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Simulation of Inspection Process for Functionally Graded Materials by Ultrasonic Time of Flight Diffraction Technique

This paper discusses simulation analysis of the time of flight diffraction (TOFD) technique for functionally graded materials (FGMs) having varied and continuous mechanical properties along their thickness. In this study, material characteristics of FGMs were assumed as an exponential model. TOFD is an ultrasonic nondestructive testing technique used to recognize and measure discontinuities and faults in parts. The TOFD technique is based on diffraction phenomena and is usually used for parts thicker than 15 mm. An important problem in the simulation of ultrasonic waves is related to undesired wave reflections from the boundaries. This point is considered as a limit for the simulation of waves. To solve this problem for time-dependent problems, one has to assume larger dimensions of part geometry. Consequently, this leads to a considerable increase in the number of elements and, subsequently, an extended time to solve the problem. In this paper, the infinite element technique was used for the proposed modeling of the procedure. Infinite elements are special types of elements with characteristics capable of being used in connection with standard finite elements; thus, it is possible to model a plate with infinite dimensions using these elements. In this paper, ultrasonic waves in a sample containing undersurface notches and the interaction of these waves with the notches were observed. Two conditions were considered in simulations of the TOFD technique: in the first, only the elasticity modulus was changed across the plate and in the form of the nth power ratio of the depth-to-plate thickness (Equation 3); and in the second, both the density and elasticity moduli were changed in the form of the nth power ratio of the depth-to-plate thickness. Results show that, by changing only the elasticity modulus, the time of receiving signals to the receiver probe increases with the n-index increment. Furthermore, in a condition where both modulus and density change, the time of arrival signals remain constant and the amplitude of received waves increases with any amount of increase in the exponential sign.

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