No 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.

Unfortunately, most of the previous work studying the fracture toughness of fibrous composites has deliberately ignored bridging the fiber onto the pre-crack/notch surfaces by creating such a crack as a through-thickness crack (TTC). Furthermore, no standard specifications for measuring the fracture toughness of fibrous composites have considered the fiber bridging through the pre-notch. Only a few pieces of research, no more than fingers on one hand, have addressed this problem by creating an actual crack, i.e., a matrix crack (MC) instead of a TTC. The challenge these researchers face is the inability to calculate the fracture toughness directly through the stress intensity factor (SIF) relationship because there is no geometry correction factor equation, f(a/d), for an MC. The main objective of the present work is to calculate f(a/d) and ascertain a relationship between the SIF and crack mouth opening displacement (CMOD) for an MC numerically using 3-D finite element analysis. An experimental program was also conducted to measure the fracture toughness of three types of concrete beams: high-strength concrete (HSC) beams with a TTC, HSC beams with an MC, and fiber-reinforced concrete (FRC) beams with an MC. The results showed that FRC beams with an MC have the highest fracture toughness and, subsequently, the highest resistance to crack growth. The numerical results revealed a suggested relationship between the SIF and CMOD of FRC beams with an MC. This relation was used to predict the fracture toughness of FRC with an MC by the critical value of CMOD measured experimentally.

No abstract

In the present work, the fracture toughness (KIC) of full-depth (FD) fiber-reinforced concrete (FRC) and layered functionally graded concrete (FGC) matrix cracked (MC) beams has been determined by the equivalent relationships of the two-parameter fracture model (ETPFM). Forty-eight MC-FGC and MC-FD FRC beam specimens with span-depth ratios (L/d) equal 4, 5, and 6 were tested under the 3PB configuration. The MC length-depth ratio (ao/d) remained constant equal to one-third. All FRC beams have the same constitutes materials with hooked-end steel fiber volume fraction equals 1%. The FGC beams are composed of three equal layers, i.e., FRC in the bottom layer at the tension side, normal strength concrete (NSC) at the middle layer, and high strength concrete at the upper layer in the compression side. The results showed that the predicted values of KIC obtained from ETPFM are considered logic according to the maximum size of the non-damaged defect concept. The crack mouth opening displacement estimated from ETPFM showed acceptable values close to the present experimental results. The KIC values calculated within the presence of fibers in front of and through the MC for FRC beam specimens having 1% SFs is more than twice the value of NSC.