Evaluation of Non-Uniform Deformation Behavior of Polycrystalline Materials Using Second-Order Homogenization Method

To evaluate the effect of the size of the microstructure on the mechanical property of the cavitated rubber blended (voided) amorphous polymer, the FEM simulation based on the rate form second-order homogenization method, in which rates of the macroscopic strain and strain gradient are given to the microstructure, was performed. Computational simulations of micro-to macroscopic deformation behaviors of amorphous polymers including different sizes and volume fractions of the voids were performed. Non-affine molecular chain network theory was employed to represent the inelastic deformation behavior of the amorphous polymer matrix. With the increase in the volume fraction of the void, decrease and periodical fluctuation of stress and localized deformation in the macroscopic field were observed, and were more emphasized with the increase in the size of the void. These results were closely related to the non-uniform deformation and volume increase of the void in the microscopic field.

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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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A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients

Journal of Function Spaces ◽

10.1155/2021/8036814 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Xiong Liu ◽

Wenming He

Keyword(s):

Elliptic Problem ◽

Homogenization Method ◽

Second Order ◽

Homogenization Theory ◽

High Demand ◽

Periodic Coefficients ◽

Order Elliptic Problem ◽

Multiscale Homogenization

In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂ / ∂ x i a i j x / ε , x ∂ u ε x / ∂ x j = f x . Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u 0 , we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u 0 satisfies than the classical homogenization theory needs.

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Multiscale computational simulation of deformation behavior of TRIP steel with growth of martensitic particles in unit cell by asymptotic homogenization method

International Journal of Plasticity ◽

10.1016/j.ijplas.2003.05.002 ◽

2004 ◽

Vol 20 (4-5) ◽

pp. 841-869 ◽

Cited By ~ 57

Author(s):

Takeshi Iwamoto

Keyword(s):

Trip Steel ◽

Deformation Behavior ◽

Computational Simulation ◽

Homogenization Method ◽

Unit Cell ◽

Asymptotic Homogenization ◽

Asymptotic Homogenization Method

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Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

Acoustics ◽

10.3390/acoustics2010005 ◽

2020 ◽

Vol 2 (1) ◽

pp. 51-72

Author(s):

Gaofeng Sha

Keyword(s):

Phase Velocity ◽

Orientation Distribution ◽

Wave Mode ◽

Homogenization Method ◽

Crystal Symmetry ◽

Polycrystalline Materials ◽

Phase Velocity Dispersion ◽

Static Phase ◽

Generalized Spherical Harmonics ◽

The Impact

This study extends the second-order attenuation (SOA) model for elastic waves in texture-free inhomogeneous cubic polycrystalline materials with equiaxed grains to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. In term of this work, one can predict both the scattering-induced attenuation and phase velocity from Rayleigh region (wavelength >> scatter size) to geometric region (wavelength << scatter size) for an arbitrary incident wave mode (quasi-longitudinal, quasi-transverse fast or quasi-transverse slow mode) in a textured polycrystal and examine the impact of crystallographic texture on attenuation and phase velocity dispersion in the whole frequency range. The predicted attenuation results of this work also agree well with the literature on a textured stainless steel polycrystal. Furthermore, an analytical expression for quasi-static phase velocity at an arbitrary wave propagation direction in a textured polycrystal is derived from the SOA model, which can provide an alternative homogenization method for textured polycrystals based on scattering theory. Computational results using triclinic titanium polycrystals with Gaussian orientation distribution function (ODF) are also presented to demonstrate the texture effect on attenuation and phase velocity behaviors and evaluate the applicability and limitation of an existing analytical model based on the Born approximation for textured polycrystals. Finally, quasi-static phase velocities predicted by this work for a textured polycrystalline copper with generalized spherical harmonics form ODF are compared to available velocity bounds in the literature including Hashin–Shtrikman bounds, and a reasonable agreement is found between this work and the literature.

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Evaluation of Non-Uniform Deformation of Multi-Layered Ceramic Sheets with Printed Electrodes during Compression

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.418-420.1647 ◽

2011 ◽

Vol 418-420 ◽

pp. 1647-1653

Author(s):

Fumio Naruse ◽

Naoya Tada

Keyword(s):

Deformation Behavior ◽

Recent Trend ◽

Video Camera ◽

Transverse Displacement ◽

Compression Tests ◽

Electronic Components ◽

Uniform Deformation ◽

Digital Video Camera ◽

Layered Ceramic

With the recent trend of down-sizing and more efficient use of electric power in electric appliances, there is a growing need of smaller electronic components, such as multi-layered ceramic capacitors (MLCCs). However, it was found that the non-uniform deformation occurred in MLCC block during the pressing process and it hinders the miniaturization of MLCCs. In this study, compression tests of multi-layered ceramic sheets with printed electrodes were carried out and the deformation behavior was observed in situ and recorded by digital video camera. The change in area fraction and transverse displacement were evaluated and the deformation mechanism was inferred from the results.

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