International Journal of Applied Glass Science--Li, Richards, and Watson Vol.5,No.1,2014 /图图 8a well established for glass because of their disordered structures, which possess a wide range of ion-pair bond distances. Estimating the a-values for oxide glasses can be found in Bridge's model 8R8三8器 For oxide glasses, Sun's binding energy approach has been adopted to calculate Youngs modulus by Makishima and Mackenzie. The binding energy represented by the product of dissociation energy per unit volume (Gi) of glass constituent (X) and glas packing density(V. The Youngs modulus model of E=2V∑(GX) The model is subsequently modified by Zou and Toratani, proposing that each glass constituent(i)con- tributes to modulus as E;=2V Gi where Vi is the pad factor of the i-constituent in an oxide form(M.oj which can be estimated from 4T/3N,(p/M(x RM+yRo ) where p is the specific gravity of glass, M the molecular weight of glass, Ny the Avogadro's number, and RM and Ro the ionic radii of cation and oxygen, respectively. Specific modulus, S, of the i-th glass constituent is defined by E/p For a given glass composition,assum- 飞E ents, the specific modulus(S)of the glass is defined by Y∑(S: Xi where y[=∑(p;X/ Pm] accounts for uncer tainty between the calculated glass density(2Ip; Xi) uncertainty in the calculated density comes from an assumption of fixed coordination numbers for the cations and oxygen of the interest. In this approach, ESEl& the glass elastic modulus is calculated according to2 E E=pS=∑(n2X)∑(S·x) The Makishima-Machenzie and Zou-Toratani 兰88R odels assume that the Youngs modulus of solids can 2才内内一 be approximated by a linear combination of each indi vidual constituent contribution 25,26 Similar approaches to glass Youngs modulus of mplex glass systems can be also found els A general representation of a linear composition model is illustrated in Fig. 4, which provides a simplified view of the listed oxide utions to the overall gl Youngs modulus. In practice, especially in complex 2到 multicomponent glass systems, significant deviations between the me g到 have been reported' and represent a gap between the
well established for glass because of their disordered structures, which possess a wide range of ion-pair bond distances. Estimating the a-values for oxide glasses can be found in Bridge’s model.23 For oxide glasses, Sun’s binding energy approach24 has been adopted to calculate Young’s modulus by Makishima and Mackenzie.25 The binding energy is represented by the product of dissociation energy per unit volume (Gi) of glass constituent (Xi) and glass packing density (Vt). The Young’s modulus model of glass is expressed as E ¼ 2Vt XðGi XiÞ ð4Þ The model is subsequently modified by Zou and Toratani,26 proposing that each glass constituent (i) contributes to modulus as Ei = 2ViGi where Vi is the packing factor of the i-constituent in an oxide form (MxOy), which can be estimated from 4p/3Nv(q/M)(x R3 M þ yR3 O ) where q is the specific gravity of glass, M the molecular weight of glass, Nv the Avogadro’s number, and RM and RO the ionic radii of cation and oxygen, respectively. Specific modulus, Si, of the i-th glass constituent is defined by Ei/qi. For a given glass composition, assuming the property is a linear additive of all glass constituents, the specific modulus (S) of the glass is defined by c Σ(Si·Xi) where c [=Σ(qi·Xi)/qm] accounts for uncertainty between the calculated glass density (Σ[qi·Xi]) and the measured value (qm). The main source of uncertainty in the calculated density comes from an assumption of fixed coordination numbers for the cations and oxygen of the interest. In this approach, the glass elastic modulus is calculated according to26 E ¼ qmS ¼ Xðqi XiÞ XðSi XiÞ ð5Þ The Makishima–Machenzie and Zou–Toratani models assume that the Young’s modulus of solids can be approximated by a linear combination of each individual constituent contribution.25,26 Similar approaches to glass Young’s modulus of complex glass systems can be also found elsewhere.27,28 A general representation of a linear composition model is illustrated in Fig. 4, which provides a simplified view of the listed oxide contributions to the overall glass Young’s modulus. In practice, especially in complex multicomponent glass systems, significant deviations between the measured and the model-derived values have been reported29 and represent a gap between theory and practice. Table I. Commercial Glass Fibers Used for Structural Composite Applications1,12–17,22 Fiber Glass SiO2 (wt%) Al O2 3 (wt%) MgO (wt%) CaO (wt%) B O2 3 (wt%) R O2 (wt%) q (g/cm3 ) rf (GPa) E† (GPa) TL (°C) TF (°C) E 52 –62 12 –16 0 –5 16 –25 0 –10 0 –2 2.60 –2.65 2.8 –3.7* 72 –82 1080 –1220 1180 –1280 S2 (AGY) 64 –66 24 –25 9.5 –10 0 –0.1 0 0 –0.3 2.46 –2.49 4.6 –5.0* 87 –91‡ 1470 1571 T (Nittobo) 64 –66 24 –26 9 –11 <0.01 0 <1 2.49 4.7 84 1465 1500 HS (Sinoma S&T) 55 –62 23 –26 11 –16 – 0–4 <1 2.53 –2.54 4.6 –4.8 86 –88 1345 –1400 1440 –1450 R (OC) 58 –60 23 –26 5 –6 9 –11 0 – 2.55 4.5* 87 1410 1330 HiPer-texTM (OC) 50 –65 12 –20 6 –12 13 –16 0 –3 0 –2 2.55 4.1 –4.6 85 1280 1351 OCVTM-H (OC) 60 15.7 8.4 13.7 0 1.3 2.61 4.1* 87 1198 1268 INNOFIBER XM (PPG) 60 –61 15 –17 6 –10 13 –16 0 <1.0 2.56 –2.58 3.7 –3.8 88 –89 1207 –1224 1275 –1290 TM (CPIC) 56 –64 13 –20 7 –12 8 –13 – 0–1 2.62 4.5 84 –86 1170 –1225 1265 –1300 ViProTM (Jushi) 57 –65 14 –20 7 –12 8 –13 0 –2 0.1 –2 2.63 4.0 –4.3 86 1203 –1228 1275 –1300 *Pristine fiber strength values determined by testing fibers in liquid nitrogen without any moisture effect, which yields higher strength. †Fiber sonic modulus method, ‡heat-treated fiber exhibiting higher modulus. 70 International Journal of Applied Glass Science—Li, Richards, and Watson Vol. 5, No. 1, 2014
amics.org/lAGS nce Glas fiber Dew Nayo n8bn号8z2 115 105 ◇A Thermal effe Na,O 3o025 AXi of given oxide in glass(mol%) Fig. 4. First-order local, linear model illustrating individual There are major factors contributing to the dis Calculated Young,s Modulus(GPa) crepancies. First, local structure or surrounding oxygen Fig. 5. Comparison between linear mixture model derived environments of glass network formers(SiO2, B2O Young's modulus and the measured Young 's modulus of glasses in etc. )and conditional network formers (Al203) vary fiber form depending on concentrations of alkalis(Li2O, Na2O, K2O, etc. ) alkaline earth (MgO, CaO, SrO, etc.),and The theory implies that a material with their relative proportions. -> The linear composition packaging or smaller ro can have higher intrinsic dels cannot account for the structural variations ength. However, in real-world applications especially for network formers, including SiO2, B2O3 and Al2O3 been observed that glass or glass fibers have measured failure strengths much lower than the theoretical expec Secondly, glass density or molar volume is affected tation by fictive temperature or thermal history of the samples in terms of glass structure relaxation 6-In turn,an One of the most detrimental factors on glass or glass fiber strength is surface contact-induced damage annealed glass has lower fictive temperature, higher or surface Raws. Another source of faws, often encoun- density, and higher Youngs modulus as tered in applications, is the attack of corrosive medium the quenched form that originates during the high-tem- on glass or glass fber surfaces, varying from acid to perature glass fiberization process. Figure 5 compares basic solutions or vapors, as well as water in the form the measured fiber glass modulus as obtained by a sonic of liquid or vapor. Surface flaws serve as a stress method(discussed later)with the calculated modulus. concentrator when the material is under an applied ten- In general, a parallel downshift correlation line can be sile load; the weakest spot(the location where the most drawn from the ideal line of 1:1 correlation, which severe surface flaw has its path perpendicular to the illustrates a primary thermal effect on glass module he thermally induced change of glass Young's modulus app lied tensile load) causes glass or glass fiber to fail at varies between 10% and up to 20%.37.3 a tensile stress level well below the theoretical expecta- tion ergy-balance criterion acture strength or apparent strength(Oapp) of a solid is Fracture of Glass and Glass Fibers defined by"> Theoretical fracture strength of solids, according to app=(2E7/rC)' /2 (plane tensile stress) (7a) Orowan,is proportional to Youngs modulus and sur face energy (yo) of the material as Gapp=[2Ey/(1-v2)C]4(plane tensile strain =(E/)
There are major factors contributing to the discrepancies. First, local structure or surrounding oxygen environments of glass network formers (SiO2, B2O3, etc.) and conditional network formers (Al2O3) vary depending on concentrations of alkalis (Li2O, Na2O, K2O, etc.), alkaline earth (MgO, CaO, SrO, etc.), and their relative proportions.30–35 The linear composition models cannot account for the structural variations, especially for network formers, including SiO2, B2O3, and Al2O3. Secondly, glass density or molar volume is affected by fictive temperature or thermal history of the samples in terms of glass structure relaxation.36–38 In turn, an annealed glass has lower fictive temperature, higher density, and higher Young’s modulus as compared to the quenched form that originates during the high-temperature glass fiberization process. Figure 5 compares the measured fiber glass modulus as obtained by a sonic method (discussed later) with the calculated modulus. In general, a parallel downshift correlation line can be drawn from the ideal line of 1:1 correlation, which illustrates a primary thermal effect on glass modulus. The thermally induced change of glass Young’s modulus varies between 10% and up to 20%.37,38 Fracture of Glass and Glass Fibers Theoretical fracture strength of solids, according to Orowan,39 is proportional to Young’s modulus and surface energy (co) of the material as rth ¼ ðEco=roÞ 1=2 ð6Þ The theory implies that a material with denser packaging or smaller ro can have higher intrinsic strength. However, in real-world applications, it has been observed that glass or glass fibers have measured failure strengths much lower than the theoretical expectation. One of the most detrimental factors on glass or glass fiber strength is surface contact-induced damage, or surface flaws. Another source of flaws, often encountered in applications, is the attack of corrosive medium on glass or glass fiber surfaces, varying from acid to basic solutions or vapors, as well as water in the form of liquid or vapor.40–44 Surface flaws serve as a stress concentrator when the material is under an applied tensile load; the weakest spot (the location where the most severe surface flaw has its path perpendicular to the applied tensile load) causes glass or glass fiber to fail at a tensile stress level well below the theoretical expectation. By the Griffith energy-balance criterion, fracture strength or apparent strength (rapp) of a solid is defined by45,46 rapp ¼ ð2Eco=pCÞ 1=2 ðplane tensile stressÞ ð7aÞ rapp ¼ ½2Eco=pð1 m2 ÞC 1=2 ðplane tensile strainÞ ð7bÞ ΔXi of given oxide in glass (mol%) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Young's Modulus of Glass (GPa) 88 90 92 94 96 98 ZrO2 ZrO2 Al2O3 TiO2 MgO Na2O K2O Li2O B2O3 CaO SiO2 B2O3 Li2O CaO SiO2 Al2O3 TiO2 MgO Na2O K2O Fig. 4. First-order local, linear model, illustrating individual oxide effects on glass Young’s modulus.27 Calculated Young's Modulus (GPa) 80 85 90 95 100 105 110 115 120 125 Measured Young's Modulus (GPa) 80 85 90 95 100 105 110 115 120 125 S-glass Thermal effect Fiber Annealed bulk glass Fig. 5. Comparison between linear mixture model derived Young’s modulus and the measured Young’s modulus of glasses in fiber form. www.ceramics.org/IJAGS High-Performance Glass Fiber Development 71