Crack tip debond stress

Determination of the crack tip debond stress, ae, at a debond length, , is contingent to the condition that the fiber axial strain is equivalent to the matrix axial strain at the boundary between the bonded and debonded regions (i.e. duf z)/dz — diP a,z)/dz at z = (L — )). Within the debonded region, the matrix axial strain at the interface is greater than the fiber axial strain due to the relative slip between fiber and matrix. Therefore, combining Eqs. (4.8), (4.9) and (4.61) at the boundary, is obtained from... 

The basic requirement necessary to satisfy the partially debonded interface is that the crack tip debond stress, cr, (and the debond length, ) must be greater than zero. From the debond criterion given by Eq. (4.68)... 

Tf is the crack tip debond stress at the boundary between the bonded and debonded regions at z = f, as defined in Section 4.2.3. It should be noted, however, that the actual values of (Tf are different for different specimen geometry even for an identical debond length, t Therefore, the solutions of FAS, and the corresponding MAS, MSS and IFSS are obtained for the bonded region ( [Pg.129]

Partial debond stress, is the applied fiber stress during the progressive debonding process that may be written as a function of the debond length, f, and the crack tip debond stress, <7f, from Eq. (4.89)... 

It follows that consists of two stress components a crack tip debond stress, at, and a friction stress component, at is not only a function of the interfacial fracture toughness, G c, but is also dependent on the debond length, t, relative to the total... 

Details of the instability conditions of the debond process and Zmax are discussed in Section 4.3.4. Further, the solution for the initial frictional pull-out stress, (T, upon complete debonding is determined when the debond length, , reaches the embedded length, L, and the crack tip debond stress, ai, is zero ... 

In these equations, the crack tip debond stress, at the boundary between the bonded and debonded regions is given by... 

It allows to estimate the first term in Eq.(6). Similarly as in Budiansky et al. work (1985) we suppose that stresses in the vicinity of the crack tip debond the particle/ matrix interface just ahead of advancing crack for a distance h on each side of the plane of the crack. Due to this symmetry with respect to the plane y = 0 it is sufficient to investigate only the upper part of the cylinder. Assume that axisyrmnetric debonding is produced by an axisymmetric distribution of load applied to the matrix cylinder that jackets the particle. The magnitude of this loading is conservatively taken as the stress... 

Fig. 6.13. The Cook-Gordon (1964) mechanisms tensile debonding occurs at the weak interface ahead of crack tip as a result of lateral stress concentration and crack tip is effectively blunted.

For example, consider the crack tip as it intersects a fiber (Fig. 16). The local stresses at the tip can cause fiber-matrix debonding. The crack tip continues to open causing the interfacial debonded region to extend. The fiber continues to interact with the matrix through a frictional sliding force even after the initial bond fails. The distance over which the force acts is the debonded length times the difference in strain between the fiber and the matrix. 

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