# Macroscopic engineering properties of polycrystalline materials: Elastic properties

@article{Gubernatis1975MacroscopicEP, title={Macroscopic engineering properties of polycrystalline materials: Elastic properties}, author={James E. Gubernatis and James A. Krumhansl}, journal={Journal of Applied Physics}, year={1975}, volume={46}, pages={1875-1883} }

We outline the formal application of integral equation methods (Green’s function techniques) to the systematic computation of the effective elastic properties of polycrystalline materials from the specification of the statistical distribution of elastic properties of the constituent grains (or pores). These methods are not entirely new, but by the use of recent developments in theory of the physics of the electronic porperties and lattice dynamics of disordered solids, we can place various…

## 162 Citations

### Elastic Properties of Polycrystals: A Review

- Materials Science
- 1990

The elastic properties of polycrystals depend on the single-crystal elastic constants of the crystallites
which build up the polycrystal and on the manner in which the crystallites are connected.…

### Thermal Conductivity of Polycrystalline Materials

- Materials Science
- 1995

A three-dimensional Poisson-Voronoi tessellation model is used to simulate the microstructure of polycrystalline materials consisting of random shape and size grains. The model is used to calculate…

### Self-consistent T-matrix calculation of the pressure derivative of elastic constants for polycrystals

- Engineering
- 1986

### Uncertainty limits for the macroscopic elastic moduli of random polycrystalline aggregates

- Materials Science
- 2000

Practical polycrystalline aggregates are expected to have macroscopic properties that depend upon the properties of constituent crystals and the aggregate geometry. Since that microgeometry is…

### The elasticity of polycrystals and rocks

- Materials Science
- 1975

We calculate the effective elastic properties of various polycrystals and rocks using a self-consistent integral equation technique developed in the theory of disordered alloys. This technique…

### Theory of elastic properties of composite materials

- Physics
- 1979

A new method of estimating effective macroscopic elastic constants for microscopically inhomogeneous materials is formulated using elastic‐wave scattering theory. The self‐consistent medium is…

### Mechanical Properties of Composites

- Engineering
- 1982

Determination of macroscopic mechanical properties of heterogeneous media from the properties of their constituents is a problem of long standing in the mechanics of solids. Current activity in the…

### The Elastic Properties of Composite Materials

- Materials Science
- 1976

The determination of the elastic properties of composite materials (multiphase aggregates, polycrystals, and porous or cracked solids) from the elastic properties of the components may be approached…

## References

SHOWING 1-10 OF 17 REFERENCES

### Elastic-plastic behaviour of polycrystalline metals and composites

- Materials ScienceProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1970

Stress-strain behaviour of polycrystals and composites is explored with self-consistent models based on the elastic-plastic properties of the single crystal constituents. Based on Hill’s (1965a)…

### Elastic Constants of Polycrystals

- Engineering
- 1973

The elastic constants of polycrystals and similar disordered materials are calculated. Exact formal solutions for the effective tensors of the elastic constants and of the compliances are given.…

### Theory of elastic constants of heterogeneous media

- Mathematics
- 1973

The theory of elastic equilibrium of heterogeneous, macrohomogeneous bodies is cast in the form of a linear integral equation with the following properties: (1) The equation contains a constant…

### Statistical Continuum Theories

- Physics
- 1965

There are presently a large number of problems in continuum physics that may be treated from a statistical point of view. In this paper we shall discuss what is meant by the statistical solution to a…

### Effective Dielectric Constant, Permeability, and Conductivity of a Random Medium and the Velocity and Attenuation Coefficient of Coherent Waves

- Geology, Physics
- 1966

Random media are considered in which the dielectric constant, permeability, and conductivity are random functions of position. For them, the average electric field, electric current, dielectric…