13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- the matrix and the particles are all assumed to be along 2x -axis. The magneto-electro-mechanical loading 0 1 σ = , 10 0 0 10 D σ − = and 8 0 0 10 B σ − = are applied along the top and bottom edges. Meanwhile, an equivalent homogeneous MEE plate of the same geometry and boundary conditions as that shown in Fig. 3(a) is adopted to compare the differences of the IFs. The material constants are given in Table 1, where the word “effective” denotes the properties of the equivalent homogeneous MEE plate. First, we discuss a horizontal crack ( 0 θ= °) with the crack length varying from / 0.2 a W= to / 0.8 a W= . Fig. 3(b) shows the mesh configuration which consists of 1009 element and 3082 nodes. Eight-node quadrilateral (Q8) elements are used over most of the mesh and six-node quarter-point (T6qp) singular elements are employed around the crack tips. The region composed of four-layer elements around each crack tip is adopted to be the integral domain. The IFs are normalized by the factors 0 0 0 I II K K a σ π = = , 0 10 0 10 IV K a σ π − = and 0 8 0 10 VK a σ π − = in this paper. Table 1. Material parameters 11 C 12 C 13 C 33 C 44 C 31 e 33 e 15 e Parameters ( 9 10 Pa) (C/m2) BaTiO3 [8] 166 77 78 162 43 -4.4 18.6 11.6 CoFe2O4 [8] 286 173 170.5 269.5 45.3 0 0 0 Effective [9] 226 125 124 216 44 -2.2 9.3 5.8 31 h 33 h 15 h 11κ 33κ 11β 33β 11γ 33γ Parameters (N/Am) ( 9 10− C2/Nm2) ( 12 10− Ns/VC) ( 6 10− Ns2/C2) BaTiO3 [8] 0 0 0 11.2 12.6 0 0 5 10 CoFe2O4 [8] 580.3 699.7 550 0.08 0.093 0 0 590 157 Effective [9] 290.2 350 275 5.64 6.35 5.367 2737.5 297 83.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.1 0.2 0.3 0.4 θ=0 solid line: particulate dash line: effective Normalized IFs a/W , KI/K 0 I , KIV/K 0 IV , KV/K 0 V Distance from crack tip to particle surface dp tip Figure 4. Normalized IFs vs crack length. Fig. 4 shows the normalized IFs obtained at the right crack tip and the distance from the crack tip to the particle surface p tip d . The results show that with the increasing of crack length / a W, the
RkJQdWJsaXNoZXIy MjM0NDE=