Analysis On The Critical Problems In Electromagnetic Materials With Multi-field Couplings

The similar critical phenomena can be seen in plastic materials, piezoelectric materials, Type-II superconductors, and so on. It is an important and attractive subject for the applications of these materials to investigate the critical phenomena in such physical systems. The present thesis is focused on theoretical research on some problems concerning on critical phenomena in the three matierials, such as the plastic zone near the crack tip in strain hardening materials, the yielding zone and polarization saturation zone in piezoelectric materials, and critical current density in Type-II superconductors.Firstly, by simplying the nonlinear constitutive equation of hardening materials, the hardening function is introduced to describe the degree of average hardening in plastic zone near the crack tip. A new strip hardening model is proposed to eliminate the singularity of stress at the crack tips. The size of strip hardening zone and crack tip opening displacement(CTOD) are derived and the dependence of strip hardening zone size and CTOD on hardeing paramenters is also discussed. The strip hardening model is successfully used to interpret the experimental results, which suggest the COD design curve is not valid for the materials with the ratio of yield stress and ultimate stress beyond 75~80%. Thereafter, the relationship beween CTOD and overall strain is also derived. By comparison, the theoretical results are in agreement with the experiments.Secondly, the effect of applied electric field on crack propagation in piezoelectric materials is investigated. It is assumed that both polarization saturation strip and stress-yielding strip appears near crack tips. The electric crack tip opending displacement(ECTOD) and mechanical crack tip opening displacement(MCTOD) are derived in two cases based on the size of polarization saturation strip and stress-yielding strip. A new fracture criterion, i.e., MCTOD is proposed for the piezoelectric materials. The MCTOD fracture criterion predicts that the existing contrary experiments may be induced by the different size of polarization saturation strip and stress-yielding strip because of different electric domain switching.Finally, the electromagnetic properties and magneto-elastic behaviors of Type-II superconducting strip in different physical fields are condisered based on arbitrary field-dependent critical state models. The current density and magnetic field distributions in superconducting strip is derived by conformal mapping and complex fields in three different cases, i.e., transport current, applied magnetic field, and in the simultaneous presence of applied field and transport current. The advantage of the method is that the integral equations are valid for arbitrary field-dependent critical state models. For the special cases with small transpirt current or applied field, analytical results are obtained rather than solving the complicate integral equations. It is demonstrated that the current density and magnetic field distributions, and penetration depth of field-dependent critical state model can be derived from the results of Bean model by a scaling factor. The characteristic of ‘current-like' and ‘field-like' current density and magnetic field distributions is discussed. The body force, strain, displacement at field ascent and descent branchs and magnetostriction loops are obtained based on Kim model and Bean model. The influence of geometry on critical current in thin high-Tc superconducting tape is also studied based on Kim model.