Constitutive Relations of Anisotropic Polycrystals: Self-Consistent Estimates.

Area of Science:

• Materials Science
• Solid Mechanics
• Crystallography

Background:

• Polycrystal elastic properties depend on microstructure and crystal symmetry.
• Existing models often simplify or fail for strongly anisotropic materials.

Purpose of the Study:

• To derive a general elastic constitutive relation for cubic polycrystals.
• To incorporate mesostructure coefficients accurately, especially for anisotropic materials.
• To simplify existing models while maintaining accuracy.

Main Methods:

• Utilized self-consistent estimates of eigenstrain following Budiansky and Wu.
• Derived average elastic constitutive relations for cubic polycrystals with arbitrary orientation symmetry.
• Expanded expressions to include quadratic terms of mesostructure coefficients for anisotropic cases.

Main Results:

• Developed an explicit form for the effective elastic constitutive relation of polycrystals.
• Showed linear terms suffice for weakly anisotropic materials (e.g., aluminum).
• Quadratic terms are necessary and accurately model strongly anisotropic materials (e.g., copper).
• The derived expression is simpler than previous methods (e.g., Morris).

Conclusions:

• The new model provides a more accurate and simpler description of polycrystal elasticity.
• The inclusion of quadratic mesostructure terms is crucial for strongly anisotropic single crystals.
• This work offers a valuable tool for predicting the mechanical behavior of diverse polycrystals.