A simple heat diffusion model to avoid singularity in estimating a crack length using sonic infrared inspection technology

• Published in: Sensors and actuators. A. Physical. 2019-07, Vol.293, p.77-86
• Main Authors: Abu-Nabah, Bassam A., Al-Said, Samer M., Gouia-Zarrad, Rim
• Format: Article
• Language: English
• Subjects: Aging aircraft; Aircraft components; Algorithms; Crack length; Crack propagation; Diffusion; Estimation; Exact solutions; Excitation; Fatigue cracks; Fatigue failure; Finite element analysis; Finite element method; Heat diffusion; Heat generation; Infrared inspection; Inspection; Inversion; Materials fatigue; Mathematical models; Nondestructive testing; Sensors; Sonic infrared; Three dimensional models; Two dimensional analysis; Two dimensional models
• ISSN: 0924-4247; 1873-3069
• DOI: 10.1016/j.sna.2019.03.001

[Display omitted] •Delivered forward analytical solution of a simple 2D heat diffusion model assuming uniform frictional heat generation along the crack.•Estimated the temperature rise and decay while applying the excitation load and after it stops, respectively.•Delivered an inverse model to estimate a crack length going under sonic IR inspection.•Demonstrated the benefits of applying predetermined heat source function to avoid singularity in crack length estimation.•Validated the model using finite element simulation and demonstrated the potential of advancing this approach using experimental data. Sonic infrared (IR) is a rapidly developing nondestructive evaluation technique for detecting and estimating the length of fatigue cracks in aircraft components. In this study, a spatial and temporal forward analytical solution of a simple 2D heat diffusion model is developed assuming uniform frictional heat generation along the crack. This model not only captures the temperature rise while applying the excitation load, but also captures the temperature decay after the excitation load stops. The simple forward analytical solution is validated in close comparison with 2D and 3D finite element modeling (FEM) results. With a validated forward model, an inversion algorithm is proposed to estimate the crack length independent of heat source values. The use of predetermined heat source function of uniform heat generation along the crack avoids singularity in estimating a crack length while feeding temperature change along but also around the crack to the inversion algorithm. The proposed algorithm showed high accuracy in predicting a crack length using thermal images generated from 2D and 3D FEM data with and without randomly added virtual temperature uncertainties. Moreover, the temperature-based inversion model as a method of estimating a crack length is tested against experimental sonic IR data to illustrate the potential capabilities of advancing this model.