Physics-based damage prediction index model and angle-matched ultrafast-laser chamfering of amorphous glass substrates

Ultrafast-laser chamfering of amorphous glass substrates is limited by subsurface lateral cracking. Guided by a cause-and-effect (Ishikawa) screening that identified the laser incidence angle as the dominant controllable lever, we formulate a physics-based, semi-empirical Damage Index Ψ = k0 ⋅ M ⋅ Φ ⋅ P, coupling geometric-optical refraction, Fresnel transmission, thermo-mechanical stress, and Lawn–Evans–Marshall lateral-crack fracture mechanics into a single screening criterion. Ψ = 1 is the nominal quasi-static onset (KI = KIC), fixed by one calibration constant at the vertical-incidence reference; all other Ψ values are exactly computable ratios. Two experimentally substantiated conditions bracket crack onset between Ψ = 0.18 (no above-threshold cracking) and Ψ = 1.0 (extensive cracking); within it, a conservative onset band Ψth ≈ 0.5–0.6 is adopted, consistent with sub-critical crack growth in silicate glasses, and the angle-matched condition operates at Ψ ≈ 0.18 (as-built faces ≤ ≈ 0.32; Sec. IV E). At the angle-matched tilt (β ≈ 30°, θ1 ≈ 75°), combined refraction, footprint, and Fresnel-transmittance effects lower the penetrating flux ≈ 5.5×. Validation on 0.455 mm borosilicate contrasts the two conditions: cracking persistent under perpendicular incidence is suppressed when angle-matched, confirmed on two independent ten-piece lots—an optical-microscopy survey (0/40 defective edges) and a scanning electron microscopy/profilometry survey resolving only sub-threshold residual micro-cracking (≤1.6 μm), with no micro-chipping. The batch is highly repeatable (chamfer depth 84.1 ± 2.0 μm, Cp > 4; chamfer angle 38.0 ± 1.05°, repeatable but offset from the 45° target by a correctable stage-centering error). Residual angle and roundness deviations are prototype-stage precision limits, not process barriers.