Fracture Mechanics of Interfaces
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FRACTURE MECHANICS OF INTERFACES SURENDRA P. SHAH AND YEOU-SHANG JENQ *Northwestern University, Department of Civil Engineering, Director, ,*Center of Concrete and Geomaterials, Evanston, IL 60201 The Ohio State University, Department of Civil Engineering, Columbus, Ohio 43210 ABSTRACT Interfacial bond properties between fibers and matrix are investigated in the present paper. A fiber pull-out test, which is commonly used to study the interfacial bond strength of fiber-matrix system, is analyzed. The bonding between fibers and matrix is assumed to be perfect before the pull-out load is applied. Griffith energy criterion is used to govern the crack propagation at the interfacial region when debonding begins. A constant frictional shear stress, which may be a result of existence of surface roughness at the interface, is assumed to exist at the wake of debonding region. Based on this mechanism, the total pull-out load can be decomposed as: resistance offered by the interfacial bond and resistance offered by the frictional stress. The proposed approach is applicable to any elastic fiber and matrix system, but only the results of steel fibers and reinforcing bar in a cementitious matrix are reported. The proposed model correctly predicts several experimental trends of bond strengths reported by other researchers. Furthermore, theoretical predictions of progressive failure of bond cracks are found to be in good agreement with a holographic interferometry study on a pull-out test. Introduction It has been shown that the addition of fibers can greatly improve the toughness and crack resistance of brittle matrices [1,2]. Due to the bridging effects offered by fibers, the steel fiber reinforced concrete maintains some load carrying capacity even after the matrix cracks. The ultimate failure of the composite system is dominated by the bridging fibers' debonding and pulling out of the matrix. This failure process is principally governed by the properties of the fiber/matrix interface. The strength of the composite interface is commonly measured using a pullout test. In this test, a fiber (which can be a reinforcing bar) is cast into a cement-based matrix and loaded in tension until the fiber debonds and is withdrawn. The pull-out test is widely used to investigate the effect of varying fiber and matrix properties. The process of fiber and debonding and pullout is not well understood, and the problem has been the subject of considerable analytical as well as experimental investigation. An excellent description and comparison of several theories has been compiled by Gray [3]. Mindess has also summarized a number of theories, specifically those based on fracture mechanics [2]. There are two principal approaches to analyzing the interfacial debonding process. The first approach assumes that debonding initiates when the shear stress between the fiber and matrix exceeds the interfacial shear strength. In this approach, the distribution of shear stress is approximated using shear lag theory. It has been pointed out that the high stre
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