J.P. Parmigiani, M.D. Thouless/J. Mech. Phys. Solids 54(2006)266-287 1.010 T!Eh=10x106 o9089%号里罡 Er后2h=0.01 Ratio of the substrate strength to interface strength, a/o Fig. 6. The for ETi/aih=0.01, 0.1, 1.0 and 10.0. The values of the other non- Ti, and d/h= 10. The plot shows h crack penetration or crack deflection will occur in Is/ri and a,/a; space.The uncertainty of the transition 。 ET后2h=Er/a2h r/h=10x10° 0.001001 Er/合2h Fig. 7. a plot showing how the strength ratio and the toughness ratio for the transition between crack deflection and penetration vary with the normalized interface fracture length scale. For this plot, the non-dimensional oups have values of Ers/0 h=Er /ah, a=B=0, T:/Eh=1.0x 10, Tu=Tmi=Ti, ai=ii,andARTICLE IN PRESS 0 1 2 3 4 5 6 7 0.0001 0.001 0.01 0.1 1 10 Interface fracture-length scale, E Γi / σi 2 h penetration into substrate deflection along interface Toughness of substrate / toughness of interface, Γs / Γi 1 0 E Γs /σs 2 h = E Γi / σi 2 h Γi /Eh = 1.0 x 10-6 ^ ^ 4 9 16 25 36 49 Strength of substrate / strength of interface, σs/ σi ^ ^ ^ Fig. 7. A plot showing how the strength ratio and the toughness ratio for the transition between crack deflection and penetration vary with the normalized interface fracture-length scale. For this plot, the non-dimensional groups have values of E¯ Gs=s^ 2 s h ¼ E¯ Gi=s^ 2 i h, a ¼ b ¼ 0, Gi=Eh¯ ¼ 1:0 10
6 , GIi ¼ GIIi ¼ Gi, s^i ¼ t^i, and d=h ¼ 10. 0 5 10 15 20 0 2 4 6 8 10 12 Γi /Eh = 1.0 x 10-6 α = 0 deflection along interface penetration into substrate Ratio of the substrate toughness to interface toughness, Γs / Γi Ratio of the substrate strength to interface strength, σs / σi ^ ^ E Γi /σi 2 h = 0.01 ^ 0.1 1.0 10 Fig. 6. The results of a set of calculations for E¯ Gi=s^ 2 i h ¼ 0:01; 0:1; 1:0 and 10:0. The values of the other non￾dimensional groups for this plot are a ¼ b ¼ 0, Gi=Eh¯ ¼ 1:0 10
6 , GIi ¼ GIIi ¼ Gi, s^i ¼ t^i, and d=h ¼ 10. The plot shows the regimes in which crack penetration or crack deflection will occur in Gs=Gi and s^s=s^i space. The error bars indicate the range of uncertainty of the transition. J.P. Parmigiani, M.D. Thouless / J. Mech. Phys. Solids 54 (2006) 266–287 277