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Hardened-layer depth measurement without prior velocity knowledge: An experimental study using FMC phased-array
Fei Hui1, Shupeng Geng1, Lei Zhang2
1School of Mechanical Engineering, Inner Mongolia University of Science and Technology, Inner Mongolia 014010, China.
Ultrasonics
|February 19, 2026
Summary
This study introduces a new ultrasonic method for measuring hardened-layer depth in steels without needing prior sound velocity data. The technique accurately determines depth, improving quality control for steel surfaces.
Area of Science:
- Materials Science
- Non-destructive Testing
- Ultrasonic Testing
Background:
- Hardened-layer depth is crucial for steel surface properties like strength and wear resistance.
- Conventional methods often require pre-existing knowledge of sound velocity, limiting their applicability.
- Phased-array full matrix capture (FMC) offers a potential alternative for quantitative measurements.
Purpose of the Study:
- To develop and validate a quantitative ultrasonic approach for hardened-layer depth measurement.
- To eliminate the need for prior knowledge of sound velocity in the hardened region.
- To provide a more reliable method for evaluating hardened-layer quality in engineering.
Main Methods:
- Utilized phased-array full matrix capture (FMC) with common-midpoint (CMP) gathers.
- Introduced an energy-stacking velocity inversion scheme to estimate sound velocities.
- Applied Kirchhoff integral migration for interface imaging using inverted velocities.
Main Results:
- Successfully measured base-material (5960 ± 10 m/s) and hardened-region (6020 ± 10 m/s) velocities.
- Achieved an average hardened-layer depth error of 2.3%, with inverted velocity differing by less than 1% from metallography.
- Demonstrated improved interface resolution and depth estimation compared to B-scan and TFM.
Conclusions:
- The proposed ultrasonic method accurately measures hardened-layer depth without prior velocity information.
- This quantitative approach offers enhanced resolution and reliability for engineering applications.
- The technique provides a practical solution for non-destructive quality evaluation of hardened steels.

