Scattering of Elastic Waves from Inhomogeneities in Solids - Application to Ultrasonic NDT
Doctoral thesis, 2002
The subject of this thesis is scattering of elastic waves from inhomogeneities in solids, with applications to ultrasonic nondestructive testing (NDT). The major part of the work concerns cracks in anisotropic solids, but the interaction of Lamb waves with circular holes in plates is considered as well. Linear elastodynamic theory is used to model the scattering problems.
In the part of the thesis where scattering of elastic waves by cracks in anisotropic solids is treated, a technique in which the scattering problem is formulated as an integral equation for the crack opening displacement (COD), by means of the Green's function, is employed. The total field in the solid can be determined once the COD has been evaluated. The integral equation is solved by expanding the COD in suitable expansion functions, which have the correct behaviour along the crack edges, followed by a projection onto the same set of functions. For all the considered crack scattering problems, complete ultrasonic NDT situations are modelled, including models for both transmitting and receiving probes. An electromechanical reciprocity relation is used to model the electrical signal in the receiver.
The scattering problem of a strip-like crack in a layered anisotropic solid has been considered for 2-D and 3-D geometries. The scattering by a rectangular crack in an anisotropic solid, without layering but with or without a planar back-surface, has also been treated. The geometry of the crack suggests how the COD best should be expressed. For a strip-like crack, a single series expansion of the COD is used, while a double series expansion of the COD is best suited for a rectangular crack.
The scattering of Lamb waves from circular through or partly through-thickness holes in isotropic plates is also considered. A mode expansion technique is used to evaluate the scattered field by employing the boundary conditions at the hole. The predicted results are validated by finite element simulations and experimental measurements for the through-thickness hole, and by a plate theory approach for the partly through-thickness hole.