A theoretical approach towards the modeling of vibrothermography using finite element methods

Abstract

Vibrothermography offers the capability to detect surface cracks mainly through capturing vibration-induced frictional heat generation of contacting crack surfaces in metallic alloys. The multidisciplinary nature of this inspection technology makes it rather difficult to theoretically capture the system response without the proper application of finite element methods (FEM). It requires relating the material mechanical and thermal properties in a coupled finite element model to properly address wave propagation, contact mechanics, fracture mechanics, friction heat generation and heat diffusion in simulated vibrothermography inspections. In this study, a theoretical model is developed to estimate the dynamic strain response at any location in commonly used cantilever beams oscillating at a given frequency. This model is utilized to assess the convergence of FEM dynamic system response while determining the element size requirements to realistically model elastic wave propagation throughout the sample. Three different meshing criteria are assessed to properly capture the singularity at the crack tip. It is demonstrated that the use of solid element circular meshing criteria around the crack tip converges to singular quarter-node solid element solution commonly used in fracture mechanics and allows coupling it with heat generation and diffusion around the vicinity of a crack to deliver a practical approach for modelling vibrothermography. This effort brings FEM a step closer towards realistic simulation of vibrothermography in the future.