Thermal and Phase-Transformation Stresses in Matrix-Whisker Composites II

Vorschau

Leseprobe, PDF (16 KB)
Inhaltsverzeichnis, PDF (40 KB)

This book presents original mathematical models for analyzing thermal and phase-transformation stresses in three-component materials. These materials consist of an isotropic matrix, cylindrical particles (whiskers), and a cylindrical envelope around the particles. The stresses are caused by differences in thermal expansion coefficients and crystalline lattice structures during cooling and phase transformation processes.

The models are based on the mechanics of elastic continua and involve:

• A detailed description of the material system’s geometry and parameters, including particle volume fraction, dimensions, and spacing.

• Use of cylindrical coordinate systems to reflect the geometry of the particles.

• Application of Cauchy’s equations, equilibrium equations, and Hooke’s law to derive the stress and strain states.

• Consideration of boundary conditions and the principle of minimum total potential energy to determine valid solutions.

The book also outlines:

• The derivation of differential equations using separation of variables,

• Analytical and numerical procedures for stress computation,

• Final formulas for both thermal and phase-transformation stresses in the matrix and particles.

The presented models are applicable to real materials like martensitic and dual-phase steels, where different phases or grains interact mechanically during thermal or structural changes.