The model gains most of its complexity from non-linearities arising from the constitutive relations, e. g., limited tensile strength of concrete and reinforcement, tension softening of the concrete, waviness of the reinforcement and non-linear bond laws. Besides a deterministic description of the material behaviour, also a stochastic formulation based on a random field approach was introduced in the model. The model has a number of advantageous features, which are provided in this combination only in a few of the existing models concerning TRC. It provides stress distributions in the reinforcement and the concrete as well as properties of concrete crack development like crack spacing and crack widths, which are in some of the existing models input parameters and not a result of the simulations. Moreover, the successive failure of the reinforcement can be studied with the model. The model was applied to three types of tests, the filament pull-out test, the yarn pull-out test and tensile tests with multiple concrete cracking. The results of the simulations regarding the filament pull-out tests showed good correspondence with experimental data. Parametric studies were performed to investigate the influence of geometrical properties in these tests like embedding and free lengths of the filament as well as bond properties between filament and matrix. The presented results of simulations of yarn pull-out tests demonstrated the applicability of the model to this type of test. It has been shown that a relatively fine subdivision of the reinforcement is necessary to represent the successive failure of the reinforcement yarns appropriately. The presented results showed that the model can provide the distribution of failure positions in the reinforcement and the degradation development of yarns during loading. One of the main objectives of the work was to investigate effects concerning the tensile material behaviour of TRC, which could not be explained, hitherto, based solely on experimental results. Hence, a large number of parametric studies was performed concerning tensile tests with multiple concrete cracking, which reflect the tensile behaviour of TRC as occurring in practice. The results of the simulations showed that the model is able to reproduce the typical tripartite stress-strain response of TRC consisting of the uncracked state, the state of multiple matrix cracking and the post-cracking state as known from experimental investigations. The best agreement between simulated and experimental results was achieved considering scatter in the material properties of concrete as well as concrete tension softening and reinforcement waviness
Die vorliegende Arbeit beschäftigt sich mit Untersuchungen zum einaxialen Zugtragverhalten von Textilbeton. Textilbeton ist ein Verbundwerkstoff bestehend aus einer Matrix aus Feinbeton und einer Bewehrung aus Multifilamentgarnen aus Hochleistungsfasern, welche zu textilen Strukturen verarbeitet sind. Die Untersuchungen konzentrieren sich auf Bewehrungen aus alkali-resistentem Glas. Das Tragverhalten des Verbundwerkstoffs ist komplex, was aus der Heterogenität der Matrix und der Garne sowie der unvollständigen Durchdringung der Garne mit Matrix resultiert. Das Hauptziel der Arbeit ist die theoretische Untersuchung von Effekten und Mechanismen innerhalb des Lastabtragverhaltens von Textilbeton, welche nicht vollständig anhand verfügbarer experimenteller Ergebnisse erklärt werden können. Das entsprechende Modell zur Beschreibung des Zugtragverhaltens von Textilbeton soll verschiedene experimentelle Versuchstypen mit einem einheitlichen Modell abbilden können. Unter Vernachlässigung von Querdehneffekten wurde ein eindimensionales Modell entwickelt und im Rahmen der Finite-Elemente-Methode numerisch implementiert. Es werden jedoch auch Lastabtragmechanismen in Querrichtung durch eine Unterteilung der Bewehrungsgarne in sogenannte Segmente berücksichtigt. Das Modell enthält zwei Typen von finiten Elementen: Stabelemente und Verbundelemente. In Längsrichtung werden Stabelemente kettenförmig angeordnet, um das Tragverhalten von Matrix und Bewehrung abzubilden. In Querrichtung sind die Stabelementketten mit Verbundelementen gekoppelt. Das Modell erhält seine Komplexität hauptsächlich aus Nichtlinearitäten in der Materialbeschreibung, z.B. durch begrenzte Zugfestigkeiten von Matrix und Bewehrung, Zugentfestigung der Matrix, Welligkeit der Bewehrung und nichtlineare Verbundgesetze. Neben einer deterministischen Beschreibung des Materialverhaltens beinhaltet das Modell auch eine stochastische Beschreibung auf Grundlage eines Zufallsfeldansatzes. Mit dem Modell können Spannungsverteilungen im Verbundwerkstoff und Eigenschaften der Betonrissentwicklung, z.B. in Form von Rissbreiten und Rissabständen untersucht werden, was in dieser Kombination nur mit wenigen der existierenden Modelle für Textilbeton möglich ist. In vielen der vorhandenen Modelle sind diese Eigenschaften Eingangsgrößen für die Berechnungen und keine Ergebnisse. Darüber hinaus kann anhand des Modells auch das sukzessive Versagen der Bewehrungsgarne studiert werden. Das Modell wurde auf drei verschiedene Versuchstypen angewendet: den Filamentauszugversuch, den Garnauszugversuch und Dehnkörperversuche. Die Berechnungsergebnisse zu den Filamentauszugversuchen zeigten eine gute Übereinstimmung mit experimentellen Resultaten. Zudem wurden Parameterstudien durchgeführt, um Einflüsse aus Geometrieeigenschaften wie der eingebetteten und freien Filamentlänge sowie Materialeigenschaften wie dem Verbund zwischen Matrix und Filament zu untersuchen. Die Berechnungsergebnisse zum Garnauszugversuch demonstrierten die Anwendbarkeit des Modells auf diesen Versuchstyp. Es wurde gezeigt, dass für eine realitätsnahe Abbildung des Versagensverhaltens der Bewehrungsgarne eine relativ feine Auflösung der Bewehrung notwendig ist. Die Berechnungen lieferten die Verteilung von Versagenspositionen in der Bewehrung und die Entwicklung der Degradation der Garne im Belastungsverlauf. Ein Hauptziel der Arbeit war die Untersuchung von Effekten im Zugtragverhalten von Textilbeton, die bisher nicht durch experimentelle Untersuchungen erklärt werden konnten. Daher wurde eine Vielzahl von Parameterstudien zu Dehnkörpern mit mehrfacher Matrixrissbildung, welche das Zugtragverhalten von Textilbeton ähnlich praktischen Anwendungen abbilden, durchgeführt. Die Berechnungsergebnisse zeigten, dass der experimentell beobachtete dreigeteilte Verlauf der Spannungs-Dehnungs-Beziehung von Textilbeton bestehend aus dem ungerissenen Zustand, dem Zustand der Matrixrissbildung und dem Zustand der abgeschlossenen Rissbildung vom Modell wiedergegeben wird. Die beste Übereinstimmung zwischen berechneten und experimentellen Ergebnissen ergab sich unter Einbeziehung von Streuungen in den Materialeigenschaften der Matrix, der Zugentfestigung der Matrix und der Welligkeit der Bewehrung