Multiaxial structure

The textile structure of fiber-reinforced plastics is built by woven fabrics (Chapter 4), knitwear (Chapter 5), nonwovens (Chapter 6), braids (Chapter 7), and two-dimensional reinforcing textiles of multiaxial structure (Chapter 8). For the matrix, both thermosets and thermoplastics are used. 

Mainly woven fabrics (Chapter 4) and nonwovens (Chapter 6) are used as geotextiles. Today also multiaxial structures such as multiaxial multi-ply warp-knitted fabrics (MAG) or stitch-bonded fabrics (NVG) (Chapter 7) are used more and more in this field of application. The yarns in this process are monofiles, filament yarns (Chapter 2), or spun yarns (Chapter 3). 

The stored strain energy can also be determined for the general case of multiaxial stresses [1] and lattices of varying crystal structure and anisotropy. The latter could be important at interfaces where mode mixing can occur, or for fracture of rubber, where f/ is a function of the three stretch rations 1], A2 and A3, for example, via the Mooney-Rivlin equation, or suitable finite deformation strain energy functional. 

As pointed out earlier, the IGDA utilizes the CIE-10 for the first three axes of its multiaxial formulation. This diagnostic model is structured as follows ... 

In a recent attempt to bring an engineering approach to multiaxial failure in solid propellants, Siron and Duerr (92) tested two composite double-base formulations under nine distinct states of stress. The tests included triaxial poker chip, biaxial strip, uniaxial extension, shear, diametral compression, uniaxial compression, and pressurized uniaxial extension at several temperatures and strain rates. The data were reduced in terms of an empirically defined constraint parameter which ranged from —1.0 (hydrostatic compression) to +1.0 (hydrostatic tension). The parameter () is defined in terms of principal stresses and indicates the tensile or compressive nature of the stress field at any point in a structure —i.e.,... 

Theories of yielding and flow expressed in terms of invariants of the applied stress tensor are examples of appropriate constitutive laws. The design of complex engineering components must consider the response of the component to realistic states of stress, which are inevitably multiaxial. Consequently, models of yielding and flow that accommodate such conditions must be employed in constructing the design. Descriptions of the structure of material that appear in such theories must likewise be expressed in tensorially invariant form. 

Failure Criterion. In the design of a propellant structure, the output of the calculation is a tensor quantity in terms of either stress or strain, which must be compared with some experimentally available failure properties. These properties are generally obtained from uniaxial and multiaxial extension... 

I had the opportunity to participate in review meetings and to meet with the researchers working in this program. Their accomplishments are presented in this book. It covers the entire spectrum of combustion applied to air breathing propulsion. Analysis, computation, experimentation, and diagnostics are blended logistically to maximize the utilization of research to practical applications. Fundamental aspects such as the detonation cell structures to applied topics such as multiaxis fluidic thrust vector control are covered in this book. 

Participation of a number of universities in the U.S. and foreign technical institutions hcis enabled significant progress in addressing these issues. Single and multicycle operations of PDEs with gaseous and liquid fuels have been demonstrated. The studies include from the fundamental understanding of the cellular structure of the detonation waves to the multiaxis thrust measurement from PDEs. 

This chapter is a revised version of Chapter 10, Fatigue of fiber reinforced composites under multiaxial loading by M. Quaresimin and R. Talreja, originally published in Fatigue Life Prediction of Composites and Composite Structures ed. A. P. Vassilopoulos, Woodhead Publishing Limited, 2010 (ISBN 978-1-84569-525-5). 

In spite of the importance that notches and stress concentrations can have in the design of structural parts, their influence on multiaxial fatigue strength has rarely been investigated [10,15,16,29,32,33]. It is difficult to draw general design indications from the few data available however, from at least one of the papers cited, some interesting conclusions can be obtained. 

The overview of the behavior of continuous hber reinforced composites under multiaxial cyclic loading presented in Section 7.4 and the assessment of certain predictive criteria reported in Section 7.5 indeed provide some support for the design of structural composite parts subjected to in-service loadings. On the other hand, they also display the complexity of the problem exacerbated by the large number of variables that... 

Another important future research activity for certification of structures under crash loads is to develop efficient stochastic analysis methods for use with explicit FE codes. Since crash events are stochastic in nature, through variability of structural mass, crash velocity, impact position and impact angle, a single crash simulation with one set of conditions is not sufficient for certification. In this case, a certification strategy should be based on a stochastic analysis with variation in crash conditions, which allows a failure envelope to be determined for a specific crash scenario. Then it is possible to consider the failure mode and crash energy absorbed under more realistic multiaxial crash loads to establish structural integrity for the worst case rather than a single crash scenario. 

An area where savings may be possible with improved materials data is on evaluation of welded joints. The material properties of the complete weld joint, as opposed to the weld metal alone, are needed. Ductility under multiaxial loading plays a key role in the structural adequacy of weldments subject to cyclic loading. 

The structure and orientation of the reinforcing fibers in the matrix system are essential for the mechanical properties of the work-piece. The choice of a particular architecture is dependent on multiple factors like drapeabiUty of the fabric, geometry/shape of the workpiece, mechanical requirements, and manufacturing process. Compraients made of unidirectional layers (laminates) are showing the best mechanical properties since the fibers are completely stretched (no undulation). Usually the single layers of a laminate are showing different fiber orientations. This causes anisotropic material behavior in the planar direction. The structure of a multiaxial layered laminate is shown in Fig. 2. 

AM Manich, M Marti, R M Sauri, M D de Castellar and J Carvalho, Effect of finishing on woven fabric structure and compressional and cyclic multiaxial strain properties . Text Res J, 2006 76 86-93... 

Three dimensional structures of multiaxial warp knitted fabrics have been recently developed for multidirectional reinforcement of composites. Multilayers of linear yams are assembled in warp (0°), weft (90°) and bias ( 0) directions to provide in-plane reinforcement in specific directions and they are stitched together by knitting yams to provide structural integrity and through the thickness reinforcement [1,2,3,4,5]. 

In this study two material groups were chosen and numbered from 1 to 4. For number 1 and 2 bamboo, polypropylene and elastomeric yams, for number 3 and 4 soybean, polyester and elastomeric yams were used. The linear density of all yams were 100 tex. Midtiaxial warp knitted structures were produced fiom these yams, directions of the yams are given in Table 1. Finally multiaxial warp knitted bandages were stitched with polyester thread for the structural integrity. 

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