composites were fabricated by hot pressing [1], and were controlled to contain the whiskers with various volume fractions from 5 to 20%. Billets hot-pressed were cut into a flexural beam with a sharp single edge notch introduced to the center. Three-point flexural test of the SENB specimen was carried using an Instron-type test machine and a crack stabilizer [2] that was requisite for realizing stable crack propagation. The stable crack propagation was observed through an optical microscope to evaluate crack extension length ∆a. Utilizing the crack length a, which is given by the addition of ∆a to the initial crack length a0, and the applied load P on the flexural beam with thickness B and width W, the critical stress intensity factor in mode I, KIc, as a function of a was determined. SIMULATION FOR CRACK FACE WHISKER BRIDGING Simulation based on a model with crack face whisker bridging was carried out in order to derive σb and crack tip opening displacement δb from an experimental R-curve. In the model, both frictional and pull-out bridging processes [3] were taken into account, and σb in each process was calculated on the basis of shear-lag theory. The δb-value was calculated in terms of the distance x from the tip using the Barenblatt relation [4] with σb thus calculated. The material parameters, such as the whisker volume fraction Vw, average radius of whiskers rw, average length of whiskers lw, elastic modulus of whiskers Ew and of matrix Em, and tensile strength of whiskers σw were employed referring to the reports of the whisker supplier and of previous works [5,6]. The frictional shear stress at whisker/matrix interface τf was appropriately determined best-fitted to the experimental R-curve results. In the present composite system, σb was represented in the following formula; ( ) ( ) w b w w w b l x x V E δ σ χ ψ σ 2 = (1) for 0 < x < d, where ψ was the orientation efficiency factor [7], ( ) − + = w m w w w f w w V E V E r l 1 1 σ τ χ and d was determined by ( ) w w w b E l d σ χ χ δ 2 2 1 1 2 − = , and ( ) f w f w b w w b w w b r E x l r x l V x τ τ δ χ δ χ ψ χ σ 1 ( ) 4 1 ( ) 4 2 − − − − = (2) for d < x < b, where b was given by ( ) χ δ 4 w b l b = . Equations (1) and (2) were only available for the condition of 1≥χ . Finally, the critical stress intensity factor of the composite was estimated as a function of relative crack length α given as α = a/W under the condition that the length of bridging zone, lb, is assumed to be much smaller than the total crack length a, as follows: ( ) ( ) dx x x K K a b Ic Ic ∫ ∆ = + 0 0 2 σ π α (3) Details of the bridging model and the procedure of calculation are given in Ref.8.
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