Zhi-Dong Zhou

An integral elasto-plastic constitutive theory

Abstract This paper proposes an integral elasto-plastic constitutive equation, in which it is considered that stress is a functional of plastic strain in a plastic strain space. It is indicated that, to completely describe a strain path, the arc-length and curvature of the trajectory, the turning angles at the corner points and other characteristic points on the path must be considered. In general, the plastic strain space is a non-Euclidean geometric space, hence its measure tensor is a function of not only properties of the material but also the plastic strain history. This recommended integral elasto-plastic constitutive equation is the generalization of Ilyushin, Pipkin, Rivlin and Valanis theories and is suited to research the responses of material under the complex loading path. The predictions of the proposed theory have a good agreement with the experimental results.

An analysis of domain reorientation in PLZT ceramics by in situ Raman spectroscopy

An in situ Raman spectroscopy in a parallel y(z,z)y configuration was employed to investigate the domain reorientation of unpoled lanthanum-doped lead zirconate titanate (PLZT) ceramics under the dc electric field of 2000 V/mm. It was found that the relative intensity ratio IE(2TO)/IE(3TO+2LO)+B1 of Raman optical modes varied periodically by 180° with the polarized direction of the laser beam. The maximum change in the intensity ratio may be correlated with the extent of the polarization within the PLZT ceramics. Upon taking the effects of the long-range electric fields associated with the polar vibrations into consideration, a formula is developed to describe the variations in the intensity ratio IE(2TO)/IE(3TO+2LO)+B1, and the average orientation within the examined grain during the application of electric field is further evaluated to be ∼33.8°.

Domain structures of ferroelectric films under different electrical boundary conditions

A two-dimensional phase field simulation of ferroelectric films is used that incorporates Landau-Devonshire energy, gradient energy and depolarization electrical energy. A new intermediate electrical boundary condition is firstly presented to study the effects on domain structures of ferroelectric films. Two-dimensional simulations of domain structures are carried out under the open circuit (OC), short circuit (SC) and intermediate (IM) electrical boundary conditions. The simulation results show that there are multi-vortices domains and 180° multi-stripes domains under OC and SC electrical boundary condition, respectively. And there is a transition from multi-vortices domains to 180° multi-stripes domains under the IM electrical boundary condition due to competition between the elastic energy and depolarization electrical energy in the films. The present IM electrical boundary condition can completely characterize different degrees of compensation for surface charges by the electrodes and further describe...

Buckling of a piezoelectric thin film bonded to compliant substrates

National Natural Science Foundation of China [10972188, 10902055, 11172252]; Natural Science Foundation of Fujian Province of China [2011J01329]; Fundamental Research Funds for the Central Universities [2011121002]; Scientific and Technological Innovation Platform of Fujian Province [2006L2003]

The influence of the electrical boundary condition on domain structures and electrocaloric effect of PbTiO3 nanostructures

The electrocaloric effect (ECE) induced by the domain switching of PbTiO3 (PTO) nanoparticles under the different electrical boundary conditions is carried out using the phase field model. The toroidal moment of polarization with vortex domain structures decreases to zero taking surface charge compensation into the electrical boundary condition, i.e. intermediate electrical boundary. There exists a critical parameter value 0.25, which decides the single domain and vortex domain structures of ferroelectric nanomaterial at the room temperature. The loops of toroidal moment as a function of the applied curled electric filed are obtained under the different electrical boundary conditions. The various domain structures in ferroelectric nanostructure are discussed in detail. Moreover negative and positive adiabatic temperature changes accompanying with vortex domain structure switching are obtained with the curled electric field under the intermediate electrical boundary. These results indicate that ferroelectr...

Continuous Modeling of the Transient and Steady Cyclic Hardening /Softening Behavior of Metallic Materials under Amplitude Change Loading

This paper is concerned with the performance of the plastic strai n amplitude measure, originally motivated and then abandoned by Haupt et al. [1]. Reasons for suc ces and failure in modeling for the amplitude dependence are discussed. It is shown that if the memory parameter in the variable to indicate the center of the plastic strain region is determined suitably, the measure gives satisfactory performance in reflecting the amplitude behavi or. By incorporating a hardening function dependent on the measure into the intrinsic time scale used in Vala is’ endochronic plasticity, various transient and steady cyclic phenomena of hardening materials can be reproduced. Introduction It has been well known that with the variation of plastic strai n amplitude, the cyclic hardening/ softening degree of the hardening materials changes continuously and appe ars memory to the prior maximum hardening history partially or completely [2,3]. In the last two decades, some proposed amplitude parameters are used to simulate these behaviors. Chaboche [ 2] proposed the concept of maximum plastic strain region. Ohno [4] proposed the cyclic non-hardening region. Improvements for Ohno’s measure have been discussed in several works [5]. Tanaka [6] used a new variable to describe the center of the plastic strain region and took the distanc e between it and the current plastic strain point as an amplitude parameter. On the other hand, Haupt et al. [1] intended to accomplish a continuous describing of the hardening and softening, where an a mplitude measure was defined and hoped to proportional to a direct measure of the plastic strain amplit ude. As a result, the measure is related to the back stress, which will lose the objectivity. To describe the amplitude effects in a continuous manner is important so that a constitutive model can easily be used for analysis of engineering components subjec ted to random loading. This presentation is intended to qualitatively study the initial amplitude measure defined in [1]. The measure, defined by the accumulation of instantaneous plastic strain a mplitude with respect to the plastic deformation process, evolves continuously and naturally includes a fading memory to the prior amplitude history. The features of the amplitude measure are discussed in detail. By incorporating it into the hardening variables used in the endochronic theory [5], it is shown that various important amplitude effects on behavior of uniaxial cyclic def ormation can be predicted in a satisfactory manner if the memory parameter in the measure is determined s uitably. In the following, stress and strain are expressed in the form of vectors in Ilyushin’s five-dimensional deviatoric vector space. Let | | x denote the absolute value of a quantity x . Key Engineering Materials Online: 2003-07-15 ISSN: 1662-9795, Vols. 243-244, pp 427-432 doi:10.4028/www.scientific.net/KEM.243-244.427

The effect of the surface electrode distributions on domain structures of ferroelectric thin films

Various domain structures in ferroelectric thin films with four different surface interdigital electrodes are simulated based on the time-dependent Ginzburg-Landau method. The four different electrode distributions are that (a) both surfaces are symmetrically arranged interdigital electrodes, (b) top surface is covered with interdigital electrode while bottom surface is covered with full electrode, (c) both surfaces are alternately arranged interdigital electrodes and (d) top surface is covered with interdigital electrodes while bottom is not covered with electrode. These electrode distributions could be converted to corresponding electrical boundary conditions of the phase field equations. Compared with ideal short circuit and open circuit electrical boundary conditions, there are some special domain structures (vortices, flux-closure structures and a/c domains) due to the change of depolarization electric energy and Landau energy with different surface electrodes. The domain structures in ferroelectric ...

Piezoelectric Effect on the Buckling of Piezoelectric Thin Film with Viscoelastic Substrate

AbstractThis work aims to study the buckling kinetic process of a piezoelectric thin film (nanoribbon) bonded to a viscoelastic compliant layer with rigid support. The piezoelectric thin film is assumed to be poled in the thickness direction and is governed by the nonlinear coupled electromechanical equations. Subsequently, on the basis of the classical elastic-viscoelastic correspondence principle, the kinetic process of the thin film buckling under the intermediate stress state is analyzed in a systematic manner. In particular the piezoelectric effect is examined with respect to the critical wavelength, the wavelength of the fastest growing mode, the critical stress, and the fastest growth rate in detail. The results evince that the piezoelectricity has an evident stiffening effect on the kinetic buckling process of the thin film with viscoelastic substrate.

BUCKLING ANALYSIS OF STRETCHABLE FERROELECTRIC THIN FILM ON ELASTOMERIC SUBSTRATES

The thin stiff films on pre-stretched compliant substrates can form wrinkles, which can be controlled in micro and nanoscale systems to generate smart structures. Recently, buckled piezoelectric/ferroelectric nanoribbons have been reported to show an enhancement in the piezoelectric effect and stretchability, which can be applied in energy harvesting devices, sensors and memory devices instead of polymeric polyvinylidine fluoride (PVDF). This paper studies the buckling and post-buckling process of ferroelectric thin films bonded to the pre-stretched soft layer, which in turn lies on a rigid support. Nonlinear electromechanical equations for the buckling of thin piezoelectric plates are deduced and employed to model the ferroelectric film poled in the thickness direction. Two buckling modes are analyzed and discussed: partially de-adhered buckling and fully adhered buckling. Transition from one buckling mode to the other is predicted and the effect of piezoelectricity on the critical buckling condition of piezoelectric film is examined.

Stress fields in the infinite electrostrictive plate with an elliptic inhomogeneity

The stress fields in the infinite electrostrictive plate with an elliptic inhomogeneity are discussed in this paper. Firstly, the general solutions of functions for electric and stress fields are derived with the help of analytical complex method. Secondly, explicit results by the complex series expanding, are given for the cases of electrostrictive material with an elliptic inhomogeneity. Finally, numerical calculations are made to discuss the effects of applied electric loading on the certain problem. It is found that, although the electric fields in the inhomogeneity are uniform, the stresses in the inhomogeneity are not uniform in general case, which is different from the solution of Eshelby theory for elastic materials.