Analytical Model for Tensile Strain Hardening and Multiple Cracking Behavior of Hybrid Fiber-Engineered Cementitious Composites

An analytical model for the design of strain-hardening and multiple-cracking behavior of engineered cementitious composites (ECC) containing hybrid fibers is proposed. The model predicts first crack strength and ultimate bridging strength of hybrid fiber ECC. The model also predicts the minimum (critical) volume fraction of fibers required to exhibit strain-hardening and multiple-cracking behavior in uniaxial tension. The model is verified with the experimental results of hybrid fiber ECC specimens. A parametric study is also performed, using this model, to evaluate the effects of fiber length, diameter, and interfacial bond strength on the first crack strength, the ultimate bridging strength and the critical volume fraction of fibers. It is shown that the critical volume fraction of fibers in hybrid fiber composites can be optimized by proper selection of fiber length, diameter, and interfacial bond strength. Low modulus fibers are found to have a more pronounced effect on the strain-hardening and multiple-cracking behaviors of hybrid fiber composites compared to high modulus fibers. The hybrid fiber concept is found to offer additional freedom in the design variables compared to composite containing one type of fiber.