Semi-analytical weight function method for center-cracked circular disk subjected to diametral compression

Abstract

Büeckner-Rice weight function method was used to analyse mixed-mode fracture of center-cracked circular disk subjected to uniaxial compression. Based on Wu-Carlsson procedure semi-analytical modes I and II weight functions were derived from corresponding reference displacement fields and stress intensity factors calculated by finite element method. Normalized mode I and mode II stress intensity factors, f_I, f_II, were derived from the obtained semi-analytical weight functions. The results were then fitted into polynomials, the precision is within 0.5%. It is interesting to note that when the inclined angle ϑ of a crack is less than 15°, the f_I values are positive. when ϑ=15°, the f_I values are positive for the crack length a varying from 0.1 to 0.7, but when a=0.8, the f_I takes the negative value −0.51. When ϑ>15°, all the f_I values become negative, which denotes that the compression-shear mode is achieved at crack tips. These results are very useful in the investigation of mixed-mode fracture of brittle materials.

Keywords

weight function / stress intensity factor / compression / center-cracked circular disk