Real fracture toughness of FRC and FGC: size and boundary effects

Abstract

The present dilemma is how to simulate the real crack in full depth (FD) fiber-reinforced concrete (FRC), FD FRC, to get the actual fracture toughness of such fibrous composites, i.e., through-thickness pre-cracks are inappropriate for such materials. To overcome this dilemma, a new technique was adopted to create a pre-matrix crack (MC) without cutting the fibers bridging the two surfaces of the pre-crack. The main objective of the present work is to study the size and boundary effects on the real fracture toughness of MC-FD FRC and functionally graded concrete (FGC). Forty-eight MC-FD FRC and MC-FGC beams with three different span to depth ratios L/d equal 4, 5, and 6, and three different beam depths of the same beam span have been tested under three-point bending. All beams have the same pre-MC length to beam depth ratio (ao/d) of 1/3. Hooked end steel fibers of 1% fiber volume fraction produced FRC. FGC beams consist of three equal layers, FRC layer at the tension side, normal strength concrete layer at the middle of the beam, and high strength concrete layer at the compression side. The applied load versus all beams' crack mouth opening displacement (CMOD) curves have been analyzed. The present load/CMOD results showed that beams having constant L/d ratios are recommended to capture independent size effect parameters. The size effect law (SEL) and boundary effect model (BEM) are good candidates to predict the size effect. According to the maximum non-damaged defect concept, the SEL is more reliable in predicting MC FD FRC fracture toughness than BEM.

Mixed-mode fracture toughness of high strength FRC: a realistic experimental approach

“…The d max /NMAS were calculated, and the results are given in Table 11. The ratios of d max /NMAS in the current study ranged between 1 and 2 in MC specimens, near the ratios found by Elakhras et al [36][37][38] for mode I, which were greater than unity.…”

“…Unfortunately, such previous work was not only a waste of time and effort but also led the scientific research compass in this field in the wrong direction for solving such problems. The first attempt in the right direction for predicting the fracture toughness of fibrous composite materials was made by Salam and colleagues [34,[36][37][38][39]. Sallam and co-workers [36,39] successfully correlated the mode I fracture toughness of FRC using MC specimens, i.e., correlating a vectorial problem with a crack path independent of the initial crack length by scalar parameters such as Griffith's energy release rate..…”

“…Using the equivalent relationships of the two-parameter fracture model, Elakhras et al [37] predicted K IC for both FRC and FGC depending on load/crack mouth open displacement (CMOD) curve results of MC specimens. The size effect law and boundary effect model showed good compatibility when applied on FRC and FGC beams using MC specimens [38]. Ali et al [39] applied the MC concept on FRC specimens subjected to mode I, investigating different a/d (0.1, 0.3, and 0.5) and fiber lengths (35 mm, 50 mm, and hybrid of them).…”

“…As aforementioned, the MC specimen approach could consider the contribution of fiber bridging during the mode I crack propagation in FRC [36][37][38][39]. Checking this potential in mixed-mode MC specimens is an interest leading to a generalized realistic experimental approach.…”

A simple fracture model for dam concrete based on the Fuller and Thompson formula

“…Many experimental studies have shown that the fracture parameters obtained from small‐ and medium‐sized specimens cast in the laboratory have significant size effects 11–16 . In other research findings, the fracture parameters of different materials were mainly studied to determine these parameters without size effects 17–24 .…”