A fatigue life prediction method for composite materials considering interlayer stress
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摘要:
针对疲劳载荷下复合材料层板容易产生分层且多是从边缘开始分层的现象，利用解析法求解复合材料层合板各层间应力，得到拉伸和弯曲载荷下各层间界面层间应力分布情况。提出了局部平均应力的概念对自由边界附近的层间应力进行处理，利用改进的Hashin分层失效准则作为分层判据选取危险层间的局部平均应力，将其引入到复合材料Stress-Fatigue life N（简称
S-N ）曲线模型当中，采用拉-拉和三点弯曲疲劳载荷下的复合材料寿命数据进行拟合，利用拟合得到的模型进行寿命预测，结果发现拟合精度较高，预测寿命均在±2倍误差带以内，并将建立的模型与目前3种常用的S -N 曲线模型进行对比，发现本文模型在整体上预测结果最好，对拉伸和弯曲疲劳寿命预测误差最小。Abstract:In response to the phenomenon that composite laminates are prone to delamination under fatigue load, which often starts from the edge, analytical methods were used to solve the interlayer stress of composite laminates and obtain the distribution of interlayer stress at each interface under tensile and bending loads. The concept of local average stress was proposed to process the interlayer stress near the free boundary. The improved Hashin delamination failure criterion was used as the delamination criterion to select the local average stress between dangerous layers, which was introduced into the composite Stress-Fatigue life N (Abbreviated as
S -N ) curve model. The composite material life data under tensile and three-point bending fatigue loads were used for fitting, and the fitted model was used for life prediction. The results showed that the fitting accuracy was high, and the predicted life was within ±2 times the error band. The model was compared with three commonly usedS -N curve models, finding that the overall prediction results of this model were the best, with the smallest prediction error for tensile and bending fatigue life.-
Key words:
- composite materials /
- edge effect /
- interlayer stress /
- S-N curve /
- life prediction
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图 1 静态载荷下无缺口层板的分层过程
Figure 1. Delamination process of non notched laminates under static load
图 2 [452/902/−452/02]S层板的拉伸疲劳失效过程
Figure 2. Tensile fatigue failure process of [452/902/−452/02]S laminates
图 3 拉伸载荷下层板各界面层间应力分布情况
Figure 3. Stress distribution between interfaces of lami-nates under tensile load
图 4 弯曲载荷下层板部分界面层间应力分布情况
Figure 4. Distribution of interlayer stress at the interface of laminate under bending load
图 5 自由边缘层间正应力随铺层角度的变化规律
Figure 5. Variation normal stress between free edge layers with ply angle
图 7 不同算例的试验寿命与预测寿命对比
Figure 7. Comparison of experimental life and predicted life for different calculation examples
图 8 本模型与其他模型对于4个算例的预测寿命
Figure 8. Predicted life of this model and the other three models for four examples
图 9 本文模型与其他模型对于4个算例的寿命预测误差箱线图
Figure 9. Life prediction error box plot of the model in this article and the other three models for four examples
表 1 两种方法计算得到的层间7的局部平均应力
Table 1. Local average stress of interlayer 7 calculated by two methods
计算方法 $ {\bar {\sigma }}_{{\textit{zz}}} $ $ {\bar {\tau }}_{x{\textit{z}}} $ $ {\bar {\tau }}_{y{\textit{z}}} $ 复化梯形公式 9.21×10−5 8.93×10−3 −1.37×10−2 拉格朗日插值法 9.07×10−5 8.23×10−3 −1.46×10−2 偏差/% 1.54 8.51 6.16 
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表 2 拉伸载荷下T300/QY8911层合板局部平均层间应力和分层判断
Table 2. Local average interlayer stress and delamination judgment of T300/QY8911 laminated plates under tensile load
自顶层至中面
铺层层间自由边界应力相对数值 $C_{\mathrm{ri}} $ 分层判断 分析 $ {\bar {\sigma }}_{{\textit{zz}}} $ $ {\bar {\tau }}_{x{\textit{z}}} $ $ {\bar {\tau }}_{y{\textit{z}}} $ 层间1 45/90 5.84×10−6 −8.92×10−3 1.36×10−2 4.84×10−3 层间7最易分层 层间2 90/−45 1.44×10−5 −8.97×10−3 1.29×10−2 4.51×10−3 层间3 −45/0 2.69×10−5 −0.9×10−2 −0. 29×10−3 1.48×10−3 层间4 0/0 3.46×10−5 2.76×10−5 1.35×10−5 7.12×10−7 层间5 0/−45 6.50×10−5 9.04×10−3 3.25×10−4 1.49×10−3 层间6 −45/90 8.19×10−5 8.98×10−3 −1.29×10−2 4.51×10−3 层间7 90/45 9.21×10−5 8.93×10−3 −1.37×10−2 4.88×10−3 最易分层 层间8 45/45 1.20×10−4 1.53×10−7 −3.23×10−5 6.68×10−7
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表 3 T300/QY8911层合板拉伸疲劳试验数据及应力参量
Table 3. Tensile fatigue test data and corresponding stress parameters of T300/QY8911 laminated plates
拉伸强度/MPa 应力水平q 寿命N/循环 应力参量 578.8 0.85 1.44×104 0.8635 0.80 1.98×104 0.8169 0.70 9.55×104 0.7222 0.65 3×105 0.6741 0.59 6×105 0.6156 0.54 106 0.5663
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表 4 本模型与其他模型对4个算例试验数据的拟合优度
Table 4. Goodness of fit between this model and other models for the experimental data of four examples
算例 本文模型 模型1 模型2 模型3 算例1 0.9838 0.6304 0.9041 0.9840 算例2 0.9839 0.9596 0.9835 0.9571 算例3 0.9716 0.5771 0.6991 0.7525 算例4 0.9900 0.9715 0.5107 0.9843
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