Y.-C. Chiang/ Engineering Fracture Mechanics 65(2000)15-28 expressed as [6 Tdv ds=2ydA+ tsdu ds+di where y is the free surface energy, j tsdu ds represents the work of friction and U is the stored strain energy of the body. For an elastic system, U is equal to Td ds- Substituting Eq(18)into Eq(17), the fracture criterion is obtained as Td ds τduds 2dA 28A If the traction T consists of n concentrated forces Pl, .. Pn and the corresponding displacements △1,…,An,Eq1.(19) then becomes 2=2∑ t du ds (20) da 28A For the interfacial debonding problem(see Fig. 2), the debonding process can be regarded as one propagating along the fiber/matrix interface. Thus, we have 2y equal to the critical strain energy re rate of interface d, A=2rald, ds= 2radz and Pi= P=taa/vf, which is the fiber force at the plane. In Eq(20), u(=)is given by Eq (14)and Ai=-wf(0)is given by Eq. (12). Then, the debonding criterion of Eq(20)becomes P awo) 1 4 au(=) Taking the derivatives of wr(O)and u(=) with respect to ld, Eq (21)becomes →ow τ.δu Fig 3 Schematic representation of a general case of a crack bodyexpressed as [6] … ST Tdw ds ˆ 2gdA ‡ … Sf tsdu ds ‡ dU …17† where g is the free surface energy, „ tsdu ds represents the work of friction and U is the stored strain energy of the body. For an elastic system, U is equal to dU ˆ  1 2  … ST Tdw ds ÿ  1 2  … SF tsdu ds …18† Substituting Eq. (18) into Eq. (17), the fracture criterion is obtained as 2g ˆ @ 2@A … ST Tdw ds ÿ @ 2@A … SF tsdu ds …19† If the traction T consists of n concentrated forces P1, ... ,Pn and the corresponding displacements D1, ... ,Dn, Eq. (19) then becomes 2g ˆ 1 2 X ST Pi @Di @A ÿ @ 2@A … SF tsdu ds …20† For the interfacial debonding problem (see Fig. 2), the debonding process can be regarded as one crack propagating along the ®ber/matrix interface. Thus, we have 2g equal to the critical strain energy release rate of interface zd, A ˆ 2pald, ds ˆ 2padz and Pi ˆ P ˆ pa2s=Vf, which is the ®ber force at the crack plane. In Eq. (20), u…z† is given by Eq. (14) and Di ˆ ÿwf…0† is given by Eq. (12). Then, the debonding criterion of Eq. (20) becomes zd ˆ ÿ P 4pa @wf…0† @ld ÿ 1 2 …ld 0 ts @u…z† @ld dz …21† Taking the derivatives of wf…0† and u…z† with respect to ld, Eq. (21) becomes Fig. 3. Schematic representation of a general case of a crack body. 20 Y.-C. Chiang / Engineering Fracture Mechanics 65 (2000) 15±28