RELAXATION OF SOME TRANSVERSALLY ISOTROPIC ENERGIES AND APPLICATIONS TO SMECTIC A ELASTOMERS

2008 ◽  
Vol 18 (01) ◽  
pp. 1-20 ◽  
Author(s):  
JAMES ADAMS ◽  
SERGIO CONTI ◽  
ANTONIO DESIMONE ◽  
GEORG DOLZMANN
Keyword(s):  
Unit Vector ◽  
Stress Strain ◽  
Isotropic Energy ◽  
Macroscopic Stress ◽  
Smectic A ◽  
Transversally Isotropic

We determine the relaxation of some transversally-isotropic energy densities, i.e. functions W : ℝ3×3 → [0,∞] with the property W(QFR) = W(F) for all Q ∈ SO (3) and all R ∈ SO (3) such that Rn0 = n0, where n0 is a fixed unit vector. One physically relevant example is a model for smectic A elastomers. We discuss the implications of our result for the computation of macroscopic stress–strain curves for this material and compare with experiment.

Stress-strain and thermomechanical characterization of nematic to smectic A transition in a strongly-crosslinked bimesogenic liquid crystal elastomer

Polymer ◽  
2018 ◽  
Vol 158 ◽  
pp. 96-102 ◽  
Author(s):  
Andraž Rešetič ◽  
Jerneja Milavec ◽  
Valentina Domenici ◽  
Blaž Zupančič ◽  
Alexey Bubnov ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Stress Strain ◽  
Liquid Crystal Elastomer ◽  
Smectic A ◽  
Thermomechanical Characterization

Pattern Formation During the Growth of Liquid Crystal Phases

MRS Bulletin ◽  
1991 ◽  
Vol 16 (1) ◽  
pp. 38-45 ◽  
Author(s):  
Patrick Oswald ◽  
John Bechhoefer ◽  
Francisco Melo
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Unit Vector ◽  
The Other ◽  
Two Dimensional ◽  
Smectic A ◽  
Anisotropic Plastic ◽  
Fundamental Research ◽  
Crystal Phases ◽  
Columnar Mesophases

Liquid crystals, discovered just a century ago, have wide application to electrooptic displays and thermography. Their physical properties have also made them fascinating materials for more fundamental research.The name “liquid crystals” is actually a misnomer for what are more properly termed “mesophases,” that is, phases having symmetries intermediate between ordinary solids and liquids. There are three major classes of liquid crystals: nematics, smectics, and columnar mesophases. In nematics, although there is no correlation between positions of the rodlike molecules, the molecules tend to lie parallel along a common axis, labeled by a unit vector (or director) n. Smectics are more ordered. The molecules are also rodlike and are in layers. Different subtypes of smectics (labeled, for historical reasons, smectic A, smectic B,…) have layers that are more or less organized. In the smectic A phase, the layers are fluid and can glide easily over each other. In the smectic B phase, the layers have hexagonal ordering and strong interlayer corrélations. Indeed, the smectic B phase is more a highly anisotropic plastic crystal than it is a liquid crystal. Finally, columnar mesophases are obtained with disklike molecules. These molecules can stack up in columns which are themselves organized in a two-dimensional array. There is no positional correlation between molecules in one column and molecules in the other columns.

Derivation of Polycrystal Creep Properties From the Creep Data of Single Crystals

1977 ◽  
Vol 44 (1) ◽  
pp. 73-78 ◽  
Author(s):  
T. H. Lin ◽  
C. L. Yu ◽  
G. J. Weng
Keyword(s):  
Single Crystals ◽  
Creep Deformation ◽  
Tensile Loading ◽  
Present Theory ◽  
Sole Source ◽  
Stress And Strain ◽  
Creep Data ◽  
Stress Strain ◽  
Macroscopic Stress ◽  
Additional Constant

A method developed for calculating the polycrystal stress-strain-time relation from the creep data of single crystals is shown. Slip is considered to be the sole source of creep deformation. This method satisfies, throughout the aggregate, both the condition of equilibrium and that of continuity of displacement as well as the creep characteristics of single crystals. A very large three-dimensional region is assumed to be filled with innumerable identical cubic blocks, each of which consists of 64 cube-shaped crystals of different orientations. This region is assumed to be embedded in an infinite elastic isotropic medium. This infinite medium is subject to a uniform loading. The average stress and strain of a cubic block at the center of the region is taken to represent the macroscopic stress and strain of the polycrystal. This method is self-consistent and considers the heterogeneous interaction effect of the creep deformation of all slid crystals. The macroscopic stress-strain-time relations of the polycrystal were calculated for three tensile loadings, one radial loading, and two nonradial loadings of combined tension and torsion. The numerical results given by the present theory agree well with those predicted by the so-called “Mechanical Equation of State.” The creep strain components calculated by the present theory for the case of a constant tensile loading followed by an additional constant tensile loading are found to be considerably higher than those predicted by von Mises and Tresca’s theories. These results agree well qualitatively with experimental results.

scholarly journals An in situ synchrotron study of the localized B2↔B19′ phase transformation in an Ni–Ti alloy subjected to uniaxial cyclic loading–unloading with incremental strains

2020 ◽  
Vol 53 (2) ◽  
pp. 335-348
Author(s):  
Xiaohui Bian ◽  
Ahmed A. Saleh ◽  
Peter A. Lynch ◽  
Christopher H. J. Davies ◽  
Azdiar A. Gazder ◽  
...  
Keyword(s):  
Phase Transformation ◽  
Cyclic Loading ◽  
Plastic Strain ◽  
Strain Curve ◽  
Transformation Strain ◽  
Gauge Length ◽  
Stress Strain ◽  
Macroscopic Stress ◽  
Residual Strains

High-resolution in situ synchrotron X-ray diffraction was applied to study a cold-drawn and solution-treated 56Ni–44Ti wt% alloy subjected to uniaxial cyclic loading–unloading with incremental strains. The micro-mechanical behaviour associated with the partial and repeated B2↔B19′ phase transformation at the centre of the sample gauge length was studied with respect to the macroscopic stress–strain response. The lattice strains of the (110)B2 and different B19′ grain families are affected by (i) the transformation strain, the load-bearing capacity of both phases and the strain continuity maintained at/near the B2–B19′ interfaces at the centre of the gauge length, and (ii) the extent of transformation along the gauge length. With cycling and incremental strains (i) the elastic lattice strain and plastic strain in the remnant (110)B2 grain family gradually saturate at early cycles, whereas the plastic strain in the B19′ phase continues to increase. This contributes to accumulation of residual strains (degradation in superelasticity), greater non-linearity and change in the shape of the macroscopic stress–strain curve from plateau type to curvilinear elastic. (ii) The initial 〈111〉B2 fibre texture transforms to [120]B19′, [130]B19′, [150]B19′ and [010]B19′ orientations. Further increase in the applied strain with cycling results in the development of [130]B19′, [102]B19′, [102]B19′, [100]B19′ and [100]B19′ orientations.

Effect of Crystal Plasticity Parameters on Microscopic Stress Distribution in Polycrystalline Aggregate Model

2013 ◽  
Vol 05 (01) ◽  
pp. 1350003 ◽  
Author(s):  
Yoshiki Mikami ◽  
Kazuo Oda ◽  
Masahito Mochizuki
Keyword(s):  
Stress Distribution ◽  
Crystal Plasticity ◽  
Strain Curve ◽  
Polycrystalline Aggregate ◽  
Aggregate Model ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Microscopic Scale ◽  
Macroscopic Stress ◽  
Hardening Modulus

Crystal plasticity parameters for numerical simulations are difficult to experimentally measure on the microscopic scale. One possible approach to avoid the difficulty is to determine the parameters that can be used to reproduce the stress–strain curve by employing a polycrystalline aggregate model. In this study, the effect of crystal plasticity parameters on stress–strain curves on a macroscopic scale and on stress distribution on a microscopic scale was investigated by using polycrystalline aggregate simulation. The parameters investigated were initial slip strength (τ0), initial hardening modulus (h0) and saturation slip strength (τs). The effect of these parameters on macroscopic stress–strain curves was found to be the followings: τ0 controls the yield stress or proof stress, and both h0 and τs control the strain-hardening behavior. The effect of these parameters on microscopic stress distribution was also investigated because similar stress–strain curve can be obtained by using different sets of crystal plasticity parameters. Consequently, even if these parameters are slightly different, a similar microscopic stress distribution can be obtained by properly reproducing the macroscopic stress–strain curve.

Material Response and Continuum Relations; or From Microscales to Macroscales

1984 ◽  
Vol 106 (4) ◽  
pp. 286-289 ◽  
Author(s):  
D. C. Drucker
Keyword(s):  
Plastic Deformation ◽  
Shear Stress ◽  
Aluminum Alloys ◽  
Single Crystals ◽  
Continuum Mechanics ◽  
Stress Strain ◽  
Material Response ◽  
Macroscopic Behavior ◽  
Macroscopic Stress ◽  
Structural Metals

Brief qualitative assessments are presented of a few approaches to macroscopic stress-strain relations for structural metals, alloys, and composites and some remarks are made about fracture. Ignoring the scale and applying continuum mechanics to the microstructure lies at one extreme, the dislocation scale treatment of single crystals and simple polycrystals at another. When, as for structural aluminum alloys, the shear stress required for continuing plastic deformation is so much higher than for the constituent single crystals, it seems unlikely that the latter approach is able to exhibit the salient features of macroscopic behavior.

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