The　service　environment　of　the　transmission　shaft　is　complex,　and　it　is　frequently　subjected　to　impact　load.　Impact　fatigue　is　the　main　cause　of　its　fatigue　failure.　In　this　study,　a　fatigue　damage　evolution　analysis　method　of　transmission　shaft　considering　residual　stress　and　hardness　gradient　is　proposed　under　the　framework　of　damage　irreversible　thermodynamics.　Firstly,　combined　with　the　wave　theory,　the　wave　effect　of　impact　stress　wave　is　analyzed,　the　evolution　equation　of　stress　wave　fluctuation　behavior　is　established,　and　the　evolution　law　of　stress　and　strain　field　under　the　action　of　stress　wave　is　analyzed.　Then,　based　on　the　irreversible　thermodynamic　framework　of　damage,　the　thermodynamic　state　potential　and　dissipation　potential　of　the　damage　process　are　studied,　and　the　coupling　characteristics　of　the　damage　evolution　dynamic　response　and　the　intrinsic　damage　dissipation　of　the　damaged　material　are　analyzed.　The　damage　evolution　model　of　fatigue　performance　degradation　considering　residual　stress　and　hardness　gradient　is　established　to　identify　the　critical　condition　of　intrinsic　damage　dissipation　and　describe　the　fatigue　damage　failure　behavior.　Finally,　the　cohesive　element　of　the　coupled　damage　constitutive　is　defined　to　simulate　the　damage　evolution　behavior　of　the　substructure,　and　the　influence　of　residual　stress　and　hardness　gradient　on　the　damage　evolution　is　explored.　The　results　show　that　different　initial　crack　forms　have　an　important　influence　on　the　stress　wave　propagation　behavior.　The　existence　of　residual　tensile　stress　accelerates　the　process　of　fatigue　damage　accumulation,　and　the　improvement　of　surface　hardness　can　improve　the　fatigue　resistance　of　the　body.　©　The　Institution　of　Engineering　&　Technology　2024.