Analysis of deformation mechanisms in superplastic yttria-stabilized tetragonal zirconia

There have been extensive experimental observations of changes in the apparent rate controlling creep parameters in studies on superplastic materials. The three most common explanations associated with these changes in the stress exponent, n, the activation energy Q and the inverse grain size exponent, p involve the effect of concurrent grain growth, the operation of a threshold stress or transitions in creep mechanisms. Each of these factors may influence experimental creep data in a similar manner. Therefore, a careful analysis of the consequences of all three factors must involve the development of a consistent set of experimental observations in order to adequately distinguish the effects of each. This paper discusses the role of concurrent grain growth, a threshold stress and transitions in creep mechanisms in superplastic materials. Specific attention is given to the analysis of data on superplastic yttria-stabilized zirconia ceramics for which an increase in n has been observed at low applied stresses. It is demonstrated that neither concurrent grain growth nor a threshold stress can account for all the relevant experimental observations in this material. It is concluded that the changes in rate controlling creep parameters are associated with the operation of two distinct sequential mechanisms as part of a grain boundary sliding process.     

Electrical double layer and rheological properties of yttria-stabilized zirconia suspensions in solutions of high molecular weight polyacrylic acid polymers

This work deals with the effect of the adsorption of two high molecular weight polyacrylic acid polymers (Carbopol) on the interfacial properties, and the rheology of aqueous zirconia suspensions. Since the Carbopol-covered particles can be thought of as soft colloids, Ohshimas theory was used to gain information on the surface potential and the charge density of the polymer layer (Ohshima H (1995) Electrophoretic mobility of soft particles. Colloids Surf A Physicochem Eng Aspects 103:249–255). The effect of the pH of the solution on the double layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The electrokinetic properties of the suspensions are studied for different pH and Carbopol concentrations in solution in order to investigate the possible stabilization of the suspensions by electrostatic repulsion between the particles. The rheological behavior of the suspensions was investigated in steady-state and dynamic conditions, and the corresponding yield stress and storage modulus were obtained in absence and presence of polymer in solution. The competition between bridging flocculation provoked by polymer adsorption and electrosteric stabilization determines the rheological properties of the suspensions. In the pH range investigated, bridging flocculation predominates at the neutral pH because of the graft of the uncoiled polymer to more than one particle, while at the extreme pH values (pH 3, pH 9) steric or electrosteric stabilization seems to be the predominant mechanism that explains the rheological results. These facts were confirmed by estimating the zirconia particle (or aggregate) diameter in the liquid medium by means of light scattering measurements.     

Study of transformation plasticity in tetragonal zirconia polycrystals by moiré interferometry

Transformation plasticity in ceria-stabilized tetragonal zirconia polycrystals due to the stress-induced tetragonal-to-monoclinic martensitic transformation under tension and bending is studied by moiré interferometry. The whole fringe patterns includingu fields andv fields are acquired. According to these patterns, the distributions of transformation plasticity in transformation zones are obtained, and the phenomenon of plastic flow localization for transformation is revealed. The above work provides a significant experimental foundation for establishing transformation constitutive relations The project supported by the National Natural Science Foundation of China     

Microstructural size effects on mechanical properties of high purity nickel

The aim of this article is to provide experimental results in order to understand the microstructural size effects which occur with a decrease in the thickness of polycrystalline nickel samples from 3.2 mm to 12.5 μm. The influence of the thickness, grain size and ratio thickness to grain size on the mechanical properties and strain hardening were investigated by mechanical tests and TEM observations. The results show the presence of three different domains of mechanical behaviour: polycrystalline, multicrystalline and quasi-single crystalline depending on the thickness and on the number of grains across the thickness. The transition between the three domains is due to the occurrence of surface effects involving a decrease in the long-range internal backstress revealed by the TEM observations.     

Thermoelasticity constants of polycrystals

Exact formulas are derived for the thermoelasticity constants of macroscopically homogeneous polycrystals. A method described earlier [1] is used as the basis. It is assumed that the local parameters form an ergodic homogeneous random field. No restriction is imposed on the degree of anisotropy of the crystals.     

Leveling and thixotropic characteristics of concentrated zirconia inks for screen-printing

Screen-printing is a cost-effective method for the mass manufacture of zirconia-based solid oxide fuel cells (SOFCs) and oxygen separation membranes. The present work outlines an investigation into the leveling, thixotropic, and screen-printing characteristics of concentrated zirconia inks by a variety of rheological and imaging methods. A combination of viscosity, shear rate jump experiments, creep and recovery analysis, and yield stress measurements were used to assess ink thixotropy. Oscillatory rheometry and scanning electron microscopy/optical microscopy revealed a consistent effect of ethyl cellulose (binder) content upon the thixotropic and leveling characteristics of zirconia inks. While the yield stress (τ ₀), extent of recovery R(%), and rate of recovery (K) increase with increasing binder content, so did the surface roughness and thickness of the screen-printed films. Increasing the binder content not only increases the network strength of the thick films but also leads to increased leveling time. As a result, rheological modifiers are proposed to be necessary to improve the leveling characteristics of zirconia inks without losing the green strength of the thick films.     

Dynamic plasticity and fracture in high density polycrystals: constitutive modeling and numerical simulation

Presented is a constitutive framework for modeling the dynamic response of polycrystalline microstructures, posed in a thermodynamically consistent manner and accounting for finite deformation, strain rate dependence of flow stress, thermal softening, thermal expansion, heat conduction, and thermoelastic coupling. Assumptions of linear and square-root dependencies, respectively, of the stored energy and flow stresses upon the total dislocation density enable calculation of the time-dependent fraction of plastic work converted to heat energy. Fracture at grain boundary interfaces is represented explicitly by cohesive zone models. Dynamic finite element simulations demonstrate the influences of interfacial separation, random crystallographic orientation, and grain morphology on the high-rate tensile response of a realistic two-phase material system consisting of comparatively brittle pure tungsten (W) grains embedded in a more ductile matrix of tungsten-nickel iron (W-Ni-Fe) alloy. Aspects associated with constitutive modeling of damage and failure in the homogenized material system are discussed in light of the computational results.     

Elastic moduli of cubic polycrystals

The averaged elastic constants of polycrystals can be found by averaging the stresses (Voigt method [1]) or the strains (Reuss method [2]). Comparison of the elastic moduli, averaged according to Voigt and Reuss, with the experimental values shows that in the first case averaging gives values that are too high, and in the second values that are too low [3]. The reason for this is that direct averaging of the moduli with respect to arbitrary orientations of the crystallites does not take account of correlation effects. There are two ways of allowing for such correlations between polycrystal grains.     

The plastic deformation of non-homogeneous polycrystals

To describe the work hardening process of polycrystals processed using various thermomechanical cycles with isochronal annealing from 500 to 900 °C, a dislocation based strain hardening model constructed in the basis of the so-called Kocks–Mecking model is proposed. The time and temperature dependence of flow stress is accounted via grain boundary migration, and the migration is related to annihilation of extrinsic grain boundary dislocations (EGBD’s) by climb via lattice diffusion of vacancies at the triple points. Recovery of yield stress is associated with changes in the total dislocation density term ρ^T. A sequence of deformation and annealing steps generally result in reduction of flow stress via the annihilation of the total dislocation density ρ^T defined as the sum of geometrically necessary dislocations ρ^G and statistically stored dislocations ρ^S. The predicted variation of yield stress with annealing temperature and cold working stages is in agreement with experimental observations. An attempt is made to determine the mathematical expressions which best describe the deformation behaviour of polycrystals in uniaxial deformation.     

Analysis of elastic-plastic deformation in TiAl polycrystals

A computational model is described for analyzing stress variations within polycrystals of γ-TiAl, including the effect of anisotropic yielding and small-scale plastic flow. Interlamellar (soft mode) slip behavior is controlled by a separate collection of slip systems whose properties are derived from measurements on polysynthetically twinned (PST) specimens. When used to represent several hundred randomly oriented material grains, the model provides distributions and statistical data about the local stress, strain, and plastic deformation resulting from a prescribed macroscopic loading.     

A finite element model of ferroelastic polycrystals

A finite element model of switching in polycrystalline ferroelastic ceramics is developed. It is assumed that a crystallite switches if the reduction in mechanically driven potential energy of the system exceeds a critical value per unit volume of switching material. Stress induced (i.e. ferroelastic) switching is a change of permanent strain in characteristic crystallographic directions. Martensitic twinning is one example, but the strain response of ferroelectric materials has the same characteristics. The model is suitable for representing ferroelastic systems such as shape memory alloys and as a preliminary model for ferroelectric/ferroelastic materials such as perovskite piezoelectrics. In the simulations, each crystallite is represented by a finite element and the crystallographic principal direction for each crystallite is assigned randomly. Different critical values for the energy barrier to switching are selected to simulate stress vs strain hysteresis loops of a ceramic lead lanthanum zirconate titanate (PLZT) at room temperature. The measured stress versus strain curves of polycrystalline ceramics designated PZT-A and PZT-B are also reproduced by the model.     

A two-dimensional finite element method for simulating the constitutive response and microstructure of polycrystals during high temperature plastic deformation

We describe a finite element method designed to model the mechanisms that cause superplastic deformation. Our computations account for grain boundary sliding, grain boundary diffusion, grain boundary migration, and surface diffusion, as well as thermally activated dislocation creep within the grains themselves. Front tracking and adaptive mesh generation are used to follow changes in the grain structure. The method is used to solve representative boundary value problems to illustrate its capabilities.     

Transition theories of elastic-plastic deformation of metallic polycrystals

Summary A general approach to the problem of determination of elastoplastic behavior of metallic polycrystals at finite deformation is presented. The relation between moving dislocation density and global slip rate for grains is developed. Transition to grain response is obtained by introducing the hardening matrix. Field equations for heterogeneous elastoplastic metals are transformed into an integral equation, using Green functions technique. This allows to find the spin of the lattice related to texture formation.Scale transition is achieved by a self-consistent approximation of the integral equation. New results concerning BCC metals (sheet steel) are presented. They apply to tensile test, Lankford coefficient, initial and subsequent yield surfaces, and evolution of the internal state of the polycrystal: second-order residual stress, stored energy and texture evolution.     

聚能装药铜射流超塑性问题的研究

通过对回收Cu射流杵体的金相分析得出药型罩在冲击波和挤压剪切变形双重作用下造成晶粒细化和温度升高,并为动态超塑性变形创造了条件,因此在形成射流之前材料已满足动态超塑性变形的条件,同时说明聚能装药射流的动态超塑性变形符合细小晶粒的转动变形机理。     

Multi-grain analysis versus self-consistent estimates of ferroelectric polycrystals

Ferroelectrics are polycrystalline materials consisting of intragranular regions with different polarization directions, called domains. The domains can be switched into different states by the application of an electric field or mechanical stress. We study the influence of grain-to-grain interactions on the overall and local switching behavior. The behavior inside each grain is represented by the micromechanics model of Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47 (8), 1663-1697]. The predictions of a self-consistent model of the polycrystal response are compared with those of a multi-grain model in which grains are represented individually. In one flavor of the multi-grain model, each grain is represented by a single finite element, while in the other the fields inside each grain are captured in more detail through a fine discretization. Different electrical and mechanical loading situations are investigated. It is found that the overall response is only mildly dependent on the accuracy with which grain-to-grain interactions are captured, while the distribution of grain-average stresses is quite sensitive to the resolution of the intragranular fields.     

Perturbation approach to elastic constitutive relations of polycrystals

Herein we obtain a formula for the effective elastic stiffness tensor C^eff of an orthorhombic aggregate of cubic crystallites by the perturbation method. The effective elastic stiffness tensor of the polycrystal gives the relationship between volume average stress and volume average strain. Under Voigt's model, Reuss’ model and Man's theory, the elastic constitutive relation accounts for the effect of the orientation distribution function (ODF) up to terms linear in the texture coefficients. However, the formula derived in this paper delineates the effect of crystallographic texture on elastic response and shows quadratic texture dependence. The formula is very simple. We also consider the influence of grain shape to elastic constitutive relations of polycrystals. Some examples are given to compare computational results of the formula with those given by Voigt's model, Reuss's model, the finite element method, and the self-consistent method. In Section 3, we also present an expression of the perturbation displacement field, in which Green's function for an orthorhombic aggregate of cubic crystallites is included.     

Mesomechanics of fatigue fracture for polycrystals with macroconcentrators

Fatigue fracture of aluminum alloys is analyzed from analysis of time-spatial mesoscale substructures. The behavior involves many stages at the mesoscale and translational–rotational movement of the bulk structure element in addition to fragmentation. Mesofragments on a trajectory of the fatigue crack were also studied.