Evolutions of stress and microstructure in multilayer ferroelectric actuators under different temperature environments

The multilayer ferroelectric actuator (MFA) with electrodes is an important smart structure and it has found wide application in engineering. Under the applied electric–elastic loads, the local stress concentration will be intensified near the tips of electrodes, and it finally may lead to the failure of the MFA. On the other hand, the temperature-dependent behavior of ferroelectrics results in the novel evolutions of local stresses and microstructure in the MFA under different temperature environments. In this work, the different temperature-induced nonlinear behavior and electroelastic field concentration around the electrode tip in the MFA is studied based on a phase-field approach containing the time-dependent Ginzburg–Landau equation. Using three-dimensional nonlinear finite element method, the temperature-induced domain switching behavior of the MFA and the evolution of the local stress near the electrode tips are simulated under different loadings and temperatures. It is found that the maximum tensile stress ahead of the electrode tip increases as the temperature increases from room temperature to a critical temperature. However, over the critical temperature, the stress decreases significantly due to the ferroelectric–paraelectric phase transition, which implies that by optimizing the environmental temperature, the local stress concentrations can be controlled.     

Thermal Stress Analysis in Magneto-Electro-Thermo-Elasticity with a Penny-Shaped Crack Under Uniform Heat Flow

ABSTRACT

The magnetoelectroelastic material possesses the dual feature that the application of magnetic field induces electric polarization and electric field induces magnetization. Piezoelectric-piezomagnetic materials exhibit magneto-electric effect. When magneto-electro-elastic materials are subjected to thermal flow, they can fracture prematurely due to their brittle behavior. Hence, it should be important to know the fracture behavior of magneto-electro- elastic materials. The penny-shaped crack problem in a medium possessing coupled electro-magneto-thermo-elastic is considered in this paper. It is assumed that the crack is isothermal. The analysis is an exact treatment of penny-shaped crack in a magneto-electroelastic solid subjected to uniform heat flow far away from the crack region. The governing equations of temperature, elastic displacements and electric potential as well as magnetic potential for an anisotropic magneto-electro-elastic medium are partial differential equations of second order, which are solved by means of the Hankel transform technique. Expressions for elastic displacements, thermal stresses, electric displacements and magnetic inductions are determined from the dual integral equation method. Exact thermal stress intensity factor of the problem is obtained, and the near crack tip solutions are provided.     

Analyses of Thermal Conduction and Stress Induced by Electric Current in an Infinite Thin Plate with an Elliptical Hole

Uniform electric current at infinity is applied to a thin infinite conductor with an elliptical hole disturbing the electric current, which gives rise to Joule heat, temperature increase and heat flux. Joule heat produces uniform and uneven temperature fields which in turn initiate thermal stress. These electrical current, Joule heat, temperature, heat flux and thermal stress analyses are carried out and their closed form solutions are obtained. The heat conduction problem is solved as a temperature boundary value problem. Figures of distribution of Joule heat, temperature, heat flux and stress are shown. A dislocation and a rotation terms for thermal stress analysis appear, which makes problem complex. Solutions of Joule heat, temperature, heat flux and thermal stress are nonlinear for the direction of electric current. For an infinite plate with a circular hole, stress components do not occur on the whole plate. As a special case, a crack problem is analyzed and intensities at the crack tip of each problem are investigated. Relations between melting temperature and electric current density, and between fracture toughness value and electric current density are investigated for some crack lengths for steel.     

Thermoelectromechanical Response of a Piezoelectric Strip with Two Parallel Cracks of Different Lengths

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal loading. The crack faces are assumed to be insulated thermally and electrically. Fourier transform techniques are used to reduce the mixed boundary value problems to two systems of singular integral equations. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the geometric parameters on the thermal stress and electric displacement intensity factors.     

Transient Thermal Fracture Analysis of Transversely Isotropic Magneto-Electro-Elastic Materials

Modern materials such as magneto-electro-elastic materials are used in the development of smart structures. The magneto-electro-elastic materials possess the dual features that the application of electric field induces magnetization and magnetic field induces electric polarization. The theory of linear magneto-electro-elasticity is applied to solve transient thermal fracture in magneto-electro-elastic cylinder under sudden heating on its outer surface. The equilibrium equations are obtained from the constitutive equations. The governing partial differential equations are deduced by using equilibrium equations of elastic, electric and magnetic fields. The heat conduction equation is solved by separation of variable technique. Hankel transform is applied to solve elastic displacements, electric potential and magnetic potential. The problem is reduced into integral equation involving Bessel functions which is treated exactly using Abel's integral equation. Transient distributions of temperature, stress, displacement and magnetic inductions are derived for magneto-electro-elastic cylinder. Thermal stress, electric displacement and magnetic induction-intensity factors are obtained. The solutions are valid for both impermeable and permeable crack models. The studies are valuable for such material analysis and design.     

Thermo-Elastic Analysis of a Cracked Half-Plane Under a Thermal Shock Impact Using the Hyperbolic Heat Conduction Theory

The transient thermal stresses around a crack in a thermo-elastic half-plane are obtained under a thermal shock using the hyperbolic heat conduction theory. Fourier, Laplace transforms and singular integral equations are applied to solve the temperature and thermal stress fields consecutively. The integral equations are solved numerically and the asymptotic fields around the crack tip are obtained. Numerical results show that the hyperbolic heat conduction have significant influence on the dynamic temperature and stress field. It is suggested that to design materials and structures against fracture under thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

The Axisymmetric Problem of a Partially Insulated Mixed-Mode Crack Embedded in a Functionally Graded Pyro Magneto-Electro-Elastic Infinite Medium Subjected to Thermal Loading

This article describes our investigation of the influence of an axisymmetric partially insulated mixed-mode crack on the coupled response of a functionally graded magneto-electro-elastic material (FGMEEM) subjected to thermal loading. The crack is embedded at the center of an infinite medium, and the material is graded in the direction orthogonal to the crack plane and is modeled as a nonhomogeneous medium with anisotropic constitutive laws. The heat conduction equation is first solved using the Hankel transform to yield the temperature field in the medium. Using the same integral transform, the magneto-electro-elasticity equations are converted analytically into a system of four singular integral equations that are solved numerically to yield the crack-tip mode I and II stress intensity factors, the electric displacement intensity factor and the magnetic induction intensity factor. The main objective of this research is to study the influence of material nonhomogeneity on the fields’ intensity factors for the purpose of gaining better understanding on the behavior of graded pyro magneto-electro-elastic materials.     

Thermal Fracture Analysis Of Nonhomogeneous Plate with Interfaces Under Uniform Heat Flow

The mixed-mode thermomechanical fracture problem in a nonhomogeneous material plate with two interfaces is studied in this research. Uniform heat flow conditions are considered. The interaction energy integral method for the thermal fracture problem is developed to calculate the thermal stress intensity factors (TSIFs) in nonhomogeneous materials. This method is proved to be domain independent for nonhomogeneous materials even when the integral domain is cut by one interface or many interfaces. Combining the interaction energy integral method with the extended Finite Element Method (XFEM), the temperature fields, the displacement fields, the thermal stress fields, and the TSIFs are calculated. In this article, both the edge crack and the internal crack are considered. Some examples are presented to study the influence of the material properties on the TSIFs. It can be found that the mismatch of the elastic modulus and thermal expansion coefficient can affect the TSIFs dramatically; however, the thermal conductivity interface will not arouse a kinking behavior of the TSIFs. It can be concluded that the existence of an interface (especially for elastic modulus and thermal expansion coefficient) affects the TSIFs greatly.     

Transient thermoelectroelastic response of a piezoelectric material strip with two parallel cracks in arbitrary positions

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks in arbitrary positions of a piezoelectric material strip under thermal shock loading. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time-dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. The temperature, stress and electric displacement distributions in a transient state are also included.     

Thermomagnetoelastic Stability of Ferromagnetic Cylindrical Shell Carrying Constant Electric Current

The modeling and study of the instability behavior of a magnetically active ferromagnetic cylindrical shell exposed to thermal and magnetic fields with a constant electric current is considered in this paper. It is assumed that the internal surface area of the shell is covered by the thin conductive cylindrical strip. The thickness of this metallic strip is small as compared to the total thickness of the shell and therefore its contribution to the elastic properties of the overall cylindrical shell can be considered negligible. The thermal and magnetic fields of the undisturbed state of the shell are determined assuming that the edges of the shell are thermo-isolated. Undisturbed state coincides with the equilibrium which was generated under the action of thermal field (in equilibrium the forces of magnetic origin are equal to zero). It is also assumed that the thermal exchanges shell-to-strip and shell-to-external media follow Newton-Rickman's law. Using the theory of thermo-magneto-elasticity of undisturbed state in conjunction with the predetermined thermal and magnetic fields the stresses of the undisturbed state are determined under the assumption that the deflection along the generators of the shell equals to zero. The solutions of the homogeneous boundary value problems are carried out and the buckling analysis of the shell is investigated. In particular, a close-form solution for the critical value of electric current for which the shell becomes statically unstable is presented.     

A NUMERICAL STUDY ON THERMAL FRACTURE OF PRECRACKED CERAMIC COATINGSIN HIGH-HEAT-FLUX ENVIRONMENT

The thermomechanical fracture and interface delamination of thermal barrier coatings (TBCs) in a high-heat-flux environment is the result of large surface temperature and thermal gradient across the coating thickness and the resulting viscoplastic deformations induced in the ceramic material. The maximum coating surface temperature has been used as the key loading parameter in previous studies. The current study explores the effects of several other thermal loading parameters on thermomechanical response and fracture behavior of TBCs with or without preexisting surface cracks. Results show that for a constant maximum surface temperature, the thermal fracture of the coating is increased by (i) an increased temperature difference across the coating, (ii) longer heating duration, and (iii) more aggressive coating surface cooling after heating. These results provide insights into TBC thermal fracture mechanisms and can potentially improve the design of the morphology of preexisting cracks in the coating to reduce fatal interface fracture.     

水平直流接地极暂态温度场分析

为分析水平直流接地极温升特性,采用ANSYS软件建立了长9m的水平电极电热耦合动态模型,仿真计算了水平直流接地极暂态温升,获得了暂态温度场的分布规律和温升曲线,与试验结果对比分析表明,水平电极的散流、温升分布呈显著的端部效应,整体呈U字型对称分布;电极端部温升速率最高,幅值最大。仿真计算焦炭床截面对电极暂态温度场的影响表明,增大焦炭床截面可显著降低电极温升,温升最高点位于焦炭床端部周围的土壤中。     

The Crack Problem in Piezoelectric Strip Under Thermoelectric Loading

This paper investigates the thermoelectromechanical fracture behavior of a parallel crack in a piezoelectric strip under thermoelectric loading. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to a system of singular integral equations, respectively, which are solved numerically. Numerical calculations are carried out, and the energy density factor as well as the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the size and the location of the crack and the magnitude of the electric loading.     

EXPERIMENTAL INVESTIGATION OF INTERFACIAL FRACTURE PARAMETERS AND CRACK INITIATION UNDER MECHANICAL AND THERMOMECHANICAL LOADING

Mechanically and thermomechanically stressed interface cracks in adhesively bonded bimaterials (PMMA-aluminum) with a large elastic and thermal property mismatch are experimentally studied. The elasto-optic effects are mapped as (sigmax+sigmay) contours in the PMAA halves and interfacial fracture parameters are estimated. Crack initiation under mechanical and thermomechanical loading conditions are shown to be controlled by different micromechanical processes. The results suggest that the micromechanical unlocking of microcavities and microprotrusions along the interface is primarily responsible for failure initiation under thermomechanical loading conditions. This is unlike the mechanical loading situations wherein fracture toughness is derived primarily from the breakage of interlocking microentanglements. The measured values of the fracture parameter DeltaIm(Kaiepsilon)T due to a temperature rise is a constant and much higher than its real counterpart (DeltapsiT (a) approxequal 76-82 degrees). The Delta(Kaiepsilon)T|cr thus obtained are much lower than the mechanical counterparts.     

Effect of Initial Imperfections on Thermal Buckling of Functionally Graded Plates

ABSTRACT

Thermal buckling analysis of rectangular functionally graded plates with initial geometrical imperfections is presented in this article. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the first-order shear deformation plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through the thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading, namely: uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect functionally graded plate. The influence of transverse shear on thermal buckling load is discussed.     

Enhancement of photovoltaic effect in nanoscale polarization graded ferroelectrics

In this work, we propose the compositionally graded ferroelectrics (CGF) as solar energy harvesting device. Such a novel geometrically frustrated system exhibits an intrinsic built-in potential which can be used to separate the hole and electron currents. It is shown that the CGF based photovoltaic devices can achieve orders of higher efficiency than bulk/non-graded ferroelectric thin films. The dependence of the photovoltaic effect on various device parameters have also been investigated.     

Derivation of Material Constants in Non-Linear Electro-Magneto-Thermo-Elasticity

All the investigations on the mechanics and physics of electro-magneto-thermo-elastic materials are based on the set of constitutive equations in which the strain, electric displacement, and magnetic induction and entropy are expressed in terms of the stress, electric field, magnetic field and temperature. A concise formulation of relevant non-linear constitutive relations is presented in this paper. The electro-magneto-thermo-elastic materials show significant interaction among the elastic, electric, magnetic and thermal fields due to the coupled nature of constitutive equations. The thermodynamic Gibbs function of state describes stress, strain, internal energy, electric field, electric displacement, magnetic field, magnetic induction, temperature and entropy. The anisotropic non-linear problem of electro-magneto-thermo-elasticity has been derived on the basis of thermodynamic principle. The Gibbs function is expanded into Taylor series. Material constants have been analyzed from strain, electric displacement, magnetic induction and entropy which are in Gibbs function. In the form of mathematical equations, relationships of material constants have been shown. The derived coefficients (tensor components) of non-linear electro-magneto-thermo-elasticity are presented in tabular forms.     

Thermal radiation effects and lifetime assessment of first wall materials

Thermal radiation problems of the first wall of fusion reactors are becoming an important factor in the design, cost, and reliability of these reactors, and will strongly affect their prospects for economical operation and future commercialisation. In this study, the thermal radiation effects of first wall fusion reactors were studied experimentally under an externally applied magnetic field. The plasma temperature was measured using the Langmuir probe technique with OA4G electron tubes.

The results showed the electron temperature became higher during propagation parallel to the magnetic field than perpendicular to the same magnetic field. The rapid increase of the electron temperature in the plasma region depends on the increase of the saturation current. It is believed that there is a threshold power level for energy exchange between the electrons and the magnetic field, below which the energy conservation of cold plasma does not apply. By suitable arrangement of the armour plating, the wall cooling effect can be enhanced and wall thermal stress can be reduced to achieve an extended wall lifetime.

For lifetime assessment, Watson's model was used for calculation of thermal stress for several materials such as AISI 316 SS, HT-9, and Inconel 617. The creep stress and swelling stress is dependent on operation time under various irradiation conditions. The effects of wall thickness on lifetime for different materials is also discussed. Evidence showed HT-9 was the best resistant alloy for void swelling. Inconel 617 also performed well with regard to the swelling resistance.     

Transient Thermoelectromechanical Response of a Piezoelectric Strip with Two Parallel Cracks of Different Lengths

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal shock loading. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations, respectively, which are solved numerically. A numerical method is employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. Temperature change, the stress and electric displacement distributions in a transient state are also included.     

A NEW MODEL OF FUNCTIONALLY GRADED COATINGS WITH A CRACK UNDER THERMAL LOADING

A new model for fracture analysis oaf functionally graded materials (FGMs) with arbitrarily varying material properties under thermal loading is developed. The FGM is modeled as a multilayered medium and in each layer both shear modulus and thermal conductivity are assumed to be a linear function of the depth and are continuous on the subinterfaces. To make the crack problem tractable, thermal expansion and conductivity of the FGMs are supposed to have the same form. With this new model, the crack problem of a functionally graded coating bonded to a homogeneous substrate under steady-state thermal loading is investigated. Employment of the Fourier integral transform technique reduces the problem to a system of Cauchy singular integral equations that are solved numerically. Thermal stress intensity factors (TSIFs) are obtained for various forms of thermal conductivity or expansion. The results reveal that the present model is very efficient and in the frame of the present model both the form of thermal conductivity/expansion and that of its derivative can influence the TSIFs significantly.