Abnormal effect of tensile strain on Young’s modulus of inorganic E-glass fibers

ISSN 0012�5016, Doklady Physical Chemistry, 2010, Vol. 433, Part 1, pp. 118–120. © Pleiades Publishing, Ltd., 2010.Original Russian Text © S.L. Bazhenov, A.K. Rogozinskii, S.S. Evstiforov, A.A. Berlin, 2010, published in Doklady Akademii Nauk, 2010, Vol. 433, No. 2, pp. 199–201.

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In this work, the effect of elongation on Young’smodulus of high�strength E�glass fibers was studied.An abnormal increase in Young’s modulus of glass attensile strain above 0.2% was detected. Such behavioris characteristic of oriented polymers.

In elastic materials at small strains, the stress isdirectly proportional to the elongation and the pro�portionality factor is called Young’s modulus. Young’smodulus is determined by the interatomic interactionpotential, which is anharmonic in crystalline materialsand metals. The anharmonicity of the potential leadsto a small deviation from Hooke’s law as early as at anelastic deformation stage. In crystals and metals, adeviation from Hooke’s law always manifests itself as adecrease in Young’s modulus with increasing strain.

Different behavior was sometimes observed in ori�ented polymers, in which Young’s modulus increaseson elongation [1–8]. There are two mechanisms ofincrease in Young’s modulus [9]. By the first mecha�nism, at large bond angles close to 180°, a polymermolecule straightens and its stiffness increases [4, 8]. Apolymer bond is similar to an elastic beam bent at anobtuse angle. The second mechanism consists in adecrease in the concentration of “soft” moleculardefects of the sort of kinks, which results in straighten�ing and stiffening of the polymer chain [5–7, 9].

The purpose of this work was to study the effect oftensile strain on Young’s modulus of high�strength E�glass fibers.

Young’s modulus was found by measuring the lon�gitudinal acoustic wave velocity [10]:

(1)

where E is Young’s modulus, ρ is density, and c is thesound velocity.

An acoustic signal was excited by an electric pulsesent to a piezoceramic transducer. The signal passedthrough a sample and arrived at a second piezoceramictransducer. The second piezoceramic transducer gen�erated an electric pulse, which was then amplified andsent to an oscillograph. The ultrasound velocity wascalculated by dividing the sample length by the pulsetravel time through the sample, which was measuredwith a Ch3�34 frequency meter. In calculations, theincrease in the sample length was taken into account.Time was measured with an accuracy of 10–8 s. Thisensured high accuracy of measuring the sound velocityand, hence, Young’s modulus. The sample length was

E ρc2,=

PHYSICALCHEMISTRY

Abnormal Effect of Tensile Strain on Young’s Modulusof Inorganic E�Glass Fibers

S. L. Bazhenov, A. K. Rogozinskii, S. S. Evstiforov, and Academician A. A. BerlinReceived February 4, 2010

DOI: 10.1134/S0012501610070031

Enikolopov Institute of Synthetic Polymer Materials,Russian Academy of Sciences, ul. Profsoyuznaya 70,Moscow, 117393 RussiaSemenov Institute of Chemical Physics,Russian Academy of Sciences,ul. Kosygina 4, Moscow, 119991 Russia

200

0.10 0.2 0.3 0.4 0.5ε, %

400

600σ, GPa

Fig. 1. Typical stress σ vs. strain ε curve for a thread ofhigh�strength E�glass fibers: (�) loading 1, (�) unloading1, (�) loading 2, and (�) unloading 2.

DOKLADY PHYSICAL CHEMISTRY Vol. 433 Part 1 2010

ABNORMAL EFFECT OF TENSILE STRAIN ON YOUNG’S MODULUS 119

0.4 m. The samples were stretched step by step with amanual micrometer screw. The elongation was mea�sured with an accuracy of 10 μm. The tensile force wasmeasured with a strain gauge. A single fiber and athread consisting of several hundreds of parallel high�strength E�glass fibers were studied. For comparison,steel wire 50 μm in diameter and unorientedpoly(methyl methacrylate) fibers 1.2 mm in diameterwere tested.

Figure 1 presents a typical pattern of elongation ofa thread consisting of high�strength E�glass fibers. Attensile strain below 0.1%, the relationship between thestrain ε and the stress σ is nonlinear because fibers inthe thread somewhat differ in length [1]. In the courseof elongation, the shortest fibers are loaded first andthen longer fibers are. During unloading, the paths ofthe forward and reverse processes coincide, whichindicates that the glass deformation is reversible. Insubsequent cycles, the loading curves are reproduced.

Curve 1 in Fig. 2 illustrates the dependence ofYoung’s modulus E of the thread of E�glass fibers onthe tensile strain ε. Initially, with increasing strain,Young’s modulus decreases, but beginning with astrain of ε ≈ 0.15%, Young’s modulus starts todecrease. Curve 2 shows a similar dependence for asingle fiber. For the single fiber, the minimum is at astrain of ~0.07%. The difference in position of theminimum between the single fiber and the thread canbe explained by difference in length between fibers inthe thread. The initial value of Young’s modulus of thesingle fiber is somewhat higher than that of the thread.This is probably because the thread contains a certainamount of ruptured fibers. Note that the loading and

unloading curves are somewhat shifted, which is indic�ative of stress relaxation in the glass. Previously, similarbehavior of Young’s modulus of glasses was notobserved.

For comparison, Fig. 3 presents the dependence ofYoung’s modulus on the tensile strain for the steel wire(curve 1) and unoriented poly(methyl methacrylate)fibers (curve 2). An increase in the strain leads to a lin�ear decrease in Young’s modulus. Both in steel and inthe amorphous polymer glass, no abnormal increase inYoung’s modulus is observed.

Elastic materials are characterized by a decrease inYoung’s modulus at small strains, which is because ofthe anharmonicity of the interatomic interactionpotential. In glass fibers at very small strains, Young’smodulus also decreases. The anharmonicity of thepotential determines the thermal expansion coeffi�cient of the glass, which is positive in the absence ofmechanical loads. Therefore, the initial decrease inYoung’s modulus is natural. However, beginning witha certain strain, Young’s modulus increases. Thisincrease is far beyond the experimental error range.The cause of it is unclear and requires further investi�gation. Nonetheless, of notice is the similarity betweenthe behavior of the glass and oriented polymers, whichalso exhibit an increase in Young’s modulus on elon�gation. In the polymers, this increase is due to molec�ular transitions at small relaxation times.

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78

0.150

~~

0.30 0.45 0.60

84

85

77

1

2

ε, %

E, GPa

5.2

0.2 0.4 0.6 0.8 1.00ε, %

5.4

228

231

E, GPa

~~1

2

Fig. 3. Young’s modulus E vs. strain ε curves for elongationof (1) a steel wire ((�) loading and (�) unloading) and (2)a single thread ((�) loading 1, (�) unloading 1, (�) loading2, and (�) unloading 2).

Fig. 2. Young’s modulus E vs. strain ε curves for elongationof (1) a thread of E�glass fibers ((�) loading and (�)unloading) and (2) poly(methyl methacrylate) fibers ((�)loading and (�) unloading).

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