An approximate model to describe the size effects of spherical contact tests, based on a modified couple stress elasticity

The size effects in spherical contact a investigated by employing a modified couple stress elasticity theory. An approximate couple stress field inside the half space is obtained by assuming that the couple stress elasticity-based displacement field is the same as the linearly elastic one. Besides, the linearly elastic stress field is expressed in a more explicit form. The stiffening effects of couple stress on contact load are expressed, and a contact load model is derived accordingly. Based on the derived load model, a modulus model which is able to describe the size effects observed in spherical contact tests is proposed. Furthermore, the validity of the modulus model is illustrated by comparing the model results with related experimental data. This work is helpful for readers to understand and calculate the size effects when measuring the modulus through spherical contact tests.