Simulation of Ultrasonic Beam Propagation From Phased Arrays in Anisotropic Media Using Linearly Phased Multi-Gaussian Beams

Abstract

Phased array ultrasonic testing is widely used to test structures for flaws due to its ability to produce steered and focused beams. The inherent anisotropic nature of some materials, however, leads to skewing and distortion of the phased array beam and consequently measurement errors. To overcome this, a quantitative model of phased array beam propagation in such materials is required, so as to accurately model the skew and the distortion. The existing phased array beam models which are based on exact methods or numerical methods are computationally expensive or time consuming. This article proposes a modeling approach based on developing the linear phased multi-Gaussian beam (MGB) approach to model beam steering in anisotropic media. MGBs have the advantages of being computationally inexpensive and remaining non-singular. This article provides a comparison of the beam propagation modeled by the developed ordinary Gaussian beam and linear phased Gaussian beam models through transversely isotropic austenitic steel for different steering angles. It is shown that the linear phased Gaussian beam model outperforms the ordinary one, especially at steering angles higher than 20 • in anisotropic solids. The proposed model allows us to model the beam propagation from phased arrays in both isotropic and anisotropic media in a way that is computationally inexpensive. As a further step, the developed model has been validated against a finite element model (FEM) computed using COMSOL Multiphysics.

A Gaussian Beam Based Recursive Stiffness Matrix Model to Simulate Ultrasonic Array Signals from Multi-Layered Media

“…The reflection coefficient can be calculated using the below equation [18]: (8) where S 33 mn is the (3,3) component of the constitutive matrices of S and…”

“…where β(ω) is the combined system function for a pair of transducer and receiver elements, R(k x 1 , 0) is the reflection coefficient of the entire structure calculated using Equation (8), and x 1 is the distance between jth element and the receiver position.…”

“…The reflection coefficient was obtained by evaluating Equation (8) for the materials in Table 1 at different frequencies and for normal incidence. The reflection coefficient is given in Figure 3a Figure 3a,b shows the reflection coefficients for aluminium and CFRP, respectively.…”

“…An alternative technique using multi-Gaussian beams to model the transducer radiation was proposed by Huang et al for isotropic materials [ 7 ]. This was extended for phased array radiation through anisotropic media [ 8 ]. This method can be used for planar or nonplanar composites but is computationally very expensive due to the number of beams that need to be traced in a multi-layered media.…”

Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media

“…A variety of approaches to simulate the array signals from multilayered materials have been reported in the literature. These approaches include applying ray methods to a homogenized layered structure [ 8 ], using hybrid ray–finite difference time domain (FDTD) methods [ 9 ], multi-Gaussian beams [ 10 , 11 ], or using plane wave models to calculate the reflection or transmission of the waves in the bounding media [ 12 , 13 , 14 , 15 ]. These approaches are either computationally expensive when used for layered materials, singular when interacting with curved interfaces, or do not reflect the real-world situation of bounded beams.…”