MECHANICS AND ENGINEERING – Numerical Computation and Data Analysis
Mechanics and Engineering — Numerical Calculations and Data Analysis 2019 Academic Conference, April 19-21, 2019, Beijing
April 19-21, 2019, Beijing, China
Study on Layered Expansion Behavior of Advanced Carbon Fiber Reinforced Composite Laminates Sheet
Gong Yu 1*, Wang Yana 2, Peng Lei 3, Zhao Libin 4, Zhang Jianyu 1
1 Chongqing University, Chongqing, 400044, China
2 China Aviation Research Institute Beijing Aeronautical Materials Research Institute, Beijing, 100095, China
3 China Commercial Aircraft Beijing Civil Aircraft Technology Research Center, Beijing, 102211, China
4 Beijing University of Aeronautics and Astronautics, Beijing, 100191, China
Abstract Laminate structure is one of the most commonly used composite configurations for composites, but delamination becomes its main failure mode due to weak interlaminar properties. Research on the multi-layer laminate stratification and expansion behavior commonly used in engineering practice has always been a hot topic for scholars. In this paper, the research results of carbon fiber reinforced composite delamination in Chongqing University and Beijing University of Aeronautics and Astronautics Fatigue Fracture Laboratory are introduced from two aspects of experimental research and numerical simulation. Finally, the development direction of the field is prospected.
Keywords: carbon fiber reinforced composite, laminate, delamination, fatigue stratification
Composite materials have excellent properties such as high specific strength and high specific stiffness, and have been widely used in aerospace, energy technology, and civil transportation and construction. During the processing and use of composite materials, the fibers and matrix will undergo different degrees of damage under load. Common failure modes for composite laminates include interlayer damage and damage within layers. Due to the lack of reinforcement in the thickness direction, the lateral mechanical properties of the laminate are poor, and delamination damage is highly likely to occur under external impact loads. The occurrence and expansion of stratified damage will lead to a decrease in structural rigidity and strength, and even cause catastrophic accidents [1-3]. Therefore, the delamination problem is more and more concerned by the structural design and strength analysis of composite materials, and it is necessary to study the layered expansion behavior of composite materials .
Research on layered expansion behavior of laminate
1. Experimental study
Interlaminar fracture toughness is a characteristic parameter of the mechanical properties between composite layers. Corresponding test standards have been established for the determination of interlaminar fracture toughness of Type I, Type II and I/II hybrid unidirectional laminates. The corresponding test apparatus is shown in Figure 1. However, the multi-directional laminates of composite materials are often used in the actual engineering structure. Therefore, the experimental study on the stratification and expansion behavior of multi-directional laminates has more important theoretical significance and engineering value. Multi-layer laminate layer initiation and expansion occur between interfaces with arbitrary layering angles, and the layered expansion behavior is significantly different from that of unidirectional laminates, and the expansion mechanism is more complicated. Researchers have relatively few experimental studies on multi-directional laminates, and the determination of interlaminar fracture toughness has not yet established an international standard. The research team used T700 and T800 carbon fiber to design a variety of composite laminates with different interface layup angles, and studied the influence of interface layup angle and fiber bridging on static and fatigue delamination behavior. It has been found that fiber bridging formed by the trailing edge of the layer has a great influence on the interlaminar fracture toughness. As the stratification expands, the interlaminar fracture toughness will gradually increase from a lower initial value, and when the stratification reaches a certain length, it reaches a stable value, that is, the R resistance curve phenomenon. The initial fracture toughness of the interlayer is almost equal and approximately equal to the fracture toughness of the resin, which depends on the fracture toughness of the matrix itself [5, 6]. However, the interlaminar fracture toughness extension values of different interfaces vary greatly. Significant interface layer angle dependence is presented. In response to this dependence, Zhao et al.  based on the physical mechanism of the stratified resistance source, it is considered that the interlaminar fracture toughness stability value consists of two parts, one part is the fracture work of the unrelated layer interface, and the other part is the intralayer damage and fiber. The work of fracture caused by bridging. Through the finite element analysis of the stress front field of the layered front, it is found that the second part of the fracture work depends on the depth of the delamination front damage zone (as shown in Figure 3), and the depth of the damage zone is proportional to the interface layup angle. A theoretical model of the I-type fracture toughness stability value expressed by the sinusoidal function of the interface layer angle is presented.
Gong et al.  carried out the I/II hybrid stratification test under different mixing ratios, and found that the I/II hybrid stratification in the laminate also has significant R resistance curve characteristics. Through the analysis of the fracture toughness between different test pieces, it is found that the initial value and the stable value of the interlaminar fracture toughness of the test piece increase significantly with the increase of the mixing ratio. In addition, the initial and stable fracture toughness of the interlayer under different mixing ratios can be described by the B-K criterion.
In terms of fatigue stratification, significant fiber bridging was also observed during the test. Through the analysis of the test data, it is found that the fatigue delamination expansion of the composite material is affected by the “resistance curve”, so that the traditional fatigue stratification expansion rate model and the threshold value are no longer applicable. On the basis of theoretical analysis, Zhang and Peng [4,8,9] introduced the fatigue delamination expansion resistance to express the energy required for the fatigue delamination expansion of composite materials, and further proposed the normalized strain energy. The release rate is the fatigue stratified expansion rate model and threshold value of the control parameters. The applicability of the model and the normalized threshold parameter is verified by experiments. Further, Zhao et al.  comprehensively considered the effects of fiber bridging, stress ratio and load-mixing ratio on fatigue stratification and expansion behavior, and established a normalized fatigue stratified expansion rate model considering the influence of stress ratio. The accuracy of the model was verified by fatigue stratification tests with different stress ratios and mixing ratios. For the physical quantity of fatigue stratified expansion resistance in the normalized fatigue stratified expansion rate model, Gong et al.  overcome the weakness of the calculation method that can only obtain limited discrete data points through experiments, and establish fatigue from the energy point of view. An analytical model for the calculation of stratified extended resistance. The model can realize the quantitative determination of fatigue stratification and expansion resistance, and provide theoretical support for the application of the proposed normalized fatigue stratified expansion rate model.
Figure 1 stratified test device diagram
Figure 2 Inter-layer fracture toughness R resistance curve 
Figure 3 Layered leading edge damage zone and stratified extended morphology 
2. Numerical simulation study
The numerical simulation of layered expansion is an important research content in the field of composite structure design. When predicting the delamination failure of composite unidirectional laminates, the existing stratification expansion criteria usually use constant interlaminar fracture toughness as the basic performance parameter , by comparing the crack tip energy release rate and interlaminar fracture toughness. Size to determine if the layering is expanding. The failure mechanism of multi-directional laminates is complex [11,12], which is characterized by significant R resistance curves [5,13]. The existing layered expansion criteria does not take this feature into account and does not apply to the simulation of the delamination behavior of fiber-containing bridged multidirectional laminates. Gong et al. [10, 13] improved the existing stratified expansion criteria and proposed to introduce the R resistance curve into the criteria, and based on this, established a stratified expansion criterion considering the effects of fiber bridging. The definition and use parameters of the bilinear constitutive cohesive unit were systematically studied by numerical methods, including the initial interface stiffness, interface strength, viscosity coefficient and the minimum number of elements in the cohesive force zone. The corresponding cohesive unit parameter model was established. Finally, the effectiveness and applicability of the improved layered expansion criterion and cohesive unit parameter model are verified by static stratification test. However, the improved criteria can only be used for one-dimensional layered simulations due to positional dependencies and not for two- or three-dimensional hierarchical extensions. In order to solve this problem, the author further proposed a new trilinear cohesive force constitutive considering fiber bridging . The constitutive relationship fits the complex process of layered expansion from a microscopic perspective, and has the advantages of simple parameters and clear physical meaning.
In addition, in order to accurately simulate the stratified migration phenomenon common in the stratification process of multi-directional laminates [11,12], Zhao et al. [11,12] proposed a crack path guidance model based on extended finite element, simulating a special design. Hierarchical migration in a composite stratification test. At the same time, a layered expansion model is proposed for the zigzag layered expansion behavior along the 90°/90° layered interface, which accurately simulates the layered expansion behavior of the 90°/90° interface.
Figure 4 Numerical simulation of layered migration and experimental results 
This paper focuses on the research results of this group in the field of composite laminate delamination. The experimental aspects mainly include the influence of the interface layup angle and fiber bridging on the static and fatigue delamination expansion behavior. Through a large number of experimental studies, it is found that the multi-directional laminate failure mechanism of composite materials is complicated. Fiber bridging is a common toughening mechanism of multi-directional laminates, which is the main reason for the R-resistance curve of interlaminar fracture toughness. At present, the R resistance curve study under the II stratification is relatively lacking and needs further research. Starting from the failure mechanism, the fatigue stratification model including various influencing factors is proposed, which is a direction of fatigue stratification research. In terms of numerical simulation, the research group proposed an improved hierarchical expansion criterion and a cohesive constitutive model to consider the influence of fiber bridging on the stratified expansion behavior. In addition, the extended finite element is used to better simulate the hierarchical migration phenomenon. This method eliminates the need for fine cell division, eliminating the problems associated with mesh re-division. It has unique advantages in simulating the stratification of arbitrary shapes, and more engineering application research of this method is needed in the future .
 Y Gong, L Zhao, J Zhang, N Hu. A novel model for determining the fatigue delamination resistance in composite laminates from a viewpoint of energy. Compos Sci Technol 2018; 167: 489-96.
 L Zhao, Y Wang, J Zhang, Y Gong, N Hu, N Li. XFEM-based model for simulating zigzag delamination growth in laminated composites under mode I loading. Compos Struct 2017; 160: 1155-62.
 L Zhao, Y Gong, J Zhang, Y Wang, Z Lu, L Peng, N Hu. A novel interpretation of fatigue delamination growth behavior in CFRP multidirectional laminates. Compos Sci Technol 2016; 133: 79-88.
 L Peng, J Zhang, L Zhao, R Bao, H Yang, B Fei. Mode I delamination growth of multidirectional composite laminates under fatigue loading. J Compos Mater 2011; 45: 1077-90.
 L Zhao, Y Wang, J Zhang, Y Gong, Z Lu, N Hu, J Xu. An interface-dependent model of plateau fracture toughness in multidirectional CFRP laminates under mode I loading. Composites Part B: Engineering 2017; 131: 196-208.
 L Zhao, Y Gong, J Zhang, Y Chen, B Fei. Simulation of delamination growth in multidirectional laminates under mode I and mixed mode I/II loadings using cohesive elements. Compos Struct 2014; 116: 509-22.
 Y Gong, B Zhang, L Zhao, J Zhang, N Hu, C Zhang. R-curve behaviour of the mixed-mode I/II delamination in carbon/epoxy laminates with unidirectional and multidirectional interfaces. Compos Struct 2019. (Under Review).
 L Peng, J Xu, J Zhang, L Zhao. Mixed mode delamination growth of multidirectional composite laminates under fatigue loading. Eng Fract Mech 2012; 96: 676-86.
 J Zhang, L Peng, L Zhao, B Fei. Fatigue delamination growth rates and thresholds of composite laminates under mixed mode loading. Int J Fatigue 2012; 40: 7-15.
 Y Gong, L Zhao, J Zhang, Y Wang, N Hu. Delamination propagation criterion including the effect of fiber bridging for mixed-mode I/II delamination in CFRP multidirectional laminates. Compos Sci Technol 2017; 151: 302-9.
 Y Gong, B Zhang, SR Hallett. Delamination migration in multidirectional composite laminates under mode I quasi-static and fatigue loading. Compos Struct 2018; 189: 160-76.
 Y Gong, B Zhang, S Mukhopadhyay, SR Hallett. Experimental study on delamination migration in multidirectional laminates under mode II static and fatigue loading, with comparison to mode I. Compos Struct 2018; 201: 683-98.
 Y Gong, L Zhao, J Zhang, N Hu. An improved power law criterion for the delamination propagation with the effect of large-scale fiber bridging in composite multidirectional laminates. Compos Struct 2018; 184: 961-8.
 Y Gong, Y Hou, L Zhao, W Li, G Yang, J Zhang, N Hu. A novel three-linear cohesive zone model for the delamination growth in DCB laminates with the effect of fiber bridging. Compos Struct 2019. (To be submitted)
 L Zhao, J Zhi, J Zhang, Z Liu, N Hu. XFEM simulation of delamination in composite laminates. Composites Part A: Applied Science and Manufacturing 2016; 80: 61-71.
 Zhao Libin, Gong Yu, Zhang Jianyu. Research progress on stratified expansion behavior of fiber reinforced composite laminates. Journal of Aeronautical Sciences 2019: 1-28.
Source: Gong Yu, Wang Yana, Peng Lei, Zhao Libin, Zhang Jianyu.Study on stratified expansion behavior of advanced carbon fiber reinforced composite laminates[C]. Mechanics and Engineering – Numerical Computation and Data Analysis 2019 Academic Conference. Chinese Society of Mechanics, Beijing Mechanics Society, 2019. via ixueshu
Post time: Nov-15-2019