Interfacial crack growth of delaminated composite laminates under hygrothermal environment
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摘要:
处于恶劣湿热环境中的复合材料层合结构，受湿热残余应变和残余应力的作用，易产生局部屈曲和分层扩展。考虑湿热效应和脱层间接触效应的影响，对含脱层复合材料中厚板的非线性屈曲和界面裂纹扩展行为进行了理论分析。基于可动边界变分原理，建立层合板在湿-热-力载荷作用下的总势能，并推导出非线性后屈曲控制方程和脱层扩展能量释放率。应用摄动法和Galerkin法求解控制方程，获得以面内压缩载荷-挠度曲线为特征的含脱层复合材料层合板的后屈曲路径。根据求得的后屈曲解及Griffith断裂准则，确定脱层扩展临界压力的理论解。通过开发MATLAB程序，综合讨论了脱层尺寸、湿热环境对脱层复合材料层合板屈曲和扩展载荷的影响。研究结果与ABAQUS有限元解和经典理论解进行比较，验证了理论分析的有效性。结果表明：湿热环境会显著降低脱层复合材料层合板的屈曲载荷和扩展载荷。此外，忽略复合材料层合板的横向剪切应变将导致对层合板承载能力的高估。
Abstract:The laminated composite structures in harsh hygrothermal environment are easy to undergo premature buckling and delamination propagation. This paper proposes a theoretical study on the nonlinear buckling and interfacial crack propagation of thick plate containing delamination by considering the hygrothermal effect and the contact effect. Based on the variational principles of variable boundary, the total potential energy of the laminates subjected to hygro-thermal-mechanical loading is established from which the governing equations for nonlinear post-buckling and the expression of energy release rate for delamination propagation are derived. The post-buckling equilibrium paths of the laminates characterized by the in-plane load vs deflection amplitude curves are determined via perturbation technique and Galerkin approach. With the available solutions from post-buckling analysis, the theoretical solution of threshold load corresponding to the delamination propagation is determined according to Griffith fracture criterion. By developing MATLAB program, numerical calculations are performed to discuss the effect of the temperature, the hygroscopic concentration and the delamination conditions on the buckling and delamination propagation threshold load. The solutions are compared with the results from ABAQUS finite element analysis and the predictions obtained from classical laminated plate theory, both showing good agreements with the presented theoretical solutions. Results show that hygro-thermal environment reduce the buckling load and the delamination propagation threshold load. Besides, neglecting the transverse shear strain may overestimate the load-carrying capacity of the laminates.
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图 1 含脱层复合材料层合板的四分区模型
Figure 1. Four region modeling of delaminated composite laminates
图 5 相对脱层深度对无量纲临界载荷Ncr和Npl的影响
Figure 5. Effect of relative delamination depth on non-dimensional critical load Ncr and Npl
图 6 相对脱层长度对无量纲临界载荷Ncr和Npl的影响
Figure 6. Effect of relative delamination length on non-dimensional critical load Ncr and Npl
图 7 温度改变对无量纲临界载荷Ncr和Npl及后屈曲路径的影响
Figure 7. Effect of change of temperature on non-dimensional critical load Ncr and Npl and post-buckling equilibrium path
图 8 湿度改变对无量纲临界载荷Ncr和Npl及后屈曲路径的影响
Figure 8. Effect of change of hygroscopic concentration on non-dimensional critical load Ncr and Npl and post-buckling equilibrium path
表 1 含脱层复合材料层合板的有限元方法与理论方法的无量纲屈曲载荷比较
Table 1. Compassion of non-dimensional buckling load between FEM and present method of delaminated composite laminates
ΔT/℃ L2/a 无量纲屈曲载荷 Diff./% FEM FSDT 0.1 8 477 8 368 1.29 0 0.3 7 031 6 720 4.42 0.5 6 091 5 844 4.06 0.1 8 329 8 220 1.31 25 0.3 6 881 6 574 4.46 0.5 5 941 5 697 4.11 0.1 8 031 7 925 1.32 75 0.3 6 581 6 280 4.57 0.5 5 640 5 402 4.22 
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表 2 含脱层复合材料层合板的经典层合板理论和剪切理论无量纲屈曲载荷和无量纲临界扩展载荷比较
Table 2. Compassion of non-dimensional buckling load and non-dimensional threshold between CLPT and present method of delaminated composite laminates
h2/h L2/a Ncr Npl Diff.Ncr/% Diff.Npl/% CLPT[18] FSDT CLPT[18] FSDT 0.1 9 527 9 050 9 706 9 055 5.01 6.71 0.1 0.2 8 991 8 553 9 039 8 620 4.87 4.64 0.3 8 549 8 145 5 578 8 181 4.73 4.63 0.1 8 001 7 623 8 031 7 721 4.72 3.86 0.3 0.2 6 633 6 349 6 658 6 395 4.28 3.95 0.3 5 738 5 516 5 758 5 548 3.87 3.65 0.1 7 029 6 753 7 065 6 831 3.93 3.31 0.5 0.2 5 477 5 294 5 501 5 338 3.34 2.96 0.3 4 562 4 428 4 583 4 462 2.94 2.64 注：Diff.Ncr为Ncr的Diff.，Diff.Npl为Npl的Diff.。
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