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Fibre Chemistry, Vol. 46, No. 2, July, 2014 (Russian Original No. 2, March-April, 2014)

COMPOSITE FIBER MATERIALS

CALCULATION OF THE LOADS ON COMPOSITEMATERIALS FORMED BY WINDING

O. V. Kashcheev,* N. A. Nikolaeva,* UDC 677.024M. I. Panin,* S. V. Knyazkin,**and S. Yu. Krotov**

To make composites reinforced with differently structured windings of glass filaments, the stresses inthe filaments of the finished composite are calculated theoretically with allowance for the type ofwinding that is used. The mutual locations of the filaments within the volume of the composite that isbeing formed need to be taken into account when calculating the stresses in them. The number offilaments in the composite and extent to which the windings structure is closed should be calculatedprior to calculating the stresses.

The ongoing pursuit of the goal of obtaining composite materials that have the optimum physico-mechanicalproperties (light in weight, nonmagnetic, heat-resistant, etc.) and any desired combination of components accounts forthe use of structures based on special wound packages as one of the foundations for creating such materials.

The development of the theory of winding [1, 2] is giving rise to completely new representations on the capabilitiesand variety of the aforementioned type of structures and, thus, on the creation of new structures for the reinforcement ofcomposites. The wide range of structures being obtained from winding filaments on mandrels of prescribed shapes isalso expanding the range of products that can be made from composites which are formed as solids of revolution in asingle-stage process. Besides making it possible to control the structure of the wound filaments (their porosity andpermeability and the direction and shape of the pores), the given method of reinforcement minimizes abrasion of thefilaments by the guides of the winding equipment and thus also minimizes the guides harmful effect on them.

Glass or carbon fibers and filaments from 5 to 20 m in diameter constitute the foundation of the reinforcingcomponents of structural materials whose strength can exceed that of steel. Up to the present, the main wound structuresthat have been used are obtained by the helical (precision) winding of continuous fibers (filaments) on mandrels ofprescribed shapes. It has been thought that such fibers (filaments) can withstand only tensile stresses, are not capable ofmaintaining a prescribed geometric shape, etc. However, these conclusions were reached by taking a three-dimensionalflat layer of wound fibers (filaments) threaded into an adhesive matrix and examining it without allowance for thestructure created by the mutual positions of the turns in several layers of the winding as the entire three-dimensionalbody of the reinforced composite is being formed.

Considering that glued strips of glass filaments are quite rigid, the stress on the filaments in a flat compositematerial subjected to uniaxial tension can be found from the expression

( )ac

m axbi

axbi

ac S

S

S

== 12cos

(1)

*Moscow State University of Design and Technology. **Dimitrovgrad Engineering-Technological Institute -an affiliate of National Nuclear Research University MIFI. E-mail: nsd0701@mail.ru. Translated from KhimicheskieVolokna, No. 2, pp. 53-55, March-April, 2014.

0015-0541/14/4602-0122 2014 Springer Science+Business Media New York

DOI 10.1007/s10692-014-9574-9

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where P is the force applied to a strip; Sac

is the area of the specimen in a cross section occupied by one of the filamentsin the strip; biax is the tensile strength of each filament, with the length of the filament after rupture being x; /2 is halfthe angle of intersection of the turns of a filament in the strip; Sbiax is the area of the ellipse, with the axes a and b, that isformed by the filaments when they are under load inside the reinforcement.

Figure 1 presents a model describing the location of glass filaments in a strip of a composite material. Figure 2presents a photograph of the actual location of the filaments in a strip.

Fig. 1. Model of the location of the glass filaments in the strip of the composite material: a) location of thefilaments in the strip; b) cross section of the strip.Fig. 2. Actual location of the glass filaments in the strip.

Fig. 1. Fig. 2.

c

b

a

Fig. 3. Types of structures of filament windings on apackage: a) compacted; b) closed; c) spiral.

ba

b

a

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To make it simpler to calculate the stress of the filaments in the strip, instead of biax and /2 in [3] we used thearithmetic mean value of the stress of the filaments in the cross section of the strip on the given segment, i.e.

m

axaxb

axbax

bbi

+++=

...21 (2)

with

m

aaaa i

+++=

...21 (3)

Having designated the expression in (1) as

01 H=

ac

axbi

SS (4)

and introducing the so-called bulk-density criterion to characterize the relative content of filaments in the volume of thecomposite

( ).cos 2 H0 = axb (5)

However, this expression does not take into account the structure of the strips winding or the mutual positionsof the filaments in the designated volume of the strip.

It is known from the results obtained in [1] that there are different types of filament-winding structures:- compacted structures, which are of the maximum possible density;- closed (honeycomb) structures, which have pores of a specified size;- spiral structures, which have pores varying in shape and in direction inside the structure of the body of the

winding.It is apparent that the mass of the binding component which is used for equivolume windings of the above three

types will depend on the number and sizes of the pores in the structure of each winding. Thus, the percentage of thevolume of composite materials that is filled and the composites strength characteristics will differ from one compositeto the next. In the case being discussed, the stress of the filaments in the structure of the materials during their tensionshould be determined not by Eq. (5) but on the basis of specific calculated values of the number and mutual positions ofthe filaments in the structure of the given type of winding.

It should be mentioned that the value calculated from Eq. (5) is sufficiently accurate for randomly structuredwindings of glass filaments, i.e. for windings in which the mutual positions of the filaments are variable. However, Eq.(5) does not give accurate results for precision windings.

The types of windings shown in Fig. 3 are precision windings. The number of filaments within a specifiedthree-dimensional layer of the winding will always be constant.

For a compacted winding, the number of filaments m will be determined from the formula

m = x/d, (6)

where x = 2rsin(/2) is the minimum distance between the turns of the winding in the given layer; r is the radius of thepackages winding; d is the diameter of the glass filaments.

The number of turns in a three-dimensional layer in closed and spiral windings should be determined based oncalculation of the angle of shear of the turns and the degree of closure of the winding (p), i.e. the number of filamentturns after which the configuration of the winding will begin to be repeated.

For a closed winding, the degree of closure( )

,

sind

Ddx

p2

= (7)

where D is the diameter of the winding of the package that is being formed.Inserting the calculated values of m and p into Eq. (1), we can more accurately determine the load applied to the

glass filaments in strips formed by the precision winding of the reinforcing components of composite materials.

125

REFERENCES

1. I.N. Panin, Creating and Studying the Structures of Special Textile Packages. Doctor of Engineering SciencesDissertation. MTI im. A. N. Kosygina, Moscow (1996).

2. I. N. Panin, Izv. Vyssh. Uchebn. Zaved. Tekhnol. Tekst. Prom-sti, No. 4, 32-34 (1993).3. O. G. Tsiplakov, Principles of the Formation of Glass-Fiber-Reinforced Plastic Shells [in Russian],

Mashinostroenie, Moscow (1968).

AbstractREFERENCES