基于频率变化预测玻璃纤维增强树脂复合材料层合板的剩余疲劳寿命

复合材料结构在疲劳过程中的累积损伤将导致结构刚度下降，并进一步引起结构的动态参数如频率发生衰减。因此，可以将结构疲劳状态与结构频率联系起来，基于频率预测结构的剩余疲劳寿命。本文首先基于复合材料在纵向、横向和面内剪切三个方向的疲劳特性，结合ABAQUS与Umat子程序开发了三维有限元模型模拟复合材料层合板中的疲劳损伤演变，并构建了不同疲劳状态下对应的模态分析模型，由此获得了疲劳过程中的频率衰减曲线。之后，基于疲劳过程的频率变化量训练了人工神经网络，用于预测玻璃纤维增强复合材料层合板的剩余疲劳寿命。特别地，在当前的数值模型中为每个单元分配了符合高斯正态分布的材料属性，以模拟实际情况下复合材料性能的离散性。结果表明，疲劳模型数值模拟结果与已有文献的疲劳实验数据吻合，基于频率变化量训练的人工神经网络可以成功预测玻璃纤维增强复合材料试件的剩余疲劳寿命。 

Prediction of remaining fatigue life of glass fiber reinforced polymer laminates based on frequency change

The cumulative damage in the composite structures during the fatigue process will lead to decrease in the stiffness of structures. This will further cause the changes in the dynamic parameters of the structure, such as the frequencies. Therefore, the fatigue status can be related to the frequencies of structures, and inversely, the frequencies can be used to predict the fatigue life of the structures. In this paper, by incorporating Umat subroutines in ABAQUS, a three-dimensional finite element model was developed to simulate the evolution of fatigue damage in glass fiber reinforced polymer (GFRP) laminates. The fatigue characteristics of composite materials in the longitudinal, transverse and in-plane shear directions have been considered in the model. The fatigue state of the glass fiber reinforced polymer laminates was exported from the fatigue model and then was imported into a second model to apply modal analysis for obtaining the frequencies which are corresponding to the fatigue status. An artificial neural network was trained based on the frequency data during the fatigue process, with the frequency shifts as the input and the remaining fatigue life as the output. The training data for ANN was generated from the finite element (FE) models, based on which the remaining fatigue life of the GFRP laminates was predicted. In particular, to consider the discreteness of material properties of fiber reinforced polymer (FRP) composite materials, each element in the finite element model (FEM) was individually assigned the material properties randomly distributed in the Gaussian normal distribution. The results show that the numerical simulation results of the present fatigue model are consistent with the fatigue test data in the existing literature. The trained artificial neural network can successfully predict the remaining fatigue life of the GFRP laminates.