Large-deformation reduced order homogenization of polycrystalline materials

In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

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Neutron time-of-flight diffraction used to study aged duplex stainless steel at small and large deformation until sample fracture

Journal of Applied Crystallography ◽

10.1107/s0021889811025957 ◽

2011 ◽

Vol 44 (5) ◽

pp. 966-982 ◽

Cited By ~ 21

Author(s):

A. Baczmanski ◽

L. Le Joncour ◽

B. Panicaud ◽

M. Francois ◽

C. Braham ◽

...

Keyword(s):

Stainless Steel ◽

Duplex Stainless Steel ◽

Large Deformation ◽

Tensile Tests ◽

Polycrystalline Materials ◽

Shear Stresses ◽

Linear Elastic ◽

Neutron Time ◽

Crystallographic Planes ◽

Damage Processes

Owing to its selectivity, diffraction is a powerful tool for analysing the mechanical behaviour of polycrystalline materials at the mesoscale (phase and/or grain scale).In situneutron diffraction during tensile tests and elastoplastic self-consistent modelling were used to study slip phenomena occurring on crystallographic planes at small and large deformation. The critical resolved shear stresses in both phases of duplex stainless steel were found for samples subjected to different thermal treatments. The evolution of grain loading was also determined by showing the large differences between stress concentration for grains in ferritic and austenitic phases. It was found that, for small loads applied to the sample, linear elastic deformation occurs in both phases. When the load increases, austenite starts to deform plastically, while ferrite remains in the elastic range. Finally, both phases undergo plastic deformation until sample fracture. By using an original calibration of diffraction data, the range of the study was extended to large sample deformation. As a result, mechanical effects that can be attributed to damage processes initiated in ferrite were observed.

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Observation of secondary slip systems in tungsten bicrystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100112361 ◽

1984 ◽

Vol 42 ◽

pp. 478-479

Author(s):

J. R. Fekete ◽

R. Gibala

Keyword(s):

Stress Field ◽

Grain Boundaries ◽

Deformation Behavior ◽

Stress Axis ◽

Polycrystalline Materials ◽

Slip Systems ◽

Metallic Materials ◽

Twist Boundary ◽

Secondary Slip ◽

Plane Normal

The deformation behavior of metallic materials is modified by the presence of grain boundaries. When polycrystalline materials are deformed, additional stresses over and above those externally imposed on the material are induced. These stresses result from the constraint of the grain boundaries on the deformation of incompatible grains. This incompatibility can be elastic or plastic in nature. One of the mechanisms by which these stresses can be relieved is the activation of secondary slip systems. Secondary slip systems have been shown to relieve elastic and plastic compatibility stresses. The deformation of tungsten bicrystals is interesting, due to the elastic isotropy of the material, which implies that the entire compatibility stress field will exist due to plastic incompatibility. The work described here shows TEM observations of the activation of secondary slip in tungsten bicrystals with a [110] twist boundary oriented with the plane normal parallel to the stress axis.

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The structure of amorphous and polycrystalline materials using energy-filtered RDF analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100130584 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1190-1191

Author(s):

David Cockayne ◽

David McKenzie

Keyword(s):

Electron Diffraction ◽

Diffraction Pattern ◽

Density Function ◽

Electron Diffraction Pattern ◽

Polycrystalline Materials ◽

Nearest Neighbour ◽

X Ray ◽

Selected Area Electron Diffraction ◽

Reduced Density ◽

System F

The technique of Electron Reduced Density Function (RDF) analysis has ben developed into a rapid analytical tool for the analysis of small volumes of amorphous or polycrystalline materials. The energy filtered electron diffraction pattern is collected to high scattering angles (currendy to s = 2 sinθ/λ = 6.5 Å-1) by scanning the selected area electron diffraction pattern across the entrance aperture to a GATAN parallel energy loss spectrometer. The diffraction pattern is then converted to a reduced density function, G(r), using mathematical procedures equivalent to those used in X-ray and neutron diffraction studies.Nearest neighbour distances accurate to 0.01 Å are obtained routinely, and bond distortions of molecules can be determined from the ratio of first to second nearest neighbour distances. The accuracy of coordination number determinations from polycrystalline monatomic materials (eg Pt) is high (5%). In amorphous systems (eg carbon, silicon) it is reasonable (10%), but in multi-element systems there are a number of problems to be overcome; to reduce the diffraction pattern to G(r), the approximation must be made that for all elements i,j in the system, fj(s) = Kji fi,(s) where Kji is independent of s.

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Morphology and atomic structure of segregated grain boundaries in Cu-Sb

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121673 ◽

1992 ◽

Vol 50 (1) ◽

pp. 254-255

Author(s):

R. W. Fonda ◽

D. E. Luzzi

Keyword(s):

Grain Boundary ◽

Grain Boundaries ◽

Intergranular Fracture ◽

Atomic Structure ◽

Copper Alloys ◽

Polycrystalline Materials ◽

Grain Boundary Embrittlement ◽

Boundary Embrittlement

The properties of polycrystalline materials are strongly dependant upon the strength of internal boundaries. Segregation of solute to the grain boundaries can adversely affect this strength. In copper alloys, segregation of either bismuth or antimony to the grain boundary will embrittle the alloy by facilitating intergranular fracture. Very small quantities of bismuth in copper have long been known to cause severe grain boundary embrittlement of the alloy. The effect of antimony is much less pronounced and is observed primarily at lower temperatures. Even though moderate amounts of antimony are fully soluble in copper, concentrations down to 0.14% can cause grain boundary embrittlement.

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Interface structures in polycrystalline ceramic materials

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143900 ◽

1986 ◽

Vol 44 ◽

pp. 468-471

Author(s):

K. J. Morrissey

Keyword(s):

Electron Microscopy ◽

Analytical Electron Microscopy ◽

Physical And Mechanical Properties ◽

High Resolution Electron Microscopy ◽

Ceramic Materials ◽

Polycrystalline Materials ◽

Transmission Electron ◽

Resolution Electron ◽

Interface Structures

Grain boundaries and interfaces play an important role in determining both physical and mechanical properties of polycrystalline materials. To understand how the structure of interfaces can be controlled to optimize properties, it is necessary to understand and be able to predict their crystal chemistry. Transmission electron microscopy (TEM), analytical electron microscopy (AEM,), and high resolution electron microscopy (HREM) are essential tools for the characterization of the different types of interfaces which exist in ceramic systems. The purpose of this paper is to illustrate some specific areas in which understanding interface structure is important. Interfaces in sintered bodies, materials produced through phase transformation and electronic packaging are discussed.

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Electron diffraction studies of amorphous and polycrystalline thin films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173728 ◽

1990 ◽

Vol 48 (4) ◽

pp. 118-119

Author(s):

D J H Cockayne ◽

D R McKenzie

Keyword(s):

Thin Films ◽

Electron Diffraction ◽

Polycrystalline Materials ◽

Good Resolution ◽

Scattered Intensity ◽

Radial Density ◽

X Ray ◽

Polycrystalline Thin Films ◽

Nitrogen Ion ◽

Diffraction Patterns

The study of amorphous and polycrystalline materials by obtaining radial density functions G(r) from X-ray or neutron diffraction patterns is a well-developed technique. We have developed a method for carrying out the same technique using electron diffraction in a standard TEM. It has the advantage that studies can be made of thin films, and on regions of specimen too small for X-ray and neutron studies. As well, it can be used to obtain nearest neighbour distances and coordination numbers from the same region of specimen from which HREM, EDS and EELS data is obtained.The reduction of the scattered intensity I(s) (s = 2sinθ/λ ) to the radial density function, G(r), assumes single and elastic scattering. For good resolution in r, data must be collected to high s. Previous work in this field includes pioneering experiments by Grigson and by Graczyk and Moss. In our work, the electron diffraction pattern from an amorphous or polycrystalline thin film is scanned across the entrance aperture to a PEELS fitted to a conventional TEM, using a ramp applied to the post specimen scan coils. The elastically scattered intensity I(s) is obtained by selecting the elastically scattered electrons with the PEELS, and collecting directly into the MCA. Figure 1 shows examples of I(s) collected from two thin ZrN films, one polycrystalline and one amorphous, prepared by evaporation while under nitrogen ion bombardment.

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