Microscopic Constitutive Models of Single Crystal and Polycrystal

2012 ◽  
pp. 85-112
Author(s):  
Ping Hu ◽  
Ning Ma ◽  
Li-zhong Liu ◽  
Yi-Guo Zhu
Keyword(s):  
Single Crystal ◽  
Constitutive Models

Application of a Smooth Approximation of the Schmid’s Law to a Single Crystal Gas Turbine Blade: Part 1—Theory and Governing Equations

2012 ◽  
Author(s):  
Alessandro D. Ramaglia
Keyword(s):  
Single Crystal ◽  
Constitutive Models ◽  
Material Model ◽  
Research Literature ◽  
Elastic Behaviour ◽  
Full Potential ◽  
Smooth Approximation ◽  
Suitable Material ◽  
Von Mises ◽  
Term Creep

In industrial practice, the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost and time for the minimum testing campaign necessary to identify the model and pre-existing standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate-independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modelled is isotropic, commercial FE packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based super-alloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behaviour. In what follows this problem is addressed by showing how single crystal plasticity modelling can be reduced to the adoption of an anisotropic elastic behaviour with a sort of von Mises yield surface.

Crystallographic Constitutive Models for Single Crystal Superalloys

2011 ◽  
Vol 197-198 ◽  
pp. 1381-1388 ◽  
Author(s):  
Qing Wu Wang ◽  
Mao Pang ◽  
Shi Hui Zhang
Keyword(s):  
Slip System ◽  
Single Crystal ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Slip Systems ◽  
Flow Equations ◽  
Hardening Law ◽  
Crystallographic Slip ◽  
Set Up ◽  
Octahedral Slip

Single crystal nickel base superalloys, such as Chinese material DD6 have been used in gas turbine blade in China more and more widely. In order to make better use of single crystal superalloys with many excellencies, constitutive models have been developed. In this paper, general method of crystallographic constitutive modeling was summarizes and a new constitutive model, based on crystallographic theory was proposed with phenomenological models' advantages. Based on crystallographic slip system principle, the basic slip-based viscoplasticity theory equations were set up on 12 octahedral slip systems and 6 cubic slip systems, total 18 slip systems. In micro-level slip system, the general unified constitutive formulations were used as the flow equations and hardening law. In the model, scalar forms were applied for constitutive equations on slip systems and the number and types of active slip systems were used to describe the material anisotropy, which was satisfied automatically by slip systems not anisotropic tensors and. The experimental and calculation results of two kind single crystal superalloys PWA1480 and DD6 were compared. The model had the capability to predict many mechanical response and analyze structure of single crystal superalloys. The modeling procedures and results showed that this crystallographic model had more clear physical meaning and was exact.

Application of a Smooth Approximation of the Schmid's Law to a Single Crystal Gas Turbine Blade

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Alessandro D. Ramaglia
Keyword(s):  
Single Crystal ◽  
Constitutive Models ◽  
Material Model ◽  
Research Literature ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Full Potential ◽  
Smooth Approximation ◽  
Suitable Material ◽  
Von Mises

In industrial practice the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost, and time for the minimum testing campaign necessary to identify the model and preexisting standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modeled is isotropic, commercial finite element (FE) packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based superalloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate, and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behavior. In what follows this problem is addressed by showing how single crystal plasticity modeling can be reduced to the adoption of an anisotropic elastic behavior with a sort of von Mises yield surface.

A Preparation of High Resolution Standards for Electron Microscopy. Part II

1971 ◽  
Vol 29 ◽  
pp. 160-161
Author(s):  
Akira Tanaka ◽  
David F. Harling
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Carbon Black ◽  
Single Crystal ◽  
Dark Field ◽  
Graphitized Carbon Black ◽  
Graphitized Carbon ◽  
Dark Field Imaging ◽  
Crystal Films ◽  
Micro Holes

In the previous paper, the author reported on a technique for preparing vapor-deposited single crystal films as high resolution standards for electron microscopy. The present paper is intended to describe the preparation of several high resolution standards for dark field microscopy and also to mention some results obtained from these studies. Three preparations were used initially: 1.) Graphitized carbon black, 2.) Epitaxially grown particles of different metals prepared by vapor deposition, and 3.) Particles grown epitaxially on the edge of micro-holes formed in a gold single crystal film.The authors successfully obtained dark field micrographs demonstrating the 3.4Å lattice spacing of graphitized carbon black and the Au single crystal (111) lattice of 2.35Å. The latter spacing is especially suitable for dark field imaging because of its preparation, as in 3.), above. After the deposited film of Au (001) orientation is prepared at 400°C the substrate temperature is raised, resulting in the formation of many square micro-holes caused by partial evaporation of the Au film.

Structure of Palladium Single-Crystal Films Prepared by Flash Evaporation onto (001) NaCl Substrates

1970 ◽  
Vol 28 ◽  
pp. 456-457
Author(s):  
L. E. Murr ◽  
G. Wong
Keyword(s):  
Single Crystal ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
High Rate ◽  
Flash Evaporation ◽  
Optimum Load ◽  
Single Crystal Films ◽  
Crystal Films ◽  
A Current

Palladium single-crystal films have been prepared by Matthews in ultra-high vacuum by evaporation onto (001) NaCl substrates cleaved in-situ, and maintained at ∼ 350° C. Murr has also produced large-grained and single-crystal Pd films by high-rate evaporation onto (001) NaCl air-cleaved substrates at 350°C. In the present work, very large (∼ 3cm2), continuous single-crystal films of Pd have been prepared by flash evaporation onto air-cleaved (001) NaCl substrates at temperatures at or below 250°C. Evaporation rates estimated to be ≧ 2000 Å/sec, were obtained by effectively short-circuiting 1 mil tungsten evaporation boats in a self-regulating system which maintained an optimum load current of approximately 90 amperes; corresponding to a current density through the boat of ∼ 4 × 104 amperes/cm2.

Dislocations, Ordering and Antiferromagnetic Domains in MnO

1970 ◽  
Vol 28 ◽  
pp. 522-523
Author(s):  
D. J. Barber ◽  
R. G. Evans
Keyword(s):  
Electron Diffraction ◽  
Single Crystal ◽  
Optical Microscopy ◽  
Defect Chemistry ◽  
Magnetic Structures ◽  
Optically Transparent ◽  
Magnetic Features ◽  
Antiferromagnetic Domains

Manganese (II) oxide, MnO, in common with CoO, NiO and FeO, possesses the NaCl structure and shows antiferromagnetism below its Neel point, Tn∼ 122 K. However, the defect chemistry of the four oxides is different and the magnetic structures are not identical. The non-stoichiometry in MnO2 small (∼2%) and below the Tn the spins lie in (111) planes. Previous work reported observations of magnetic features in CoO and NiO. The aim of our work was to find explanations for certain resonance results on antiferromagnetic MnO.Foils of single crystal MnO were prepared from shaped discs by dissolution in a mixture of HCl and HNO3. Optical microscopy revealed that the etch-pitted foils contained cruciform-shaped precipitates, often thick and proud of the surface but red-colored when optically transparent (MnO is green). Electron diffraction and probe microanalysis indicated that the precipitates were Mn2O3, in contrast with recent findings of Co3O4 in CoO.

Electron Microscopy of Shock Loaded Polycrystalline Beryllium

1974 ◽  
Vol 32 ◽  
pp. 506-507 ◽  
Author(s):  
J. M. Galbraith ◽  
L. E. Murr ◽  
A. L. Stevens
Keyword(s):  
Electron Microscopy ◽  
Wave Propagation ◽  
Structural Change ◽  
Single Crystal ◽  
Diffraction Pattern ◽  
Shock Loading ◽  
Slip Systems ◽  
Compression Tests ◽  
X Ray Diffraction ◽  
X Ray

Uniaxial compression tests and hydrostatic tests at pressures up to 27 kbars have been performed to determine operating slip systems in single crystal and polycrystal1ine beryllium. A recent study has been made of wave propagation in single crystal beryllium by shock loading to selectively activate various slip systems, and this has been followed by a study of wave propagation and spallation in textured, polycrystal1ine beryllium. An alteration in the X-ray diffraction pattern has been noted after shock loading, but this alteration has not yet been correlated with any structural change occurring during shock loading of polycrystal1ine beryllium.This study is being conducted in an effort to characterize the effects of shock loading on textured, polycrystal1ine beryllium. Samples were fabricated from a billet of Kawecki-Berylco hot pressed HP-10 beryllium.

Studies of Oxide Formation on Copper Thin Films by Electron Microscopy

1977 ◽  
Vol 35 ◽  
pp. 316-317
Author(s):  
G. G. Hembree ◽  
M. A. Otooni ◽  
J. M. Cowley
Keyword(s):  
Electron Microscopy ◽  
Electron Diffraction ◽  
Single Crystal ◽  
Crystal Surface ◽  
Crystal Defects ◽  
Diffraction Reflection ◽  
Reaction Products ◽  
Intermediate Energies ◽  
Crystal Films ◽  
Reflection Electron Microscopy

The formation of oxide structures on single crystal films of metals has been investigated using the REMEDIE system (for Reflection Electron Microscopy and Electron Diffraction at Intermediate Energies) (1). Using this instrument scanning images can be obtained with a 5 to 15keV incident electron beam by collecting either secondary or diffracted electrons from the crystal surface (2). It is particularly suited to studies of the present sort where the surface reactions are strongly related to surface morphology and crystal defects and the growth of reaction products is inhomogeneous and not adequately described in terms of a single parameter. Observation of the samples has also been made by reflection electron diffraction, reflection electron microscopy and replication techniques in a JEM-100B electron microscope.A thin single crystal film of copper, epitaxially grown on NaCl of (100) orientation, was repositioned on a large copper single crystal of (111) orientation.

Mechanical Properties and Dislocation Structure of Single Crystal Cdte Deformed in Compression at 300°C

1976 ◽  
Vol 34 ◽  
pp. 592-593
Author(s):  
Ernest L. Hall ◽  
J. B. Vander Sande
Keyword(s):  
Mechanical Properties ◽  
Single Crystal ◽  
Dislocation Structure ◽  
Room Temperature ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Optical Devices ◽  
Semiconductor Compound ◽  
Wide Range ◽  
Sample Orientation

The present paper describes research on the mechanical properties and related dislocation structure of CdTe, a II-VI semiconductor compound with a wide range of uses in electrical and optical devices. At room temperature CdTe exhibits little plasticity and at the same time relatively low strength and hardness. The mechanical behavior of CdTe was examined at elevated temperatures with the goal of understanding plastic flow in this material and eventually improving the room temperature properties. Several samples of single crystal CdTe of identical size and crystallographic orientation were deformed in compression at 300°C to various levels of total strain. A resolved shear stress vs. compressive glide strain curve (Figure la) was derived from the results of the tests and the knowledge of the sample orientation.

Reconstruction of electron holograms recorded in a non-FEG, non-biprism TEM

1995 ◽  
Vol 53 ◽  
pp. 618-619
Author(s):  
Z.L. Wang
Keyword(s):  
Electron Microscope ◽  
Single Crystal ◽  
Experimental Technique ◽  
Transmission Electron Microscope ◽  
The Other ◽  
Electron Holography ◽  
Transmission Electron ◽  
Coherent Sources ◽  
Imaging Theory ◽  
Normal Specimen

An experimental technique for performing electron holography using a non-FEG, non-biprism transmission electron microscope (TEM) has been introduced by Ru et al. A double stacked specimens, one being a single crystal foil and the other the specimen, are loaded in the normal specimen position in TEM. The single crystal, which is placed onto the specimen, is responsible to produce two beams that are equivalent to two virtual coherent sources illuminating the specimen beneath, thus, permitting electron holography of the specimen. In this paper, the imaging theory of this technique is described. Procedures are introduced for digitally reconstructing the holograms.

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