考虑界面接触效应的复合材料层合板分层屈曲的三维有限元分析
|
摘要
运用Abaqus有限元软件模拟含脱层的复合材料层合板的屈曲过程。运用实体单元构建复合材料层合板模型,采用线弹性本构关系,考虑脱层间的接触效应,在脱层界面处施加硬接触的法向行为,防止脱层界面上下两部分的相互贯穿,保证变形的协调性。通过数值算例,综合讨论了不同深度、不同宽度、不同长宽比以及有无接触效应时对屈曲极限荷载的影响。同时对无损伤层合板在相同参数的情况下的屈曲进行了模拟,获得了临界荷载值,将有限元结果与理论解比较后数值吻合,结果表明,所建立的模型能够准确的模拟脱层板屈曲过程。
This paper presents a finite-element approach to simulate the buckling process of the composite laminated plate containing a buried delamination. The delaminated composite laminates are analyzed using solid elements. In order to prevent the mutual penetration between the two parts above and below the delamination and to ensure coordinated deformation, a normal behavior of hard contact is applied at the interfaces of the delamination to take into consideration of the nonlinear contact effect between the debonded regions. Parametric analyses are conducted to investigate the effects of delamination depth, delamination length and aspect ratio on the buckling loads. Furthermore, buckling of a perfect laminate with the same geometrical parameters is simulated to obtain the critical buckling load. A comparison between the finite element prediction and the classic theoretical solution for the perfect laminate is carried out. It is found that they are in good agreement. The established model can simulate the buckling process of the composite laminated plate accurately.
This paper presents a finite-element approach to simulate the buckling process of the composite laminated plate containing a buried delamination. The delaminated composite laminates are analyzed using solid elements. In order to prevent the mutual penetration between the two parts above and below the delamination and to ensure coordinated deformation, a normal behavior of hard contact is applied at the interfaces of the delamination to take into consideration of the nonlinear contact effect between the debonded regions. Parametric analyses are conducted to investigate the effects of delamination depth, delamination length and aspect ratio on the buckling loads. Furthermore, buckling of a perfect laminate with the same geometrical parameters is simulated to obtain the critical buckling load. A comparison between the finite element prediction and the classic theoretical solution for the perfect laminate is carried out. It is found that they are in good agreement. The established model can simulate the buckling process of the composite laminated plate accurately.
引文
[1] Whitcomb J D. Finite element analysis of instability related delamination growth [J]. Journal of Composite Materials,1981(5):403-428.
[2] Bisagni C, Walters C. Experimental investigation of the damage propagation in composite specimens under biaxial loading. Composite Structures,2008,85(4):293-310.
[3] Rhead A T, Butler R, Hunt GW. Post-buckled propagation model for compressive fatigue of impact damaged laminates. International Journal of Solid and Structures.2008,45(16):4349-4361.
[4] 王平安,矫桂琼,王波,等.复合材料加筋板载剪切荷载下的屈曲特性研究[J].机械强度,2009,31(1):078-082.WANG PingAn, JIAO GuiQiong, WANG Bo, et al.Buckling performance analysis of stiffened composite plate under shear loading[J].Journal of Mechanical Strength, 2009,31(1):078-082(In Chinese).
[5] Kachanov L M. Separation failure of composites materials[J]. Polymer Mechanics,1976,22(3):533-560.
[6] Chai H, Babcock C D, Knauss W G. One dimensional modeling of failure in laminated plates by delamination buckling[J]. International Journal of Solids and Structurees, 1981,17(11):1069-1083.
[7] Simitses G J, Sallam S, Yin W L. Effect of delamination of axially loaded homogeneous laminated plates[J]. AIAA Journal, 1985,23(9):1437-1444.
[8] Yin W L, Wang J T. The energy-release rate in the growth of a one-dimensional delamination[J]. Journal of Applied Mechanics, 1984,51(4):939-941.
[9] Lee J, Gurdal Z, Griffin O H, Buckling and postbuckling of circular plates containing concentric penng-shaped delaminations[J]. Computers & Structures, 1996,58(5):1045-1054.
[10] Yap Chun Wee, Chai Gin Boay. Analytical and numerical studies on the buckling of delaminated composite beams[J]. Composite Structures, 2007(80):307-319.
[11] 徐永锋,张志民,王俊奎.复合材料夹层板面芯二维分层屈曲研究[J]. 复合材料学报,1997,14(4):101-107.XU YongFeng, ZHANG ZhiMin, WANG JunKui. Buckling study of two-dimensional face-core delaminations in composite sandwich plates[J]. Acta Materiae Compositae Sinica, 1997,14(4):101-107(In Chinese).
[12] 刘从玉,许希武,陈康. 考虑脱粘的复合材料加筋板屈曲后屈曲及承载能力数值分析[J].复合材料学报,2010,27(6):158-166.LIU CongYu, XU XiWu, CHEN Kang. Buckling, post-buckling and collapse analysis of stiffened composite panels with debonding damage[J]. Acta Materiae Compositae Sinica,.2010,27(6):158-166(In Chinese).
[13] 孙浩,许希武,郭树祥. 含分层损伤缝合复合材料层板的剩余压缩强度[J]. 材料科学与工程学报,2012,30(4),615-624.SUN Hao, XU XiWu, GUO ShuXiang. Prediction of residual compressive strength of stitched composite laminates with a delamination[J]. Journal of Materials Science &Engineering. 2012,30(4),615-624(In Chinese).
[14] 卢子兴,王晓英,俸翔.复合材料层合板临界屈曲荷载分散性[J].复合材料学报,2013,30(1):194-200.LU ZiXing, WANG XiaoYing, FENG Xiang. Critical buckling load discrepancy of composite laminates[J].Acta Materiae Compositae Sinica, 2013,30(1):194-200(In Chinese).
[15] Barbero, E. J. and Reddy, J. N. Modeling of delamination in composite laminates using a layer-wise plate theory. International Journal of Solids and Structures,1991,28(3),373-388.
[16] Robbins D H, Reddy J N, Krishna M A V. On the modeling of delamination in thick composites with delaminations. AIAA Journal,1993,31(2),331-338.
[17] Qing G H, Liu Y H., Li D H. A semi-analytical model for the energy release rate analyses of composite laminates with a delamination. Finite Element in analysis and Design, 2011,47,1017-1024.
[18] 王泽武,李耀宙,夏良志,等.圆筒形薄壳热屈曲临界温度理论解及修正[J].机械强度,2017,39(1):149-153.WANG ZeWu, LI YaoZhou, XIA LiangZhi, et al. Theoretical solution and its correction of thermal buckling critical temperature for cylindrical thin-shell[J]. Journal of Mechanical Strength, 2017,39(1):149-153(In Chinese).
[19] Xue J H, Luo Q Z, Han F, Liu R H. Two dimensional analyses of delamination buckling of symmetrically cross-ply, rectangular laminates [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(5):1-16.
[20] Tang M Q, Xue J H, Yuan H, Liu R H. Macro-micro analysis for anti-penetrating postbuckling of fiber reinforce, debonded laminates with contact effects [J]. International Journal of Applied Mechanics,2014,6(4):1-24.
[21] Xue J H, Zi L, Yuan H, Lin R H. Contact analysis is for fiber reinforced, delaminated laminates with kinematic nonlinearity [J]. Acta Mechanica Solida Sinica, 2013,26(4):388-402.
[22] Jones, R. M. Mechanics of Composites Materials, 2nd ed., Philadelphia, USA,1980.
[23] 沈观林,胡更开. 复合材料力学[M]. 第二版.北京:清华大学出版社,2006:143-153.SHEN GuanLin, HU GengKai. Mechanics of composite materials[M].Second Edition.Beijing: Tsinghua University Press, 2006:143-153.
[2] Bisagni C, Walters C. Experimental investigation of the damage propagation in composite specimens under biaxial loading. Composite Structures,2008,85(4):293-310.
[3] Rhead A T, Butler R, Hunt GW. Post-buckled propagation model for compressive fatigue of impact damaged laminates. International Journal of Solid and Structures.2008,45(16):4349-4361.
[4] 王平安,矫桂琼,王波,等.复合材料加筋板载剪切荷载下的屈曲特性研究[J].机械强度,2009,31(1):078-082.WANG PingAn, JIAO GuiQiong, WANG Bo, et al.Buckling performance analysis of stiffened composite plate under shear loading[J].Journal of Mechanical Strength, 2009,31(1):078-082(In Chinese).
[5] Kachanov L M. Separation failure of composites materials[J]. Polymer Mechanics,1976,22(3):533-560.
[6] Chai H, Babcock C D, Knauss W G. One dimensional modeling of failure in laminated plates by delamination buckling[J]. International Journal of Solids and Structurees, 1981,17(11):1069-1083.
[7] Simitses G J, Sallam S, Yin W L. Effect of delamination of axially loaded homogeneous laminated plates[J]. AIAA Journal, 1985,23(9):1437-1444.
[8] Yin W L, Wang J T. The energy-release rate in the growth of a one-dimensional delamination[J]. Journal of Applied Mechanics, 1984,51(4):939-941.
[9] Lee J, Gurdal Z, Griffin O H, Buckling and postbuckling of circular plates containing concentric penng-shaped delaminations[J]. Computers & Structures, 1996,58(5):1045-1054.
[10] Yap Chun Wee, Chai Gin Boay. Analytical and numerical studies on the buckling of delaminated composite beams[J]. Composite Structures, 2007(80):307-319.
[11] 徐永锋,张志民,王俊奎.复合材料夹层板面芯二维分层屈曲研究[J]. 复合材料学报,1997,14(4):101-107.XU YongFeng, ZHANG ZhiMin, WANG JunKui. Buckling study of two-dimensional face-core delaminations in composite sandwich plates[J]. Acta Materiae Compositae Sinica, 1997,14(4):101-107(In Chinese).
[12] 刘从玉,许希武,陈康. 考虑脱粘的复合材料加筋板屈曲后屈曲及承载能力数值分析[J].复合材料学报,2010,27(6):158-166.LIU CongYu, XU XiWu, CHEN Kang. Buckling, post-buckling and collapse analysis of stiffened composite panels with debonding damage[J]. Acta Materiae Compositae Sinica,.2010,27(6):158-166(In Chinese).
[13] 孙浩,许希武,郭树祥. 含分层损伤缝合复合材料层板的剩余压缩强度[J]. 材料科学与工程学报,2012,30(4),615-624.SUN Hao, XU XiWu, GUO ShuXiang. Prediction of residual compressive strength of stitched composite laminates with a delamination[J]. Journal of Materials Science &Engineering. 2012,30(4),615-624(In Chinese).
[14] 卢子兴,王晓英,俸翔.复合材料层合板临界屈曲荷载分散性[J].复合材料学报,2013,30(1):194-200.LU ZiXing, WANG XiaoYing, FENG Xiang. Critical buckling load discrepancy of composite laminates[J].Acta Materiae Compositae Sinica, 2013,30(1):194-200(In Chinese).
[15] Barbero, E. J. and Reddy, J. N. Modeling of delamination in composite laminates using a layer-wise plate theory. International Journal of Solids and Structures,1991,28(3),373-388.
[16] Robbins D H, Reddy J N, Krishna M A V. On the modeling of delamination in thick composites with delaminations. AIAA Journal,1993,31(2),331-338.
[17] Qing G H, Liu Y H., Li D H. A semi-analytical model for the energy release rate analyses of composite laminates with a delamination. Finite Element in analysis and Design, 2011,47,1017-1024.
[18] 王泽武,李耀宙,夏良志,等.圆筒形薄壳热屈曲临界温度理论解及修正[J].机械强度,2017,39(1):149-153.WANG ZeWu, LI YaoZhou, XIA LiangZhi, et al. Theoretical solution and its correction of thermal buckling critical temperature for cylindrical thin-shell[J]. Journal of Mechanical Strength, 2017,39(1):149-153(In Chinese).
[19] Xue J H, Luo Q Z, Han F, Liu R H. Two dimensional analyses of delamination buckling of symmetrically cross-ply, rectangular laminates [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(5):1-16.
[20] Tang M Q, Xue J H, Yuan H, Liu R H. Macro-micro analysis for anti-penetrating postbuckling of fiber reinforce, debonded laminates with contact effects [J]. International Journal of Applied Mechanics,2014,6(4):1-24.
[21] Xue J H, Zi L, Yuan H, Lin R H. Contact analysis is for fiber reinforced, delaminated laminates with kinematic nonlinearity [J]. Acta Mechanica Solida Sinica, 2013,26(4):388-402.
[22] Jones, R. M. Mechanics of Composites Materials, 2nd ed., Philadelphia, USA,1980.
[23] 沈观林,胡更开. 复合材料力学[M]. 第二版.北京:清华大学出版社,2006:143-153.SHEN GuanLin, HU GengKai. Mechanics of composite materials[M].Second Edition.Beijing: Tsinghua University Press, 2006:143-153.