The effect of reinforcement bridging on the elastic fracture energy of concrete

Abstract

Failure of structures may be analyzed based on strength criterion or fracture mechanics criterion. Strength criterion deals with material resistance beyond the critical conditions such as yield, and ultimate strength. In fracture mechanics the critical condition is defined by toughness which can be stress intensity factor (K) or fracture energy (G). This study explores the critical point during loading up to the limit of elasticity based on linear elastic fracture mechanics – LEFM. However, nonlinearity frequently appears due to the existence of a relatively large fracture process zone – FPZ located at the crack-tip. The assumption of LEFM in quasi – brittle material such as concrete is therefore limited to large size structures only. The well-known approach to obtain the fracture energy Gf for infinite large structures is size effect law – SEL. Gf is defined as the specific energy, i. e. energy per unit crack plane area. This is elastic energy which is linear. To answer a question whether reinforcement affect the elastic fracture energy, a research was conducted following the principles of work-of-fracture – WOR using the RILEM Specification Test Method. Three-point-bend beam specimens were made of normal concrete, subjected to monotonic load P, until they failed. P–u relationship prevails the real work. The elastic fracture energy based on WOR that is was found by divided the area under P–u curve of elastic range with ligament. The result is, equal to 397.87 N/m for beam A1 (bending failure l/h=5.5), 133.6 N/m for beam B1 (Shear failure, l/h=5.0). 101.93 N/m for beam B2 (shear failure, l/h=5.0), 153.75 N/m for beam B3 (shear failure, l/h=5.0). The greater value comparing to Gf implies that reinforcement affect significantly the elastic fracture energy.