Ultrasonic evaluation of anisotropic damage in multiaxially textile-reinforced thermoplastic composites made from hybrid yarns

The basic damage and failure models of multiaxially reinforced composites with a thermoplastic matrix are presented and verified. Within the framework of continuum damage mechanics, a phenomenological model is introduced, where the damage is defined as a change in the elasticity tensor. For damage identification, a specific ultrasonic device was developed. A combination of an immersion set-up and a contact coupling device formed a system for an efficient determination of stiffness-tensor components from convenient sets of velocity measurements. Linked to a tensile machine, it allowed us to measure the anisotropic damage of the new materials group caused by tensile loading. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 221–234, March–April, 2006.     

Material-Adapted Design of Textile-Reinforced Composite Structures with Optimized Vibro-Acoustic and Damping Properties Including Shear Effects

Advanced analytical models have been developed at the ILK, which offer a possibility of calculating the vibro-acoustic and damping behavior of textile-reinforced composite shells and plates with account of shear effects. The simulation models elaborated have been verified on selected examples, and the analytical results were fully corroborated by accompanying numerical calculations for typical lay-ups.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 289–302, May–June, 2005.     

Kerbspannungsanalyse anisotrop faserverstärkter Scheiben

Übersicht Da Kerben vor allem die versagensrelevanten Schwachstellen einer Konstruktion darstellen, ist für die Auslegung von Faserverbundbauteilen in besonderem Maße ein Kerbspannungsnachweis geboten. Denn bei anisotropen Werkstoffen sind die maximalen Kerbspannungsfaktoren erheblich höher als bei den herkömmlichen isotropen Werkstoffen, wobei das Kerbspannungsverhalten stark vom AnisotropiegradE /E des Faserverbundes sowie von geometrie- und belastungsspezifischen Kenngrößen abhängt. Das ebene Kerbspannungsfeld wird mittels der Methode der konformen Abbildung durch komplexwertige Spannungsfunktionen ermittelt. Dabei dient als mathematisches Modell die anisotrope homogene Scheibe unendlicher Ausdehnung mit verschiedenen Ausschnittskonturen. Für einige Standardfälle von Kerbkonturen und Belastungsarten sowie im Leichtbau eingesetzten Faserverbundwerkstoffen wird der Kerbspannungsfaktor in Abhängigkeit allfälliger Einflußparameter untersucht. Im einzelnen handelt es sich dabei um folgende Konstruktionsparameter: Kerbform, Faser/Matrix-Kombination, Art und Richtung der Belastung, Faserorientierung.

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Stress concentration in notched anisotropically fibre-reinforced plates

Summary As notches represent the most relevant sites of failure in a construction, a calculation of the stress distribution around holes is essential for the design of fibre-reinforced materials. Especially in the case of anisotropic materials the maximal stress concentration factor on the cutout is considerably higher than in conventional isotropic materials. In fibre-reinforced materials the stress distribution around holes is strongly dependent on the degree of anisotropyE /E as well as on the notch geometry and load parameters. The plain stress field around a notch of known geometry will be calculated by means of the method of conformal mapping and complex stress functions, based on the mathematical model of an infinite anisotropic plate with various shapes of the aperture. For some standard types of notches and load cases, the stress concentration factor as a function of various construction parameters will be studied for fibre-reinforced materials used in lightweight construction. Particularly, the following construction parameters are considered: Hole geometry, fibre/matrix combination, load cases and directions orientation of fibres.

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Zum 80. Geburtstag Herrn Univ.-Prof. (em.) Dr. Manfred Schäfer gewidmet.     

An analytical method for the determination of stress and strain concentrations in textile-reinforced GF/PP composites with elliptical cutout and a finite outer boundary and its numerical verification

Stress concentrations in the vicinity of cutouts can often be regarded to be the limiting factor for a whole structure. As a further development of prior research at the Institute of Lightweight Engineering and Polymer Technology, an analytical method for the determination of the whole stress-strain fields in the vicinity of holes in multilayered textile-reinforced composites has been developed, which takes into consideration the influences of a finite outer boundary of the specimen. The analytical method is based on the classical laminate theory and the use of complex-valued potential functions. To account for the shape of the specimen, the method of conformal mappings is applied for the inner boundary, while a combination of boundary collocation and least squares method is used for the outer boundary. The method allows a layer-by-layer analysis of stress concentrations. For the verification of the developed calculation model, extensive experimental and numerical finite-element (FE) studies have been carried out on multilayered GF/PP plates with different laminate layups, notches, and specimen dimensions. The comparison of the experimentally or numerically determined results with the analytically calculated ones shows a very good correlation, of which the numerical studies are presented here for the first time. In a second step, the applicable boundary conditions on the outer boundary have been extended in such a way that varying stress and moment resultants can be applied, so that the calculation method can be used as an analytical sub-model in combination with FE techniques.     

Design of Dynamically Loaded Fiber-Reinforced Structures with Account of Their Vibro-Acoustic Behavior

Dynamically loaded structures for high-technology applications generally require high material damping combined with low construction weight and adequate stiffness. Advanced lightweight structures will have to meet not only these dynamic demands but also improved acoustic (low noise) standards. High-performance materials like magnesium, aluminum, or titanium, which are mainly used in today's lightweight applications, reach their limits with respect to these dynamic and especially vibro-acoustic requirements. They offer a high specific stiffness and strength, but a relatively low damping, which leads to intense acoustic radiation. Therefore, composites or compound materials with a dynamically and vibro-acoustically optimized property profile are needed. The structural dynamic and vibro-acoustic behavior of these types of lightweight structures cannot be described by the use of classical models. Here, the advanced methods developed at ILK are considered, which take into account the special mechanical properties of the fiber-matrix compound. Also, sophisticated numerical simulation techniques such as the finite and the boundary element method are successfully applied.     

Fatigue failure criteria and degradation rules for composites under multiaxial loadings

To develop design rules for dynamically loaded composite structures, extensive static and cyclic tension/compression-torsion tests were carried out on carbon-fibre-reinforced composites, in which especially the important influence of multiaxial loading conditions on their fatigue behaviour was investigated. Physically based failure criteria for static loadings are modified for multiaxial cyclic loadings, and a good agreement with experiments is achieved. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 631–641, September–October, 2006.     

Adjustment of Residual Stresses in Unsymmetric Fiber-Reinforced Composites Using Genetic Algorithms

During the manufacturing process of multilayered fiber-reinforced composites with variable fiber orientations, residual stresses build up in these composites due to the directional expansion of single unidirectionally reinforced layers. Depending on the laminate lay-up, the inhomogeneous residual stresses, which are caused by thermal effects, moisture absorption, and chemical shrinkage, can lead to large multistable out-of-plane deformations. Instead of avoiding these curvatures, they can be advantageously used for technical applications following the near-net-shape technology. In order to adjust the deformations to the technical requirements, genetic algorithms in combination with a nonlinear calculation method have been developed, which can purposefully adapt the laminate lay-up depending on the loading and process parameters.     

Design of novel morphing structures based on bistable composites with piezoceramic actuators

Instead of attempts to avoid the large out-of-plane deformations of multilayered fiber-reinforced composites caused by residual stresses, these deformations can be advantageously used for technical applications such as novel morphing structures, where only a discontinuous energy impulse of an actuator is necessary to change the configuration of the structure. For the design of such innovative morphing structures with piezoelectric actuators, novel nonlinear semi-analytical and numerical simulation models have been developed and verified experimentally. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 475–494, July–August, 2006.     

Berechnung des Spannungs- und Verschiebungsfeldes anisotroper Scheiben mit elliptischem Ausschnitt

Übersicht Für die anisotrope linear-elastische Scheibe unter beliebiger Zugkraft- und Faserorientierung wird analytisch das ebene Spannungs- und Verschiebungsfeld um die elliptische Innenkerbe mittels komplex-wertiger Spannungsfunktionen ermittelt. Dabei dient als mathematisches Modell der (gezogene) Scheibenstreifen unendlicher Breite. Am Beispiel orthotrop glasfaserverstärkter Werkstoffe wird gezeigt, daß die vom isotropen Werkstoff her bekannten Aussagen über das Spannungs- und Verschiebungsverhalten an elliptischen und kreisförmigen Kerben auf anisotrope Werkstoffe nicht übertragbar sind. Insbesondere gilt dies bei Auseinanderklaffen von Last- und Orthotropiehauptrichtung (off-axis-Belastung). Für einige ausgezeichnete Fälle werden die für die Dimensionierung maßgebenden Spannungsüberhöhungsfaktoren in Polardiagrammen dargestellt sowie der Ort der maximalen Spannungsüberhöhung angegeben, der — im Unterschied zum isotropen Werkstoff — i. allg. nicht mehr mit dem Kerbgrund zusammenfällt.

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Calculation of the stress and displacement field of anisotropic plates with elliptical hole

Summary The plane stress and displacement field around the elliptical hole of an anisotropic linear elastic plate under arbitary orientation of tension force and fibres is analytically determined by the method of stress functions of a complex variable. For this purpose the infinite plate under uniaxial tension is used as mathematical model. For the example of glass fibre reinforced plastics with orthotropic properties it is shown that the data gathered from isotropic materials on the behaviour of stress and displacement around elliptical and circular holes are not applicable to anisotropic materials. This is especially true when load and orthotropic principal directions (off-axis-load) diverge. For several particular cases, the hole stress concentration factors which are decisive for the design are depicted in polar diagrams. The position of the maximum stress is also given which — in contrast to isotropic materials — generally no longer coincides with the notch base.