Fiber composite

from Wikipedia, the free encyclopedia

A fiber composite material is a composite material , a multi-phase or mixed material, which generally consists of two main components: the reinforcing fibers and an embedding "matrix" (the filler and adhesive between the fibers). Due to the mutual interactions of the two components, the entire material receives higher-quality properties than either of the two components involved alone.


In contrast to earlier composite materials with very thick “fibers”, such as reinforced concrete , the introduction of extremely thin fibers (a few µm in diameter), among other things, makes use of the specific strength effect . This connection was discovered in the twenties by AA Griffith and reads: A material in fiber form has a strength many times greater in the direction of the fiber than the same material in another form. The thinner the fiber, the greater its strength. The reason for this lies in the increasing straightening of the molecular chains as the available area decreases. In addition, flaws leading to breakage (weakest link theory - "Every chain is only as strong as its weakest link." ) In the material are distributed over very large distances so that the fibers are largely free of flaws that could cause a break. Since material can be saved with the same strength, a material is created with a high specific strength (ratio of strength and weight). In addition, a fault in the material does not lead to failure of the entire component, but only to the breakage of a single fiber in the composite for the time being (no crack propagation).

Components made of fiber composite materials are usually more expensive than normal (metal) components.

Endless and long fiber material

The fibers can be aligned depending on the load and their density (number per area) can be adjusted (often up to a "fiber volume proportion" of 60%). The fibers are mainly aligned according to the load paths . In order to influence the strength in different directions, instead of individual fibers, woven or non- woven fabrics are used, which are produced before contact with the matrix.

There are four main consequences (according to Andre Stieglitz) for the selection of a component to convert into a continuous fiber-reinforced composite structure. If one of the following four requirements is not met, its use for the selected component must be viewed critically:

  1. There must be relevant loads in the component.
  2. The load curves must be known or assessable.
  3. There must be main directions of the loads - if the component is loaded evenly regardless of direction, the use of a more isotropic material is recommended ( metal , short fiber composite, ...).
  4. You have to be able to align the fibers according to the load directions.

Short fiber composite

In contrast to the long fiber composite, the fibers of a short fiber composite material, which are just a few millimeters long, are usually not aligned according to the (main) load direction on the component, but are arranged randomly. This creates a framework or lattice structure that has isotropic properties, similar to a homogeneous material.


The higher-quality properties of a fiber composite material are only achieved through the interaction of both components. Two components result in three active phases in the material: very tensile fibers, a relatively soft matrix that embeds them and a boundary layer that connects both components.

Conditions for the reinforcing effect of fibers

Not all combinations of fiber and matrix materials lead to an increase in the strength and rigidity of the new composite. Three conditions must be met for a reinforcement effect to take place in the direction parallel to the fibers:

  1. E fiber, longitudinal > E matrix
    The modulus of elasticity of the fiber in the longitudinal direction must be greater than the modulus of elasticity of the matrix material.
  2. ε break, matrix > ε break, fiber
    The elongation at break of the matrix material must be greater than the elongation at break of the fibers.
  3. R fiber, lengthways > R matrix
    The breaking strength of the fibers must be greater than the breaking strength of the matrix material.

Clearly: (1), (3): The fiber has to withstand higher loads than the matrix, otherwise a component made solely from the matrix material would be more stable.

An important feature here is the “critical fiber length”. The longer they are, the better the fibers can transfer forces to other fibers and to the matrix. For optimal tension and load transfer between fiber and matrix, the fibers must exceed the critical fiber length.

As a rule, there is no increase in strength perpendicular to the fiber. The reason is the increase in elongation .

Functions of the components

  • The matrix holds the reinforcing fibers in place and transfers and distributes stresses between them. In terms of durability, it has the task of protecting the fibers from external mechanical and chemical influences.
  • The fibers give the fiber composite the necessary strength. In addition to tensile strength, if the material is subjected to compression, flexural strength can also play a role.
  • The boundary layer is used to transfer stress between the two components. It only transmits thrust and can take on very abstract forms if the thrust occurs, for example, through pure friction. In other cases, however, for example in the case of shear via adhesive bonding, it is intentional and physically present in terms of production technology. In the latter case, the fibers are coated with a coupling agent before the first contact with the matrix, which can react chemically with both components and guarantees a transition as uninterrupted as possible.

An important factor when dimensioning fiber composite materials is the volume ratio ( fiber volume fraction ) between fibers and matrix. The higher the proportion of fibers, the stronger, but also more rigid and brittle the material becomes. This can lead to problems if certain deformations are exceeded.

Principle of power transmission

Fig .: 1 Illustration of the stress transfer in fiber composite materials with representation of the length involved and the stress distribution in the fiber.

As shown in Figure 1, if the tensile force is applied in a concentrated manner, it is impossible to let it attack the fibers directly, as these are always covered by a matrix layer. The tensile force therefore only acts on the matrix in the form of concentrated tensions and is distributed by this to the closest fibers. The size of this "spreading field" (the effective length of a fiber) depends on the tension between the fiber and the matrix: a soft matrix combined with stiff fibers result in large effective lengths, a stiff matrix with soft fibers results in small effective lengths. However, stresses do not necessarily have to be applied in concentrated form; a variant for generating tensile stresses is, for example, applied torque . The operating principle does not change.

Fig.:2 Illustration of the functional principle of pressure-loaded fibers embedded in a matrix.

In the case of pressure acting along the fiber path, as it also occurs when bending, the matrix functions like a bedding and the fiber (the fiber bundle) like an elastically embedded beam , see also Figure 2. Important material properties are the matrix stiffness k and the bending stiffness of the fiber E · I (stiffness multiplied by the geometrical moment of inertia). The calculation is now much more complex, since, in addition to the sheer tensile strength of the fiber, its diameter also plays a role due to the area moment of inertia . The pressure case has been researched since the mid-1960s and is still a scientific challenge today. Attempts are currently being made to numerically prove and understand the theoretical approaches using computers and modern FEM programs. On the one hand, the problems lie in the fact that there is a stability problem and thus even the smallest changes in the material composition can have considerable effects on the forces that can be tolerated. On the other hand, a highly developed multi-phase material fails in a variety of ways and different mechanisms alternate during the failure and are sometimes mutually dependent. Pressure failure occurs very suddenly, quickly and sometimes without warning. It is therefore very difficult to observe, which makes analysis difficult.


In addition to the purely mechanical properties, i.e. the necessary calculated strength, durability and price issues play a major role in the choice of materials. In order to ensure good functioning, the rigidity of the two components should be matched to one another so that force peaks that occur can be well distributed in the material. The following materials are used:


Residual strength of various fibers
  • Glass
    Glass fibers are the most commonly used types of fibers mainly because of their relatively low price. There are fiber types for different areas of application.
  • Carbon fiber
    See there.
  • Ceramic
    fibers Endless ceramic
    fibers made of aluminum oxide, mullite (mixed oxide of aluminum oxide and silicon dioxide ), SiBCN, SiCN, SiC etc. are expensive special fibers for high-temperature-resistant composite materials with a ceramic matrix. Similar to carbon fibers, non-oxide fibers are made from organic resins that contain silicon as well as carbon.
  • Aramid fibers
    See there.
  • Boron fibers
  • Basalt fibers
    Basalt fiber is a mineral fiber that is mainly used in container and vehicle construction because of its good chemical and temperature resistance.
  • Steel
    Steel fibers are mainly used in construction for steel fiber concrete . This application is growing rapidly and has particularly economic advantages.
  • Natural fibers
    fibers most frequently used for the production of fiber composite materials are local wood fibers, flax and hemp fibers as well as subtropical and tropical fibers such as jute , kenaf , ramie or sisal fibers .
  • Nylon
    fibers Fibers with a high elongation at break are advantageous when the component has to absorb impacts and this property is decisive for the design.


The choice of the matrix divides the fiber composite materials into two groups: fiber-plastic composites (reinforced plastic, fiber-reinforced plastics) and others.

While synthetic resins and elastomers are liquid until they harden, thermoplastics are solid up to approx. 150 ° C (sometimes up to 340 ° C). The thermosetting synthetic resins are usually glass brittle and do not deform plastically. Fiber-reinforced plastics with a thermoplastic matrix are subsequently, i. H. after the primary forming, hot formable. The micro and macro impregnation of the fibers is easier with synthetic resins than with solid thermoplastics. Thermoplastics are heated for impregnation or dissolved in a solvent.

Research in the field of biopolymers has been intensified in recent years . By using thermoset and thermoplastic bioplastics, biodegradable or permanent composite materials can be produced on the basis of renewable raw materials, which often have properties comparable to those of natural and glass fiber reinforced petroleum-based polymers.

Types and manufacturing processes


The group of laminates takes full advantage of the individual fiber orientation. They usually consist of several semi-finished fiber products (e.g. woven fabrics, non-woven fabrics, mats) with different main fiber directions. There are several processes for their production:

  • Manual laying process
    semi-finished fiber products (fabric / scrim / fiber mats) are placed in a mold by hand and soaked with synthetic resin . Then they are vented with the help of a roller by pressing. This is intended to remove not only the air present in the laminate structure, but also excess resin. This procedure is repeated until the desired layer thickness is available. One also speaks of a “wet on wet” process. After all layers have been applied, the component hardens due to the chemical reaction of the resin with the hardener. The process does not place great demands on the tools and is also suitable for very large components. It is often used in series production, where lightweight components are desired, but should also be produced inexpensively.
    The advantages are lower tool and equipment costs, on the other hand the lower component quality (lower fiber content) and the high manual effort, which requires trained laminators. The open processing of the resin places high demands on occupational safety.
  • Laying on hands with vacuum presses
    After all reinforcement and sandwich materials have been introduced, the mold is covered with a separating film, a suction fleece and a vacuum film. A negative pressure is created between the vacuum film and the mold. This causes the composite to be pressed together. Any remaining air is sucked out. Excess resin is absorbed by the suction fleece. In this way, an even higher component quality can be achieved compared to the hand lay-up process.
  • Prepreg technology
    Fiber mats pre-impregnated (i.e. already impregnated) with matrix material are placed on the mold. The resin is no longer liquid, but has a slightly sticky, solid consistency . The composite is then vented using a vacuum bag and then, often in an autoclave , cured under pressure and heat. The prepreg process is one of the most expensive manufacturing processes due to the necessary operating equipment (cooling systems, autoclave) and the demanding process control (temperature management). In addition to fiber winding and injection and infusion processes, it enables the highest component quality. The process is mainly used in the aerospace industry, in motorsport and for competitive sports equipment.
  • Vacuum infusion
    Vacuum build-up
    Finished component
    In this process, the dry fiber material (rovings, mats, scrim, fabric, ...) is placed in a mold coated with a release agent. A separating fabric and a distribution medium are placed over this, which should facilitate the even flow of the resin. The film is sealed against the mold by means of a vacuum sealing tape and the component is then evacuated with the aid of a
    vacuum pump (usually rotary vane pumps ). The air pressure presses the inserted parts together and fixes them. The liquid resin, which is often tempered, is sucked into the fiber material by the applied vacuum. To prevent excess resin from getting into the vacuum pump after passing through the fibers, a resin brake and / or resin trap is installed in front of the pump . After the fibers are completely soaked, the supply of resin is cut off and the soaked FRP can be removed from the mold after curing. The curing times depend on the selected matrix material (resin) and the temperature. The advantage of this process is the uniform and almost bubble-free impregnation of the fibers and thus the high quality of the components produced and the reproducibility. Components such as rotor blades for wind turbines with a length of more than 50 meters are already being manufactured using this process. Further developments to the vacuum infusion process are the differential pressure resin transfer molding ( DP-RTM ) and single line injection process (SLI).
  • Fiber winding
    The filament winding process is a technique for laying down continuous fiber strands (rovings) on an (at least approximately) cylindrical shape. With this method, fibers are positioned very tightly and closely together with a high degree of dimensional accuracy. To wind the fibers, a body is required that gives the component its later shape. This body is called the
    core , as is customary with archetypes . A distinction is also made between lost and reusable cores in fiber winding. Lost cores are usually made of lightweight rigid foam that either remains in the component or is chemically dissolved. The special feature of wound pressure vessels is that the thin-walled core (made of HD polyethylene, for example) remains inside as a gas-tight barrier. If these so-called liners are made of metal, they can also be load-bearing and, together with the matrix made of composite material, form a hybrid system. Here the core is also "lost", but at the same time it is a functional part of the construction. Reusable cores are mostly made of aluminum; they naturally restrict the freedom of design in the construction, since the core must be removable from the component. Examples of fiber-wound parts are lighthouses , shells of tram cars and buses or silos . The usual impregnation methods are:

    • The continuous fiber or the strand is first passed through an impregnation bath in which it is wetted with the matrix material and then wound around a form.
    • There are prepreg wound -Faserbahnen, which are cured only by heating.
    • Unimpregnated fibers are wound, which are then impregnated with a resin injection process (see above).
  • Fiber spraying
    Strictly speaking, fiber spraying is not a lamination technique, as the material is not applied in layers (lat .: lamina). However, the result and the application of the material are comparable to laminated products, so this technique is included here.
    In fiber spraying, continuous fibers (rovings) are cut to the desired length by a cutting unit and then brought into the mold together with resin and hardener using a fiber spray gun. In addition, as with hand lamination, a lamination roller is used to compact the laminate. The main disadvantage of this variant is the significantly lower strength compared to laminated fabric.

Injection molded parts

Most parts made of fiber-reinforced plastics are manufactured inexpensively by injection molding . Typical glass fibers for reinforcement can, for. B. 11 microns thick and 300 microns long. Fibers over a millimeter long are already considered "long" in plastics processing. A common matrix material is, for example, polyamide 6.6, the admixture of glass fibers is usually between 20 and 50% by weight. A corresponding material that is 35% by weight filled with glass fibers is marked with "PA66GF35". The plastics manufacturer supplies the material in the form of pellets in which the glass fibers are already embedded in the matrix material. When this mixture is melted in the extruder and this mixture is injected into the mold, the fibers align themselves to a greater or lesser extent according to the direction of flow, so that the strength in the finished component is not the same at all points and not in all directions. Glass fibers also have an abrasive effect, so that the processing of glass fiber reinforced thermoplastic leads to increased material wear of the mostly steel injection mold compared to unreinforced plastic.

Injection molded parts

In transfer molding or resin transfer molding (RTM), dry fibers can be inserted into a mold and then flowed around with liquid resin under pressure. The resin is cured by heat. The fiber orientation can be adapted to the load cases by means of sewing and embroidery processes in the preform .

Extruded parts

Compact and hollow profiles with dimensions of 1 mm in diameter up to about 250 mm × 500 mm outer dimensions and largely constant cross-sections are produced very efficiently using the extrusion process. All fibers are aligned in the same direction in length, which leads to very good reproducibility. The mechanical properties can be influenced to a limited extent by the addition of fiber rovings, mats and fleeces.

Sheet Molding Compounds (SMC)

With sheet molding compounds, a type of fiber-reinforced plastics, a so-called resin mat is made in a prefabrication from resins, hardeners, fillers, additives etc. and pieces of glass fiber up to 50 mm in length. After a maturing time (storage time), a few days at approx. 30–40 ° C, the viscosity of the resin mat increases from honey-like to wax-resistant to leather-like. With this defined viscosity, depending on the resin mat formulation, the mat can be processed further.

Further processing then takes place in heated tools using the pressing process. The resin mat is cut into precisely defined sizes, depending on the component size and geometry, and placed in the tool according to a defined insertion plan. When the press is closed, the resin mat is distributed throughout the mold. The viscosity increase previously achieved during the ripening period drops almost back to the level of semi-finished product production.

There are two phenomena:

  1. The flow of the resin mat in the tool means that different flow fronts can come together at the corners of the tool (but also at reinforcement ribs and domes). If there is insufficient penetration of the flow fronts, so-called weld lines occur. At these bonding seams, the mechanical properties of the component are sometimes significantly reduced compared to the rest of the component.
  2. The lighter and finer components of the resin mat (resins, additives, etc.) flow faster than the larger components (glass fibers, fillers). This can lead to an accumulation of the smaller components at long flow paths at the component boundaries and a "resin layer" forms. This resin layer is brittle and can lead to minor flaking when exposed to mechanical stress.

The advantage of this class of materials is the easy representation of three-dimensional geometries and wall thickness differences in just one work step. The final component shape is given by the cavity of an at least two-part tool and usually shows smooth, visually appealing surfaces on both sides.

After a curing time of 30 seconds to several minutes at temperatures of 140 ° C to 160 ° C - the duration and height of which depends on the component thickness and the reaction system used - the finished component can be removed from the mold. However, due to the still high component temperatures, the component must be carefully and evenly cooled to prevent microcracks in the component. Due to the longer fiber length than BMC , SMC components are usually more resilient than BMC components. With the appropriate design, SMC components can also be used in painted visible areas.

Fiber concrete

The strength (tension and pressure) of concrete or cement can be increased by adding fibers. The fibers are only a few centimeters long (the high modulus of elasticity of the concrete makes long fibers nonsensical) and are distributed in the matrix without orientation. The result is an isotropic material. The fibers are mixed with the concrete like normal aggregate and cured together in a formwork.

Processing security precautions

Safety glasses and protective gloves provide a minimum level of protection against contact with the resin system. Resin, and especially hardeners and accelerators, often contain substances which, in addition to being toxic, also promote allergies. In the cured state, however, food safety is sometimes even achieved.

Accelerator and hardener are never put together directly. Both components can react violently with each other, and there is a risk of injury. This is why the accelerator is usually added to the resin before it is mixed with the hardener.

During the mechanical processing ( machining ) of fiber-reinforced plastics, very fine particles are created which, depending on the fiber type, can be respirable. That is why a face mask is mandatory.

Due to its electrical conductivity, carbon fiber dust can damage electrical devices. Therefore, the processing is carried out under explosion protection .

Calculation of the elastic properties

The elastic properties of fiber composite materials are calculated on the basis of the properties of elementary individual layers ( unidirectional layers ). This calculation method is known as the classical laminate theory . Tissues are displayed as two unidirectional layers rotated at an angle of 90 °. Influences caused by the undulation of the fibers in the tissue are taken into account by reducing factors. A design method for weight-optimal laminates is the network theory .

The result of the classic laminate theory are the so-called engineering constants of the composite material and the pane-plate stiffness matrix. This matrix consists of the following elements:

  • Disc stiffness matrix
  • Plate stiffness matrix
  • Coupling matrix

Based on these matrices, the reactions of the composite material can be

  • Disc loads: normal stresses and shear in the plane
  • Plate loads : bending moments and torsional moment

be calculated.

The coupling matrix couples the disk loads with the disk deformations and vice versa. It is of interest in practice that an occupied coupling matrix leads to thermal distortion. Since thermal expansions are also coupled, fiber composite components whose coupling matrix is ​​occupied distort. The aim of many research projects is to use the couplings in the disk-plate stiffness matrix in a targeted manner.

For the exact calculation procedure, please refer to the literature and textbooks.

Calculation and verification

The proof of strength, especially of fiber-reinforced plastics, is based on breakage criteria. Due to the brittleness and strength anisotropy of most fiber composite materials, special breakage criteria are necessary for fiber plastic composites .

There are a number of different break criteria and thus also detection methods. Often individual companies (for example in the military or civil aircraft construction) have developed their own verification procedures.

Calculation programs


This Excel -based program was developed by the Institute for Plastics Processing (IKV) at RWTH Aachen University . In addition to the calculation of the layer stresses and the engineering constants according to the classic laminate theory , it contains a module in which Puck's action plane criteria (see: Rupture criteria for fiber-reinforced plastic composites ) are implemented for a strength analysis . In addition to the layer-by-layer stresses, failure loads can also be calculated.


ESAComp was developed on behalf of the European space agency ESA . It offers an interface to FE programs, but it can also be used without an FE program. In addition to the layer-by-layer stress analysis, failure loads can be determined with the help of various fracture criteria .

ESAComp was developed at the Institute for Lightweight Construction at the TU Helsinki.

Lami Cens

A free, easy-to-use Excel application for determining important properties of fiber-reinforced plastic laminates was developed by H. Funke. This enables semi-finished products to be selected and stacked using a menu, just like when laminating. Lami Cens determines production-specific parameters such as laminate thickness and weight, fiber weight, resin consumption and cost parameters. The engineering constants for the homogeneous load on the pane (modulus of elasticity and , shear modulus , Poisson's ratio and ) are calculated using the classical laminate theory . A strength analysis is not possible.

Composite Star

This software was developed by the Belgian company Material SA, Brussels . In particular, it is to be used in connection with wound components made of fiber-plastic composite and the corresponding simulation software Cadwind (same company).

eLamX - expandable laminates eXplorer

eLamX is a freely usable laminate calculation program written in Java, which was and is being developed at the professorship for aircraft technology at the Technical University of Dresden. The calculations are based on the classic laminate theory . The software has a modular structure and is constantly being expanded. Currently (January 2020) there are modules for laminate calculation including strength analysis based on various failure criteria, engineering constants and hygrothermal effects, for stability, deformation and natural frequency investigations of fiber composite panels with and without stiffening elements, for the design of cylindrical pressure tanks and for comparing various strength criteria (3D- Representation of the fracture bodies) available. Furthermore, the tension around holes (circle, ellipse, square, rectangle) in symmetrical and asymmetrical laminates and the spring-in angle can be calculated. The materials used can be defined by entering all material parameters directly or on the basis of various micromechanical models and the corresponding fiber matrix data. It is also possible to optimize the laminate structure on the basis of given loads for a given layer material. Extensions for calculations on sandwich and the analytical consideration of repair solutions are in development. eLamX 2.6 has been available since January 2020.

R&G laminate calculator

Free online laminate calculator that can be used to calculate parameters such as thickness and resin consumption as well as the fiber content of laminates. Depending on the type of fiber, reinforcement textiles and processing methods, practical fiber volume proportions are suggested. The parameters are selected based on the menu. A reverse function is also built in; the number of layers can be determined based on a given laminate thickness. You can enter your own values.

FB-Bem or FC-calc

This Excel -based program was developed by the civil engineer Bernhard Wietek and is available in German (FB-Bem) and English (FC-calc) versions. The dimensioning of fiber concrete for the load cases bending, bending with longitudinal force, buckling, shear and punching is calculated here. All concrete grades can be reinforced with fibers made of steel, plastic or glass.

Natural fiber composite

Wood in its naturally grown form is often used as a template for the design of fiber-plastic composites. The reason for this is that wood fibers, just like other natural fibers , are composed of different "individual building blocks". Stiff cellulose fibrils are embedded in a matrix of hemicellulose and lignin and serve as a strengthening element in the cell wall. Even in its artificially created forms, pressboard or MDF , at least the natural fibers are incorporated as a component .

Bone is a fiber composite material in two ways: in the nanometer range , the collagen fibers are embedded in hydroxylapatite crystals , in cortical bone in the micrometer range osteons also act as fibers.

application areas

Fiber composite materials surround us in all areas of life, mostly without our being aware of it. The spectrum ranges from clothing, furniture and household appliances to multi-storey buildings, bridges, boats and the aerospace industry. The main area of ​​application for the natural fiber reinforced plastics is the automotive industry.

Economical meaning

The fiber composite materials with the greatest economic importance are glass fiber reinforced plastics (GRP) with a share of over 90%. In 2009, 815,000 t of glass fiber reinforced plastics were produced in Europe. The largest producers in the European market are Spain, Italy, Germany, Great Britain and France. As a result of the economic crisis, the production volume in all application industries has shrunk by around a third compared to 2007. Open processing methods such as hand lamination or fiber spraying are hardest hit by this market development. Only bio-based fiber composites oppose this general trend. A comparison of the economic development in the various sub-sectors showed that only natural fiber-reinforced plastics are growing - with a significant economic plus of a good 20%.


  • AA Griffith. The phenomenon of rupture and flow in solids. Philosophical Transactions of the Royal Society of London , 221A: 163-198, 1920.
  • M. Flemming and S. Roth. Fiber composite construction methods , Springer 2003, ISBN 3-540-00636-2
  • Michaeli, Huybrechts and Wegener. Dimensioning with fiber composite plastics , Hanser 1994, ISBN 3-446-17659-4
  • Bernhard Wietek : Steel fiber concrete. Basics and practical application. 2nd Edition. Vieweg + Teubner, Wiesbaden 2010, ISBN 978-3-8348-0872-1 .
  • Ehrenstein (Hrsg.): Fiber composite plastics - materials, processing, properties , Hanser 2006, ISBN 3-446-22716-4
  • A. Puck: Strength analysis of fiber matrix laminates , Hanser 1996, ISBN 3-446-18194-6
  • PA Fowler, JM Hughes & RM Elias, "Review Biocomposites: technology, environmental credentials and market forces", Journal of the Science of the Food and Agriculture Issue 86, 2006, pp. 1781-1789
  • B. Wietek , Fiber Concrete , Springer Vieweg Verlag 2015, ISBN 978-3-658-07763-1

See also

Individual evidence

  1. Fracture model of fiber-reinforced plastics - Lexicon of plastics testing. In: Retrieved July 15, 2016 .
  3. Elmar Witten (2009): The Composites Market Europe 2008/2009. Industrial Association for Reinforced Plastics ( [1] (PDF; 106 kB) download)
  4. Elmar Witten (2009) at the Biomaterials Congress


  1. A load path is the "path" that the force takes in the event of an impact.