Issue 35

O. Demir et alii, Frattura ed Integrità Strutturale, 35 (2016) 340-349; DOI: 10.3221/IGF-ESIS.35.39 341 There are various studies that exist in the literature for mixed mode-I/II fracture. One of the most common fracture criterion for in-plane mixed mode problems is maximum tangential (circumferential) stress (MTS), which was proposed by Erdogan and Sih [1]. This criterion assumes that, crack propagation starts from the crack tip radially when the tangential stress reaches a maximum value and exceeds a critical value or if an equivalent stress intensity factor ( Keq ) reaches the fracture toughness ( K IC ) propagation becomes unstable and fracture occurs. In this criterion K eq and crack deflection angle are given by: 2 0 0 0 3 cos cos sin 2 2 2 eq I II IC K K K K             (1) 2 2 2 0 2 2 3 8 arccos 9 II I I II I II K K K K K K               (2) Another common fracture criterion developed by Sih [2], is minimum strain energy density criterion. It is based on the elastic energy density. According to this criterion crack extends in the direction of minimum strain energy density factor and if the minimum strain energy density factor reaches a critical value, which depends on material, crack becomes unstable. Substituting the stress intensity factor, k I and k II into the following equations crack deflection angle, θ , can be obtained:       2 2 I I II II 2cosθ 1 sin θk 2 2cos 2θ 1 cosθ k k 1 6cosθ sin θ k 0                         (3)       2 2 I I II II 2 cos 2θ 1 cos θ k 2 1 sin θ 4 sin 2θ k k 1)cosθ 6cos 2θ k 0                         (4) Nuismer [3] and Hussain [4] expressed the maximum energy release rate criterion according to the Griffith’s theory [5] in several different forms. According to this criterion, crack propagates in the direction that strain energy release rate is maximum and crack becomes unstable if the maximum strain energy release rate exceeds a critical value. Crack deflection angles obtained from maximum circumferential stress criterion and maximum strain energy release rate criterion are the same. Consequently, the results of crack deflection angles according to Erdogan and Sih, and Nuismer and Hussain criterion are identical. Koo and Choy [6] developed the maximum tangential strain criterion proposed by Chang [7] and expressed a new criterion called maximum tangential strain energy density criterion. Initial crack growth occurs in the direction of maximum tangential strain energy density factor and if the factor reaches a critical value crack initiation occurs. The tangential strain energy density factor C and coefficients are defined by: 2 2 11 1 12 1 2 22 2 k k k k C b b b    (5)   11 1/ 64 (1 cos )( 2 cos ) b           12 1/ 64 (sin 3/ 2 3cos ) b         (6)   2 22 1/ 64 (3sin )( 3cos ) b       where ߢ =3-4ν for plane strain and ߢ =(3-ν)/(1+ ν) for plane stress conditions, ν is Poisson's ratio and μ is shear modulus. Then the crack initiation angle θ can be obtained by: 0 C     and 2 2 0 C     (7)