Cracking behavior and control of β-solidifying Ti-40Al-9V-0.5Y alloy produced by selective laser melting

•A crack-free β-solidifying Ti-40Al-9V-0.5Y (at. %) alloy was successfully fabricated by selective laser melting (SLM).•The influence factors for cracking sensitivity are explored based on heat transfer mode of molten pool and cooling rate.•The formation and inhibition mechanism of solidification and cold cracking are proposed based on solidified microstructure and phase transformation.•The crack-free Ti-40Al-9V-0.5Y alloy produced by SLM is provided with fine equiaxed microstructures and favorable mechanical properties.