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 continuous glass fibers and discontinuous wool fibers are explored in terms of structural anisotropy, enthalpy relaxation, defect orientation, and surface inhomogeneities. The fibers are spun from the E-glass and the basaltic glass melts, respectively. It is revealed 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 increase 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 decay 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 subTg annealing. I. Introduction THE strength of glass has been attracting the interest of scientists for more than a century. In spite of progress in understanding 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 practical strength is not a physical value like density because it depends both on internal factors (e.g., chemical composition, microstructure, and defects) and on external factors (e.g., manners of both sample production and strength measurements). The rupture strength of chemical bonds, often called the theoretical 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 theoretical strength. This discrepancy between theoretical and practical 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 history,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 continuous 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 (diameter height). In the middle of the bottom of the crucible, there is a die with the dimension of 2.0 mm 3.0 mm (diameter 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 collected using a metallic drum. Different drawing speeds gave different axial stresses to the fibers, and hence generated different fiber diameters. The drawing temperatures were 1413 K for the basaltic fibers and 1393 K for the E-glass fibers, which correspond 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 microscope (SEM) (Philips XL30 ESEM, Hillsboro, OR). Sample name stands for the glass type and the drawing speed. For instance, 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 threewheel 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 direction. 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 estimated using a method reported elsewhere.19 The fiber diameters 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 airannealed 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 determine Cp of the samples, the heat flow data both for the baseline (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, respectively. 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 released 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 below 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 elsewhere.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 calculated 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 <11.4 um tribution evaluations. The strength values are separated in two 50 vol% is of d<6. 4 um, and only 16 vol% has d<3. I um. For distributions based on the slope of the distributions shown in continuous fibers, the distribution is rather narrow as long as the Fig. 1: a high-strength distribution with strength values above iber-drawing parameters are fixed. Figures 2(a)and(b) show 2700 MPa and a low-strength distribution with values below the tensile strength as a func inverse tber 2700 MPa. The characteristic tensile strength go and weibull,s both E-glass and basaltic compositions, respectively modulus m are found for each distribution and listed in table ll From Figs. 2(a) and(b). it is seen that the tensile strength of The slopes of the strength curves in the region between 1000 he fibers is more than one order of magnitude higher than tha of bulk glasses with the same composition. For continuous ba and 2700 MPa are parallel for both wool fibers and continuous salic fibers, the strength first increases with the decreasing fiber been found that these slopes reflect a broad distribution in diameter, and then reaches a plateau where the strength is in flaws including voids or bubbles positioned in the volume of dependent of the fiber diameter in the diameter range between the fibers and small flaws near or at the surface of the fibers .--In 5 and 17 um. Furthermore, Fig. 2 shows a significant differ- addition the continuous fibers exhibit a narrow high-strengtl ence in strength between continuous fibers and wool fibers for distribution above 2700 MPa and the basaltic wool fibers show similar fiber diameters. The tensile strengths of the wool fibers a narrow low-strength distribution in the region below 900 MPa. are considerably lower than those of the continuous fibers for The continuous fiber e40 has a single strength distribution, but both glass compositions. For the E-glass com n(Fig. 2(a)) with a low-strength tail caused only by a single data point. This the tensile strength of the wool fibers is about 1500 MPa, whereas low-strength tail is frequently observed in strength tests of glass that of the continuous fibers is about 2250--3000 MPa. The difference is also seen for the basaltic com (Fg.2(b), distribution. However, from fractography, the E-glass wool in which the tensile strength is around 1250 MPa for the wool fibers possess a bimodal flaw distribution, which is also shown For the continuous fiber-drawing process, the relation tween the fiber diameter d and the drawing speed v can The fiber diameter is often believed to have an impact on the described by the expression 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 d=4v-O5 Table ll Weibull,'s Parameters of All Samples Ob Tensile str Lower gr distribution Higher ar distribution Samp 〈d>(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; <d>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 measuring 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 immersion liquid with a refractive index of 1.558 was used for quantitative 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 evaluations of the fiber strength values need (at least) bimodal distribution 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 basaltic fibers, the strength first increases with the decreasing fiber diameter, and then reaches a plateau where the strength is independent of the fiber diameter in the diameter range between B5 and 17 mm. Furthermore, Fig. 2 shows a significant difference 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 between 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 drawing, 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 simulation 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 between 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 continuous 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 anisotropy due to annealing is much faster than the enthalpy relaxation.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 significantly higher than that of bulk glasses of similar compositions. 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 following 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 relaxation 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 anisotropy 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 anisotropy 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 continuous fibers and the wool fibers for similar diameters; Interval 2, the s0 difference between the wool fibers and the bulk glass of same compositions. 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 Table II). Above this strength region, tensile strength data are achievable only for the continuous fibers. The narrow highstrength 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 continuous 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 discrepancy 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 corresponds 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 intrinsic 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 anisotropy.18 Thus, it can be inferred that the increases of the structural 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 linearly 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