Design of Ultrasonic Probe Configuration Using Finite-Difference Time Domain Simulation

Abstract

An analysis tool has been developed for optimizing ultrasonic transmitter-receiver configurations for in-situ monitoring of crack propagation during cyclic loading in order to develop better crack tip models for fatigue life estimation. Time-of-flight diffraction technique is simulated using finite-difference time-domain method to study the interaction of ultrasonic waves from probes with defects/cracks. Governing equations relating velocities to stresses are discretized using central finite-difference formulation and solved on a staggered grid in an explicit time-marching scheme, with velocity and stress components offset in time and space. This leads to a leap frog scheme in which the velocity and stress components are calculated alternately from each other. Grid size is taken as the ratio of minimum wavelength and number of steps per wavelength $(N = \text {15} -\text {20})$ to ensure stability. Time step is obtained from Courant stability criteria. Defect surface is modelled as traction-free. Perfectly matching layer with small damping factor is applied to minimize the amplitude of waves reflected from boundaries created at the edges of domain. Simulation matches well with results from finite element model using ABAQUS / EXPLICIT solver. FDTD method can be used for designing optimum transmitter-receiver configuration since it is computationally less expensive and easy to implement as compared to FEM.