tailieunhanh - Engineered Interfaces in Fiber Reinforced Composites Part 6

Tham khảo tài liệu 'engineered interfaces in fiber reinforced composites part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Engineered interfaces in fiber reinforced composites L 10mm In light of the foregoing discussion concerning the functional partitioning of the partial debond stress the characteristic debond stresses can be evaluated. The initial debond stress ơữ is obtained for an infinitesimal debond length where the frictional stress component is zero . The maximal debond stress ffj is determined immediately before the load instability Karbhari and Wilkins 1990 Kim et al. 1991 of the partial debond stress 7J when the debond length becomes i L zmax Details of the instability conditions of the debond process and zmax are discussed in Section . Further the solution for the initial frictional pull-out stress ơfr upon complete debonding is determined when the debond length reaches the embedded length L and the crack tip debond stress ơi is zero In Eq. it is assumed that the influence of the instantaneous fiber displacement relative to the matrix due to the sudden load drop after instability is negligible. 7 ơdí- 0 - 4. - _ Q exp 2 z. - zmax - 1 1 4- ớj exp Á Á zmax ƠỊ Ỡ - Tf 1 - exp -z L - zmax . __ mexp ẤL -l . . gfr g r Ơ 1 - exp -ẤẢ 1 w exp 2Z. - 1 1 2 L 50mm L 30mm ể mm Fig. . Plot of partial debond stress ffJJ as a function of debond length. f for untreated SiC fiber glass matrix composite. After Kim et al. 1991 . Chapter 4. Microtnechanics of stress transfer 135 . Instability of debond process The instability condition requires that the derivative of the partial debond stress with respect to the remaining bond length z L - Ể is equal to or less than zero . dffj dz o Kim et al. 1991 . Therefore the fiber debond process becomes unstable if L - f is smaller than a critical bond length zmax where the slopes of the curves become zero in Figs. and . At these bond lengths the partial debond stress ffj corresponds to the maximum debond stress ơj. The zmax value is determined from Eq. as Numerical treatment of Eq. .