Calculation of effective elastic moduli of polycrystalline materials including nontextured samples and fiber textures

1994 ◽  
Vol 50 (1) ◽  
pp. 5-16 ◽  
Author(s):  
H. Kiewel ◽  
L. Fritsche
Keyword(s):  
Elastic Moduli ◽  
Polycrystalline Materials ◽  
Effective Elastic Moduli

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.

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.

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.

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