Angle Beam Nondestructive Testing

Introduction

Ultrasonic testing is useful for detecting the flaws in solid objects, mainly metals.

The emitted ultrasonic signal frequency varies from 1 to 10 MHz.

The operating principle of an angle beam transducer lies in the generation of a refracted wave that propagates in the test sample at a certain angle, typically 45˚, 60˚, or 70˚.

A flaw in the test sample results in a reflection of the wave that is detected by the transducer (the same that emits the signal or a different one).

The transducer sends an ultrasonic longitudinal (pressure) wave of the speed 𝑐p1 through the wedge, typically made of acrylic glass, at an angle 𝛼.

The incident wave results in refracted longitudinal and shear waves that propagate in the test sample with the speeds 𝑐p2 and 𝑐s2, respectively.

The angles of refraction are defined according to Snell’s law as

sin 𝛼

𝑐p1=sin𝛽

𝑐p2=sin 𝛾

𝑐s2.

The angles 𝛼 that yield 𝛽 = 90∘ and 𝛾 = 90∘ are called the first and the second critical angles, respectively.

Theory

Test sample

Incident pressure wave path

Ultrasonic transducer wedge

Flaw

Refracted pressure wave path

Refracted shear wave path

In this model, the transducer wedge is made of acrylic plastic and the test sample of aluminum.

The refracted shear wave propagates at the angle 𝛽 = 45∘, which results in 𝛼 = 28∘.

The angle of incidence is greater than the first critical angle for the given pair of materials, 𝛼cr1 = 19.6∘.

This means that the refracted longitudinal wave skims along the test sample surface.

Model Setup

Test sample

Incident pressure wave path

Ultrasonic transducer wedge

Flaw

Refracted pressure wave path

Refracted shear wave path

The model uses the Elastic Waves, Time Explicit physics interface that implements the time-explicit discontinuous Galerkin finite element method (dG-FEM).

The source signal is given by a modulated Gaussian pulse with a center frequency 𝑓0 = 1.5 MHz.

The Absorbing Layers together with the Low-Reflecting Boundary condition imposed at the left and the right sides of the test sample suppress spurious reflections from its ends.

The use of a geometry assembly and the Continuity pair boundary condition makes it possible to have nonconforming meshes at the transducer wedge/test sample interface.

Model Setup

Absorbing layer

Continuity pair boundary condition

Absorbing layer

Results

Velocity magnitude profiles at 3, 6, 9, and 12 µs: wave refraction and reflection from the flaw are clearly seen.

Results

Average pressure signal over the transducer surface: The reflection from the flaw is registered at 𝒕 ≈ 𝟏𝟓 µs.

Conclusions

The Elastic Waves, Time Explicit interface shows high efficiency in the applications that require modeling of transient wave propagation in linear elastic media

• Solving for 5.5 ⋅ 105 DOFs in this model only required 1.7 GB of RAM.

• Increasing the signal frequency twice results in 2.1 ⋅ 106 DOFs and requires 3 GB of RAM.

• The use of the Solid Mechanics interface (that is based on a time-implicit second-order FEM method) to solve the same problems results in poor scaling and higher consumption of RAM: 4 GB and 11.5 GB for 𝑓0 and 2𝑓0, respectively.

Taking advantage of the geometry assembly and the nonconforming mesh reduces the number of DOFs and the computational time.

The use of Absorbing Layers and Low-Reflecting Boundary conditions makes it possible to model the wave propagation in an unbounded domain.

Further Resources for Inspiration comsol.com

Further Resources for Inspiration comsol.com