《复合材料 Composites》课程教学资源（学习资料）第二章 增强体_glass fiber-16 Impact of Drawing Stress on the Tensile Strength of Oxide Glass Fibers

J.Am. Ceram.Soc,9303236-3243(2010) Dol:10.ll11551-29162010.03879x C 2010 The American Ceramic Society urna Impact of Drawing Stress on the Tensile Strength of Oxide Glass Fibers Majbritt D. Lund and Yuanzheng Yue Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark The sources of the tensile strength and fracture of both contin- show the role of both the microstructure and the relaxation uous glass fibers and discontinuous wool fibers are explored in behavior of oxide glass fibers in influencing the fiber strength. 8 terms of structural anisotropy, enthalpy relaxation, defect ori- In this paper, we attempt to answer the following long-standing entation, and surface inhomogeneities. The fibers are spun from questions. What causes the difference in strength between fibers the e-glass and the basaltic glass melts, respectively. It is d bulk glasses with the same chemical composition? How does vealed that axial stress plays an important role in enhancing the the axial stress(oax), the cooling rate, structural heterogeneity strength of the oxide glass fibers. The increase of axial stress and the technological defects(e. g, striae, bubbles, etc. ) influence leads to the increase of both the structural anisotropy and the the fiber strength? defect (flaws, bubbles, striae, etc )orientation, and hence the increase of the tensile strength. besides the axial stress, the in- crease of the cooling rate also increases the tensile strength of the continuous fibers These findings are further substantiated by IL. Experimental Procedure annealing experiments on both continuous and wool fibers below (1) Fiber Drawing Tg. The onset annealing temperature of the tensile strength de- Fibers used in this study were produced either from the contin- cay is close to that of the anisotropy relaxation of the continuous uous drawing process with a single orifice or from the cascade fibers. The relative contributions of the different factors to the process. Two types of glass fibers were produced from basaltic fiber strength are schematically scaled with the help of the sub- and E-glass compositions shown in Table I. The differences in the basaltic glass compositions are attributed to the chemical variation of the basalt raw material The glasses for the fiber spinning were obtained by melti L. Introduction the raw materials in an electrical furnace for 2 h at 1773-1803K and then casting the melt into the fiber-drawing crucible of HE strength of glass has been attracting the interest of sci- 90/10Pt/Rb(for continuous fiber drawing) or quenching it into ntists for more than a century. In spite of derstanding the fracture of glass, there are still challenges both iber drawing has a dimension of 40 mm x 70 mm(dia- in clarifying the origin and in determining the controlling meter x height). In the middle of the bottom of the crucible, parameters of the tensile strength of glasses and glass fiber there is a die with the dimension of 2.0 mm x 3.0 mm(dia These challenges are partly due to effects of numerous factors or meter x height). The crucible filled with glass was placed in the strength of glass, e.g., chemical composition, the thermal an electrically heated cylinder furnace(SCANDIA type STTF and mechanical histories, the sample shape and the size, and the 115/400-1550C, Allerod, Denmark), from which the fibers were surrounding atmosphere and so forth. In other words, the prac- ontinuously drawn at speeds between 1 and 50 m/s, and col- tical strength is not a physical value like density because it de- lected using a metallic drum. Different drawing speeds gave composition, different axial stresses to the fibers, and hence generated differ microstructure, and defects)and on external factors(e. g, man- ent fiber diameters. The drawing temperatures were 1413 K for ners of both sample production and strength measurements) the basaltic fibers and 1393 K for the E-glass fibers, which cor o, The rupture strength of chemical bonds, often called the the- respond to the viscosities of 180 and 220 Pa-s, respectively. The btained in practice. It is known that thin 10 um) glass fibers exhibit 10-100 times higher strength than its counterp Table I. Chemical Compositions of Both E-Glass and Basaltic bulk glasses. This value is, however, much lower than thethe Glasses for the produced fibers oretical strength. This discrepancy between theoretical and prac- Basalt glas long time. The work of Griffith greatly influenced the field of Oxide(wt%) Continuous E Cascade E Continuous B Cascade B glass strength research, and initiated the debate on the relation etween the tensile strength and the fiber diameters. 2-10 It has Sio, 0.453.6 49.3 hypothesized that the high fiber tensile strength might be D2O ed to orientated molecules predisposed in the fibers duri the fiber-drawing process. 1. 8 Recent studies of the effect of different parameters such as cooling rate, 1, 12 melting his- tory,>,"and mechanical stretching on the fiber strength .223.5 23.5 leincontributing editor NaO 0.9 0.9 K,O 0.l 0.7 0.9 BO F 0.2 0.7 August 24, 2009: approved April 22, 2010. May 17-21, 200g tent of this paper was presented at 2008 GOMD meeting.Tucson,USA Tg(K) 952 by Rockwool International A/s FezO /2Fe determined by Mossbauer spectroscopy. The compositions wer measured using X-ray fluorescence(XRF). The Ts value from differential scanning 'Author to whom correspondence should be addressed. e-mail: yy a bio aau.dk calorimetry (DSC) measurements is listed below each composition. 3236

Impact of Drawing Stress on the Tensile Strength of Oxide Glass Fibers Majbritt D. Lund and Yuanzheng Yue,w Section of Chemistry, Aalborg University, DK-9000 Aalborg, Denmark The sources of the tensile strength and fracture of both contin￾uous glass fibers and discontinuous wool fibers are explored in terms of structural anisotropy, enthalpy relaxation, defect ori￾entation, and surface inhomogeneities. The fibers are spun from the E-glass and the basaltic glass melts, respectively. It is re￾vealed that axial stress plays an important role in enhancing the strength of the oxide glass fibers. The increase of axial stress leads to the increase of both the structural anisotropy and the defect (flaws, bubbles, striae, etc.) orientation, and hence the increase of the tensile strength. Besides the axial stress, the in￾crease of the cooling rate also increases the tensile strength of the continuous fibers. These findings are further substantiated by annealing experiments on both continuous and wool fibers below Tg. The onset annealing temperature of the tensile strength de￾cay is close to that of the anisotropy relaxation of the continuous fibers. The relative contributions of the different factors to the fiber strength are schematically scaled with the help of the sub￾Tg annealing. I. Introduction THE strength of glass has been attracting the interest of sci￾entists for more than a century. In spite of progress in un￾derstanding the fracture of glass, there are still challenges both in clarifying the origin and in determining the controlling parameters of the tensile strength of glasses and glass fibers. These challenges are partly due to effects of numerous factors on the strength of glass, e.g., chemical composition, the thermal and mechanical histories, the sample shape and the size, and the surrounding atmosphere and so forth. In other words, the prac￾tical strength is not a physical value like density because it de￾pends both on internal factors (e.g., chemical composition, microstructure, and defects) and on external factors (e.g., man￾ners of both sample production and strength measurements). The rupture strength of chemical bonds, often called the the￾oretical strength, is much higher than any strength values obtained in practice.1 It is known that thin (B10 mm) glass fibers exhibit 10–100 times higher strength than its counterpart, bulk glasses. This value is, however, much lower than the the￾oretical strength. This discrepancy between theoretical and prac￾tical strength values has been puzzling glass researchers for a long time. The work of Griffith1 greatly influenced the field of glass strength research, and initiated the debate on the relation between the tensile strength and the fiber diameters.2–10 It has been hypothesized that the high fiber tensile strength might be related to orientated molecules predisposed in the fibers during the fiber-drawing process.1,8 Recent studies of the effect of different parameters such as cooling rate,11,12 melting his￾tory,13,14 and mechanical stretching15–17 on the fiber strength show the role of both the microstructure and the relaxation behavior of oxide glass fibers in influencing the fiber strength.18 In this paper, we attempt to answer the following long-standing questions. What causes the difference in strength between fibers and bulk glasses with the same chemical composition? How does the axial stress (sax), the cooling rate, structural heterogeneity and the technological defects (e.g., striae, bubbles, etc.) influence the fiber strength? II. Experimental Procedure (1) Fiber Drawing Fibers used in this study were produced either from the contin￾uous drawing process with a single orifice or from the cascade process. Two types of glass fibers were produced from basaltic and E-glass compositions shown in Table I. The differences in the basaltic glass compositions are attributed to the chemical variation of the basalt raw material. The glasses for the fiber spinning were obtained by melting the raw materials in an electrical furnace for 2 h at 1773–1803 K and then casting the melt into the fiber-drawing crucible of 90/10Pt/Rb (for continuous fiber drawing) or quenching it into water (for the cascade process). The crucible for continuous fiber drawing has a dimension of 40 mm 70 mm (dia￾meter height). In the middle of the bottom of the crucible, there is a die with the dimension of 2.0 mm 3.0 mm (dia￾meter height). The crucible filled with glass was placed in an electrically heated cylinder furnace (SCANDIA type STTF 115/400–15501C, Aller^d, Denmark), from which the fibers were continuously drawn at speeds between 1 and 50 m/s, and col￾lected using a metallic drum. Different drawing speeds gave different axial stresses to the fibers, and hence generated differ￾ent fiber diameters. The drawing temperatures were 1413 K for the basaltic fibers and 1393 K for the E-glass fibers, which cor￾respond to the viscosities of 180 and 220 Pa s, respectively. The Table I. Chemical Compositions of Both E-Glass and Basaltic Glasses for the Produced Fibers Oxide (wt%) 7 E-glass Basalt glass Continuous E Cascade E Continuous B Cascade B SiO2 0.4 53.6 53.6 49.3 47.1 Al2O3 0.3 14.6 14.6 15.6 15.3 TiO2 0.1 — — 1.8 1.6 FeO — — 6.8w 9.1w Fe2O3 0.2 0.3 0.3 4.1w 2.1w CaO 0.2 23.5 23.5 10.4 7.3 MgO 0.2 — — 6.6 7.2 Na2O 0.2 0.9 0.9 3.9 3.6 K2O 0.1 — — 0.7 0.9 B2O3 0.2 6.3 6.3 — — F2 0.2 0.7 0.7 — — Tg (K) 952 952 908 926 w Fe2O3/SFe determined by Mo¨ssbauer spectroscopy. The compositions were measured using X-ray fluorescence (XRF). The Tg value from differential scanning calorimetry (DSC) measurements is listed below each composition. L. Klein—contributing editor Part of the content of this paper was presented at 2008 GOMD meeting, Tucson, USA, May 17–21, 2008 This work was financially supported by Rockwool International A/S. Member, The American Ceramic Society. w Author to whom correspondence should be addressed. e-mail: yy@bio.aau.dk Manuscript No. 26734. Received August 24, 2009; approved April 22, 2010. Journal J. Am. Ceram. Soc., 93 [10] 3236–3243 (2010) DOI: 10.1111/j.1551-2916.2010.03879.x r 2010 The American Ceramic Society 3236

October 2010 Tensile Strength of Oxide Glass Fibers fiber diameters were determin electron mi- the samples measured during the first and second croscope(SEM)(Philips XL30 OR). Sample spectively. By using a method proposed previously, the glass name stands for the glass type peed. For in- transition temperatures (T, of the basaltic glasses were found le bs refers to and are listed in Table I. The area between the CpI and Cp basaltic glass drawn at 8 m/s curves represents the excess enthalpy of the hyperquenched he discontinuous wool fibers were obtained using a three- glasses, AH, relative to that of the standard glass. The excess wheel cascade spinning machine. In detail, a glass produced enthalpy was trapped in fibers during the spinning process, and previously was remelted in an electrical furnace(Hasle Isom referred to as the total excess enthalpy AHtot. AHtot will A/ /S, Roenne, Denmark)at 1803 K for I h. Subsequently, the ased when the fibers are reheated in dsc to a temperature melt was poured onto the outer rim of a spreader wheel that is where the Cn curves for the first and the second scan merge rotating at a given speed. While some material was spun off, When the fibers undergo a sub-Tg annealing, i.e., annealing be- most of the melt was transferred to either of the two adjacent low Te for a given duration, part of AH,ot will be released, while wheels spinning at a high rotational speed in the opposite di part of it remains. The remaining part is denoted here by AHr rection. Fibers were formed when droplets were thrown from The details of how to calculate the AHrem values are given else- the wheels by centrifugal force. During the spinning process, the where. 9 fibers were hyperquenched at a rate of 106K/s that was es- timated using a method reported elsewhere. The fiber diame- ters were determined using SEM(Philips XL30 ESEM (4) Tensile Strength Tests The tensile strength tests(uniaxial tension test) of individual fi- bers were performed using a Raith FTM testing rig(Rockwool International A, Hedehusene, Denmark) for a single gla strength, fibers were annealed in atmospheric air at different fiber operating at a constant speed of 10 m/s. The applied temperatures(Ta)chosen in the range of 0.5 Tg to T(in Kelvin) force, F, could be calculated from the controlled speed and the distance that is changeable by moving the flexible end of the for 3 h. Because annealing occurred below Tg, it is thus referred to as sub-T. annealing. The fibers were annealed in a muffle testing rig. The gauge length of the tested fibers was between furnace at constant temperatures with a variation of +2 k, and and 3 mm. All tensile tests were made at room temperature afterward taken out directly from the furnace. It should under ambient conditions The diameters of the tested fibers oted that part of basaltic wool fiber samples were annealed ina were measured using SEM(Philips XL30 ESEM) close to the point of fracture, and thus the cross-section area, A, could be ube furnace in a N2 atmosphere, so that comparison in tensile rength can be made between the N2-annealed and the air- alculated. The tensile strength of the samples, of, were calcu lated from the relation or= F/A. Evaluation of the tensile trengths was performed using Weibull,s statistics, which is based on"the weakest-link theory" and assume a random (3) Differential Scanning Calorimetry(DSC) location of independent flaws causing mechanical failure. The The isobaric heat capacity (Cp) of a crushed fiber sample of probability of failure, Pr, is defined as c20 mg was measured as a function of temperature using a DSC(Netzsch STA 449C Jupiter, Selb, Germany)in argon. The le was placed in a platinum crucible situated on a sample Pr= holder of the dsC at room temperature. The samples were held for 5 min at an initial temperature of 333 K, then heated at 20 K/min to 1. I Tg, and then cooled back at 20 K/min to 573 K where go is a scale parameter (also called the characteristic After natural cooling to room temperature, the second upsc trength), corresponding to the fracture strength with a failure was performed using the same procedure as for the first. To de- bability of 63. 2%, and hence is related to the mean value of termine Cp of the samples, the heat flow data both for the base the distribution. The Weibull modulus, m, re ts the scatter line(using two empty crucibles) and for the reference sample in the fracture strength. The tensile strength data were plotted in (Sapphire)were measured CpI and Cp2 are the heat capacities of a Weibull plot, i.e., In(In(1/1-PD)vs In(or)(see Fig. 1),from Tensile strength o,(MPa) 5001000 3000 5001000 3000 (a)E-glass fibers Wool 8 0 ≥ ●xC 5 Inat( o, in MPa) is the probability of failure, for both linear fits of or in the high-strength region

fiber diameters were determined using a scanning electron mi￾croscope (SEM) (Philips XL30 ESEM, Hillsboro, OR). Sample name stands for the glass type and the drawing speed. For in￾stance, E10 refers to E-glass drawn at 10 m/s, while B8 refers to basaltic glass drawn at 8 m/s. The discontinuous wool fibers were obtained using a three￾wheel cascade spinning machine. In detail, a glass produced previously was remelted in an electrical furnace (Hasle Isomax A/S, Roenne, Denmark) at 1803 K for 1 h. Subsequently, the melt was poured onto the outer rim of a spreader wheel that is rotating at a given speed. While some material was spun off, most of the melt was transferred to either of the two adjacent wheels spinning at a high rotational speed in the opposite di￾rection. Fibers were formed when droplets were thrown from the wheels by centrifugal force. During the spinning process, the fibers were hyperquenched at a rate of B106 K/s that was es￾timated using a method reported elsewhere.19 The fiber diame￾ters were determined using SEM (Philips XL30 ESEM). (2) Annealing To study the influence of the structural relaxation on the fiber strength, fibers were annealed in atmospheric air at different temperatures (Ta) chosen in the range of 0.5 Tg to Tg (in Kelvin) for 3 h. Because annealing occurred below Tg, it is thus referred to as sub-Tg annealing. The fibers were annealed in a muffle furnace at constant temperatures with a variation of 72 K, and afterward taken out directly from the furnace. It should be noted that part of basaltic wool fiber samples were annealed in a tube furnace in a N2 atmosphere, so that comparison in tensile strength can be made between the N2-annealed and the air￾annealed samples. (3) Differential Scanning Calorimetry (DSC) The isobaric heat capacity (Cp) of a crushed fiber sample of B20 mg was measured as a function of temperature using a DSC (Netzsch STA 449C Jupiter, Selb, Germany) in argon. The sample was placed in a platinum crucible situated on a sample holder of the DSC at room temperature. The samples were held for 5 min at an initial temperature of 333 K, then heated at 20 K/min to 1.1 Tg, and then cooled back at 20 K/min to 573 K. After natural cooling to room temperature, the second upscan was performed using the same procedure as for the first. To de￾termine Cp of the samples, the heat flow data both for the base￾line (using two empty crucibles) and for the reference sample (Sapphire) were measured. Cp1 and Cp2 are the heat capacities of the samples measured during the first and second upscans, re￾spectively. By using a method proposed previously,19 the glass transition temperatures (Tg) of the basaltic glasses were found and are listed in Table I. The area between the Cp1 and Cp2 curves represents the excess enthalpy of the hyperquenched glasses, DH, relative to that of the standard glass. The excess enthalpy was trapped in fibers during the spinning process, and referred to as the total excess enthalpy DHtot. DHtot will be re￾leased when the fibers are reheated in DSC to a temperature where the Cp curves for the first and the second scan merge. When the fibers undergo a sub-Tg annealing, i.e., annealing be￾low Tg for a given duration, part of DHtot will be released, while part of it remains. The remaining part is denoted here by DHrem. The details of how to calculate the DHrem values are given else￾where.19 (4) Tensile Strength Tests The tensile strength tests (uniaxial tension test) of individual fi- bers were performed using a Raith FTM testing rig (Rockwool International A/S, Hedehusene, Denmark) for a single glass fiber operating at a constant speed of 105 m/s. The applied force, F, could be calculated from the controlled speed and the distance that is changeable by moving the flexible end of the testing rig. The gauge length of the tested fibers was between 2 and 3 mm. All tensile tests were made at room temperature under ambient conditions. The diameters of the tested fibers were measured using SEM (Philips XL30 ESEM) close to the point of fracture, and thus the cross-section area, A, could be calculated. The tensile strength of the samples, sf, were calcu￾lated from the relation sf 5 F/A. Evaluation of the tensile strengths was performed using Weibull’s statistics,20 which is based on ‘‘the weakest-link theory’’ and assume a random location of independent flaws causing mechanical failure. The probability of failure, Pf, is defined as Pf ¼ 1  exp  sf s0   m (1) where s0 is a scale parameter (also called the characteristic strength), corresponding to the fracture strength with a failure probability of 63.2%, and hence is related to the mean value of the distribution. The Weibull modulus, m, represents the scatter in the fracture strength. The tensile strength data were plotted in a Weibull plot, i.e., ln(ln(1/1Pf)) vs ln(sf) (see Fig. 1), from 5678 56789 –4 –3 –2 –1 0 1 2 B8 o 5 16 50 84 1000 o 99 Fracture propability Pf (%) ln(ln(1/(1– Pf))) lnf ( f in MPa) Tensile strength f (MPa) 200 500 3000 200 500 1000 3000 (b) Basaltic fibers Wool Casc B Continuous B21 B33 B51 Wool Case E Continuous E10 E20 E30 E40 (a) E-glass fibers Fig. 1. Tensile strength (sf) distribution in Weibull diagrams, i.e. the plot of ln(ln(1(1Pf))) vs ln(sf), where Pf is the probability of failure, for both wool fibers and continuous fibers drawn at different speeds. (a) E-glass fibers; and (b) basaltic fibers. Straight graygray lines in the diagram represent the linear fits of sf in the high-strength region. October 2010 Tensile Strength of Oxide Glass Fibers 3237

3238 Journal of the American Ceramic Society--Lund and Yue Vol 93. No. 10 which the Weibull parameters oo and m can be found by linear regression of the data. Each test series contains 2540 fibers 4000 (5 Optical Birefringence Mechanically induced anisotropy can be quantified by ing the optical birefringence of fibers under pe light. Measurements of the birefringence of 1000 ot possible due to small optical phase differences. Therefore fiber bundles fixed in parallel orientation and fixed in a glass I-Bulk glass tube were used. a fiber bundle immersed in commercial imm 0.000.050.100.150.000050.100.15020 sion liquid with a refractive index of 1.558 was used for quan- 1/d(1/m titative birefringence measu Brace-Kohler ompensator using a monochromatic light of 546 nm. Details Fig. 2. Tensile strength oo as a function of the reciprocal diameter of E-glass (a) and basaltic fibers(b). Vertical rectangular gray box. the go ta of bulk samples in a certain rang Solid circles, the go data of the wool fibers. The go data of continuous basaltic fibers shown in(b) were obtained from the fibers drawn with II. Results both the 1. 8 mm (diameter) die(see the inverted triangles) and the 2.0 mm die(see triangles), respectively. Error bars are shown in the The challenge in evaluating the strength of brittle materials is the large scattering in data obtained within a single sample. For the glass fibers tested in this work, the data variation is visualized in fibers. For basaltic wool fibers, the distribution is represented by Weibull's plots shown in Fig. 1. The figure shows that the eval- uations of the fiber strength values need(at least) bimodal dis- a fiber volume of 84 vol%, which has a diameter (pm) d>(um) dlass fibers l690 44 14.9 2810 0.94 1820 9.9 2450 E40 1070 6.5 2970 8.4 0.95 6 Cascade e 1870 Basaltic fibers 1830 3.6 0.93 16.9 0.6 3210 l2.8 0.4 340 3.1 0.96 0.3 3990 7.9 0.87 B33 2710 3.0 0.96 0.5 15.9 0.79 B51 2630 3.2 0.96 2.0 4160 9.9 0.76 6.8 10 Cascade B 1890t 4.4 0.91 6.4 2. Obtained from the higher strength region for wool fibers. the slopes of which are close to those of the lower strength region for continuous fibers(see Fig. 1) do is th characteristic strength taken at the failure probability of 63%: m is Weibull's modulus representing the slope of the strength distribution; is the average fiber diameter and Std is the standard deviation of <d

which the Weibull parameters s0 and m can be found by linear regression of the data. Each test series contains 25–40 fibers. (5) Optical Birefringence Mechanically induced anisotropy can be quantified by measur￾ing the optical birefringence of fibers under polarized light. Measurements of the birefringence of single fibers are not possible due to small optical phase differences. Therefore, fiber bundles fixed in parallel orientation and fixed in a glass tube were used. A fiber bundle immersed in commercial immer￾sion liquid with a refractive index of 1.558 was used for quan￾titative birefringence measurements with a Brace–Ko¨hler compensator using a monochromatic light of 546 nm. Details of the methods are given elsewhere.21 III. Results The challenge in evaluating the strength of brittle materials is the large scattering in data obtained within a single sample. For the glass fibers tested in this work, the data variation is visualized in Weibull’s plots shown in Fig. 1. The figure shows that the eval￾uations of the fiber strength values need (at least) bimodal dis￾tribution evaluations. The strength values are separated in two distributions based on the slope of the distributions shown in Fig. 1: a high-strength distribution with strength values above 2700 MPa and a low-strength distribution with values below 2700 MPa. The characteristic tensile strength s0 and Weibull’s modulus m are found for each distribution and listed in Table II. The slopes of the strength curves in the region between 1000 and 2700 MPa are parallel for both wool fibers and continuous fibers (Fig. 1). By studying fractography of wool fibers, it has been found that these slopes reflect a broad distribution in flaws including voids or bubbles positioned in the volume of the fibers and small flaws near or at the surface of the fibers.22 In addition, the continuous fibers exhibit a narrow high-strength distribution above 2700 MPa, and the basaltic wool fibers show a narrow low-strength distribution in the region below 900 MPa. The continuous fiber E40 has a single strength distribution, but with a low-strength tail caused only by a single data point. This low-strength tail is frequently observed in strength tests of glass fibers. The E-glass wool fibers show an apparent single strength distribution. However, from fractography, the E-glass wool fibers possess a bimodal flaw distribution, which is also shown by basaltic wool fibers.22 The fiber diameter is often believed to have an impact on the tensile strength. Before such an impact is discussed, the diameter distributions of fibers must be determined. Usually, the wool fibers have a larger variation in diameter than the continuous fibers. For basaltic wool fibers, the distribution is represented by a fiber volume of 84 vol%, which has a diameter o11.4 mm, 50 vol% is of do6.4 mm, and only 16 vol% has do3.1 mm. For continuous fibers, the distribution is rather narrow as long as the fiber-drawing parameters are fixed. Figures 2(a) and (b) show the tensile strength as a function of the inverse fiber diameter for both E-glass and basaltic compositions, respectively. From Figs. 2(a) and (b), it is seen that the tensile strength of the fibers is more than one order of magnitude higher than that of bulk glasses with the same composition. For continuous ba￾saltic fibers, the strength first increases with the decreasing fiber diameter, and then reaches a plateau where the strength is in￾dependent of the fiber diameter in the diameter range between B5 and 17 mm. Furthermore, Fig. 2 shows a significant differ￾ence in strength between continuous fibers and wool fibers for similar fiber diameters. The tensile strengths of the wool fibers are considerably lower than those of the continuous fibers for both glass compositions. For the E-glass composition (Fig. 2(a)), the tensile strength of the wool fibers is about 1500 MPa, whereas that of the continuous fibers is about 2250–3000 MPa. The difference is also seen for the basaltic composition (Fig. 2(b)), in which the tensile strength is around 1250 MPa for the wool fibers, and around 3500 MPa for the continuous fibers. For the continuous fiber-drawing process, the relation be￾tween the fiber diameter d and the drawing speed v can be described by the expression21: d ¼ Av0:5 (2) Table II Weibull’s Parameters of All Samples Obtained from Linear Fits of the Data of the Entire, the Lower, and the Higher Tensile Strength (rf) Distributions, Respectively, as Shown in Fig. 1 Samples Lower sf distribution Higher sf distribution s0 (MPa) m R2 /dS (mm) Std s0(high) (MPa) m R2 /dS (mm) Std E-glass fibers E10 1690 4.4 0.93 14.9 0.1 2880 7.2 0.95 14.9 0.5 E20 2080 4.4 0.97 10.4 0.7 2810 17.2 0.94 10.2 0.2 E30 1820 7.1 0.97 9.9 0.5 2450 14.1 0.83 9.5 0.3 E40 1070 — — 6.5 — 2970 8.4 0.95 7.6 0.5 Cascade E 1870w 3.9 0.95 7.4 2.5 — — — — — Basaltic fibers B8 1830 3.6 0.93 16.9 0.6 3210 12.8 0.92 16.7 0.4 B21 2340 3.1 0.96 9.4 0.3 3990 7.9 0.87 8.9 0.4 B33 2710 3.0 0.96 8.7 0.5 3970 15.9 0.79 8.3 0.5 B51 2630 3.2 0.96 8.1 2.0 4160 9.9 0.76 6.8 1.0 Cascade B 1890w 4.4 0.91 6.4 2.1 — — — — — w Obtained from the higher strength region for wool fibers, the slopes of which are close to those of the lower strength region for continuous fibers (see Fig. 1). s0 is the characteristic strength taken at the failure probability of 63%; m is Weibull’s modulus representing the slope of the strength distribution; /dS is the average fiber diameter, and Std is the standard deviation of /dS. 0 (a) E-glass compositions (b) Basaltic compositions 4000 3000 2000 1000 Bulk glass Bulk glass 0.00 0.05 0.10 0.15 0.00 0.05 0.10 0.15 0.20 1/d (1/μm) 0 (MPa) Fig. 2. Tensile strength s0 as a function of the reciprocal diameter of E-glass (a) and basaltic fibers (b). Vertical rectangular gray box, the s0 data of bulk samples in a certain range due to the scattering of data. Solid circles, the s0 data of the wool fibers. The s0 data of continuous basaltic fibers shown in (b) were obtained from the fibers drawn with both the 1.8 mm (diameter) die (see the inverted triangles) and the 2.0 mm die (see triangles), respectively. Error bars are shown in the figure. 3238 Journal of the American Ceramic Society—Lund and Yue Vol. 93, No. 10

October 2010 Tensile Strength of Oxide Glass Fibers 3239 where A is a constant, which is found to be 4.66(+0.09)x 10-s m"/s.for the basaltic fibers and 5.12(+0.6)x 10-5m/s0.5 a,(MPa) 5001000 3000 for the E-glass fibers. From the finite element simulation of the drawing process of ntinuous basaltic glass fibers, a linear relationship is found Ta(ki between v and the axial stress applied to the fibers during draw Oax. as follo where B is a slope. For the continuous basaltic glass fibers, the (2)with Eq(3), a direct relationship between the fiber ning Eq and the axial stress is obtained In o,(a, in MPa) This relation also applies for the continuous E-glass fibers, Fig 4. Tensile strength (or) decay of continuous E-glass fibers as a because these fibers are produced under drawing conditions onsequence of sub-Tg annealing at various temperatures between 0.5 Tg similar to those of the continuous basaltic glass fibers. For the nd Tg, which is visualized in a Weibull diagram. ool fibers, the Oax during forming was estimated by FEM sim- ulation to be around o02 mPa MPa. However, this final strength level of the glass fibers is sig basaltic fibers, the tensile strength first rises rapidly with Oax, and nificantly higher than that of bulk glasses of similar composi then approaches a plateau at oax >20 MPa. The difference be- tions. To reveal the origin of the higher tensile strength of glas tween the maximum strength of the continuous fibers and that fibers relative to bulk glass and wool fibers, the actual tensile of the bulk glasses is separated into two intervals. Interval 1 strength(Go) of as-produced basaltic fibers is described by three represents the do difference between the fibers(including con- distinct Go drops in Fig. 5(b). AGor is the difference in strength tinuous and wool fibers)drawn at the lowest oax and the fibers between the as-produced continuous fibers and the as-produced drawn at the highest Gax Interval 2 represents the Go difference wool fibers. AGo2 is the drop in strength from as-produced wool between wool fibers and bulk glass. These intervals will be used fibers to that of fully relaxed fibers. Aoo is the difference in in the discussion of the origin of the fiber strength in the next strength between the fully relaxed fibers and bulk glass of the section Recent studies show that relaxation of the structural anisot Figures 6(a) and(b) show the dependences of the remaining ropy due to annealing is much faster than the enthalpy relax- excess enthalpy scaled by AHlot excess enthalpy, AHrem/AHtot ation. To see whether the anisotropy and enthalpy relaxation (here also called the enthalpy relaxation index), on the annealing are linked to the evolvement of the tensile strength of glass fibers temperature Ta for both the E-glass(Fig. 6(a) and the basaltic pon annealing, tensile strength of both the annealed wool and fibers(Fig. 6(b)). This dependence can be described by the fol- the annealed continuous fibers is measured. Figure 4 shows the lowing expression strength decay of continuous E-glass fibers with the increasing pendence of o the oo data are plotted against the T -scaled △Bos △Hrcm temperature, Ta/Te in Fig. 5 for both the E-glass fibers (Fig. 5(a)) and the basaltic fibers(Fig. 5(b), respectively As shown in Figs. 5(a) and(b), the onset temperature of the where Tr is the characteristic annealing temperature and C is a ength decay is around 0.5-0.6 Tg for continuous fibers, constant reflecting the rate at which AHrem decreases with Ta. ereas it is around 0.7-0 8 Tg for the wool fibers. It is also Figure 6(b)shows that there is a similarity in the enthalpy re- seen that the strength decay occurs faster for the continuous fi- laxation between the basaltic continuous and the wool fibers(see bers than for the wool fibers. Upon a 3-h annealing near Tg, the the fitting curves). When the fibers undergo annealing near Tg tensile strength of all samples reduces to a level around 800-900 for 3 h, the excess enthalpy is reduced to zero. It is known that the enthalpy relaxation in continuous glass fibers begins at higher annealing temperatures than the anisot 4000 ropy relaxation process 3000 3 fibers decay of the optical birefringence(Anm)of glass fibers normalized 乏200 isotropy relaxation index), with the increasing Ta. To compare Wool fibers Wool fibers the anisotropy relaxation with the enthalpy relaxation, the An/ interval Antot data are plotted against Ta in Fig. 6(a). This plot can be 20406080020 dashed curve in Fig. 6(a). It is observed in Fig. 6(a)that birefringence decays much faster than the excess enthalpy Fig 3. Tensile strength do as a function of the axial stress to fibers during drawing for both E-glass(a)and basaltic co ) and comparisons of the tensile strength data between wool, and bulk samples Interval 1, the do difference betweer tinuous fibers and the wool fibers for similar diameters: Interval To explore the origin of the difference in the fracture behavior difference between the wool fibers and the bulk glass of between the wool and the continuous glass fibers, it is useful to Ik samp sitions. Vertical rectangular grey box, the do data of bulk e scattering range. Error bars are calculated following AS 二 compare the Weibull moduli m, i. e, the slopes of the strength distributions between the two types of fibers(Fig. 1). Figure 1 shows that the two types have comparable Weibull

where A is a constant, which is found to be 4.66 (70.09) 105 m1.5/s0.5 for the basaltic fibers and 5.12 (70.6) 105 m1.5/s0.5 for the E-glass fibers. From the finite element simulation of the drawing process of continuous basaltic glass fibers, a linear relationship is found between v and the axial stress applied to the fibers during draw￾ing, sax, as follows: sax ¼ Bv (3) where B is a slope. For the continuous basaltic glass fibers, the constant B is found to be 1.07 106 N s/m3 . By combining Eq. (2) with Eq. (3), a direct relationship between the fiber diameter and the axial stress is obtained sax ¼ BA2 d2 (4) This relation also applies for the continuous E-glass fibers, because these fibers are produced under drawing conditions similar to those of the continuous basaltic glass fibers. For the wool fibers, the sax during forming was estimated by FEM sim￾ulation to be around 0.02 MPa. Figures 3(a) and (b) show that, for both E-glass fibers and basaltic fibers, the tensile strength first rises rapidly with sax, and then approaches a plateau at sax420 MPa. The difference be￾tween the maximum strength of the continuous fibers and that of the bulk glasses is separated into two intervals. Interval 1 represents the s0 difference between the fibers (including con￾tinuous and wool fibers) drawn at the lowest sax and the fibers drawn at the highest sax. Interval 2 represents the s0 difference between wool fibers and bulk glass. These intervals will be used in the discussion of the origin of the fiber strength in the next section. Recent studies show that relaxation of the structural anisot￾ropy due to annealing is much faster than the enthalpy relax￾ation.18 To see whether the anisotropy and enthalpy relaxations are linked to the evolvement of the tensile strength of glass fibers upon annealing, tensile strength of both the annealed wool and the annealed continuous fibers is measured. Figure 4 shows the strength decay of continuous E-glass fibers with the increasing annealing temperature (Ta) in a Weibull plot. To observe the Ta dependence of s0, the s0 data are plotted against the Tg-scaled temperature, Ta/Tg, in Fig. 5 for both the E-glass fibers (Fig. 5(a)) and the basaltic fibers (Fig. 5(b)), respectively. As shown in Figs. 5(a) and (b), the onset temperature of the strength decay is around 0.5–0.6 Tg for continuous fibers, whereas it is around 0.7–0.8 Tg for the wool fibers. It is also seen that the strength decay occurs faster for the continuous fi- bers than for the wool fibers. Upon a 3-h annealing near Tg, the tensile strength of all samples reduces to a level around 800–900 MPa. However, this final strength level of the glass fibers is sig￾nificantly higher than that of bulk glasses of similar composi￾tions. To reveal the origin of the higher tensile strength of glass fibers relative to bulk glass and wool fibers, the actual tensile strength (s0) of as-produced basaltic fibers is described by three distinct s0 drops in Fig. 5(b). Ds01 is the difference in strength between the as-produced continuous fibers and the as-produced wool fibers. Ds02 is the drop in strength from as-produced wool fibers to that of fully relaxed fibers. Ds03 is the difference in strength between the fully relaxed fibers and bulk glass of the same composition. Figures 6(a) and (b) show the dependences of the remaining excess enthalpy scaled by DHtot excess enthalpy, DHrem/DHtot (here also called the enthalpy relaxation index), on the annealing temperature Ta for both the E-glass (Fig. 6(a)) and the basaltic fibers (Fig. 6(b)). This dependence can be described by the fol￾lowing expression24: DHrem DHtot ¼ Tr Ta C 1  exp  Ta Tr C ! " # (5) where Tr is the characteristic annealing temperature and C is a constant reflecting the rate at which DHrem decreases with Ta. Figure 6(b) shows that there is a similarity in the enthalpy re￾laxation between the basaltic continuous and the wool fibers (see the fitting curves). When the fibers undergo annealing near Tg for 3 h, the excess enthalpy is reduced to zero. It is known that the enthalpy relaxation in continuous glass fibers begins at higher annealing temperatures than the anisot￾ropy relaxation process.18,21 The latter is often reflected by the decay of the optical birefringence (Dn) of glass fibers normalized by the initial birefringence (Dntot), Dn/Dntot (here also called an￾isotropy relaxation index), with the increasing Ta. To compare the anisotropy relaxation with the enthalpy relaxation, the Dn/ Dntot data are plotted against Ta in Fig. 6(a). This plot can be described by an expression similar to Eq. (5) as shown by the dashed curve in Fig. 6(a). It is observed in Fig. 6(a) that optical birefringence decays much faster than the excess enthalpy during annealing. IV. Discussion To explore the origin of the difference in the fracture behavior between the wool and the continuous glass fibers, it is useful to compare the Weibull moduli m, i.e., the slopes of the strength distributions between the two types of fibers (Fig. 1). Figure 1 shows that the two types of fibers have comparable Weibull’s 0 20 40 60 80 0 20 40 60 80 0 (a) E-glass compositions (b) Basaltic compositions Continuous fibers Continuous fibers Wool fibers Bulk glass Wool fibers Bulk glass interval 1 1000 interval 2 2000 3000 4000 0 (MPa) ax (MPa) Fig. 3. Tensile strength s0 as a function of the axial stress sax applied to fibers during drawing for both E-glass (a) and basaltic composition (b), and comparisons of the tensile strength data between continuous, wool, and bulk samples. Interval 1, the s0 difference between the con￾tinuous fibers and the wool fibers for similar diameters; Interval 2, the s0 difference between the wool fibers and the bulk glass of same compo￾sitions. Vertical rectangular grey box, the s0 data of bulk samples with the scattering range. Error bars are calculated following ASTM standard 1239.23 56789 –4 –3 –2 –1 0 1 2 5 16 50 84 99 ln(ln(1/(1– Pf))) 279 473 523 673 773 873 973 Ta (K) E-glass fibers Pf (%) ln f (f in MPa) 200 500 1000 3000 f (MPa) Fig. 4. Tensile strength (sf) decay of continuous E-glass fibers as a consequence of sub-Tg annealing at various temperatures between 0.5 Tg and Tg, which is visualized in a Weibull diagram. October 2010 Tensile Strength of Oxide Glass Fibers 3239

3240 Journal of the American Ceramic Society--Lund and Yue Vol 93. No. 10 4000(a)E-glass fibers(continuous) (b)Basaltic fibers continuous 3000 2000 0.4 0.6 1.0 040.60.81.01.21.4 T/T(K/K) Fig. 5. Characteristic tensile strength ao. as a function of the Tg-scaled annealing temperature, Ta/Tg for durations of 3 h. altic fibers(both co us and discontinuous wool fibers). Wool I and II refer to the samples that w eated in air and in ely. ool, Oo2, and oo] are the drop in the tensile strength from not annealed continuous to wool fibers not annealed wool relaxed fibers, and that from the fully relaxed fibers to the bulk sample, respectively. Error bars are following ASTm ensile str e ameter range, ne the error range achievable only for the continuous fibers. The narrow high- is taken into account. The maximun ength of contin- strength distribution of the continuous glass fibers is reflected by ous E-glass fibers is close to 10-um-diame the relatively large Weibull's modulus m ranging from 8 to 17 ontinuous E-glass fibers reported by e.g., Kurkjian et al Table ID). Within this narrow distribution, the average diameter For continuous basaltic fibers( Fig. 2(b)), the data of the wool fibers significantly deviate from the general tendency of the strength level of the continuous fibers of similar fiber diameters Figs. 2(a)and(b). Importantly, oax applied to the wool fibers magnitude lower than that applied to continuous fibers. This plies that the large ax difference could explain the large dis- 02 he wool and continuous fibers To con- 0.0 (a)E-glass fibers 0.0 3(a)and(b). Thus, a good agreement is found between the go data of the wool fibers and those of the continuous fibers. This 1.0△ suggests that the large Oax difference between the two types of Figs. 3(a)and(b)show a rapid increase in tensile strength at ax 10 MPa, which is then followed by a plateau, which corre- 3500 MPa for the continuous basaltic fibers, respectively and sponds to 2800 MPa for the continuous E-glass fibers △ Following the Griffith-Orowan fracture criterion,27the maximum of the tensile strength corresponds to flaw sizes of 20-40 nm. Flaws of these sizes are not associated with the (b) nd atomistic bonding in gla hence the maximum strength cannot be referred to as an intron- sic strength. However, the present authors argue that the glass 0.6 0.8 structure could influence the apparent strength of glass fibers Ta/Tg(K/K) and its distribution in a different way. This statement is based on Fig. 6. (a)Comparison between the Tr-scaled annealing temperature the findings shown in Figs. 3(a)and(b), i.e., the fibers subjected (Ta/Ty) dependence of the enthalpy relaxation index(AHrem/AHtot)and a smaller Oax have a lower do than those subjected to a larger that of the anisotropy relaxation index(An/Atot)for E-glass Shers. results in a linear increase of the degree of structural an/so Oax. In a previous study, it was found that an increase of the oa AHtot the total excess enthalpy of the original fibers, An the optical ropy. Thus, it can be inferred that the increases of the struc- (e, orientation of structural units along the of the original fibers. The solid and the dash curves represent the fits of fiber axis) enhances the tensile strength of glass fibers. As is experimental data to Eq (5)both for the enthalpy relaxation and for the known, the structural anisotropy of continuous glass fibers lin- ntinuous fibers and wool fibers for basaltic co The solid and the dash curve represent the fits of the experimental data However, unlike the anisotropy, the tensile strength reaches a to Eq. (5)both for the continuous basaltic fibers and for the wool fibers. plateau or maximum above a certain Oax value. This suggests espectively. All samples were annealed in atmospheric air for 3 h. The that above a critical Oax value the fiber strength is controlled not measured using differenti nly by the structural anisotropy but also by other factors such as inhomogeneity in atomic range, imperfect bonds on the

moduli in the strength region of about 1000–2700 MPa (see Ta￾ble II). Above this strength region, tensile strength data are achievable only for the continuous fibers. The narrow high￾strength distribution of the continuous glass fibers is reflected by the relatively large Weibull’s modulus m ranging from 8 to 17 (Table II). Within this narrow distribution, the average diameter of fibers ranges from 7.5 to 15 mm. In this diameter range, no diameter dependence of strength is detected if the error range is taken into account. The maximum tensile strength of contin￾uous E-glass fibers is close to that of the 10-mm-diameter continuous E-glass fibers reported by e.g., Kurkjian et al. 25 and Cameron.26 For continuous basaltic fibers (Fig. 2(b)), the data of the wool fibers significantly deviate from the general tendency of the change of the continuous fiber strength with the fiber diameter. In detail, the characteristic strength s0 falls far below the strength level of the continuous fibers of similar fiber diameters (Figs. 2(a) and (b)). Importantly, sax applied to the wool fibers during fiber spinning was found to be almost four orders of magnitude lower than that applied to continuous fibers. This implies that the large sax difference could explain the large dis￾crepancy in s0 between the wool and continuous fibers. To con- firm this, the tensile strength data are plotted against sax in Figs. 3(a) and (b). Thus, a good agreement is found between the s0 data of the wool fibers and those of the continuous fibers. This suggests that the large sax difference between the two types of fibers is indeed the origin of the s0 discrepancy. In addition, Figs. 3(a) and (b) show a rapid increase in tensile strength at sax o10 MPa, which is then followed by a plateau, which corre￾sponds to B2800 MPa for the continuous E-glass fibers and B3500 MPa for the continuous basaltic fibers, respectively. Following the Griffith–Orowan fracture criterion,27 the maximum of the tensile strength corresponds to flaw sizes of 20–40 nm. Flaws of these sizes are not associated with the atomistic local structure and atomistic bonding in glasses, and hence the maximum strength cannot be referred to as an intrin￾sic strength. However, the present authors argue that the glass structure could influence the apparent strength of glass fibers and its distribution in a different way. This statement is based on the findings shown in Figs. 3(a) and (b), i.e., the fibers subjected to a smaller sax have a lower s0 than those subjected to a larger sax. In a previous study, it was found that an increase of the sax results in a linear increase of the degree of structural anisot￾ropy.18 Thus, it can be inferred that the increases of the struc￾tural anisotropy (i.e., orientation of structural units along the fiber axis) enhances the tensile strength of glass fibers. As is known, the structural anisotropy of continuous glass fibers lin￾early increases with the drawing speed, and hence with the sax. However, unlike the anisotropy, the tensile strength reaches a plateau or maximum above a certain sax value. This suggests that above a critical sax value the fiber strength is controlled not only by the structural anisotropy but also by other factors such as inhomogeneity in atomic range,28 imperfect bonds on the 0 Δ Δ Δ (a) E-glass fibers (continuous) (b) Basaltic fibers continuous wool I wool II 4000 3000 2000 1000 0 (MPa) 0.4 0.6 0.8 1.0 0.4 0.6 0.8 1.0 1.2 1.4 Ta/Tg (K/K) 01 02 03 Fig. 5. Characteristic tensile strength s0, as a function of the Tg-scaled annealing temperature, Ta/Tg for durations of 3 h. (a) E-glass fibers (continuous fibers); and (b) basaltic fibers (both continuous and discontinuous wool fibers). Wool I and II refer to the samples that were heat treated in air and in nitrogen, respectively. s01, s02, and s03 are the drop in the tensile strength from not annealed continuous to wool fibers, that from not annealed wool fibers to the fully relaxed fibers, and that from the fully relaxed fibers to the bulk sample, respectively. Error bars are calculated following ASTM standard C-1239.23 1.0 0.8 Δn/Δntot ΔHrem/ΔHtot Δ Hrem/Δ Htot Δ Hrem/Δ Htot (b) Basaltic fibers (a) E-glass fibers Continuous Wool Δn/Δntot 0.6 0.4 0.2 0.0 0.4 0.6 0.8 1.0 Ta/Tg (K/K) 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 Fig. 6. (a) Comparison between the Tg-scaled annealing temperature (Ta/Tg) dependence of the enthalpy relaxation index (DHrem/DHtot) and that of the anisotropy relaxation index (Dn/Dntot) for E-glass fibers. DHrem is the excess enthalpy remaining in the fibers after annealing, DHtot the total excess enthalpy of the original fibers, Dn the optical birefringence remaining in fibers, and Dntot the total optical birefringence of the original fibers.18 The solid and the dash curves represent the fits of experimental data to Eq. (5) both for the enthalpy relaxation and for the anisotropy relaxation, respectively. (b) Comparison in DHrem/DHtot between continuous fibers and wool fibers for basaltic compositions. The solid and the dash curve represent the fits of the experimental data to Eq. (5) both for the continuous basaltic fibers and for the wool fibers, respectively. All samples were annealed in atmospheric air for 3 h. The enthalpy data were measured using differential scanning calorimetry in argon at an upscan rate of 20 K/min. 3240 Journal of the American Ceramic Society—Lund and Yue Vol. 93, No. 10

fiber surface, stress corrosion,29 surface roughness, and so on. In other words, the tensile strength of the continuous fibers cannot be enhanced just by increasing the structural anisotropy. It is known that sax causes anisotropy of microstructure in glass fibers, i.e., orientation of structural units along the fiber axis21,30 or extruded glass rods.31 In Fig. 3, the interval 1 must be related to the structural orientation due to the sax dependence of the optical birefringence.18,21 However, due to the presence of defects in the melts before fiber drawing, sax also induces the orientation of defects along the fiber axis. The defects here in￾clude microbubbles, striae, and structural clusters. By applying the sax to fibers, not only the chemical structure but also striae, microbubbles, and anisometric inhomogeneous domains are stretched and simultaneously orientated along the fiber axis. Before fiber drawing, the defects are randomly oriented in the melt. When they are frozen-in in fibers, they could become po￾tential sources of fracture of the fibers. However, when the de￾fects remain oriented, the probability for the fracture of the fibers will be greatly reduced, just as many other materials con￾taining the oriented species or structural unites do not fracture catastrophically.32 It should be noted that the defect orientation is initiated at a much smaller shear stress or axial stretching stress compared with the structural orientation. This is verified by the fact that structural orientation in glass melts occurs much easier than crystal orientation33 or than bubble squeezing.34 The structural orientation involves the slight elongation of the intermediate￾range voids in the glass network,35 whereas the defect orienta￾tion involves the long-range alignment of the defects.36 As illustrated in Fig. 3(b), interval 2 represents the excess of the tensile strength of the basaltic wool fibers (also the basaltic continuous fiber subjected to equal sax) over that of bulk glasses. This excess strength is most likely ascribed to three effects. First, the probability of the appearance of the flaws in the wool fibers, and hence the probability of the fibers to frac￾ture are much lower than that of bulk glasses. Second, the ori￾entation of the above-mentioned defects along the fiber axis occurs both in the interior and on the surface of the wool fibers due to the sax, 37 whereas it does not occur in bulk glasses. Such a defect orientation contributes to the strength of both the wool and the continuous fibers. Third, the fictive temperature (Tf) of wool fibers is much higher than that of bulk glasses, because wool fibers undergo a cooling process that is 106 –107 times faster than the cooling of standard bulk samples.38 It has long been known that a glass with a higher Tf is less heterogeneous, and hence higher in the tensile strength than a glass with a lower Tf. 28 Because of these three effects, the strength of the wool fi- bers can even exceed 1500 MPa, which is considerably higher than that of a bulk glass (usually 80–200 MPa).39 To further clarify why the strength of the continuous fibers is much higher than that of the wool fibers of the same diameter, annealing experiments were performed on both types of glass fibers, by which the relation between the fiber strength and the relaxation behavior should be revealed. The annealing results in decay in strength of both continuous E-glass fibers (Fig. 5(a)) and of continuous and wool basaltic fibers (Fig. 5(b)). This de￾cay is reflected by a parallel shift of the Weibull distribution curves (with same slopes) from the highest to the lowest strength as seen in Fig. 4. The parallel shift indicates that the strength decay caused by the annealing might have similar fracture or￾igins for all the glass fibers studied in this work. There is a nar￾row (or steep) high-strength distribution for both untreated continuous fibers and the slightly annealed continuous fibers. The narrow high-strength distribution can no longer be ob￾served in E-glass fibers annealed at 673 K and in basaltic fibers annealed at 743 K, respectively (see Fig. 4). Obviously, the dis￾appearance of the narrow high-strength distributions strongly influences the overall reduction in strength. In Fig. 5(b), three distinct s0 drops are highlighted, which describe the three possible mechanisms that determine the fiber strength. They are s01, s02, and s03, which are explained in the figure caption of Fig. 5. For the same diameter of basaltic fibers, the strength decay pattern is different from continuous to wool fibers (Fig. 5(b)). At low Ta (o0.8 Tg), the strength of the con￾tinuous fibers decays much faster than that of the wool fibers. In fact, the latter remain almost unchanged until Ta reaches 0.8 Tg. The drop Ds01 might be correlated with the relaxation of anisotropy. This statement is substantiated by four facts. First, the onset temperature of the strength decay of continuous fibers is roughly in coincidence with that of the anisotropy relaxation, i.e., 0.5 Tg, as shown in Fig. 6(a). Second, the surface of the fibers should degrade to some extent, when the fibers are an￾nealed at Tao0.8 Tg. However, the surface degradation does not affect the strength of the wool fibers, as it remains nearly con￾stant at Tao0.8 Tg. This implies that the strength decay is not related to the surface degradation. Third, the enthalpy relax￾ation occurs in both the wool and the continuous fibers. But the enthalpy relaxation does not affect the strength of the wool fi- bers. Hence, it should not affect the strength of the continuous fibers either. Fourth, the orientation of defects (striae and bub￾bles) along the fiber axis does not easily relax toward the ran￾dom orientation at Ta well below the viscous region. Thus, the degree of the orientation of defects does not vary, and hence, does not determine the drop Ds01. The drop Ds02 might be mainly attributed to both the surface degradation and structural heterogeneity. This statement is sub￾stantiated by three facts. First, the anisotropy in the continuous fibers almost completely disappears at Ta 5 0.8 Tg. Further￾more, there is almost no anisotropy in the wool fibers. Thus, the anisotropy should not be responsible for Ds02. Second, the de￾cays in strength of both wool and continuous fibers follow a similar slope above 0.8 Tg (Fig. 5(b)) and probably have same origin. It is known that severe surface degradation must occur at such high annealing temperatures above 0.8Ta. Third, the enth￾alpy relaxation most intensely takes places in the Ta range cor￾responding to Ds02 (Fig. 6(a)). This leads to a decrease in the fictive temperature, and hence to an increase in the structural heterogeneity or clustering. As a consequence, the fiber strength drops to a final value of about 800–900 MPa. The drop Ds03 indicates that after the full release of the excess enthalpy, both the wool fibers and the continuous fibers still maintain a higher strength than the bulk glasses. The high strength of the annealed fibers might be attributed predomi￾nantly to the fact that the defect orientation both in the interior and on the surface of the fibers remains the same after anneal￾ing. It is unlikely that the long-range arrangement of orientated defects relaxes toward the random orientation, unless the fibers are heated to a viscous state. In contrast, all sorts of defects are randomly distributed in the bulk glasses. In Fig. 5(b), similar decay patterns of the tensile strength are observed for wool fibers annealed both in air and in nitrogen. This indicates that the strength decay is not associated with the oxidation of the wool fibers. The annealing-induced decay of the tensile strength of E-glass fibers was reported in an earlier study.40 Figure 5(b) shows that the onset temperature of the strength decays is around 0.5 Tg (454 K) for continuous fibers, and around 0.8 Tg (726 K) for the basaltic wool fibers. Interestingly, the onset temperature of the strength decay is close to that of the local structural anisotropy relaxation of continuous E-glass fibers (Fig. 6(a)). For the con￾tinuous fibers, the maximum sax applied in this work is 70 MPa for the continuous E-glass fibers and 52 MPa for the continuous basaltic fibers. These values lead to a high degree of structural orientation and are close to the onset stress of the shear thinning flow of a silicate network glass.41 The oriented local structure is energetically very unstable that it relaxes at very low tempera￾tures, e.g., already at 0.5 Tg. 18 It should be noted that the axial stretching or shear-induced anisotropy in silicate glass is detect￾able only by optical birefringence21,30 and not by nuclear mag￾netic resonance (NMR).42 As shown in Fig. 4, the narrow high-strength distribution re￾mains at a lower Ta and disappears at a higher Ta. This implies that the narrow high-strength distribution of continuous fibers could arise from the existence of the optical birefringence. At October 2010 Tensile Strength of Oxide Glass Fibers 3241

3242 Journal of the American Ceramic Society--Lund and Yue Vol 93. No. 10 Ta>0.7 Te, the narrow high-strength distribution does not exist deities are also factors responsible for th trength of an- any longer, because the structural anisotropy is nearly relaxed nealed glass fibers compared with bulk Finally, the (Fig. 6). It is expected that the continuous basaltic fibers should relative contributions of the above-mentio ctors to the fi- ave a degree of structural anisotropy similar to that of the ber strength are estimated in terms of the continuous E-glass fibers for comparable dax due to the similar as a function of annealing temperature glass systems, i.e., aluminosilicate. The optical birefringence (An) of the basaltic continuous fibers is not measurable using the present technique due to the rather limited optical transp ency of basaltic glasses. The authors thank R. von der( L Jensen, S. Primdahl, and D. Lybye for From Fig. 6(a), a strong decoupling is observed between the useful discussions. They also thank P. Nielsen for performing the tensile strength isotropy and the enthalpy relaxation for E-glass fibers with a diameter of about 9 um. In other words, the anisotropy rela ation starts at a much lower annealing temperature than the enthalpy relaxation. This decoupling is associated with the References difference in relaxation mechanism. The anisotropy relaxation A. A. Griffith, "The Phenomena of Rupture and Flow in Solids, Philos. is related, as the modifying ion motion, to local structural ar Trans. R. Soc. London, 221, 163-98(1921 rangements, whereas the enthalpy relaxation appears to be dom- ength of Glass Fibres, " Ind. Eng. Chem., 31. 290-8(1939). inated by the relaxation of the silicate melt network. The anisotropy relaxation occurs easier when the initial anisotropy J.Am. Ceram.So,38.122-5(1955) R E Mould. ""Crossbending Tests of Glass Fibers and the Limiting Strength ol is larger, i.e., the ax is larger. In other words, the larger GI py is, the more unstable is the orientated glass ngth of Glass Fibres, Nature, 181. 1006(1958 hence the faster and easier the structure relaxes. In a 6G. M. Bartenev, "The Structure and Strength of Glass Fibers. "J. Non Cryst. recent study, the stress relaxation is contingent on the simul taneous enthalpy relaxation in thick chalcogenide glass fibers ture of Glass Fibers, Sov. Phys. Solid State, 6. 920(1964) the stress relaxation and the enthalpy relaxation for relatively Fibers "J. Soc. Glass Technol. 34.63-8(1950). ""Evidence against oriented structure in glass thick fibers, i.e., the fibers with a low anisotropy. It would be of the Factors Likely to Afect the Strength highly interesting in the future to conduct a systematic stud and Properties of Glass Fibres, "Plrys. Chem. Glass, 1, 418(1960 about the dependence of the extent of the decoupling on the fiber diameter and hence on the g Fibers-Re-Examination, " J. Non Cryst. Solids. 286, 132-8(2001)- From Fig. 6(b), it is observed that the enthalpy relaxation Rate, and Viscosity of Glasses. " J. Chem. Phys., 120, 8053-9(2004). curve of the wool fibers is slightly below that of the continuous IN. M. Cameron. "Relation Between Melt Treatment and Glass Fiber fibers. This is attributed to the fact that the wool fibers hav undergone a faster cooling(10 K/s)than the continuous fi- IR.K.Brow, N. Lower, C.R. Kurkjian, and H Li. "The Effects of Melt His- bers(10 K/s), and hence tory on the Failure Characteristics of Pristine GLass Fibres. Plus Chen Glasses. er e enthalpy(AHtot) and a higher fictive temperature(To than the ahler and R. Bruckner. "Structural and Mechanical Properties of Glass latter. Consequently, the excess enthalpy of the wool fibers re- Fibers with Linear and Three Dimensional Network "Glastechn. Ber.. 58. 33-45 laxes at a lower Ta than that of the continuous fibers. (1985) All tensile strength tests were performed in an ambient at ns on alkali silicate Glass Fibers, J. Non Cryst. Solids, 204. 282-93(1996 mosphere, and hence interaction between fiber surfaces and hu and G. E. Mostovoi."The Effect of Basalt idity in the air could occur, and this could result in a decrease Fiber Production Techology on Mechanical Properties of Fiber,Glass Cer in the tensile strength. On the other hand because of the same 5625(201 ambient conditions, the tensile strength data can be reasonabl Birefringence Decay, Enthalpy Relaxation and Viscous Flow in Calcium Boroak- ompared between different types of fibers, and therefore the 256,299-30502008) main conclusions drawn from this work are not influenced by the surrounding conditions of measurements quenched Glass, "Appl. Phys. Letf. 81. 2983-5(2002) stical Theory on the Strength of Materials." Ing (193 Wool Fibres, "J. Ceran. Soc. Jpn, 116, 8 From E-glass and basaltic compositions, both continuous and 2ASTM International Standard Practice for Reporting Uniaxial Strength Data wool glass fibers were drawn under similar conditions. All the and Estimating Weibull Distribution Parameters for Advanced Ceramics, C-1239-07. fibers underwent tensile strength tests under ambient conditions ASTM International. West Conshohocken. PA. 20 The results show that the tensile strength of the continuous fi- 2Y. Z. Yue, "Influence of Physical Ageing on the Excessive Heat Capacity of bers increases with a decrease of the fiber diameter. i.e. from urkjian, P. K. Gupta, R. K. Brow, and N. Lower."TI bulk glass to the thick glass fibers(about 10-17 um), and then approaches a plateau. However, the tensile strength of the wool fibers does not follow the diameter dependence of the tensile of E-Glass Fibres Part 2. Heating and strength of the continuous fibers. But when the strength is plot 2H. Rawson, "Internal Stresses Caused by Disorder in Vitreous Materials, ted against the o.. the strength data of the wool fibers beau- tifully fit the main trend of the continuous fibers. By considering crhorn and L. H. Boltz, "" Stress Corrosion and Static Fatigue of the oax dependence of the optical birefringence, it is inferred that Glass. J. A. Ceram Soc., 53, 543-8(1970). Bruckner."Structure Sensitive Measurements the structural anisotropy (or orientation) induced by the E-Glass Fibers. "J Non-Cryst. Solids, 49, 471-84(1982) plays an important role in determining the tensile strength of the continuous fibers. In addition, the defect orientation caused by Magnetic Resonance Evidence for Structural Order in Extruded Phosphate the oax contributes to the fiber strength as well ssel, ""Oriented Crystallization of Glass. A Review, " J. Non Cryst. By comparing the annealing-induced decay of the tensile strength with both enthalpy relaxation and structural anisot R. Bruckner. Y. Z. Yue and J. Deubener Rheology of Glass opy relaxation, it is confirmed that the structural anisotropy is an important source of the higher strength of continuous glass Lime-Silica Glasses"Glass Technol, 43C,43-5(2002) Flow of Foamed soda- fibers than the bulk glass of same composition. However, defect BR. Bruckner, "Anisotropic Glasses and Glass Melts-A Survey, "Glastechn orientation, elevated fictive temperature, and surface homoge- 396-411(1996

Ta40.7 Tg, the narrow high-strength distribution does not exist any longer, because the structural anisotropy is nearly relaxed18 (Fig. 6). It is expected that the continuous basaltic fibers should have a degree of structural anisotropy similar to that of the continuous E-glass fibers for comparable sax due to the similar glass systems, i.e., aluminosilicate. The optical birefringence (Dn) of the basaltic continuous fibers is not measurable using the present technique due to the rather limited optical transpar￾ency of basaltic glasses. From Fig. 6(a), a strong decoupling is observed between the anisotropy and the enthalpy relaxation for E-glass fibers with a diameter of about 9 mm. In other words, the anisotropy relax￾ation starts at a much lower annealing temperature than the enthalpy relaxation. This decoupling is associated with the difference in relaxation mechanism.18 The anisotropy relaxation is related, as the modifying ion motion, to local structural ar￾rangements, whereas the enthalpy relaxation appears to be dom￾inated by the relaxation of the silicate melt network. The anisotropy relaxation occurs easier when the initial anisotropy of fibers is larger, i.e., the sax is larger. In other words, the larger the anisotropy is, the more unstable is the orientated glass struc￾ture, and hence the faster and easier the structure relaxes. In a recent study,43 the stress relaxation is contingent on the simul￾taneous enthalpy relaxation in thick chalcogenide glass fibers (d 5 400 mm). This implies that there is no decoupling between the stress relaxation and the enthalpy relaxation for relatively thick fibers, i.e., the fibers with a low anisotropy. It would be highly interesting in the future to conduct a systematic study about the dependence of the extent of the decoupling on the fiber diameter, and hence on the sax. From Fig. 6(b), it is observed that the enthalpy relaxation curve of the wool fibers is slightly below that of the continuous fibers. This is attributed to the fact that the wool fibers have undergone a faster cooling (B106 K/s) than the continuous fi- bers (B105 K/s), and hence the former have a higher excess enthalpy (DHtot) and a higher fictive temperature (Tf) than the latter. Consequently, the excess enthalpy of the wool fibers re￾laxes at a lower Ta than that of the continuous fibers. All tensile strength tests were performed in an ambient at￾mosphere, and hence interaction between fiber surfaces and hu￾midity in the air could occur, and this could result in a decrease in the tensile strength. On the other hand, because of the same ambient conditions, the tensile strength data can be reasonably compared between different types of fibers, and therefore the main conclusions drawn from this work are not influenced by the surrounding conditions of measurements. V. Conclusions From E-glass and basaltic compositions, both continuous and wool glass fibers were drawn under similar conditions. All the fibers underwent tensile strength tests under ambient conditions. The results show that the tensile strength of the continuous fi- bers increases with a decrease of the fiber diameter, i.e., from bulk glass to the thick glass fibers (about 10–17 mm), and then approaches a plateau. However, the tensile strength of the wool fibers does not follow the diameter dependence of the tensile strength of the continuous fibers. But when the strength is plot￾ted against the sax, the strength data of the wool fibers beau￾tifully fit the main trend of the continuous fibers. By considering the sax dependence of the optical birefringence, it is inferred that the structural anisotropy (or orientation) induced by the sax plays an important role in determining the tensile strength of the continuous fibers. In addition, the defect orientation caused by the sax contributes to the fiber strength as well. By comparing the annealing-induced decay of the tensile strength with both enthalpy relaxation and structural anisot￾ropy relaxation, it is confirmed that the structural anisotropy is an important source of the higher strength of continuous glass fibers than the bulk glass of same composition. However, defect orientation, elevated fictive temperature, and surface homoge￾neities are also factors responsible for the higher strength of an￾nealed glass fibers compared with bulk samples. 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