HOLMES ET AI physics of the sequential fragmentation process that fragmentation of E-glass/DGEBA/m-PDA specimens occurs in the sfFt and carbon fiber/DGEBA/m-PDA specimens, where It is important to note that the theories and the DGEBa denotes the diglycidyl ether of bisphenol-A supporting Monte Carlo simulations assume that the and m-PDA denotes meta-phenylenediamine matrix is elastic-perfectly plastic (EPP). Although this assumption has been repeatedly shown to be incorrect for most polymer matrices, the EPP EXPERIMENTAL assumption is generally considered to be a reasona- Unsized E-glass fibers, w 15 um in diameter, were ble approximation for capturing the key features of obtained from Owens Corning. The fibers were the sequential fragmentation process in the SFFT either used as received(bare E-glass fibers)or methodology The EPP assumption leads to the con- treated with the n-octadecyl triethoxysilane clusion that the smallest breaks in the final fragment (NOTS) or glycidyloxypropyl trimethoxysilane length distribution are formed early in the test when (GOPS), with the GOPS surface treatment performed the critical transfer length is shortest. This assump- by the procedure given in Ref. 17. The AS-4 carbon tion anchors the filtered distribution concept that fibers were obtained from the Hexcel Corporation. was advanced by Curtin to develop his theory and The mold preparation procedure and curing proce- found to be plausible by Hui et al. in the develop- dure for the E-Glass SFCs made using the diglycidyl ment of their theory. The experimental data ether of bisphenol-A(DGEBA)resin(Epon 828, Shell) published by Kim et al. on E-glass SFCs showed the cured with meta-Phenylenediamine (n-PDA, Fluka, opposite effect, so that the filtered distribution con- or Sigma-Aldrich) have been published previously by cept utilized by the two theories cannot be applied Holmes et al. 5, 16, 18, 9 McDonough et al. have to the kim et al. data described the procedure for preparing the poly In addition to casting doubt upon the universality isocyanurate SFCs, and Kim et al. have described of the theories, the Kim et al. data suggest that the the procedure for preparing the combinatorial micro- physics of the sequential fragmentation process may composite SFC specimens used in this report. The composite failure behavior since the key input Rich et al. using the procedure described in Re 1 not be well-enough understood to reliably predict AS-4 carbon fiber SFC specimens were prepared arameters are obtained from the efft methodolo- The testing protocols for the E-glass SFC speci- gies. As an example, these composite failure models mens are most completely described in Ref. 18 and indicate that the density of fiber breaks increases as the test protocol associated with the AS-4 SFC speci the interfiber distance between fibers decreases. mens is described in Ref. 15. Finally, the automated Results by Li et al. on micromechanics specimens testing procedure used for the combinatorial micro- composed of 2D Nicalon multifiber arrays, and later composites has been previously described by Kim confirmed by Kim and Holmes on 2D E-glass et al. 121 The standard uncertainty in determining multifiber arrays, indicate that the break density the break locations was determined to be 1.1 um along the length of a fiber decreases as the interfiber whereas the standard uncertainty in the reported distance decreases. This result contradicts the predic- fragment lengths is 1.6 um. tion arrived at from shear lag models derived by ano Therefore, the Kim et al. and Li et al. experi RESULTS AND DISCUSSIONS results indicate that additional investigations are The effects of matrix behavior, adhesion strength, required of the EFFT methodologies to determine and testing rate on uniform break formation in the efficacy of these approaches in assessing interfa- E-glass SFCs cial phenomena in composite materials, in providing The locations of the fiber breaks along the length of useful input parameters for composite failure an E-glass fiber embedded in a SFC composed of models, and in assessing critical flaw nucleation in DGEBA/m-PDA epoxy resin conform to a uniform composite materials. In this article, the fragmenta- distribution, where the probability plot correlation tion of embedded E-glass fibers is further investi- coefficients of the break locations for the uniform gated by assessing the impact of the matrix type, distribution from multiple samples were consistently IFSS, and fiber-fiber interactions on the evolution of the sequential fiber fragmentation process. greater than or equal to 0.999(Fig. 1). From the For completeness, the relative break locations that occurred in SFCs tested by the 2nd VAMAS(the Certain commercial materials and equipment are identified Versailles Project on Advanced Materials and in this paper to specify adequately the experimental proce- Standards) Round Robin testing protoco/'5 are fitted dure. In no case does such identification imply recommenda- tion or endorsement by the National Institute of Standards to the uniform distribution function to illuminate and Technology, nor does it imply necessarily that the prod- differences that may arise between the sequential uct is the best available for the purpose Journal of applied Polymer Science DOI 101002/appphysics of the sequential fragmentation process that occurs in the SFFT. It is important to note that the theories and the supporting Monte Carlo simulations assume that the matrix is elastic-perfectly plastic (EPP). Although this assumption has been repeatedly shown to be incorrect8,9 for most polymer matrices, the EPP assumption is generally considered to be a reasona￾ble approximation for capturing the key features of the sequential fragmentation process in the SFFT methodology. The EPP assumption leads to the con￾clusion that the smallest breaks in the final fragment length distribution are formed early in the test when the critical transfer length is shortest. This assump￾tion anchors the filtered distribution concept that was advanced by Curtin6 to develop his theory and found to be plausible by Hui et al.7 in the develop￾ment of their theory. The experimental data published by Kim et al. on E-glass SFCs showed the opposite effect, so that the filtered distribution con￾cept utilized by the two theories cannot be applied to the Kim et al. data. In addition to casting doubt upon the universality of the theories, the Kim et al. data suggest that the physics of the sequential fragmentation process may not be well-enough understood to reliably predict composite failure behavior since the key input parameters are obtained from the EFFT methodolo￾gies. As an example, these composite failure models indicate that the density of fiber breaks increases as the interfiber distance between fibers decreases. Results by Li et al.10 on micromechanics specimens composed of 2D Nicalon multifiber arrays, and later confirmed by Kim and Holmes11 on 2D E-glass multifiber arrays, indicate that the break density along the length of a fiber decreases as the interfiber distance decreases. This result contradicts the predic￾tion arrived at from shear lag models derived by Cox12 and others.13,14 Therefore, the Kim et al. and Li et al. experimental results indicate that additional investigations are required of the EFFT methodologies to determine the efficacy of these approaches in assessing interfa￾cial phenomena in composite materials, in providing useful input parameters for composite failure models, and in assessing critical flaw nucleation in composite materials. In this article, the fragmenta￾tion of embedded E-glass fibers is further investi￾gated by assessing the impact of the matrix type, IFSS, and fiber–fiber interactions on the evolution of the sequential fiber fragmentation process. For completeness, the relative break locations that occurred in SFCs tested by the 2nd VAMAS (the Versailles Project on Advanced Materials and Standards) Round Robin testing protocol15 are fitted to the uniform distribution function to illuminate differences that may arise between the sequential fragmentation of E-glass/DGEBA/m-PDA specimens and carbon fiber/DGEBA/m-PDA specimens, where DGEBA denotes the diglycidyl ether of bisphenol-A and m-PDA denotes meta-phenylenediamine. EXPERIMENTAL Unsized E-glass fibers,  15 lm in diameter, were obtained from Owens Corning.* The fibers were either used as received (bare E-glass fibers) or treated with the n-octadecyl triethoxysilane (NOTS)16 or glycidyloxypropyl trimethoxysilane (GOPS), with the GOPS surface treatment performed by the procedure given in Ref. 17. The AS-4 carbon fibers were obtained from the Hexcel Corporation.15 The mold preparation procedure and curing proce￾dure for the E-Glass SFCs made using the diglycidyl ether of bisphenol-A (DGEBA) resin (Epon 828, Shell) cured with meta-phenylenediamine (m-PDA, Fluka, or Sigma-Aldrich) have been published previously by Holmes et al.9,15,16,18,19 McDonough et al.20 have described the procedure for preparing the poly￾isocyanurate SFCs, and Kim et al.21 have described the procedure for preparing the combinatorial micro￾composite SFC specimens used in this report. The AS-4 carbon fiber SFC specimens were prepared by Rich et al. using the procedure described in Ref. 15. The testing protocols for the E-glass SFC speci￾mens are most completely described in Ref. 18 and the test protocol associated with the AS-4 SFC speci￾mens is described in Ref. 15. Finally, the automated testing procedure used for the combinatorial micro￾composites has been previously described by Kim et al.11,21 The standard uncertainty in determining the break locations was determined to be 1.1 lm, whereas the standard uncertainty in the reported fragment lengths is 1.6 lm.16 RESULTS AND DISCUSSIONS The effects of matrix behavior, adhesion strength, and testing rate on uniform break formation in E-glass SFCs The locations of the fiber breaks along the length of an E-glass fiber embedded in a SFC composed of DGEBA/m-PDA epoxy resin conform to a uniform distribution, where the probability plot correlation coefficients of the break locations for the uniform distribution from multiple samples were consistently greater than or equal to 0.999 (Fig. 1). From the * Certain commercial materials and equipment are identified in this paper to specify adequately the experimental proce￾dure. In no case does such identification imply recommenda￾tion or endorsement by the National Institute of Standards and Technology, nor does it imply necessarily that the prod￾uct is the best available for the purpose. 510 HOLMES ET AL. Journal of Applied Polymer Science DOI 10.1002/app