13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- || 12 21 1 3 ( , ) ( , ) cos cos 2 2 2 IK r r r σ θ σ θ θ θ π = = , (23) || 21 11 3 3 5 ( , ) sin 2sin sin cos 2 2 2 2 I d K H r r θ θ θ θ θ π ⎛ ⎞ =− + ⎜ ⎟ ⎝ ⎠ , || 2 21 22 3 5 ( , ) sin cos 2 2 2 I d K H r r θ θ θ π = , || 2 21 12 3 5 ( , ) sin sin 2 2 2 I d K H r r θ θ θ π =− , || 21 21 3 3 5 ( , ) sin 2cos sin sin 2 2 2 2 I d K H r r θ θ θ θ θ π ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ , (24) where ( ) ( ) 1 2 21 2 1 4 R K K d MK R − = − , 22 0 lim 2 ( ,0) I r K r r π σ → =P , (25) and 11 12 ( )/2 M c c = − . 4. Numerical examples In the first example a straight central crack in a finite quasicrystal strip under a pure phonon load is analyzed (Fig. 1). The strip is subjected to a stationary or impact mechanical load with Heaviside time variation and the intensity 0 1Pa σ = on the top side of the strip. The material coefficients of the strip correspond to Al-Ni-Co quasicrystal and they are given by 10 2 11 2 23.43 10 c L M Nm− = + = ⋅ , 10 2 12 5.74 10 c L Nm− = = ⋅ , 10 2 1 12.2 10 K Nm− = ⋅ , 10 2 2 2.4 10 K Nm− = ⋅ , 3 4180 / kg m ρ= , 19 3 4.8 10 / w m s kg − Γ = ⋅ . The crack-length 2 1.0 a m = , strip width ratio / 0.4 a w= , and strip-height 1.2 h w = are considered. Due to the symmetry of the problem with respect to the crack-line as well as vertical central line, only a quarter of the specimen is numerically analyzed. Both phonon and phason displacements in the quarter of the specimen are approximated by using 930 (31x30) nodes equidistantly distributed.
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