Rate-dependent, finite elasto-plastic deformation of polycrystals

1986 ◽  
Vol 407 (1833) ◽  
pp. 343-375 ◽  
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Finite Deformation ◽  
Constitutive Relations ◽  
Slip Rate ◽  
Large Strains ◽  
Rate Dependent ◽  
Crystallographic Slip ◽  
Self Consistent ◽  
Consistent Method

Based on Hill’s method, a self-consistent averaging scheme is proposed for estimating the overall, finite deformation response of polycrystalline aggregates consisting of single crystals which undergo plastic flow by rate-dependent crystallographic slip, accompanied by elastic lattice distortion. First, constitutive relations for such single crystals are developed assuming that the slip-rate and the associated resolved shear stress are governed by: (1) a power-law relation, and (2) a viscoplastic relation. Then, Hill’s idea that the constraint imposed on a single crystal by the remaining aggregates may be represented by embedding the single crystal in a homogeneous, infinitely extended matrix having the instantaneous overall moduli, is used to formulate a completely self-consistent averaging procedure, valid for rate-dependent materials at finite strains and rotations. This method includes both the Hill and the Krӧner‒Budiansky‒Wu (K. B. W.) methods as limiting cases; when rate-effects are negligible, it reduces to Hill’s self-consistent method as formulated by Iwakuma and Nemat-Nasser for finite deformations, while it reduces to a generalized finite deformation version of the K. B. W. method for strongly rate-dependent materials. Illustrative numerical examples are presented for a plane uniaxial deformation, using a two-dimensional poly crystalline model. These examples clearly show that the rate-dependent crystallographic slip on the level of single crystals produces a more stable overall behaviour of poly crystals. This supports similar results arrived at by other investigators for single crystals and for polycrystals, by using the Taylor averaging scheme. It is shown that, while Taylor’s averaging scheme gives accurate estimates of the incremental quantities at large strains, the total overall quantities differ considerably from the ones obtained by the self-consistent method.

scholarly journals Growth of single crystals in the (Na1/2Bi1/2)TiO3–(Sr1–xCax)TiO3 system by solid state crystal growth

2021 ◽  
Author(s):  
Phan Gia Le ◽  
Huyen Tran Tran ◽  
Jong-Sook Lee ◽  
John G. Fisher ◽  
Hwang-Pill Kim ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Solid State ◽  
Single Crystal ◽  
Single Crystals ◽  
Piezoelectric Properties ◽  
Single Crystal Growth ◽  
Crystal Growth Rate ◽  
Large Strains ◽  
Growth Technique ◽  
The Matrix

AbstractCeramics based on (Na1/2B1/2)TiO3 are promising candidates for actuator applications because of large strains generated by an electric field-induced phase transition. For example, the (1−x)(Na1/2Bi1/2)TiO3-xSrTiO3 system exhibits a morphotropic phase boundary at x = 0.2–0.3, leading to high values of inverse piezoelectric constant d*33, which can be further improved by the use of single crystals. In our previous work, single crystals of (Na1/2B1/2)TiO3-SrTiO3 and (Na1/2B1/2)TiO3-CaTiO3 were grown by the solid state crystal growth technique. Growth in the (Na1/2B1/2)TiO3-SrTiO3 system was sluggish whereas the (Na1/2B1/2)TiO3-CaTiO3 single crystals grew well. In the present work, 0.8(Na1/2Bi1/2)TiO3-0.2(Sr1−xCax)TiO3 single crystals (with x = 0.0, 0.1, 0.2, 0.3, 0.4) were produced by the solid state crystal growth technique in an attempt to improve crystal growth rate. The dependence of mean matrix grain size, single crystal growth distance, and electrical properties on the Ca concentration was investigated in detail. These investigations indicated that at x = 0.3 the matrix grain growth was suppressed and the driving force for single crystal growth was enhanced. Replacing Sr with Ca increased the shoulder temperature Ts and temperature of maximum relative permittivity Tmax, causing a decrease in inverse piezoelectric properties and a change from normal to incipient ferroelectric behavior.

scholarly journals On rate-dependent polycrystal deformation: the temperature sensitivity of cold dwell fatigue

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150214 ◽  
Author(s):  
Zhen Zhang ◽  
M. A. Cuddihy ◽  
F. P. E. Dunne
Keyword(s):  
Stress Relaxation ◽  
Temperature Sensitivity ◽  
Slip Rate ◽  
Cyclic Stress ◽  
Load Shedding ◽  
Rate Dependent ◽  
Dwell Fatigue ◽  
Dislocation Hardening ◽  
Crystallographic Slip ◽  
Local Slip

A temperature and rate-dependent crystal plasticity framework has been used to examine the temperature sensitivity of stress relaxation, creep and load shedding in model Ti-6Al polycrystal behaviour under dwell fatigue conditions. A temperature close to 120°C is found to lead to the strongest stress redistribution and load shedding, resulting from the coupling between crystallographic slip rate and slip system dislocation hardening. For temperatures in excess of about 230°C, grain-level load shedding from soft to hard grains diminishes because of the more rapid stress relaxation, leading ultimately to the diminution of the load shedding and hence, it is argued, the elimination of the dwell debit. Under conditions of cyclic stress dwell, at temperatures between 20°C and 230°C for which load shedding occurs, the rate-dependent accumulation of local slip by ratcheting is shown to lead to the progressive cycle-by-cycle redistribution of stress from soft to hard grains. This phenomenon is termed cyclic load shedding since it also depends on the material's creep response, but develops over and above the well-known dwell load shedding, thus providing an additional rationale for the incubation of facet nucleation.

Latent Hardening in Copper and Copper Alloys

2005 ◽  
Vol 495-497 ◽  
pp. 1043-1048 ◽  
Author(s):  
K.P. Boyle
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Crystal Plasticity ◽  
Copper Alloys ◽  
History Dependence ◽  
Hardening Material ◽  
Hardening Model ◽  
Rate Dependent ◽  
Latent Hardening ◽  
Single Crystal Plasticity

A new phenomenological latent hardening model is developed for rate-dependent single crystal plasticity. The model quantitatively predicts the latent hardening evolution and latent hardening material dependence for f.c.c. single crystals. Increased overshoot, typically observed in copper alloys as opposed to copper, is rationalized based on the history dependence of latent hardening.

scholarly journals Anisotropic Hydraulic Permeability Under Finite Deformation

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Jeffrey A. Weiss
Keyword(s):  
Transport Properties ◽  
Finite Deformation ◽  
Large Deformations ◽  
Constitutive Relations ◽  
Biological Tissues ◽  
Normal Function ◽  
Large Strains ◽  
Hydraulic Permeability ◽  
Fluid Mixture ◽  
Anisotropic Transport

The structural organization of biological tissues and cells often produces anisotropic transport properties. These tissues may also undergo large deformations under normal function, potentially inducing further anisotropy. A general framework for formulating constitutive relations for anisotropic transport properties under finite deformation is lacking in the literature. This study presents an approach based on representation theorems for symmetric tensor-valued functions and provides conditions to enforce positive semidefiniteness of the permeability or diffusivity tensor. Formulations are presented, which describe materials that are orthotropic, transversely isotropic, or isotropic in the reference state, and where large strains induce greater anisotropy. Strain-induced anisotropy of the permeability of a solid-fluid mixture is illustrated for finite torsion of a cylinder subjected to axial permeation. It is shown that, in general, torsion can produce a helical flow pattern, rather than the rectilinear pattern observed when adopting a more specialized, unconditionally isotropic spatial permeability tensor commonly used in biomechanics. The general formulation presented in this study can produce both affine and nonaffine reorientations of the preferred directions of material symmetry with strain, depending on the choice of material functions. This study addresses a need in the biomechanics literature by providing guidelines and formulations for anisotropic strain-dependent transport properties in porous-deformable media undergoing large deformations.

SLIP PLANES IN Fe – 3% Si SINGLE CRYSTALS DEFORMED AT 77 °K

1967 ◽  
Vol 45 (2) ◽  
pp. 1031-1040 ◽  
Author(s):  
B. Šesták ◽  
N. Zárubová ◽  
V. Sládek
Keyword(s):  
Shear Stress ◽  
Large Deviations ◽  
Single Crystal ◽  
Single Crystals ◽  
Room Temperature ◽  
Four Point Bending ◽  
Crystallographic Slip ◽  
Slip Planes

Macroscopic slip planes were determined on specimens of different orientations, cut from a single crystal of Fe – 3% Si alloy after slow deformation [Formula: see text] by four-point bending at 77 °K. On the compression side of the specimens with orientations [Formula: see text] the slip planes were found to be very close to those with maximum resolved shear stress. On the compression side of the specimens with [Formula: see text] and on the tension side of specimens with [Formula: see text] (except the specimens with χ = ±30°) either crystallographic slip along {110} planes or large deviations of slip planes from maximum resolved shear stress planes to {110} planes were observed. The ψ(χ) curves obtained at 77 °K are compared with those obtained similarly at room temperature. The ψ(χ) curves for 77 °K cannot be explained microscopically on the basis of the composite slip on {110} and {112} planes if only the effect of the slip sense is assumed.

The observation of defects on (100) CdTe surfaces by chemical etching

1992 ◽  
Vol 50 (2) ◽  
pp. 1424-1425
Author(s):  
M.E. Lee
Keyword(s):  
Single Crystal ◽  
Grain Boundaries ◽  
Single Crystals ◽  
Chemical Etching ◽  
Crystalline Perfection ◽  
Crystalline Defects ◽  
High Incidence ◽  
Crystallographic Defects ◽  
Cdznte Substrates ◽  
Device Technology

The crystalline perfection of bulk CdTe substrates plays an important role in their use in infrared device technology. The application of chemical etchants to determine crystal polarity or the density and distribution of crystallographic defects in (100) CdTe is not well understood. The lack of data on (100) CdTe surfaces is a result of the apparent difficulty in growing (100) CdTe single crystal substrates which is caused by a high incidence of twinning. Many etchants have been reported to predict polarity on one or both (111) CdTe planes but are considered to be unsuitable as defect etchants. An etchant reported recently has been considered to be a true defect etchant for CdTe, MCT and CdZnTe substrates. This etchant has been reported to reveal crystalline defects such as dislocations, grain boundaries and inclusions in (110) and (111) CdTe. In this study the effect of this new etchant on (100) CdTe surfaces is investigated.The single crystals used in this study were (100) CdTe as-cut slices (1mm thickness) from Bridgman-grown ingots.

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