Embedded fiber length

Fig 3.8 shows the interface shear bond strength, tb, determined from Eq. (3.7), which is not a material constant but varies substantially with embedded fiber length, L. However, to evaluate all the relevant interface properties properly, which include the interface fracture toughness, Gic, the coefficient of friction, p, and the residual clamping stress, qo, it is necessary to obtain experimental results for a full range of L and plot these characteristic fiber stresses as a function of L. More details of the... 

Fig. 3.8. Plots of interface bond strength, Tt, versus embedded fiber length, L. (a) for a carbon fiber-epoxy matrix system and (b) for a Hercules IM6 carbon fiber-acrylic matrix system. After Pilkethly and Doble (1990) and Desarmont and Favre (1991).

Fig. 4.7. Distributions of (a) fiber axial stress, a, (b) matrix axial stress, Om., and (c) interface shear stress. T along half the embedded fiber length, L, in the fiber fragmentation test.

Theoretical analyses of interfacial debonding and frictional pull-out in the fiber pull-out test were initially modeled for ductile matrices (e.g. tungsten wire-copper matrix (Kelly and Tyson, 1965, Kelly, 1966)) assuming a uniform IFSS. Based on the matrix yielding over the entire embedded fiber length, as a predominant failure mechanism at the interface region, a simple force balance shown in Fig. 4.19 gives the fiber pull-out stress, which varies directly proportionally to the cylindrical surface area of the fiber... 

Fig. 4.19. Fiber pull-out stress as a function of embedded fiber length, /./2a, for a tungsten wire embedded copper matrix composite system. Open symbols for pulled-out specimens solid symbols for fractured specimens. After Kelly and Tyson (1965).

Specific results are calculated for SiC fiber-glass matrix composites with the elastic constants given in Table 4.1. A constant embedded fiber length L = 2.0 mm, and constant radii a = 0.2 mm and B = 2.0 mm are considered with varying matrix radius b. The stress distributions along the axial direction shown in Fig. 4.31 are predicted based on micromechanics analysis, which are essentially similar to those obtained by FE analysis for the two extremes of fiber volume fraction, V[, shown in Fig. 4.32. The corresponding FAS distribution calculated based on Eqs. (4.90) and (4.120), and IFSS at the fiber-matrix interface of Eqs. (4.93) and (4.132) are plotted along the axial direction in Fig. 4.32. 

Fig. 4.39. Comparisons of initial debond stress,

Gray, R..1. (1984). Analysis of the effect of embedded fiber length on the fiber debonding and pull-out from an elastic matrix. J. Mater. Sci. 19, 861-870. 

Zmax maximum embedded fiber length for unstable debond process... 

Chua and Piggott [44,45] considered only the extensional strain energy (Ui) stored in the embedded fiber length and the shear strain energy (Gm) in the matrix immediately surrounding the fiber which is given in the following equation where... 

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