Formation of annular cracks in glass during contact interaction

Abstract

Experimental results are presented on the indentation of steel balls of various diameters into glass samples having a rectangular parallelepiped shape. The ultimate load in the formation of an annular crack in the vicinity of the contact region and the radius of this crack were determined experimentally. The annular crack appeared outside the contact area almost in all tests. Due to the fact that the diameter of the contact area was much smaller than the dimensions of the samples, the glass samples were considered as an elastic half-space. Huber’s solution for Hertz’s problem of pressing a ball into an elastic half-space was used to determine the field of contact stresses in the fracture zone. Local criterion for maximum stresses and nonlocal failure criteria (average stress criterion, the Nuismer criterion, and the gradient criterion) were used to model fracture in a contact interaction. The ultimate tensile stress and the critical stress intensity factor of the glass were experimentally determined on beams without a notch and with a notch for calculating a parameter having a dimension of length and entering nonlocal failure criteria. It is shown that the estimates of the radius of the annular crack that are closest to the experimental data give a gradient criterion among the applied criteria. Estimates of the ultimate tensile stress according to this criterion exceed the values obtained when the beams are bent, which can be explained by the scale factor.