Modeling of the detection of surface-breaking cracks by laser ultrasonics

A model for the Scanning Laser Source (SLS) technique, a novel laser-based inspection method for the ultrasonic detection of small surface-breaking cracks, is presented. The modeling approach is based on the decomposition of the field generated by a line-focused laser in a half-space containing a surface-breaking crack, by using linear superposition of the incident and the scattered fields. The incident field is that generated by laser illumination of a defect-free half-space. A model which accounts for the effects of thermal diffusion and optical penetration, as well as the finite width of the line-source and the duration of the laser pulse, is formulated, and solved by Fourier-Laplace transform techniques. The inversion of the transforms is performed numerically. The well-known dipole model follows from appropriate limits, and it is shown by simple elasticity arguments that the strength of the dipole can be related a-priori to the heat input and certain material properties. Some illustrative results provide insight on the relevance of the different mechanisms that have been taken into account in the model. The scattered field incorporates the interactions of the incident field with the surface-breaking crack. It is analyzed numerically by the boundary element method. A simple and elegant technique for the treatment of non-decaying Rayleigh waves propagating along the unbounded surface of a half-spaces is developed and verified. An efficient practical implementation of the method is obtained by an application of the reciprocal theorem of elastodynamics. A computational exploration of the acoustic emissions from nucleating cracks which benefits from this numerical technique is presented. Simulations of the SLS technique are compared with an experiment for a large defect, showing that the model captures the observed phenomena. An example for a small crack illustrates the ability of the SLS technique to detect small defects, beyond the sensitivity of conventional ultrasonic methods.