## 4 Results and Discussion
### Delamination Migration  
The delamination migration problem, in which delamination normally grows and migrates into different interfaces together with matrix cracks, is a good example to check the capability of the FE model to reflect the interaction between the matrix crack and delamination. Many studies on experimental methods and simulation techniques for the purpose of investigating a delamination migration have been done in recent years [35; 60; 37; 61]. After [PERSON] and his colleagues performed a numerical simulation of delamination migration by using the Abaqus continuum damage model for intralaminar cracks and the cohesive zone for delamination [62], they concluded that the migration initiation and subsequent delamination could not be predicted by this method. This is because this numerical method did not capture the relationship of the interaction between intralaminar and interlaminar failure. The approach proposed in this work, which reflected the interaction between delamination and intralaminar cracks, is believed to be  
Figure 5: Deformed shape of the unidirectional specimen. Figure 6: The predicted remote stress-displacement curve. suitable for modeling the delamination migration behavior in FRP composites. Therefore, a typical delamination migration problem in a laminated composite specimen is investigated to validate the capability of the proposed model. In this section, the results of numerical damage simulation of the delamination migration of carbon fiber-reinforced polymer (CFRP) composite are presented, and the numerical results and experimental data [61] are compared together to validate the FE model. The loading, boundary conditions, and geometric dimensions of specimens for verifying the performance of our approach are illustrated in Figure 7, and the material elastic properties of CFRP composites are illustrated in Table 1.  
A specimen has 44 plug, and its layup sequence is as follows: \([0_{4}/90_{12}/0_{10}/90_{4}/\mathbf{T}/0/90/0_{2}/90_{6}/0_{2}/90/0]\). Script \"\(\mathbf{T}\)\" means the initial crack made by inserting PTFE (polytetrafluoroethylene) at an interface between a zero-degree ply and a stack of four 90-degree plies, and the length of the initial crack is 48 mm. Both ends of the specimen are clamped, and the upper surface suffers the tensile force controlled by the vertical tensile displacement. As the load increases, the initial crack propagates at the interface between the 0\({}^{\circ}\) and 90\({}^{\circ}\) layers. The propagating interface crack is then kinked into the adjacent upper 90\({}^{\circ}\) layer and becomes an intralaminar matrix crack. After matrix cracking, the crack reaches the upper interface and changes into an interlaminar crack. The red dashed line in Figure 7 is the expected crack path, which is the experimentally-tested delamination migration. To simulate multiple delaminations at interfaces between the individual plies, four longitudinal cohesive layers are used. A refined mesh using an element length of 0.12 mm was used in the simulation of a specimen and contained a total of 45,568 solid elements and 1616 interface elements, which changed a little by the calculation results with further mesh refining. The contour plots of the damage variable at various load levels are presented in Figure 8, and the sequence of the interlaminar delamination and intralaminar matrix failure can be seen from the evolution of the damage contour. The cohesive element failure initiates at 73.2% of the ultimate load and progresses in the initial crack direction of the specimen, as shown in Figure 8a. The solid elements are not damaged before the matrix damage initiates and the interface crack has migrated. The initial interface crack propagates for some time and then begins to penetrate into the adjacent upper 90\({}^{\circ}\) solid layer. The intralaminar damage (migration) occurs at solid elements, while delamination stops at a certain point (migration point) and does not propagate, as shown in Figure 8b.