Finite Element Analysis And Frequency Domain Analysis Of3-D Braided Composite Under Impact Loading

Comparing to laminates, three-dimensional (3-D) braided composites have mechanical advantages along the thickness direction due to the net-shape structure. Because of the high inter-laminar shear strength,3-D braided composites have not delaminations subjected to impact loading. Due to high stiffness, high strength, and high impact damage tolerance,3-D braided composites have been widely applied to the impact situations.This paper aims to simulate the dynamic response of3-D braided composites with finite element method, which will help reduce the manufacturing and test costs while optimizing structural design. Meanwhile, some dynamic characteristics of the impact stress wave, hidden in time domain, can be revealed in frequency domain analysis. The frequency domain analysis improves the understanding of the failure mechanism of the3-D composites, so as to further benefit the structure design.Our research includes three parts. First, the transverse impact and low-velocity impact response of3-D braided composite are tested by split Hopkinson pressure bar and Instron9250drop-weight instrument, respectively. The dynamic response characteristics and failure morphologies are obtained under different loading conditions and impact velocities. Based on which, the failure mechanism can be analyzed. Second, a unit cell model and its constitutive equation are derived based on the micro-structure of the3-D braided composites. A user defined material subroutine VUMAT is compiled based on the unit cell model, constitutive equation, the maximum stress theory, and the critical damage area theory (CDA). Incorporated with the VUMAT, the load-displacement curve of3-D braided composites under transverse impact and low-velocity impact can be calculated by the dynamic explicit solver ABAQUS/Explicit. Finally, the experimental load-time curves are transformed into frequency domain by Fast Fourier Transform (FFT) and Hilbert-Huang Transform (HHT) method. Therefore, the dynamic response of the impact loading can be analyzed in frequency domain.The main conclusions of this investing are as follows:(1) For the quasi-static test of3-D braided composites, the load increases linearly and decreases gradually after the maximum value. The damage area and severity are small since the3- D braided composites have enough time to reach stress equilibrium. The main failure mode is resin crack on the surface and de-bonding on the back.(2) For the transverse impact of3-D braided composites, the incident bar hits the specimen several times due to the multi-reflection of stress wave in the incident bar. Therefore, there are several load peaks in the load-displacement curve while the peak loads decreases as the increase of impact cycles. The peak loads and absorbed energy increase with the increase of impact velocity. Based on the failure morphologies, the failure mode is resin crack at relative low impact velocity and fiber breakage at other high impact velocities.(3) For the low-velocity impact of3-D braided composites, the peak load, the absorbed energy at peak load, and total absorbed energy increase with the increase of impact velocity. The failure modes change from elastic deformation at1m/s to resin crack and de-bonding at2m/s～4m/s and finally to fiber breakage at6m/s.(4) The load-displacement curve calculated by finite element method agrees well with the experimental results. The agreement proves the accuracies and effectiveness of the unit-cell mode and the VUMAT. The unit cell mode and VUMAT can be applied in the structural designing of3-D braided composite. Furthermore, this method can also expand to designing of other structural composites.(5) The frequency and amplitude characteristics of impact loading can be obtained by the Fast Fourier Transform of load-time curve from experimental test. The result shows that the energy of impact loading centralized in the low-frequency area. The amplitude increases with the increase of impact velocity, but the frequency does not change significantly. With another signal transform method Hilbert-Huang Transform, the relationship between time, frequency, and amplitude of impact loading can be obtained. The relationship between time and frequency provides more information about the dynamic response of3-D braided composite. The discontinuity in time-frequency curve implies the dynamic response of3-D braided composite change from elastic deformation stage to plastic damage stage. The discontinuity happens earlier when the impact velocity increases.