Nonlinear Constitutive Behavior Of Ferroelectric Materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Growth Mechanism And Corrosion Behavior Of Ceramic Coatings On Aluminum Produced By Autocontrol Ac Pulse Peo

Ceramic coatings are produced on aluminum alloy by autocontrol AC pulse Plasma Electrolytic Oxidation (PEO) with stabilized average current. Transient signal gathering system is used to study the current, voltage, and the transient wave during the PEO process. SEM, OM, XRD and EDS are used to study the coatings evolution of morphologies, composition and structure. TEM is used to study the micro profile of the outer looser layer and inner compact layer. Polarization test is used to study the corrosion property of PEO coatings in NaCl solution. According to the test results, AC pulse PEO process can be divided into four stages with different aspects of discharge phenomena, voltage and current. The growth mechanism of AC PEO coating is characterized as anodic reaction and discharge sintering effect. PEO coating can increase the corrosion resistance of aluminum alloy by one order or two; however, too long process time is not necessarily needed to increase the corrosion resistance. In condition of this paper, PEO coating at 60 min is the most protective coating for aluminum alloy substrate. (C) 2008 Elsevier B.V. All fights reserved.

Deformation Behavior Of Fe-Based Bulk Metallic Glass During Nanoindentation

Fe-based bulk metallic glasses (BMGs) normally exhibit super high strength but significant brittleness at ambient temperature. Therefore, it is difficult to investigate the plastic deformation behavior and mechanism in these alloys through conventional tensile and compressive tests due to lack of distinct macroscopic plastic strain. In this work, the deformation behavior of Fe52Cr15Mo9Er3C15B6 BMG was investigated through instrumented nanoindentation and uniaxial compressive tests. The results show that serrated flow, the typical plastic deformation feature of BMGs, could not be found in as-cast and partially crystallized samples during nanoindentation. In addition, the deformation behavior and mechanical properties of the alloy are insensitive to the applied loading rate. The mechanism for the appearance of the peculiar deformation behavior in the Fe-based BMG is discussed in terms of the temporal and spatial characteristics of shear banding during nanoindentation.

Molecular Dynamics Study Of The Mechanical Behavior Of Nickel Nanowire: Strain Rate Effects

We present the analysis of uniaxial deformation of nickel nanowires using molecular dynamics simulations, and address the strain rate effects on mechanical responses and deformation behavior. The applied strain rate is ranging from 1 x 10(8) s(-1) to 1.4 x 10(11) s(-1). The results show that two critical strain rates, i.e., 5 x 10(9) s(-1) and 8 x 10(10) s(-1), are observed to play a pivotal role in switching between plastic deformation modes. At strain rate below 5 x 10(9) s(-1), Ni nanowire maintains its crystalline structure with neck occurring at the end of loading, and the plastic deformation is characterized by {111} slippages associated with Shockley partial dislocations and rearrangements of atoms close to necking region. At strain rate above 8x10(10) s(-1), Ni nanowire transforms from a fcc crystal into a completely amorphous state once beyond the yield point, and hereafter it deforms uniformly without obvious necking until the end of simulation. For strain rate between 5 x 10(9) s(-1) and 8 x 10(10) s(-1), only part of the nanowire exhibits amorphous state after yielding while the other part remains crystalline state. Both the {111} slippages in ordered region and homogenous deformation in amorphous region contribute to the plastic deformation. (C) 2007 Published by Elsevier B.V.

Microstructure Observation And Mechanical Behavior Modeling For Limnetic Nacre

In the present research, microstructure of a kind of limnetic shell (Hyriopsis cumingii) is observed and measured by using the scanning electron microscopy, and mechanical behavior experiments of the shell nacre are carried out by using bending and tensile tests. The dependence of mechanical properties of the shell nacre on its microstructure is analyzed by using a modified shear-lag model, and the overall stress-strain relation is obtained. The experimental results reveal that the mechanical properties of shell nacre strongly depend on the water contents of the limnetic shell. Dry nacre shows a brittle behavior, whereas wetting nacre displays a strong ductility. Compared to the tensile test, the bending test overestimates the strength and underestimates the Young's modulus. The modified shear-lag model can characterize the deformation features of nacre effectively.

Influence Of Different Amount Of Au On The Wetting Behavior Of Pdms Membrane

Polydimethylsiloxane (PDMS) has been widely used as a base material for bio-MEMS/NEMS devices. It is difficult for PDMS to transfer and spread aqueous solution as a kind of highly hydrophobic material. Therefore, surface modification is necessary for PDMS to make it hydrophilic. In this paper, a method of hydrophilization of PDMS surface is proposed. Gold is sputtered to the PDMS substrate by sputter coater in different average thicknesses. Relationship between the average thickness of gold on the PDMS substrate and the contact angle of the surface was studied. It was found that even gold of average thickness less than 1 nm can result in about 25 degrees change of contact angle. AFM is also used to get topographic information of PDMS surface coated with gold. Three cases are classified with different amount of Au: (1) Heterogeneous zone; (2) Transition zone; (3) Film zone. For heterogeneous zone, a simple model about heterogeneous phase wetting is put forward to interpret this phenomenon.

Influence of thermal residual stresses on the composite macroscopic behavior

The influence of the thermal residual stress on the deformation behavior of a composite has been analyzed with a new micromechanical method. The method is based on secant moduli approximation and a new homogenized effective stress to characterize the plastic state of the matrix. It is found that the generated thermal residual stresses after cooling and their influence on the subsequent deformation behavior depends significantly on the aspect ratio of the inclusions. With prolate inclusions, the presence of thermal residual stresses generate a higher compressive hardening curves of the composite, but it is reversed with oblate inclusions. For particle reinforced composite, thermal residual stresses induce a tensile hardening curve higher than the compressive one and this is in agreement with experimental observations. (C) 1998 Elsevier Science Ltd.

Avalanche behavior and statistical properties in a microcrack coalescence process

Fracture owing to the coalescence of numerous microcracks can be described by a simple statistical model, where a coalescence event stochastically occurs as the number density of nucleated microcracks increases. Both numerical simulation and statistical analysis reveal that a microcrack coalescence process may display avalanche behavior and that the final failure is catastrophic. The cumulative distribution of coalescence events in the vicinity of critical fracture follows a power law and the fracture profile has self-affine fractal characteristic. Some macromechanical quantities may be traced back and extracted from the mesoscopic process based on the statistical analysis of coalescence events.

Electromechanical influence of crack velocity at bifurcation for poled ferroelectric materials

The piezoelastodynamic field equations are solved to determine the crack velocity at bifurcation for poled ferroelectric materials where the applied electrical field and mechanical stress can be varied. The underlying physical mechanism, however, may not correspond to that assumed in the analytical model. Bifurcation has been related to the occurrence of a pair of maximum circumferential stress oriented symmetrically about the moving crack path. The velocity at which this behavior prevails has been referred to as the limiting crack speed. Unlike the classical approach, bifurcation will be identified with finite distances ahead of a moving crack. Nucleation of microcracks can thus be modelled in a single formulation. This can be accomplished by using the energy density function where fracture initiation is identified with dominance of dilatation in relation to distortion. Poled ferroelectric materials are selected for this study because the microstructure effects for this class of materials can be readily reflected by the elastic, piezoelectic and dielectric permittivity constants at the macroscopic scale. Existing test data could also shed light on the trend of the analytical predictions. Numerical results are thus computed for PZT-4 and compared with those for PZT-6B in an effort to show whether the branching behavior would be affected by the difference in the material microstructures. A range of crack bifurcation speed upsilon(b) is found for different r/a and E/sigma ratios. Here, r and a stand for the radial distance and half crack length, respectively, while E and a for the electric field and mechanical stress. For PZT-6B with upsilon(b) in the range 100-1700 m/s, the bifurcation angles varied from +/-6degrees to +/-39degrees. This corresponds to E/sigma of -0.072 to 0.024 V m/N. At the same distance r/a = 0.1, PZT-4 gives upsilon(b) values of 1100-2100 m/s; bifurcation angles of +/-15degrees to +/-49degrees; and E/sigma of -0.056 to 0.059 V m/N. In general, the bifurcation angles +/-theta(0) are found to decrease with decreasing crack velocity as the distance r/a is increased. Relatively speaking, the speed upsilon(b) and angles +/-theta(0) for PZT-4 are much greater than those for PZT-6B. This may be attributed to the high electromechanical coupling effect of PZT-4. Using upsilon(b)(0) as a base reference, an equality relation upsilon(b)(-) < upsilon(b)(0) < upsilon(b)(+) can be established. The superscripts -, 0 and + refer, respectively, to negative, zero and positive electric field. This is reminiscent of the enhancement and retardation of crack growth behavior due to change in poling direction. Bifurcation characteristics are found to be somewhat erratic when r/a approaches the range 10(-2)-10(-1) where the kinetic energy densities would fluctuate and then rise as the distance from the moving crack is increased. This is an artifact introduced by the far away condition of non-vanishing particle velocity. A finite kinetic energy density prevails at infinity unless it is made to vanish in the boundary value problem. Future works are recommended to further clarify the physical mechanism(s) associated with bifurcation by means of analysis and experiment. Damage at the microscopic level needs to be addressed since it has been known to affect the macrocrack speeds and bifurcation characteristics. (C) 2002 Published by Elsevier Science Ltd.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

Effect of Fe content on the thermal stability and dynamic mechanical behavior of NdAlNiCu bulk metallic glasses

The dependence of microstructure and thermal stability on Fe content of bulk Nd60Al10Ni10Cu20-xFex (0 less than or equal to x less than or equal to 20) metallic glasses is investigated by means of differential scanning calorimetry (DSC), X-ray diffraction (XRD) and high-resolution transmission electron micrograph (HRTEM). All samples exhibit typical amorphous feature under the detect limit of XRD, however, HRTEM results show that the microstructure of Nd60Al10Ni10Cu20-xFex alloys changes from a homogeneous amorphous phase to a composite structure consisting of clusters dispersed in amorphous matrix by increasing Fe content. Dynamic mechanical properties of these alloys with controllable microstructure are studied, expressed via storage modulus, the loss modulus and the mechanical damping. The results reveal that the storage modulus of the alloy without Fe added shows a distinct decrease due to the main a relaxation. This decrease weakens and begins at a higher temperature with increasing Fe content. The mechanism of the effect of Fe addition on the microstructure and thermal stability in this system is discussed in terms of thermodynamics viewpoints. (C) 2004 Elsevier B.V. All rights reserved.

Effect of quasicrystalline phase on the deformation behavior of Zr62Al9.5Ni9.5Cu14Nb5 bulk metallic glass

Quasicrystalline phase with different volume fraction were formed by isothermally annealing the as-castZr(62)Al(9.5)Ni(9.5)Cu(14)Nb(5) bulk metallic glass at 723 K for different times. The effects of quasicrystals on the deformation behavior of the materials were studied by nanoindentation and compression test. It revealed that the alloys with homogeneous amorphous structure exhibit pronounced flow serrations during the nanoindentation loading, while no obvious flow serration is observed for the sample with quasicrystals more than 10 vol.%. However, further compression tests confirm that the no-serrated flows are formed due to different reasons. For annealed samples containing quasicrystals less than 35 vol.%, continuous plastic deformation occurs due to propagation of multiple shear bands. While the disappearance of serrated flow cannot be explained by the generation of multiple shear bands for samples containing quasicrystals more than 35 vol.%, which will fracture with a totally different fracture mode, namely, dimple fracture mode under loading instead of shear fracture mode. (c) 2005 Published by Elsevier B.V.