Commercially pure zirconium was processed by the surface mechanical attrition treatment (SMAT),and the microstructure observation showed that a gradient structure was induced.Nanoindentation measurements were taken to obtain the load-displacement curves at different depths below the treated surface.Using dimensional analysis,the local yield stress,hardness,strain hardening exponent,and elastic modulus at the corresponding depths were derived.The results showed that the yield stress and hardness varied with depth,while the strain hardening exponent and elastic modulus were approximately invariable.The finite element method was used to simulate nanoindentation at different depths below the treated surface to verify the derivation of the local elastic-plastic constitutive relationship.Stressstrain curves were computed for the treated samples through the rule of mixtures,and they agreed well with the experimental results.The analysis showed that the surface and subsurface hardening layers as well as the transition layer shared a high load applied to the samples,even though their volume fraction was small.