疲劳有限元分析

Finite Element Analysis of near the Fatigue Crack Tip Parameters in the Glass Fibre Reforced Aluminum alloy laminates under tension-compression loading Bai Shigang1,3, Zhang Jiazhen1, Zhou Zhengong1 1 Composite Materials and Structure Research Centre, Harbin Institute of Technology, Harbin 150001 2 Northeast Agricultural University, School of Science，150030 In this paper a finite element analysis for fatigue crack in the glass fiber reforced aluminum alloy laminates (GLARE) is studied. For comparison of parameters near the tip of fatigue crack in the GLARE under tension-compression and tension-tension loading have also been studied. The crack opening displacement and plastic zone were studied as the main parameters near the tip of fatigue crack. The differences of parameters near the tip of fatigue crack in GLARE under tension-compression and tension-tension loading was observed. The analysis shows that the fatigue crack growth rate is faster under tension-compression than the one under tension-tension loading. Key words: Introduction Fiber metal Laminates (FMLs) were firstly developed at Delft University of Technology as a family of hybrid materials that consist of bonded thin mental sheets and fibers embedded in expoxy. Two variants of FMLs were successively developed: Arall, containing aramid fibers, and Galare, containing glass fibers. The current investigation into fatigue crack propagation behavior focuses on Glare, which consists of aluminium 2024-T3, S2-glass fibers and the FM94 adhesive system. Glare has become known for its excellent fatigue and has been successively applied to the Airbus A380 as skin materials. In recent years, several authors [ ] have been published their research on fatigue crack propagation investigation of FMLs. Some methods to describe the fatigue crack propagation behavior and to predict the fatigue crack growth life have been presented. R. Marissen presented the analytical method to pridict the fatigue crack growth rate of the FMLs using the assumption that the bridging stress along the crack line is uniform. R.C. Alderliesten established of mathematical model of fatigue crack propagation and interface delamination using linear elastic fracture mechanics method. Wu Xueren and Guo Yajun presented a phenomenological method to predict the the fatigue crack growth rate [9,10]. But the existing method usually insist that the compresssion load under tension-compression loading has no effect on the fatigue crack propagation. That is based on the the crack closure theory that believes the cack has closed when the loading stress is zero. ASTM E647-95a [ ] denoted that only the tension loading has effect on the fatigue crack propagation and believes that the crack growth rate under stress rate R=0 is the same as the one under stress rate R<0. However, the recent researching result shows that the crack is not necessarily closed and the crack tip forms a hole as the external loading is zero. So it is necessary to investigate the near the fatigue crack tip parameters in the fibre reforced Aluminum alloy laminates under tension-compression loading. Finite element model The specimens used in the current finite element analyses with centre crack. The height of the specimen, L is 116.84mm, 2W is 44.55mm as shown in Fig. 1. The lengths of the half cracks a=8mm. The stress-plastic strain curve used in this analysis is shown in Fig. 2. Because of symmetry conditions only one quarter of the specimen is modeled. Fig. 3 shows the detailed arrangement which represents a quarter of the specimen. Fig. 4 shows the whole finite element model finite element model which represents a quarter of the specimen. The delamination shape of triangle was given. The geometry parameters of delamination in fig.3 was b= 5mm and c=10mm. Three dimensional finite element model was established. The grid size was 0.1mm. Traction Separation laws and cohesive element were used to model the delamination of interface of aluminium alloy and glass fiber epoxy. The Young’s modulus and Poisson’s ratio and Damage Parameters for Traction Separation laws used in this analysis are showed in the table.1. Table 1 Material constants Aluminum alloy Glass fiber reinforced epoxy Parameters of traction separation laws Young's modulus EAl/GPa Yield strength σys/MPa Young's modulus Ela/GPa Delamination zone Other zone Maxs Energy Maxs Energy 70 120.1 45 0.01 2 × 10-6 5× 108 2× 109 Fig. 1 Test model Fig. 2 Stress strain curve Fig. 3 Finite element mesh Fig. 4 Boundary condition The loading history can be calculated at the same nominal stress intensity factor. A representation of the result is shown in Table.1 and the loading history curve is shown in Fig.5. ta is the time from maximum compression loading to zero. Results and discussion Fig. 7 show the crack opening profiles for a=8mm. It can be seen that the near crack tip opening displacements at t=tb for R=0 was not zero. When the external load is zero the crack still open for glass fiber reinforced aluminum laminates under the bridging stress of the intact glass fiber, as the crack opening displacement was composed of two parts. One is the elastic displacement and the other is plastic displacement. It also can be seen that the near crack opening displacements have been reduced with the increase in compressive stress and the closed crack lengths have been increased. It is noted that the closing of the cracks starts from the elements far away from the crack tip and gradually spreads to the crack tip. From the maximum tensile loading and unloading to zero, the process of elastic deformation caused the displacement back to zero. However, the plastic deformation of unloading less than the plastic deformation loading, residual plastic deformation caused the cracks tip still open at zero applied stress. Therefore, the crack tip behaves like a notch and efficiently as a stress raiser during the compressive loading part of the load cycle. The stress concentration exists near the crack tip under the following compression loading. ig. 5 Crack loading history Fig. 7 Crack opening profiles Fig.8 gives the plastic zone size at the minimum external load for stress rate R=0 and R=-1. It shows the effect of the compression loading on the plastic zone size near the crack tip. The maximum positive plastic zone at external load σ=60MPa is far less thanσ=-60MPa. It is due to the bridging stress of intact fiber that reduces the stress intensity factor. However, the reverse plastic zone is formed from the reverse stress concentration exists near the crack tip without the fiber’s bridging function. Fig. 8 the relation of plastic zone size and external load Conclusion (1) The fatigue crack growth rate is faster under tension-compression than the one under tension-tension loading. (2) Reference [1] Van Lipzig H T M. Retardation of fatihue crack growth [D]. Netherlands: Department of Aeronautical Engineering, Delft University, 1973. 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