Flexural-guided-wave mode F(1,1) based inspections for small-bore tubes with bends

Small-bore tubes, which typically serve as critical industrial components, are challenging to inspect due to their inaccessibility and small dimensions. This paper investigates inspections of small-bore tubes with bends using the flexural guided-wave mode F(1,1). A magnetostrictive patch transducer for F(1,1) excitation is proposed, sharing the same architecture as conventional T(0,1) transducers but driven by opposite alternating currents. To address the challenge arising from the significant curvature of small-bore tubes when exciting pure F(1,1) modes, magnetic field simulations were performed to optimize the transducer's magnetic field uniformity and directivity. The wave motion of F(1,1) is thoroughly studied. It is found that the F(1,1) mode has two focusing regions separated by 90 degrees in circumstance, one for the circumferential vibration focus and the other for the radial vibration focus. Then, the scattering of the F(1,1) mode with varying circumferential or radial focusing positions as it propagates through the bend is numerically analyzed. It is found that when the F(1,1) mode's circumferential displacement focus aligns with the outward bend, it converts to the T(0,1) mode with each passage through the bend, with no L(0,1) mode generated, and the wave energy at the outward bend is enhanced. When the F(1,1) mode's radial displacement focus aligns with the outward bend, it converts to the L(0,1) mode with no T(0,1) mode observed, and the wave energy is further focused at the inward bend. When the F(1,1) mode's circumferential displacement focus is located 45° from the outward bend, both the T(0,1) and L(0,1) modes are scattered. Experiments were conducted to validate the F(1,1) excitation and the numerical simulation results for F(1,1) bend scattering. Furthermore, F(1,1)-based inspections of bent tubes were conducted to experimentally assess the bend scattering behavior and defect detectability. The weak reflections of the F(1,1) mode from the bend itself do not mask flaw signals, thereby enabling the effective detection of crack-like defects with a 6% cross-sectional area loss. The F(1,1) mode with its circumferential displacement focus aligned with the outward bend is more sensitive to flaws located at the outward bend, whereas the F(1,1) mode with its radial displacement focus aligned with the outward bend is more sensitive to flaws located at the inward bend, in good agreement with the simulation results.