Analytical Models of Coherent-Interface-Induced Stresses in Composite Materials II


Ladislav Ceniga – Research Professor, Institute of Material Research, Kosice, Slovak Republic

Series: Materials Science and Technologies
BISAC: TEC021000

This book presents original analytical models of coherent-interface-induced stresses in three-component materials. These materials consist of isotropic particles with an isotropic continuous envelope on their surface, where the particles are distributed in an isotropic matrix. Dimensions of an isotropic crystalline lattice of these components are different. The particle and envelope lattices on the particle-envelope boundary, as well as the envelope and matrix lattices on the matrix-envelope boundary, represent a coherent or semi-coherent interface. Due to this interface, the lattices are deformed. The coherent/semi-coherent-interface-induced stresses, which are a consequence of this deformation, exhibit an influence on material properties.

The deformation is usually considered within the boundaries. This well-known concept of the coherent or semi-coherent interfaces, which is applied to a one-particle-matrix system, does not consider the particle volume fraction v, the particle radius R and the inter-particle distance d, which represent fundamental structural characteristics of two-component materials. Accordingly, the one-particle model system does not correspond to real multi-particle materials, e.g., two-component materials.

The analytical models in this book, which are determined for a multi-particle model system with coherent and semi-coherent interfaces on the particle-envelope and matrix-envelope boundaries, consider these characteristics. The deformation is determined within the boundaries, as well as within the particles, envelope and matrix. Additionally, critical values of these characteristics, which are a reason of a transformation of coherent/semi-coherent particle-matrix boundaries to incoherent ones, are determined. If tensile mechanical stresses act at these incoherent boundaries, then cavities are formed around the particles. The cavities represent defects in the matrix, which degrade material properties. These critical values define a limit state with respect to this degradation.

Limit states represent an important phenomenon in material engineering. Analytical models of limit states are a considerable contribution to materials science. Accordingly, this book presents unique analytical results, which are determined for coherent and semi-coherent interfaces at the particle-envelope and matrix-envelope boundaries. These results, which are determined by fundamental equations of solid continuum mechanics, are applicable within basic research (solid continuum mechanics, theoretical physics, materials science), as well as within the practice of engineering.

Table of Contents


Chapter 1. Solid Continuum Mechanics
1.1. Model Material System
1.2. Coordinate System
1.3. Reason of Interface-Induced Stresses
1.4. Fundamental Equations
1.5. Energy of Model Material System
1.6. Limit State
1.7. Analysis of Solutions

Chapter 2. Mathematical Boundary Conditions
2.1. Spherical Particle
2.2. Spherical Envelope
2.3. Cell Matrix

Chapter 3. Analytical Model 1
3.1. Mathematical Procedure 1
3.2. Condition
3.3. Condition
3.4. Condition

Chapter 4. Analytical Model 2
4.1. Mathematical Procedure 1
4.2. Condition
4.3. Condition
4.4. Condition

Chapter 5. Analytical Model 3
5.1. Mathematical Procedure 1
5.2. Condition
5.3. Condition
5.4. Condition

Chapter 6. Appendix
6.1 Cauchy’s and Equilibrium Equations
6.2 Numerical Determination




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