scholarly journals Effect of the Grain Shape on the Elastic Constants of Polycrystalline Materials

1996 ◽  
Vol 28 (1-2) ◽  
pp. 17-33 ◽  
Author(s):  
H. Kiewel ◽  
H. J. Bunge ◽  
L. Fritsche
Keyword(s):  
Boundary Value Problem ◽  
Coordination Number ◽  
Elastic Constants ◽  
Elastic Moduli ◽  
Grain Shape ◽  
Polycrystalline Materials ◽  
Stress And Strain ◽  
Effective Elastic Moduli ◽  
Real Material ◽  
Effective Constants

We examine the influence of the grain shape on the effective elastic moduli of polycrystalline materials. For that purpose the real material is simulated by a cluster of Wigner-Seitz cells. For clarity each aggregate consists of grains with only one type of shape. Therefore we can classify each cluster by the coordination number of its grains. To determine the elastic moduli a homogeneous deformation is subjected to the surface of the cluster. The solution of this boundary value problem yields the average stress and strain governing inside the material whose interconnection by Hooke's law leads to the sought-for effective constants.The most important result is that with increasing coordination number the elastic moduli decrease.

scholarly journals Calculation of Linear and Non-Linear Elastic Properties of Polycrystalline Materials by Use of a Cluster Model

1997 ◽  
Vol 28 (3-4) ◽  
pp. 261-271 ◽  
Author(s):  
H. Kiewel ◽  
H. J. Bunge ◽  
L. Fritsche
Keyword(s):  
Elastic Properties ◽  
Grain Shape ◽  
Cluster Method ◽  
Elastic Behavior ◽  
Polycrystalline Materials ◽  
Linear Elastic ◽  
Effective Elastic Constants ◽  
Real Material ◽  
Non Linear ◽  
Effective Constants

In the present paper we have put together some results of a cluster method that allows the calculation of linear and also non-linear effective elastic constants of polycrystalline materials within an iterative self-consistent scheme. The conceptual idea consists in simulating the real material by a suitably chosen cluster of single grains. One can then determine the elastic properties of the material under study by examining the elastic behavior of the cluster. The method is capable of resolving the effect of the grain shape, that is determined by the coordination number of the grains on the effective constants.

scholarly journals Evaluation of Effective Elastic Properties of Nitride NWs/Polymer Composite Materials Using Laser-Generated Surface Acoustic Waves

2018 ◽  
Vol 8 (11) ◽  
pp. 2319 ◽  
Author(s):  
Evgeny Glushkov ◽  
Natalia Glushkova ◽  
Bernard Bonello ◽  
Lu Lu ◽  
Eric Charron ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Composite Materials ◽  
Elastic Constants ◽  
Acoustic Waves ◽  
Composite Structures ◽  
Elastic Moduli ◽  
Surface Acoustic Waves ◽  
Dispersion Curves ◽  
Effective Elastic Moduli ◽  
Asymptotic Representations

In this paper we demonstrate a high potential of transient grating method to study the behavior of surface acoustic waves in nanowires-based composite structures. The investigation of dispersion curves is done by adjusting the calculated dispersion curves to the experimental results. The wave propagation is simulated using the explicit integral and asymptotic representations for laser-generated surface acoustic waves in layered anisotropic waveguides. The analysis of the behavior permits to determine all elastic constants and effective elastic moduli of constituent materials, which is important both for technological applications of these materials and for basic scientific studies of their physical properties.

Elastic Moduli of Two Dimensional Materials With Polygonal and Elliptical Holes

1994 ◽  
Vol 47 (1S) ◽  
pp. S18-S28 ◽  
Author(s):  
I. Jasiuk ◽  
J. Chen ◽  
M. F. Thorpe
Keyword(s):  
Elastic Constants ◽  
Conformal Transformation ◽  
Elastic Moduli ◽  
Far Field ◽  
Effective Elastic Moduli ◽  
Two Dimensional ◽  
Effective Elastic Constants ◽  
Two Dimensional Materials ◽  
Elliptical Holes ◽  
General Relations

We study the effective elastic moduli of two-dimensional composite materials containing polygonal holes. In the analysis we use a complex variable method of elasticity involving a conformal transformation. Then we take a far field result and derive the effective elastic constants of composites with a dilute concentration of polygonal holes. In the discussion we use the recently-stated Cherkaev-Lurie-Milton theorem, which gives general relations between the effective elastic constants of two-dimensional composites. We also discuss known results for elliptical holes in the context of the present work.

Effective Elastic Moduli of Composite Materials: Reduced Parameter Dependence

1997 ◽  
Vol 50 (11S) ◽  
pp. S39-S43 ◽  
Author(s):  
John Dundurs ◽  
Iwona Jasiuk
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Elastic Moduli ◽  
Plane Elasticity ◽  
Parameter Dependence ◽  
Effective Elastic Moduli ◽  
Independent Variables ◽  
Effective Elastic Constants

In this paper, we focus on the effective elastic constants of composite materials and pay attention to the possibility of reducing the number of independent variables. Surprisingly, this important issue has hardly been explored before. In our analysis, we rely on a new result in plane elasticity due to Cherkaev, Lurie, and Milton (1992), and use Dundurs constants (Dundurs, 1967, 1969). As an example, we consider a result for the effective elastic moduli of a composite containing a dilute concentration of perfectly-bonded circular inclusions.

scholarly journals Calculation of Effective Elastic Moduli of Textured Materials

1995 ◽  
Vol 23 (1) ◽  
pp. 43-59 ◽  
Author(s):  
N. J. Park ◽  
H. J. Bunge ◽  
H. Kiewel ◽  
L. Fritsche
Keyword(s):  
Elastic Moduli ◽  
Expansion Method ◽  
Polycrystalline Materials ◽  
Effective Elastic Moduli ◽  
Actual Material ◽  
Finite Sum ◽  
Textured Materials ◽  
The Hill ◽  
Very High ◽  
Series Expansion Method

Effective elastic constants of polycrystalline materials were determined with a recently developed method. This method bases on the modelation of the actual material by a cluster of 100 to 500 single crystals. In the present version of the scheme parallelepipeds are used. The ODF was calculated with the series expansion method. The transformation of this ODF into a finite sum of single orientations permits to assign any grain an individual orientation.Reliable results for the effective elastic moduli of textured materials are reported. They lie always within the bounds of Voigt and Reuss. The very high anisotropic substances, e.g. shape-memory-alloys, show a significant deviation from the Hill values.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

The dislocations contrast factors of cubic crystals in the Zener constant range between zero and unity

2002 ◽  
Vol 17 (2) ◽  
pp. 104-111 ◽  
Author(s):  
I. C. Dragomir ◽  
T. Ungár
Keyword(s):  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Profile Analysis ◽  
Anisotropy Constant ◽  
Diffraction Peak ◽  
Polycrystalline Materials ◽  
Ionic Crystals ◽  
Strain Anisotropy ◽  
Cubic Crystals ◽  
Lattice Distortions

Diffraction peak profiles broaden due to the smallness of crystallites and the presence of lattice defects. Strain broadening of powders of polycrystalline materials is often anisotropic in terms of the hkl indices. This kind of strain anisotropy has been shown to be well interpreted assuming dislocations as one of the major sources of lattice distortions. The knowledge of the dislocation contrast factors are inevitable for this interoperation. In a previous work the theoretical contrast factors were evaluated for cubic crystals for elastic constants in the Zener constant range 0.5≤Az≤8. A large number of ionic crystals and many refractory metals have elastic anisotropy, Az, well below 0.5. In the present work the contrast factors for this lower anisotropy-constant range are investigated. The calculations and the corresponding peak profile analysis are tested on ball milled PbS and Nb and nanocrystalline CeO2.

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