Three　kinds　of　Dy3+　ion-doped　(LuxY1-x)3Al5O12　(x　=　0,　1/3,　1/2)　single　crystals　fabricated　by　the　Czochralski　method　with　4　at.%　Dy3+　ion　doping　were　investigated　by　indentation　and　scratch　techniques　under　Vickers,　Knoop,　Berkovich,　and　spherical　indenters　to　understand　the　influence　of　Lu　ion　on　micromechanical　properties　and　fracture　behavior　of　Y3Al5O12　(i.e.　YAG　for　x　=　0)　single　crystals.　The　largest　(or　smallest)　values　of　hardness,　elastic　modulus,　and　fracture　toughness　were　found　for　x　=　1/3　(or　1/2).　The　indentation　size　effect　was　explained　by　four　different　models　with　the　Hays-Kendall　approach　being　the　most　suitable　one　to　determine　the　true　hardness.　Fracture　toughness　values　of　YAG　crystals　obtained　by　the　Vickers　hardness　method　agreed　with　those　obtained　by　scratching　with　a　spherical　indenter　based　on　linear　elastic　fracture　mechanics.　©　2022　Elsevier　Ltd　and　Techna　Group　S.r.l.