Three-dimensional Analyses Of Penny-shaped Crack Problems In Thermo-Electro-Magneto-Elastic Solids And Their Applications

With the rapid development of modern science and technology,a variety of smart and advanced materials,such as,piezoelectric ceramics,multiferroic composite materials and shape memory alloys,etc,have emerged to satisfy various specific requirements in manufacturing industry.In engineering practice,these materials are often subjected to the impact of multi-physical fields,such as,temperature field,electric field and magnetic field,etc.Therefore,when the mechanical behaviors of these materials are investigated,the multi-field coupling effects have to be taken into consideration.Due to the coupling of multi-physical fields,the mathematical equations involved in the corresponding fracture theory become notoriously complicated and tedious,and to develop the analytical solutions for a three-dimensional crack problem becomes extremely difficult.In the past two decades,studies on the fracture behaviors in the framework of multi-physical coupling analysis have attracted considerable academic attentions,and a great deal of scientific research achievement has been got by scholars.However,there are still many unsolved problems in the fracture theory for both traditional and new materials with multi-field coupling effects.In general,the crack problems encountered in engineering practice are of irregular three-dimensional geometries.In view of the complexity of three-dimensional fracture theory in the framework of multi-physical coupling analysis,the three-dimensional crack problems are often degenerated into two-dimensional cases.It should be pointed out that the physical quantities corresponding to the three-dimensional crack analyses may be different from those in the two-dimensional cases.The three-dimensional crack analyses could be a nature benchmark to various simplified models and numerical simulations.In order to thoroughly reveal the influences of multi-field coupling loads on the three-dimensional fracture behaviors,this thesis has carried out the following studies:(1)The problems of an infinite isotropic medium containing a penny-shaped crack under point temperature,uniform temperature or uniform heat flux loads are analytically investigated.Based on the thermo-elastic general solution and making use of the generalized potential theory method,the exact three-dimensional thermo-elastic solutions to the problems are explicitly obtained.By virtue of the obtained thermo-elastic solutions,the penny-shaped Dugdale crack problem is solved,and the extent of the plastic zone at the crack tip is determined.Numerical calculations are carried out to show the distributions of the three-dimensional thermo-elastic fields.(2)The problem of an infinite magneto-electro-thermo-elastic medium weakened by a penny-shaped crack,which is symmetrically subjected to four pairs of generalized concentrated loads on the upper and lower surfaces,is analytically investigated.Theseloads could be mechanical pressures,electric displacements,magnetic inductions and temperature increments.The crack surfaces may be electrically and magnetically impermeable,electrically permeable and magnetically impermeable,electrically impermeable and magnetically permeable,and electrically and magnetically permeable.Based on the thermo-electro-magneto-elastic general solution,the thermo-magneto-electro-elastic coupling field variables in the three-dimensional full space for various boundary cases are explicitly obtained by means of the generalized potential theory method.For the case of uniform loads,the thermo-magneto-electro-elastic coupling field variables could be derived by integrating the fundamental solutions over the crack surface.Numerical calculations are performed to show the distributions of the 3D coupled fields.The influences of the magneto-electric properties of the crack surfaces on the numerical results are revealed.(3)Based on the thermo-electro-elastic fundamental solution,the electric polarization saturation at the front of a thermally loaded penny-shaped crack in an infinite thermo-piezo-elastic medium is investigated in both analytical and numerical manners.This crack is assumed to be electrically semi-permeable,and the electric field in the crack cavity is taken into account.By virtue of the hypothesis of the electric polarization saturation model,an approximate analytical solution to the present non-linear crack problem is derived.The validity of the analytical solution is checked via the numerical discrete method together with an iterative approach.A good agreement is observed.The influences of some material constants on the electric yielding zone are numerically revealed.An empirical formula is developed for the extent of electric yielding zone at the crack tip.(4)The thermal-induced electric and magnetic polarization saturations at the tip of a penny-shaped crack embedded in an infinite space of thermo-magneto-electro-elastic medium are analytically investigated.By virtue of the solution to the Abel type integral equation,the governing equations corresponding to the present problem are analytically solved and the generalized crack surface displacement and field intensity factors are obtained in closed-forms.Applying the hypothesis of the electric and magnetic polarization saturation model to the analytical results,the sizes of the electric and magnetic yielding zones are determined.Numerical calculations are carried out to reveal the influences of the thermal load and the electric and magnetic yielding strengths on the results.