Analysis of a penny-shaped crack in a magneto-electro-elastic medium
Analysis of a penny-shaped crack in a magneto-electro-elastic medium
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DOI：
10.1080/14786430600724439
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发表时间：
2006-10
影响因子：
1.6
通讯作者：
M. Zhao;F. Yang;T. Liu
中科院分区：
文献类型：
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作者：
M. Zhao;F. Yang;T. Liu
本文导出了无限横观各向同性电磁弹性介质中椭球形孔洞在远距离轴对称力-电-磁联合载荷作用下的解。通过使椭圆孔的短轴趋近于零，得到了硬币形裂纹的精确解。结果表明，应力强度因子仅与外加机械载荷有关，而电位移强度因子和磁感应强度因子与外加复合载荷有关，并与β/α和γ/α两个比值有关。参数α是椭球腔的短轴与长轴之比，β是腔中材料的介电常数与磁电弹性介质的有效介电常数之比，γ是腔中材料的磁导率与磁电弹性介质的有效磁导率之比。这两个比率表征裂纹对电场和磁场的磁导率。研究了β/α和γ/α的几种极限情况。采用自洽方法确定了力-电-磁复合载荷作用下真实的裂纹张开度α。计算了BaTiO 3-CoFe 2 O 4复合材料中硬币形裂纹在不同体积分数和不同复合载荷下的应力、电位移和磁感应强度因子。
The solution for an ellipsoidal cavity in an infinite transversely isotropic magneto-electro-elastic medium under remotely applied axisymmetric, combined mechanical–electric–magnetic loading is derived. The exact solution for a penny-shaped crack is obtained by letting the minor axis of the ellipsoidal cavity approach zero. The results demonstrate that the stress intensity factor depends only on the applied mechanical loading, but the electric displacement intensity factor and the magnetic induction intensity factor depend on the applied combined loading, as well as the two ratios of β/α and γ/α. Parameter α is the ratio of the minor axis to the major axis of the ellipsoidal cavity, β is the ratio of the dielectric constant of the material in the cavity to the effective dielectric constant of the magneto-electro-elastic medium, and γ is the ratio of the magnetic permeability of the material in the cavity to the effective magnetic permeability of the magneto-electro-elastic medium. The two ratios characterize the permeability of the crack to electric and magnetic fields. Several limiting cases for β/α and γ/α are studied. A self-consistent method is adopted to determine the real crack opening α under the combined mechanical–electric–magnetic loading. The stress, electric displacement and magnetic induction intensity factors of a penny-shaped crack in BaTiO3–CoFe2O4 composites are calculated for different volume fractions and different applied combined loadings.