Multiaxial behavior of ferroelectric single and polycrystals with pressure dependent boundary effects

The external electric and mechanical fields applied at angles to the initial poled direction of the ferroelectric ceramics produce a significantly different nonlinear behavior to that of external fields applied parallel to the poling direction. This angle dependent response of ferroelectric single and polycrystals are predicted by the model proposed based on irreversible thermodynamics and physics of domain switching. The dissipation associated with boundary constraints in thin ferroelectric single crystals are incorporated in the model. As well, the pressure dependent constraints imposed by the surrounding grains on the grain of interest at its boundary during domain switching is correlated with the resistance experienced by a ferroelectric single crystal on its boundary during domain switching. Taking all the domain switching possibilities, the volume fractions of each of the variants in a grain are tracked and homogenized for macroscopic behavior. Numerical simulations were carried out for the multiaxial behavior of ferroelectric single and polycrystals under electrical, mechanical and electromechanical loading conditions.     

Multiscale finite element modeling of superelasticity in Nitinol polycrystals

An efficient method is proposed for modeling superelastic polycrystalline NiTi by solving a two-scale problem. The RVE size of the fine scale is determined using a statistics-based approach. Both problems are discretized in space using the finite element method and their communication is effected using MPI. Representative simulations illustrate the modeling capabilities of the proposed approach.     

Toughening due to domain switching in single crystal ferroelectric materials

In this paper Mode I steady state crack growth in single crystal ferroelectric materials is investigated. Specifically, the fracture toughness enhancement due to domain switching near a steadily growing crack tip is analyzed. For this purpose, an incremental phenomenological constitutive law for single crystal ferroelectric materials is implemented within a finite element model to calculate the stress and remanent strain fields around the crack tip. Also, the ratio of the far field applied energy release rate to the crack tip energy release rate, i.e. the toughening, is calculated. The numerical computations are carried out for single crystal ferroelectric materials of tetragonal or rhombohedral structure with different switching hardening and irreversible remanent strain levels. Toughening levels for crack growth along different crystallographic directions and planes are obtained and compared. Results from numerical computations for the toughening anisotropy for both tetragonal and rhombohedral crystals are presented and discussed.     

Micromechanical formulation and 3D finite element modeling of microinstabilities in composites

A 3D micromechanical formulation and a FE-model of fiber micro-buckling in materials with isotropic and transversal isotropic fibers in compression is presented. Three variants of geometrical modeling of the characteristic cell are proposed and compared. An appropriate one is then selected. An eigenvalue analysis of a characteristic cell is performed. The results show that the fiber anisotropy reduces significantly the critical loads and must be taken into account.     

Time-dependent cohesive zone modelling for discrete fracture simulation

The cohesive crack tip model became very popular in fracture and failure mechanics, starting with the original publications of (Dugdale, 1960) [1] and (Barenblatt, 1962) [2] and first practical applications in the early 1980s. A compact representation of the fracture mechanical basis, kinematic and constitutive issues as well as some special characteristics of the related finite element formulation are given in the first part of this contribution. The main part is dedicated to the presentation and discussion of recent developments of cohesive finite element methods for time-dependent fracture. On the basis of a rheological model assumption, a novel viscoelastic extension for cohesive traction separation laws is presented and the resultant characteristic behaviour is depicted and compared for different loading conditions. Adopting an industrial application of a peel foil specimen, the time-dependent characteristics as well as some aspects of parameter identification and application of the material model are shown.     

Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing (1) the polycrystalline structure, (2) the location of the cracks, and (3) the ferroelectric domain microstructure. Different polycrystalline microstructures are obtained from computer simulations of grain growth. Then, a phase-field model for fracture in ferroelectric single-crystals is extended to polycrystals by incorporating the differential fracture toughness of the bulk and the grain boundaries, and the different crystal orientations of the grains. Our simulation results show intergranular crack propagation in fine-grain microstructures, while transgranular crack propagation is observed in coarse grains. Crack deflection is shown as the main toughening mechanism in the fine-grain structure. Due to the ferroelectric domain switching mechanism, noticeable fracture toughness enhancement is also obtained for transgranular crack propagation. These observations agree with experiment.     

On the fracture toughness anisotropy of mechanically poled ferroelectric ceramics

In this paper an incremental constitutive theory for the deformation due to switching in ferroelectrics is applied to predict the fracture toughness anisotropy in these materials after mechanical poling. Mechanical poling of an initially unpoled specimen differs from electrical poling in that only mechanical stresses are applied to the material. Therefore, no electrical polarization can develop. After mechanical poling, for example by a uniaxial applied stress, the fracture toughness of a ferroelectric ceramic for cracks running parallel or orthogonal to the poling direction will differ. Finite element computations of the steady crack growth process have been carried out to quantify these differences. Results are generated for a range of constitutive properties for three crack growth directions with respect to the initial mechanical poling direction. The results are discussed in relation to available experimental data and to the toughness anisotropy due to electrical poling.     

Mechanics of extended continua: modeling and simulation of elastic microstretch materials

The investigation of microstretch and micromorphic continua (which are prominent examples of so-called extended continua) dates back to Eringens pioneering works in the mid 1960, cf. (Eringen in Mechanics of micromorphic materials. Springer, Berlin Heidelberg New York, pp 131–138, 1966; Eringen in Int J Eng Sci 8:819–828; Eringen in Microcontinuum field theories. Springer, Berlin Heidelberg New York, 1999). Here, we re-derive the governing equations of microstretch continua in a variational setting, providing a natural framework within which numerical implementations of the model equations by means of the finite element method can be obtained straightforwardly. In the application of Dirichlets principle, the postulation of an appropriate form of the Helmholtz free energy turns out to be crucial to the derivation of the balance laws and constitutive relations for microstretch continua. At present, the material parameters involved in the free energy have been assigned fixed values throughout all numerical simulations—this simplification is addressed in detail as the influence of those parameters must not be underestimated. Since only few numerical results demonstrating elastic microstretch material behavior in engineering applications are available, the focus is here on the presentation of numerical results for simple twodimensional test specimens subjected to a plane strain condition and uniaxial tension. Confidence in the simulations for microstretch materials is gained by showing that they exhibit a “downward-compatibility” to Cosserat continuum formulation: by switching off all stretch-related effects, the governing set of equations reduces to the one used for polar materials. Further, certain material parameters can be chosen to act as penalty parameters, forcing stretch-related contributions to an almost negligible range in a full microstretch model so that numerical results obtained for a polar model can be obtained as a limiting case from the full microstretch model.     

Modeling and experimental verification of thermo-mechanical coupled behavior of face-centered-cubic polycrystals

An improved integration model based on crystal plasticity is presented to model the thermo-mechanical processes of face-centered-cubic (FCC) polycrystals. In this model, the thermal part of deformation gradient is introduced into the multiplicative decomposition of the total deformation gradient and the plastic deformation gradient is chosen as the basic integration variable. The effects of temperature, temperature changing rate and dissipation of plastic deformation are considered in the finite deformation computation. The obtained plastic deformation gradient includes the plastic deformation as well as the thermal effects. In applications, the mechanical behaviors of 1100 Al in warm forming and 22MnB5 boron steel in hot tensile deformation were computed using this model. In experiments, the hot tensile tests of 22MnB5 boron steel were performed in the isothermal and non-isothermal conditions. The predicted results can reflect the thermal effects in forming process and agree well with the experimental data.     

Micromechanical modeling and experimental characterization on viscoelastic behavior of 1–3 active composites

A study on the temperature-dependent viscoelastic behavior of (1–3 active composites) 1–3 piezocomposites and bulk piezoceramic subjected to electromechanical loading is carried out. The temperature-dependent effective properties are obtained experimentally using resonance based measurement technique. Experiments are also preformed for various fiber volume fractions of 1–3 piezocomposites subjected to constant compressive prestress and cyclic electric field at elevated temperature to understand the time-dependent behavior. Based on the measurements it is observed that the viscoelastic behavior has a significant influence on the electromechanical responses of 1–3 piezocomposites. Hence a viscoelastic based numerical model (unit cell approach) is proposed to predict the time-dependent effective properties of 1–3 piezocomposites. The evaluated effective properties are incorporated in a finite element based 3-D micromechanical model to predict the time-dependent thermo-electro-mechanical behavior of 1–3 piezocomposites and compared with the experimental observations.     

Enhancement of ferroelectric and piezoelectric characteristics in europium substituted SrBi2Ta2O9 ferroelectric ceramics

Europium substituted samples of compositions Sr_1 − xEu_xBi₂Ta₂O₉ were synthesized by solid-state reaction method. The prepared samples were characterized for their structural and electrical properties. X-ray analysis confirms the formation of the single-phase layered perovskite structure. The microstructural studies reveal that the average grain size increases with increase in Eu content. An increase in remanent polarization and d₃₃ values with increasing concentration of europium has been observed. The maximum 2P_r ~ 14 μC/cm² is observed in the sample with x = 0.20. The observed results have been discussed in terms of contribution from the cation vacancies introduced into the lattice structure due to donor doping.     

Micromechanical modeling of intrinsic and specimen size effects in microforming

Size effect is a crucial phenomenon in the microforming processes of metallic alloys involving only limited amount of grains. At this scale intrinsic size effect arises due to the size of the grains and the specimen/statistical size effect occurs due to the number of grains where the properties of individual grains become decisive on the mechanical behavior of the material. This paper deals with the micromechanical modeling of the size dependent plastic response of polycrystalline metallic materials at micron scale through a strain gradient crystal plasticity framework. The model is implemented into a Finite Element software as a coupled implicit user element subroutine where the plastic slip and displacement fields are taken as global variables. Uniaxial tensile tests are conducted for microstructures having different number of grains with random orientations in plane strain setting. The influence of the grain size and number on both local and macroscopic behavior of the material is investigated. The attention is focussed on the effect of the grain boundary conditions, deformation rate and the grain size on the mechanical behavior of micron sized specimens. The model is intrinsically capable of capturing both experimentally observed phenomena thanks to the incorporated internal length scale and the crystallographic orientation definition of each grain.     

Microstructural modeling and simulation for GCr15 steel during elevated temperature deformation

The microstructural evolution of GCr15 steel, one of the most commonly used bearing steels, was investigated and simulated by physical experiments and finite element method (FEM). Physical experiments were conducted on the Gleeble-3500 thermo-simulation system. Effects of initial grain size and plastic strain on the microstructural of the materials were investigated by setting different heating temperature, holding time and deformation degree, respectively. Based on the results of stress–strain curves and metallographic analysis, the constitutive equations for flow stress, austenite grain growth and dynamic recrystallization of GCr15 steel were formulated by linear regression method and genetic algorithm. In addition, the coupled thermo-mechanical finite element method integrated with the developed constitutive models was used to simulate the microstructural evolution of GCr15 steel during hot compression. Good agreement between the calculated and experimental results was obtained, which confirmed that the developed constitutive models can be successfully used to predict microstructural evolution during hot deformation process for GCr15 steel.     

Mechanical property characterization and simulation of fused deposition modeling Polycarbonate parts

Building end-use functional parts with additive manufacturing (AM) technologies is a challenging task. Several factors influence their surface finish, dimensional accuracy, mechanical properties and cost. Their orientation inside the building chamber is one of the most significant factors in AM processes. When using Fused Deposition Modeling (FDM) to build such parts, additional factors must be considered.This paper aims to accomplish two purposes: finding a good model to simulate FDM parts and correlating a finite element analysis (FEA) simulation with physical testing.The first objective was achieved by experimental tensile test of specimens to determine the nine mechanical constants that defines the stiffness matrix of an orthotropic material. Three Young’s modulus, three Poisson’s ratio and three shear modulus were experimentally obtained as well as yield tensile and ultimate strength of each specimen.A simple part was designed and manufactured in different orientations to be physically tested and simulated to achieve the second objective. Polycarbonate (PC) was used as part material. Combined loading including bending and torsion was used. Differences on mechanical response were observed during the physical test of the parts depending on the building direction. Conclusions comment results and the convenience of using a different constitutive model depending on the design and use specifications.     

Crack tip displacements of microstructurally small surface cracks in single phase ductile polycrystals

A planar double slip crystal plasticity model is applied to the evaluation of crack tip opening (CTOD) and sliding (CTSD) displacements for microstructurally small stationary cracks under monotonic loading for a material with nominal stress-strain behavior that is representative of a relatively high strength helicopter rotor hub material. Two-dimensional plane strain finite element calculations are presented for CTSD and CTOD of microstructurally small transgranular surface cracks in a polycrystal subjected to monotonic loading. The effects of crack length relative to grain size, orientation distribution of nearest neighbor grains, stress state and stress level are considered for nominal stress levels below the macroscopic yield strength. The CTOD and CTSD are computed for stationary crystallographic surface cracks with various realizations of crystallographic orientations of surrounding grains. It is found that (i) the opening displacement is dominant for remote tension even for crystallographic cracks oriented along the maximum shear plane in the first surface grain, (ii) there is a strong dependence of the CTOD on the proximity to grain boundaries, but lesser dependence of the CTSD, and (iii) that the elastic solutions for CTOD and CTSD are valid below about 30% of the 0.2% offset-defined yield strength.     

Ductile fracture simulation of hydropiercing process based on various criteria in 3D modeling

Hydropiercing has been used widely in the past decade in the automotive industry. So far, the ductile fracture of hydropiercing process considering the effect of hydroforming has not been studied in detail due to the complicated deformation process. In order to simulate hydropiercing process accurately, a 3D model considering the effect of hydroforming process has been developed in this study. Six ductile criteria were implemented to predict crack initiation and propagation by means of the user subroutine VUMAT of ABAQUS. The comparative study among the results obtained by the simulations using the different ductile criteria and the experiments was explored. The model using the Rice and Tracey Criterion shows good agreement with the experiment at loading pressure of 60–60 MPa, however the others could not. Moreover, the simulation errors using the Rice and Tracey Criterion at different loading pressure and hydropiercing type are small enough too compared with experiments so that this criterion could be used to simulate the hydropiercing process. Finally, the deformation mechanism of hydropiercing process has been discussed on the bases of simulations with the Rice and Tracey Criterion and experiments.     

高速主轴动力学建模及速度效应分析

考虑高速旋转部件的离心力和陀螺力矩效应,利用Timoshenko梁单元和转盘单元建立主轴转子、转盘、主轴箱等部件有限元模型,并对Jones轴承模型进行扩展建立高速滚动轴承非线性模型。将各子部件模型进行集成,得到整个高速主轴系统的非线性动力学方程,并进行试验验证。分别从转子陀螺力矩、转子离心力和轴承软化这三个角度,系统地研究高速旋转状态下主轴-轴承系统内部的速度效应及其对整个系统动态特性的影响规律。结果表明:当系统存在较大的阻尼比(1%~5%)时,陀螺力矩对系统的直接频率响应函数影响不明显,但是对交叉传递函数的影响显著;随着主轴转速的升高,主轴转子的离心力效应会逐渐削弱主轴系统的刚度,最终使整个高速主轴系统的固有频率降低;必须综合考虑主轴转子的离心力效应和轴承的软化效应,才能比较准确地仿真高速主轴系统的动力学特性。     

Micromechanical modeling of cohesive thermoelastic steady-state and transient cracking in polycrystalline materials

In this paper, a micromechanical formulation is proposed for modeling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model is based on a multiregion boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic isotropic behavior, and multiphase aggregates have been considered. Damage evolution along (intergranular or transgranular) interfaces is modeled using thermomechanical cohesive laws, and upon failure, nonlinear frictional contact analysis is introduced to model separation, stick or slip. Steady-state and transient thermoelastic formulations have been modeled, and numerical simulations are presented, not only to demonstrate the validity but also to study the physical implications of the proposed formulation, in comparison with other numerical methods as well as experimental observations and literature results.