The effect of using fractional single and dual-phase lag on temperature distributions during laser drilling process

Abstract

Abstract This study presents the development and validation of a mathematical model designed to simulate laser beam percussion micro-drilling in the aerospace nickel-based superalloy Hastelloy X, using microsecond-pulsed lasers. The primary objective is to accurately predict and optimize hole quality by minimizing taper angles and inlet/outlet diameters while enhancing inlet circularity. The research incorporates five non-Fourier heat conduction models, encompassing both classical and fractional frameworks, to effectively characterize the laser drilling process. These models account for the influence of single and dual phase-lags on temperature distribution and resultant hole geometry. The governing equations are systematically resolved using L1 and L2 approximation techniques for time-fractional derivatives, coupled with the meshless local Petrov-Galerkin method to address spatial derivatives. The validation process involves comparing the inlet and outlet diameters, as well as taper angles of drilled holes, against both experimental data and finite element model predictions. This study introduces a more realistic representation of heat propagation, thereby enhancing the accuracy of the results. Furthermore, both the fractional single-phase lag and dual-phase lag models reduce error rates in predicting diameters and taper angles compared to traditional models. Notably, the fractional dual-phase lag model demonstrates superior performance, achieving minimal errors of 1.6% and 15% in the inlet and outlet diameters, respectively, along with a relatively low taper angle error of 0.573°, closely aligning with experimental observations. This advanced modelling framework significantly optimizes micro-drilling quality, particularly in high-performance aerospace alloys.