CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

Material Models of Composites for Crash Simulation

Many different types of composites exist today, but generally there is a common aim to combine two or more constituents to give a better material than each of the individual constit- uents. The most popular composites today combine strong stiff fibres (e.g. Carbon, Glass or Aramid) with a low strength polymer matrix (e.g. Epoxy or Polyester). Great flexibility is possible in combining these materials to obtain required cost and performance. The fibres are first brought together as yarns having, typically, 6k (k=1000) and possibly up to 48k fibres. These yarns may be directly used to manufacture a ‘preform’, which is the basic textile structure of the composite; or they may be further processed into fabrics. The fabrics would then be formed (draped), combined and trimmed for the preform. Generally, Aerospace applications use 6k or 12k tows for best performance, whereas ‘thicker’ 24k or even 48k tows are preferred for Automotive applications where low cost fast preforming is the priority. Many different types of fabrics are produced having widely different drape, infusion or final part mechanical properties for stiffness, strength or impact. Gen- erally, fabrics fall into two groups and either have intertwined yarns (e.g. Plain weaves and Twills) or have straight yarns (Non Crimp Fabrics) for better stiffness. In this case yarns are overlaid and held together with light stitching.

composites broadly fall into two camps. First, there are the high performance pre-preg composites in which a laminate is made from stacking plies which have resin pre-impregnated into the fibres; and second, there are Liquid Resin Infusion technologies where resin is only added after the dry fabrics are placed and shaped. Regardless of the fibre, fabric or resin types there are usually common analysis methods available to predict composites mechanical performance; these range from simple analytical methods for stiffness to advanced Finite Element methods for stiffness, failure and impact or crash loading. Some simple formulae based on mechanics of materials can be helpful to obtain basic mechanical data; these so-called micro-me- chanics laws combine fibre and matrix properties to give homogenized composite properties.

Voigt model: This law of mixtures gives accurate axial composite modulus E 1 from fibre modulus (E f ), resin modu- lus (Em), fibre volume ratio (V f = vol. fibres/ total vol.) and the matrix volume ratio V m (=1-V f / total vol.). Reuss model: This reciprocal law of mixtures for E 2 gives a poor estimate for transverse modulus since transverse stresses are non-uniform and poorly represented by the assumed simple spring model. Improved relations are given by the Halpin-Tsai or Hopkins-Chamis models.

Bi-axial NCF (tricot stitch)

Despite considerable research it has been difficult to extend micro-mechanics models to woven textile composites for accurate failure prediction. If homogenized properties are available, from test or micro-mechanics, then Classical Lami- nate Theory (CLT) can be used to compute laminate stiffness of a stack of plies. Software tools are available to help auto- mate these calculations. Typically, for a given applied loading, these codes compute overall laminate strains and individual ply stresses and strains in the fibre directions. Classical failure criteria can then be used to compute maximum load limits. During the past 30 years many ply failure criteria have been proposed with the main ones being Maximum Stress (or Strain) and the Tsai-Hill and Tsai-Wu ‘quadratic’ criteria. Each of these describes a failure envelope in stress, or strain space,

Uni-directional NCF The function of the resin is to protect fibers and transfer stresses between them; particularly for load redistribution at the ends of any fibres that may break. Again, an enormous variety or resin types are commercially available ranging from low performance, low cost, polyester systems to high perfor- mance epoxy resins and super high performance/cost PEEK thermoplastic resins. Finally, manufacturing methods for

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