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The use of composites is increasing in the world, especially in the aviation world. The most common failure of composite is delamination. Delamination can be caused by static or cyclic loads. One numerical method that can be used to analyze delamination is cohesive zone modeling. In an era of increasing use of finite element method, cohesive zone modeling has the advantage that it can be applied to finite elements easily by using a damage variable. Currently, cohesive zone modeling for quasi-static loading has been successfully developed and has been widely used. However, the application of cohesive zone modeling in the finite element method for cyclic loading is still being developed because it has challenges in the form of elements that must experience damage under cyclic loading with the same maximum displacement. In this thesis, the model developed by Turon is used to predict fatigue crack propagation. The developed cohesive element was built using the UEL subroutine in ABAQUS software. Several simulations have been conducted under quasi-static and cyclic loading using two models, i.e. single element and double cantilever beam test. The single-element tests have shown suitable results under quasi-static and cyclic loading compared to the ABAQUS built-in cohesive element. The double cantilever beam simulation under quasi-static loading has provided a promising result compared to the reference which is followed by a convergence test. Meanwhile, the double cantilever beam simulation under cyclic loading has presented a similar trend to the experimental results. However, the result of fatigue simulation is still not fully in accordance with the experimental results and leads to the need for parametric studies, containing cycle jump value and mode-I fracture toughness. From the results of these simulations, potential future works will be obtained that can be developed from this thesis.