A method for determination of intrinsic material length base on strain gradient study in spherical indentation

The strain gradient in spherical indentation was studied and a new method to determine the material intrinsic length was proposed. Through analytic study, strain gradient in spherical indentation was found to depend on both indenter radius and indentation penetration. When the penetration is deep, the strain gradient will increase rapidly. With the help of numerical method, the analytic relation obtained was proved to be reliable. At the same time, the distribution of strain gradient underneath the spherical indenter was found to be inhomogenous. It increases along the contact surface from the bottom to the material surface. Based on the analytic relation between strain gradient and penetration, an attempt was made to determine the material intrinsic length with spherical indentation under deep penetration. Annealed oxygen-free copper, (220) single crystal copper, AA5052 and AA7050-T7451 were studied and the material intrinsic lengths determined were 5.5 µm, 18.8 µm, 45.5 µm, and 50.3 µm respectively. The results of annealed oxygen-free copper and (220) single crystal copper were close to the results obtained by other researchers but the results of AA5052 and AA7050-T7451 seemed large. The possible reasons were discussed.