Home - Education Resources - NDT Course Material - Ultrasound

Introduction to Ultrasonic Testing

Basic Principles
Present State
Future Direction

Physics of Ultrasound
Wave Propagation
Modes of Sound Waves
Properties of Plane Waves
Wavelength/Flaw Detection
Elastic Properties of Solids

Acoustic Impedance
Refraction & Snell's Law
Mode Conversion
Signal-to-noise Ratio
Wave Interference

Equipment & Transducers
Piezoelectric Transducers
Characteristics of PT
Radiated Fields
Transducer Beam Spread
Transducer Types
Transducer Testing I
Transducer Testing II
Transducer Modeling
Tone Burst Generators
Function Generators
Impedance Matching
Data Presentation
Error Analysis

Measurement Techniques
Normal Beam Inspection
Angle Beams I
Angle Beams II
Crack Tip Diffraction
Automated Scanning
Velocity Measurements
Measuring Attenuation
Spread Spectrum
Signal Processing
Flaw Reconstruction

Calibration Methods
Calibration Methods
DAC Curves
Curvature Correction
Thompson-Gray Model
Grain Noise Modeling

Selected Applications
Rail Inspection

Reference Material
UT Material Properties


Curvature Correction

Curvature in the surface of a component will have an effect on the shape of the ultrasonic beam.  The image to the right shows the beam from a focused immersion probe being projected on to the surface of a component.  Lighter colors represent areas of greater beam intensity.  It can be seen that concave surfaces work to focus the beam and convex surfaces work to defocus the beam.  Similar effects are also seen with contact transducers.  When using the amplitude of the ultrasonic signal to size flaws or for another purpose, it is necessary to correct for surface curvature when it is encountered.  The "correction" value is the change in amplitude needed to bring signals from a curved surface measurement to the flat surface or DAC value.

A curvature correction curve can be generated experimentally in a manner similar to that used to generate a DAC curve,  This simply requires a component with a representative reflector at various distances below the curved surface.  Since any change in the radius will change the focus of the sound beam, it may be necessary to develop reference standards with a range of surface curvatures. 

However, computer modeling can also be used to generate a close approximation of the curvature correction value.  Work by Ying and Baudry (ASME 62-WA175, 1962) and by Birchak and Serabian (Mat. Eval. 36(1), 1978) derived methods for determining "correction factors" to account for change in signal amplitude as a function of the radius of curvature of convex, cylindrical components.

An alternative model for contact and immersion probe inspection was more recently by researchers at the Center for NDE at Iowa State University. This mathematical model further predicts transducer radiation patterns using the Gauss-Hermite model, which has been used extensively for simulation of immersion mode inspections. The resulting model allows computationally efficient prediction of the full ultrasonic fields in the component for

  1. any frequency, including broadband measurements.
  2. both circular and rectangular crystal shapes.
  3. general component surface curvature
  4. both normal and oblique incidence (e.g., angle beam wedges) transducers.

When coupled with analytical models for defect scattering amplitudes, the model can be used to predict actual flaw waveforms.  The image shown above was generated with this model.











The plot to the right shows an example curvature correction curve and DAC curve.  This curvature correction curve was generated for the application of detecting a #4 flat bottom hole under a curved surface as shown in the sketch and photograph.  An immersion techniques was used generate a shear wave since the reflective surface of the target flaw was not parallel with the surface. The DAC curve drops monotonically since the water path ensures that the near field of the sound beam is always outside the part. The correction factor starts out negative because of the focusing effect of the curved surface. At greater depths, the correction factor is positive due to the increased beam spread beyond the focal zone caused by the surface curvature.

A table of correction values and the DAC and curvature correction curves for different size radiuses can be found at the following link.

Click here for the Curvature Correction Table