Crack stability in simply supported four-point and three-point loaded beams of brittle materials

Abstract

The feasibility of utilizing simple beam specimens as candidates for fracture-toughness testing of brittle nonmetallic materials was explored. Four-point and three-point loaded beams were examined via theoretical considerations with regard to crack growth stability and constant deflection loading, taking into account the stiffness or compliance of the loading system. It was found that the compliance of the loading system played a major role with regard to crack growth stability. Also, a three-point loaded beam exhibited greater stability than a four-point loaded beam. Nevertheless, the geometry of both beam specimen configurations was optimized within practical limits to yield a test system that would serve as a potentially successful candidate for fracture-toughness testing, if the compliance of the testing machine and ancillary equipment could be kept below a practicable level. Experimental verification of the theoretical predictions of stability of both the four-point and three-point loaded beams was accomplished. Load—displacement curves were determined for beams fabricated from a quasi-brittle material, polymethylmethacrylate (PMMA), having various initial crack lengths. Fracture toughness of PMMA was also obtained via two methods: the critical stress intensity approach and the energy of fracture. The results from these two methods corroborated each other and established data available in the literature.