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 dis￾crepancies. 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-tem￾perature 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 sur￾face 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 expec￾tation. 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 encoun￾tered 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 ten￾sile 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 expecta￾tion. 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