Response Of Individual Grains Research Articles

Multiple-mechanism and microstructure-based crystal plasticity modeling for cyclic shear deformation of TRIP steel

The transformation-induced plasticity (TRIP) steel has an excellent synergy between strength and ductility and is widely used in industry. Cyclic loading is often seen in its industrial application. Therefore, it is of great significance to study cyclic plastic behavior of the TRIP steel. The TRIP steel's cyclic shear behavior and microstructure evolutions were investigated by mechanical testing, electron backscatter diffraction (EBSD) characterization, and in-situ electron channeling contrast imaging (in-situ ECCI) observation. Then, a multiple-mechanism crystal plasticity constitutive model was developed, considering both dislocation slip and martensitic transformation mechanisms. Furthermore, an isotropic hardening law and a modified kinematic hardening rule were taken into account. The crystal plasticity model was implemented into DAMASK with the spectral method. A polycrystalline RVE with realistic grain morphology was constructed from the EBSD data. The simulations of the TRIP steel under cyclic shear loading showed that the samples under higher strain amplitude exhibit stronger cyclic shear hardening. The activation of the martensitic transformation mechanism promotes cyclic hardening. In grain level, the grains with Taylor factor (related to orientation) between 3.3 and 3.9 can activate more slip systems and have a better cyclic hardening ability. So, the Taylor factor is defined as an indicator describing the cyclic response of individual grains in polycrystalline materials. Considering the capability of the established modeling framework, it is of great significance to guide the TRIP steel to serve safely and help the microstructural design in grain scale.

Texture-sensitive prediction of micro-spring performance using Gaussian process models calibrated to finite element simulations

This paper explores the viability and benefits of building a computationally low-cost surrogate model relating the mechanical performance of micro-springs to crystallographic texture and single-crystal elastic constants. This task is accomplished by leveraging advances in (i) computationally-expensive finite element (FE) models that explicitly incorporates the constitutive response of individual grains in to simulate the overall mechanical response of the micro-spring, (ii) efficient parametrization of the extremely large space of textures using Fourier basis (i.e., generalized spherical harmonics), (iii) sequential design of FE simulations to maximize model fidelity while also minimizing the overall computational expense incurred in generating the data, and (iv) the use of Gaussian process models for incorporating uncertainty quantification into the development of the desired surrogate model. The strategy implemented in this work proved to be remarkably efficient in producing the desired surrogate model. The utility of the surrogate model established in this work is demonstrated with a case study addressing an inverse solution for the specific crystallographic texture that maximizes the micro-spring performance for a selected material.

Size effect on plastic anisotropy in microscale deformation of metal foil

Metal foils are extensively used for manufacturing microparts with a high depth-to-thickness ratio by microforming processes. Since there are few grains participating in the deformation of metal foil, the mechanical response of each individual grain intensively affects the deformation behavior and the quality of the formed micropart, which leads to strong anisotropy in microforming. To clarify the size effect on material anisotropy and the impact of scale-dependent plastic anisotropy on the formability of metal foil, a series of tensile experiments and geometrically scaled-down deep-drawing tests of SUS304 foil with different thicknesses of 50–200 μm and grain sizes of 10.2–80.5 μm were performed. The experimental results indicate that the anisotropy of flow stress, yield tensile ratio (i.e., ratio of the yield strength to the tensile strength) and elongation at angles of 0°, 45° and 90° to the rolling direction is prominently enhanced with decreasing thickness and that the anisotropy generally shows a substantial sensitivity to grain size. In addition, the abnormally increased hardening rate of flow behavior for metal foil with few grains in thickness direction arises from the deformation-induced transformation from austenite to martensite. The Lankford values in different orientations, the planar anisotropy and normal anisotropy coefficients decrease with increasing grain size and decreasing foil thickness. The foil manifests strong plastic anisotropy when the grain size is comparable to the foil thickness due to the dominant response of individual grains in terms of crystal orientation, texture, size and shape at a low value of t/d ratio (i.e., the ratio of the thickness to the grain size). Furthermore, several macroscale yield criteria are adopted to characterize the anisotropic phenomenon in the multi-scaled deep drawing process. The results suggest that the Yld2000-2d criterion is more suitable than Hill’48 and Von Mises functions to predict the anisotropic behavior of metal foil with a large number of grains involved in microforming. However, the prediction precision is worsened with decreasing t/d ratio, and the use of Yld2000-2d becomes problematic when the foil thickness is of the same magnitude as grain size, which is closely linked to the interactive effects of grain size, foil thickness and crystallographic texture in microscale plastic deformation.

Microstructure and Micromechanical Properties of Mg Microtubes Prepared by Laser Dieless Drawing

The paper presents microscale experimental investigation performed on microtubes that were prepared with a novel laser dieless drawing (LDD) technique from difficult-to-work AZ31 magnesium alloy (nominally 3wt.%Al-1wt.%Zn-0.3wt.%Mn-Mg balanced). A microstructure analysis was performed via various microscopic techniques. Mechanical response of individual grains with various orientations was tested using instrumental nanoindentation and the results were compared with the microstructure. Distributions of elastic modulus, hardness and visco-elastic properties were analyzed. In addition, microtubes were also characterized in terms of their surface roughness and morphology based on different modes of surface treatment. The grain size is practically not changed when LDD is applied after extrusion showing low thermal and straining effect of the process. Local mapping of mechanical properties does not show weak spots and imply feasibility of the novel production technology.

Evaluation of an inverse methodology for estimating constitutive parameters in face-centered cubic materials from single crystal indentations

Abstract The feasibility to determine the adjustable parameters of single crystal plasticity constitutive laws by an inverse approach that minimizes the deviation between the measured and simulated indentation response of individual grains (of a polycrystalline sample) is investigated for the case of face-centered cubic (fcc) lattice structure. Optimization uses the Nelder–Mead (NM) simplex algorithm, which was modified to navigate parameter space regions where objective function evaluations fail. A phenomenological power-law is assumed as the constitutive description for crystal plasticity. Simulated cases of indentation with prescribed constitutive parameter values serve as the virtual reference. A sensitivity analysis revealed that the initial and saturation slip resistance τ 0 and τ sat are the most dominant parameters while the hardening slope h 0 has less influence. Reproducibility and robustness are analyzed for different objective functions involving the load–displacement response and residual surface topography for several indentation crystal orientations . Concurrent optimization of load–displacement and topography consistently provided the least scatter in the optimized parameter values from the target solution compared to either one individually and essentially independent of indentation crystal orientation. Deviations in slip activity were typically of the same order of magnitude as the combined deviations of load–displacement and surface topography response. Optimization of more than one crystallographic indentation response at once did not improve the parameter estimation quality but proportionally increases the evaluation effort. It is concluded that for fcc materials one single crystal indentation experiment suffices to closely quantify the two most influential parameters of a phenomenological constitutive plasticity law when the objective function of the modified NM simplex algorithm proposed herein combines the load–displacement response and residual surface topography.

Electromechanical Response of Polycrystalline Barium Titanate Resolved at the Grain Scale

Ferroic materials are critical components in many modern devices. Polycrystalline states of these materials dominate the market due to their cost effectiveness and ease of production. Studying the coupling of ferroic properties across grain boundaries and within clusters of grains is therefore critical for understanding bulk polycrystalline ferroic behavior. Here, three‐dimensional X‐ray diffraction is used to reconstruct a 3D grain map (grain orientations and neighborhoods) of a polycrystalline barium titanate sample and track the grain‐scale non‐180° ferroelectric domain switching strains of 139 individual grains in situ under an applied electric field. The map shows that each grain is located in a very unique local environment in terms of intergranular misorientations, leading to local strain heterogeneity in the as‐processed state of the sample. While primarily dependent on the crystallographic orientation relative to the field directions, the response of individual grains is also heterogeneous. These unique experimental results are of critical importance both when building the starting conditions and considering the validity of grain‐scale modeling efforts, and provide additional considerations in the design of novel ferroic materials.

Fracture toughness characterization of single-crystalline tungsten using notched micro-cantilever specimens

The fracture toughness of tungsten is strongly influenced by microstructural features including crystal orientation and grain structure as well as specimen or component size. In order to gain insight into the mechanical response of individual grains, an experimental study using small scale fracture specimens was conducted and closely accompanied by finite element simulations. Free-standing notched single-crystalline tungsten micro-bending beams with an orientation of the {011}〈01¯1〉-crack system along the loading direction were loaded using a nanoindenter and modelled using crystal plasticity and cohesive zones. This combined numerical and experimental approach successfully demonstrates a procedure to determine the fracture toughness of such small non-standard specimens despite the occurrence of plastic deformation.

A computational study of the microstructural effect on the deformation and fracture of friction stir welded aluminum

A computational analysis of the microstructural effect on the deformation and fracture of friction stir welded aluminum is performed. A dynamic boundary-value problem using a plane strain approximation is solved numerically by the finite difference method. The calculations take an explicit account of experimental polycrystalline microstructures typical for different weld zones, like the base material, weld nugget, and thermo-mechanically affected zones. The mechanical response of individual grains is simulated within an elastic–plastic formulation of the problem with isotropic strain hardening. A fracture model allowing for crack generation and propagation in maximum equivalent plastic strain regions is used. It is shown that the localization of plastic strain and the strength of aluminum in different weld zones are determined by the microstructure of the material on the advancing side of the weld.

A mesomechanical analysis of the stress–strain localisation in friction stir welds of polycrystalline aluminium alloys

A numerical analysis is presented of the microstructural effects on the deformation and fracture of friction stir welds in aluminium alloys. A dynamic boundary-value problem in a plane strain formulation is solved numerically by the finite-difference method. Experimental polycrystalline microstructures inherent in different weld zones—base material, weld nugget, and thermo-mechanically affected zones—were accounted for explicitly in the calculations. To simulate the mechanical response of individual grains, use was made of an elastic–plastic formulation of the problem accounting for isotropic strain hardening, including the Hall–Petch effect, and of a fracture model allowing for crack initiation and growth in the regions of maximum equivalent plastic strains. Plastic strain and fracture localisation is shown to depend on the strength of welded materials.

Orientation Dependence of the Fracture Behavior of Single-crystal Tungsten

Polycrystalline tungsten at room temperature shows a brittle fracture behavior, which is also strongly influenced by the grain structure and texture as well as sample dimensions. To gain insight into the mechanical response of individual grains, an experimental program has been set up to test small scale samples under microbending starting with a notched tungsten single crystal oriented with the {110}<▪> crack system along the loading direction. Related to this experimental program a finite element study has been performed to analyze the crack propagation in such single-crystal tungsten micro cantilevers. The aim of the present numerical work is to investigate the influence of the single-crystal orientation on the fracture process.A finite element (FE) model of the notched microbeam was created taking plastic deformation at the crack tip into account. Plastic deformation is implemented using a crystal plasticity approach formulated by Asaro (1983) and written by Huang (1991). Furthermore, the fracture process with crack propagation is described by a cohesive zone model. The simulations of microbending allow for evaluating the details of the fracture process more accurately. The results reveal details of the developing plastic zone as well as the current crack propagation and the J-integral in dependence of the crystal orientation and notch geometry.

Rheological Hardness Index for Assessing Hardness of Hexaploids and Durums

ABSTRACTKernel hardness of cereal grains is a fundamental phenotype, and various protocols for its characterization have been proposed. Although, from different perspectives, each has proved useful, these methods do not directly address the rheological (fracturing) response of a grain when subjected to compression. Such information is hidden in the individual crush response profiles (iCRPs) obtained by measuring the response of individual grains to crushing on an SKCS 4100 device. Here, the appropriateness and utility of rheological phenotypes, based on single‐kernel measurements, are demonstrated by proposing and validating a new wheat grain hardness phenotype, the rheological hardness index (RHI). It is defined in terms of the rheological phenotype phases (RPPs) of the averaged CRPs (aCRPs) obtained by averaging a large number of iCRPs. The utility of RHI is illustrated by showing how it provides improved insight about the differences in brittleness and compactness of grains from different wheat varieties. This investigation highlights the opportunity that the RPP of the aCRPs represent for obtaining specific quantitative phenotypes for the study of hardness in cereal grains. In particular, successful plant breeding relies on segregating a breeding population into appropriate end‐use categories, for which RHI has a potential role to play.

Deformation heterogeneity of Ti under cryogenic channel-die compression

AbstractCommercial purity Ti was subjected to channel die compression in liquid nitrogen for the purpose of studying its deformation characteristics from the viewpoint of the grain refinement induced by severe plastic deformation. Deformed specimens showed microstructural heterogeneity in that the initial blocky grains of about 50 μm in size turned into a mixture of the easily deforming soft grains and the hard grains revealing local concentration of dislocations and deformation twins. Using electron back scattered diffraction analysis the in-grain misorientation-axis distribution was studied, from which it was found that the deformation heterogeneity resulted from the anisotropy of individual grains with respect to the compression die: while the soft grains were those oriented favorably for the prism <a> slip, the hard ones were oriented for non-prism slips and deformation twinning. The difference in the response of individual grains, therefore, led to a remarkable effect of the crystal texture of specimens on the maximum strain that can be imposed on specimens without cracking. Based on the present results, a way to achieve expedient grain refinement through the cryogenic plane-strain compression was suggested.

A uniaxial tensile stage with tracking capabilities for micro X-ray diffraction applications

First results are presented for a uniaxial tensile stage designed to operate on a scanning micro X-ray diffraction synchrotron beamline. The new tensile stage allows experiments at typical loading cycles used in standard engineering stress–strain tests. Several key features have been implemented to supportin situloading experiments at the intragranular length scale. The physical size and weight of the load cell were minimized to maintain the correct working distance for the X-ray focusing optics and to avoid overloading the high-resolution raster scan translation stages. A high-magnification optical microscope and image correlation code were implemented to enable automated online tracking capabilities during macroscopic elongation of the sample. Preliminaryin situtensile loading experiments conducted on beamline 12.3.2 at the Advanced Light Source using a polycrystalline commercial-purity Ti test piece showed that the elastic–plastic response of individual grains could be measured with submicrometre spatial resolution. The experiments highlight the unique instrumentation capabilities of the tensile stage for direct measurement of deviatoric strain and observation of dislocation patterning on an intragranular length scale as a function of applied load.

A nonlinear model of piezoelectric polycrystalline ceramics under quasi-static electromechanical loading

Nonlinear characteristics of tetragonal perovskite type polycrystalline piezoelectric ceramics under electromechanical loading are theoretically simulated using a threedimensional micromechanical model. The model consists of many differently oriented grains which form the bulk material. Uni-axial, quasi-static loading is applied in the simulations. The calculations which are based on a linear constitutive and nonlinear domain switching model are performed at each grain. All grains are assumed to be statistically random oriented at the virgin state.The behavior of piezoelectric ceramics under constant compressive stress which is applied in the same direction of the cyclic electric field is investigated. The macroscopic response of the bulk ceramics to the applied loading is predicted by averaging the response of individual grains. It is assumed that a domain or a microstructure switches if the reduction in potential energy of the polycrystal exceeds a threshold of critical energy per unit volume of the material. Due to intergranular effects domain switching may occur in reality even for those grains, for which the critical energy level is not reached. This effect is modeled by introducing a probability for domain switching as a function of the actual energy level related to the critical energy level. By use of the probability functions, it is possible to model the nonlinearity even in a small electromechanical loading range. The effect of different probability functions, and material parameters are also analysed. The results of simulations have been compared with experimental data from literature.

Rate dependent properties of perovskite type tetragonal piezoelectric materials using micromechanical model

In this paper, a three-dimensional micromechanical model is presented for simulation of the rate dependent properties of certain perovskite type tetragonal piezoelectric materials. The model is based on linear constitutive, nonlinear domain switching, and linear kinetics theories. The simulation starts with a virgin bulk material of randomly oriented grains. Then the material is electrically loaded with an alternating voltage of various frequencies, which are in the order of 0.01 Hz to 1 Hz. An energy equation in combination with a probability function is used to determine the onset of the domain switching inside the grains. Such a probability function leads to a better phenomenological model for the domain switching even for electrical loadings, which are in a range far below the coercive fields. The propagation of the domain wall during the domain switching process in grains is modeled by means of linear kinetics relations after domain nucleation. The response of the bulk ceramic is predicted by averaging the response of individual grains using Euler angles for the transformation from local coordinates of the grains to global coordinate. Electric displacement hysteresis loops for different frequencies and amplitudes of the alternating electric fields are simulated. A simple micromechanical model without the probabilistic approach is compared with the one that takes it into account. Both models give important insights into the rate dependency of piezoelectric materials, which was observed in some experiments reported in the literature.

Local elastic response of individual grains in lead‐free Nb‐doped Bi4Ti3O12 piezoelectric ceramics

AbstractThe local elastic response of individual grains in lead‐free Nb‐doped Bi4Ti3O12 piezoelectric ceramics have been examined by atomic force microscopy in the acoustic mode. Subsurface features with different elasticity down to 60 nm are imaged from the cantilever deflection vibration at a modulation frequency much lower than the cantilever resonance. Local elastic regions parallel and perpendicular to the long axis of the plate‐like grains are found in the Bi4Ti3O12 piezoelectric ceramics, which are most likely a result of the crystal structure arrangement undergone in the grain growth of the Nb‐doped Bi4Ti3O12 piezoelectric ceramics during sintering. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Ferroelectric/ferroelastic interactions and a polarization switching model

Ferroelectric and ferroelastic switching cause ferroelectric ceramics to depolarize and deform when subjected to excessive electric field or stress. Switching is the source of the classic butterfly shaped strain vs electric field curves and the corresponding electric displacement vs electric field loops [1]. It is also the source of a stress—strain curve with linear elastic behavior at low stress, non-linear switching strain at intermediate stress, and linear elastic behavior at high stress [2, 3]. In this work, ceramic lead lanthanum zirconate titanate (PLZT) is polarized by loading with a strong electric field. The resulting strain and polarization hysteresis loops are recorded. The polarized sample is then loaded with compressive stress parallel to the polarization and the stress vs strain curve is recorded. The experimental results are modeled with a computer simulation of the ceramic microstructure. The polarization and strain for an individual grain are predicted from the imposed electric field and stress through a Preisach hysteresis model. The response of the bulk ceramic to applied loads is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The observed strain and electric displacement hysteresis loops and the nonlinear stress—strain curve for the polycrystalline ceramic are reproduced by the simulation.

On modeling anisotropy in deformation processes involving textured polycrystals with distorted grain shape

A mathematical formulation is presented which uses rate-dependent polycrystalline plasticity to model the development of plastic anisotropy in bulk forming processes. The formulation assumes that underlying a material point on a continuum scale is a collection of anisotropic, contiguous grains. The mechanical response at a continuum level is derived from the response of individual grains suitably averaged over all grains in the aggregate. The effects of preferred orientation (texture) and of the evolving grain shape on the directionality to the flow properties of the polycrystal are included. A general numerical framework is described for incorporating this complex material behavior in a finite element formulation. As an application, texture development during the flat rolling of aluminum sheets is presented. The simulation predictions have been compared with reported experimental data and with a previous study where the effects of grain shape were neglected.