13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Figure 5. Two randomly slant micro cracks in an infinite specimen under uniform tension with the spacing, S=2b 4.1. Effects of inclination and randomness of micro cracks on SIF Two random and completely non-parallel micro cracks are shown in Fig. 5. These micro cracks are known as micro crack 1 and micro crack 2. Their vertical and horizontal distances (center to center) are defined by S, and their inclination angles are denoted by β and ψ. The micro cracks are located in an infinite specimen under uniform tension (parallel to y axis). The normalized stress intensity factors b kI and b kII are shown graphically in Figs. 6 and 7. These normalized intensity stress factors are evaluated for four original tips of the two micro cracks (keeping a constant inclination angle, β=60°, for micro crack 1 but different angles, ψ= 150°, 140°,120°, 100°,80° and 60° for micro crack 2). For the original micro crack tips 3, 4, which have the most effect compared to other original tips, Ik value has decreased with an increase in the inclination angle of micro crack 2 (angle ψ) from 50° to 90°. In fact, Ik gets negative values when ψ is close to 90°. In tension field, the closing of micro crack is due to shear stress because shearing mode occurs sooner than opening mode in this field. The stress intensity factor Ik increases considerably as the inclination angle ψ increases from 90° to 150°. For the original micro crack tips 1 and 2, the effects of randomness are lower than those of other tips. The maximum value of Ik (~0.772) occurs at ψ=150° due to the complete non-orientation of both the micro cracks. The behavior of mode II SIFs of four original tips of micro cracks is notably different from that of mode I SIFs. For original tips 3, 4, | II k | value S tip1 θ σ∞ σ∞ Micro crack 2 Micro crack 1 tip2 Spacing(S) tip4 tip3 θ β ψ
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