Explicit model for ultrasonic attenuation in equiaxial hexagonal polycrystalline materials.
L Yang1, O I Lobkis, S I Rokhlin
1The Ohio State University, Department of Materials Science and Engineering, Edison Joining Technology Center, 1248 Arthur E. Adams Dr., Columbus, OH 43221, USA.
Ultrasonics
|November 2, 2010
Summary
This study provides explicit equations for ultrasonic wave attenuation in hexagonal polycrystalline materials. These formulas aid in microstructure characterization and accurately predict experimental results without adjustable parameters.
Area of Science:
- Materials Science
- Acoustics
- Solid Mechanics
Background:
- Ultrasonic wave attenuation is crucial for material characterization.
- Existing models may lack explicit forms or broad applicability for polycrystalline materials.
- Understanding wave scattering mechanisms is key to microstructure analysis.
Purpose of the Study:
- To derive explicit equations for ultrasonic attenuation coefficients in untextured hexagonal polycrystalline materials.
- To provide a model for interpreting and evaluating experimental ultrasonic data.
- To establish a framework for analyzing wave scattering and microstructure interactions.
Main Methods:
- Derivation of analytical expressions for attenuation coefficients.
- Separation of attenuation into terms for longitudinal and transverse wave scattering.
- Analysis of long wavelength (Rayleigh) and short wavelength (stochastic) scattering regimes.
- Development of equations for estimating the transition frequency range.
Main Results:
- Explicit formulas for longitudinal and transverse wave attenuation coefficients were obtained.
- The derived expressions correctly transition to classical asymptotics in Rayleigh and stochastic regimes.
- A method for estimating the transition frequency between scattering regimes was developed.
- Experimental validation using a Ti alloy demonstrated good agreement with the model.
Conclusions:
- The derived explicit equations offer a practical tool for ultrasonic microstructure characterization.
- The model accurately describes wave attenuation across different scattering regimes.
- The findings are applicable to untextured hexagonal polycrystalline materials, validated by experimental data.
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