Fracture toughness of matrix cracked FRC and FGC beams using equivalent TPFM

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