The half elliptical hole with an edge crack in a thermopiezoelectric material is studied by using the complex variable method. First, the mapping function which maps the outside of the elliptical hole and the crack in the right half plane into the outside of a circular hole in a full plane is given by the method of conformal mapping. Then, the complex potential functions and the field intensity factors (FIF) are presented according to the boundary conditions, respectively. Some useful results can be found by numerical analysis: 1) The influence of the heat flux on FIF depends on the model of the crack; 2) The shape and the size of the hole possess a significant effect on the field distribution at the crack tip.
W.C. Shen, L.L. Lin, C.Y. Shen, S. Xing and Z.B. Pan
TbxHo0.9−xNd0.1(Fe0.8Co0.2)1.93/epoxy (0 ⩽ x ⩽ 0.40) composites are fabricated in the presence of a magnetic field. The structural and dynamic magnetoelastic properties are investigated as a function of both magnetic bias field Hbias and frequency f at room temperature. The composites are formed as textured orientation structure of 1–3 type with 〈1 0 0〉 preferred orientation for x ⩽ 0.10 and 〈1 1 1〉-orientation for x ⩾ 0.25. The composites generally possess insignificant eddy-current losses for frequency up to 50 kHz, and their dynamic magnetoelastic properties depend greatly on Hbias. The elastic modulus (E3H and E3B) shows a maximum negative ΔE effect, along with a maximum d33, at a relatively low Hbias ~ 80 kA/m, contributed by the maximum motion of non-180° domain-wall. The 1–3 type composite for x ⩾ 0.25 shows an enhanced magnetoelastic effect in comparison with 0 to 3 type one, which can be principally ascribed to its easy magnetization direction (EMD) towards 〈1 1 1〉 axis and the formation of 〈1 1 1〉-texture-oriented structure in the composite. These attractive dynamic magnetoelastic properties, e.g., the low magnetic anisotropy and d33,max as high as 2.0 nm/A at a low Hbias ~ 80 kA/m, along with the light rare-earth Nd element existing in insulating polymer matrix, would make it a promising magnetostrictive material system.