COMPARISON OF E-GLASS DATA WITH STATISTICAL THEORIES 511 nitial strain tion fit(ppcc >0.99)was initially achieved at less than 12 breaks/cm Analysis of the GOPS SFC specimens showed that uniform distributions of fiber break locations were also achieved at saturation, correlations from(0.9990 Nth strain Tensile stress profile to 0.9997), with break densities at the end of the test varying from(19.4 to 26.3)breaks /cm(Fig. 2). The onset of uniformity in these specimens occurred between 16 and 26 breaks/cm. Therefore, 94.7% of the 19 E-glass samples analyzed yield break loca- tions that are strongly modeled by a uniform distri- bution, with the set with one outlier coming from the NOTS treated E-glass SFC samples Figure 1 Schematic representation of fiber fragments correlation coefficient for the fiber breaks fitted to a occurring in the single fiber fragmentation test uniform distribution of o 9972. These results indicate that the expected outcome from the sequential statistical theory of spacings, this result leads to the fragmentation of E-glass fiber SFCs at saturation are conclusion that the ordered distribution of the break locations that correspond to a uniform distri. spacings (i.e., fragment lengths) produced by a SFFT bution, with standard statistics spacing theories indi- conforms to(1) cating that the ordered spacings (i.e,fragment To assess the generality of the Kim et al. results, lengths) at saturation conform to the distribution single bare (i. e, unsized) E-glass fibers were embed- function given in (1) ded in a polyisocyanurate matrix and tested using These results appear to contradict the experimen- fast, intermediate, and slow test protocols. In con- tal data of Gulino and Phoenix who studied the se- trast to the bare E-glass DGEBA/m-PDA SFC speci- quential fragmentation of carbon fiber hybrid micr mens, the fiber break densities of these specimens composites. However, it is worthwhile noting that were unaffected by the testing rate. However, all of the E-glass SFCs tested by Holmes et al. exhib analyses of the break locations from these specimens ited debonded regions whose total length comprised indicate that they conform, like the DGEBA/m-PDA less than 5% of the total sample length. As an exam- SFC specimens, to a uniform distribution as satura- ple, the NOTS SFC specimens yielded the largest tion is approached with probability plot correlation average debond regions around each fiber break coefficients greater than 0.999. Consistent with the ( 26 um), with the range of the values for the four behavior observed in the bare E-glass DGEBA/m- specimens being between(11 and 37) um. Therefore, PDA SFC specimens, the break locations evolve to a the debond regions occurring in the fracture of uniform distribution at fiber break densities of 21 breaks/cm and remain uniform for the remainder of he test, with break densities on the order of 099 2 30 breaks/ cm being observed To span the range of interfacial shear strengths, ea 1 tests were also performed on E-glass fibers treated 3 a97 with n-octadecyl triethoxysilane(NOTs) and glyci- a9 dyloxypropyl triethoxysilane (GoPS) that were also 2 awns Polyiso cant ae. All Protocols embedded in the DGEBA/m-PDa matrix. As expected the NOTS SFC specimens exhibited a marked reduction in the fiber break density at satu- ration since the n-octadecyl group does not cova- Minimum value for 0.999 correlation coemcient lently bond to the DEGBA/m-PDA matrix. For the four specimens tested, the saturation break densities ged from(13 to 17)breaks/cm, significantly lower than those observed for the bare E-glass fibers Figure 2 Correlation coefficients for probability plot fit of matrices. Despite these low-break densities, the fiber tion (a) Solid symbols: E-Glass fiber SFCs with various sur break locations at saturation conformed in each face treatments(bare, NOTS, and GOPS), test protocols(fast, specimen to a uniform distribution with probability intermediate, and slow), and matrices(DGEBA/m-PDA ep- plot correlation coefficients ranging from 0.9972 to fiber SFCs in DGEBA/m-PDA tested by fast(or VAMAS) 0.9994 for the four specimens tested(Fig. 2). For the testing protocol. 15 [Color figure can be viewed in the online NotsdatadepictedinFigure2,auniformdistribuissuewhichisavailableatwww.interscience.wiley.com.j Journal of applied Polymer Science DOI 10.1002/ appstatistical theory of spacings, this result leads to the conclusion that the ordered distribution of the spacings (i.e., fragment lengths) produced by a SFFT conforms to (1). To assess the generality of the Kim et al. results, single bare (i.e., unsized) E-glass fibers were embed￾ded in a polyisocyanurate matrix and tested using fast, intermediate, and slow test protocols.18 In con￾trast to the bare E-glass DGEBA/m-PDA SFC speci￾mens, the fiber break densities of these specimens were unaffected by the testing rate. However, analyses of the break locations from these specimens indicate that they conform, like the DGEBA/m-PDA SFC specimens, to a uniform distribution as satura￾tion is approached with probability plot correlation coefficients greater than 0.999. Consistent with the behavior observed in the bare E-glass DGEBA/m￾PDA SFC specimens, the break locations evolve to a uniform distribution at fiber break densities of  21 breaks/cm and remain uniform for the remainder of the test, with break densities on the order of 30 breaks/cm being observed (Fig. 2). To span the range of interfacial shear strengths, tests were also performed on E-glass fibers treated with n-octadecyl triethoxysilane (NOTS) and glyci￾dyloxypropyl triethoxysilane (GOPS) that were also embedded in the DGEBA/m-PDA matrix. As expected the NOTS SFC specimens exhibited a marked reduction in the fiber break density at satu￾ration since the n-octadecyl group does not cova￾lently bond to the DEGBA/m-PDA matrix. For the four specimens tested, the saturation break densities ranged from (13 to 17) breaks/cm, significantly lower than those observed for the bare E-glass fibers tested in the DGEBA/m-PDA and polyisocyanurate matrices. Despite these low-break densities, the fiber break locations at saturation conformed in each specimen to a uniform distribution with probability plot correlation coefficients ranging from 0.9972 to 0.9994 for the four specimens tested (Fig. 2). For the NOTS data depicted in Figure 2, a uniform distribu￾tion fit (ppcc > 0.99) was initially achieved at less than 12 breaks/cm. Analysis of the GOPS SFC specimens showed that uniform distributions of fiber break locations were also achieved at saturation, correlations from (0.9990 to 0.9997), with break densities at the end of the test varying from (19.4 to 26.3) breaks/cm (Fig. 2). The onset of uniformity in these specimens occurred between 16 and 26 breaks/cm. Therefore, 94.7% of the 19 E-glass samples analyzed yield break loca￾tions that are strongly modeled by a uniform distri￾bution, with the set with one outlier coming from the NOTS treated E-glass SFC samples, yielding a correlation coefficient for the fiber breaks fitted to a uniform distribution of 0.9972. These results indicate that the expected outcome from the sequential fragmentation of E-glass fiber SFCs at saturation are break locations that correspond to a uniform distri￾bution, with standard statistics spacing theories indi￾cating that the ordered spacings (i.e., fragment lengths) at saturation conform to the distribution function given in (1). These results appear to contradict the experimen￾tal data of Gulino and Phoenix who studied the se￾quential fragmentation of carbon fiber hybrid micro￾composites. However, it is worthwhile noting that all of the E-glass SFCs tested by Holmes et al. exhib￾ited debonded regions whose total length comprised less than 5% of the total sample length. As an exam￾ple, the NOTS SFC specimens yielded the largest average debond regions around each fiber break ( 26 lm), with the range of the values for the four specimens being between (11 and 37) lm. Therefore, the debond regions occurring in the fracture of Figure 1 Schematic representation of fiber fragments occurring in the single fiber fragmentation test. Figure 2 Correlation coefficients for probability plot fit of fiber break locations at saturation to the uniform distribu￾tion. (a) Solid symbols: E-Glass fiber SFCs with various sur￾face treatments (bare, NOTS, and GOPS), test protocols (fast, intermediate, and slow), and matrices (DGEBA/m-PDA ep￾oxy and polyisocyanurate). (b) Open symbols: AS-4 carbon fiber SFCs in DGEBA/m-PDA tested by fast (or VAMAS) testing protocol.15 [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.] COMPARISON OF E-GLASS DATA WITH STATISTICAL THEORIES 511 Journal of Applied Polymer Science DOI 10.1002/app