非理想缺陷层合板的界面参数分析

doi:10.19936/j.cnki.2096-8000.20250828.009

摘要/Abstract

摘要： 考虑到纤维桥联影响,引入一种具有消失厚度损伤区域的代表性体积单元(RVE),并建立无厚度弹簧模型,通过两个独立的界面参数来表征裂纹的理想和非理想程度(在敏感区间内,界面参数可用于模拟非理想程度),从而用于具有横向基体裂纹的层合板估算。对于具有张开和闭合裂纹的层合板,在静不定边界区域引用待定的分区载荷。本文不仅考虑了光滑平面张开裂纹、光滑平面闭合裂纹以及完全啮合张开裂纹三种理想裂纹情况,还分析了非理想裂纹即非理想张开裂纹和非理想闭合裂纹两种情况。研究不仅验证了柔度元素的对称性和闭合情况下剪切柔度元素变化率的相等性,同时也表明裂纹的非理想程度对有效耦合系数和有效剪切柔度的影响显著。

关键词: 横向基体裂纹, 理想裂纹, 非理想裂纹, 变分分析, 界面参数, 刚度退化, 复合材料

Abstract: Considering the influence of bridge fibers, a representative volume element(RVE) with damaged regions of vanishing thickness and a spring model with no thickness is established to characterize the ideal and non-ideal degree of cracks by two independent interface parameters(interface parameters can be used to simulate non-ideal degree in the sensitive interval) is developed to study for estimation of lanimates with transverse matrix cracks. For laminates with open and closed cracks, pending partition loads are applied in the statically indeterminate boundary. This paper not only consider three cases of the idela cracks, the smooth plane-surface open crack, the smooth plane-surface closed crack and the perfect meshing open crack, but also two cases of the non-ideal cracks, the open cracks and the closed cracks. The study not only verifies the symmetry of the flexibility element and the equality of the change rate of the shear flexibility element under closed cracks, but also shows that the non-ideal degree of cracks has a great influence on the effective coupling coefficient and the effective shear flexibility.

Key words: transverse matrix crack, ideal crack, non-ideal crack, variational analysis, interface parameters, stiffness reduction, composites

中图分类号:

TB332

徐栋, 黄志强, 陈松, 谢晶晶. 非理想缺陷层合板的界面参数分析[J]. 复合材料科学与工程, 2025, 0(8): 74-85.

XU Dong, HUANG Zhiqiang, CHEN Song, XIE Jingjing. Interface parameter analysis of laminates with non-ideal defects[J]. COMPOSITES SCIENCE AND ENGINEERING, 2025, 0(8): 74-85.

参考文献

[1] REIFSNIDER K L, SCHULTE K, DUKE J C. Long-term fatigue behavior of composite materials[M]//Long-term behavior of composites. West Conshohocken: ASTM International, 1983.
[2] HIGHSMITH A L, REIFSNIDER K L. Stiffness-reduction mechanisms in composite laminates[M]//Damage in composite materials: basic mechanisms, accumulation, tolerance, and characterization. West Conshohocken: ASTM International, 1982.
[3] HOOVER J W, KUJAWSKI D, ELLYIN F. Transverse cracking of symmetric and unsymmetric glass-fibre/epoxy-resin laminates[J]. Composites Science and Technology, 1997, 57(11): 1513-1526.
[4] KATERELOS D G, MCCARTNEY L N, GALIOTIS C. Local strain re-distribution and stiffness degradation in cross-ply polymer composites under tension[J]. Acta Materialia, 2005, 53(12): 3335-3343.
[5] AMARA K H, TOUNSI A, BENZAIR A. Transverse cracking and elastic properties reduction in hygrothermal aged cross-ply laminates[J]. Materials Science and Engineering: A, 2005, 396(1-2): 369-375.
[6] OGIHARA S, TAKEDA N. Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates[J]. Composites Science and Technology, 1995, 54(4): 395-404.
[7] JOFFE R, VARNA J. Analytical modeling of stiffness reduction in symmetric and balanced laminates due to cracks in 90 layers[J]. Composites Science and Technology, 1999, 59(11): 1641-1652.
[8] KASHTALYAN M, SOUTIS C. Stiffness degradation in cross-ply laminates damaged by transverse cracking and splitting[J]. Composites Part A: Applied Science and Manufacturing, 2000, 31(4): 335-351.
[9] HASHIN Z. Analysis of orthogonally cracked laminates under tension[J]. Journal of Applied Mechanics, 1987, 54(4): 872-879.
[10] VINOGRADOV V, HASHIN Z. Probabilistic energy based model for prediction of transverse cracking in cross-ply laminates[J]. International Journal of Solids and Structures, 2005, 42(2): 365-392.
[11] HUANG Z Q, NIE G H, CHAN C K. An exact solution for stresses in cracked composite laminates and evaluation of the characteristic damage state[J]. Composites Part B: Engineering, 2011, 42(5): 1008-1014.
[12] HUANG Z Q, YI S H, CHEN H X, et al. Parameter analysis of damaged region for laminates with matrix defects[J]. Journal of Sandwich Structures & Materials, 2021, 23(2): 580-620.
[13] ZHANG J, FAN J, SOUTIS C. Analysis of multiple matrix cracking in[±θ_m/90_n] _S composite laminates. Part 1: In-plane stiffness properties[J]. Composites, 1992, 23(5): 291-298.
[14] KASHTALYAN M, SOUTIS C. Analysis of local delaminations in composite laminates with angle-ply matrix cracks[J]. International Journal of Solids and Structures, 2002, 39(6): 1515-1537.
[15] KASHTALYAN M, SOUTIS C. Analysis of composite laminates with intra-and interlaminar damage[J]. Progress in Aerospace Sciences, 2005, 41(2): 152-173.
[16] TOUNSI A, AMARA K. Stiffness degradation in hygrothermal aged cross-ply laminate with transverse cracks[J]. AIAA Journal, 2005, 43(8): 1836-1843.
[17] ZHANG H, MINNETYAN L. Variational analysis of transverse cracking and local delamination in[θ_m/90_n] _S laminates[J]. International Journal of Solids and Structures, 2006, 43(22-23): 7061-7081.
[18] LI S, HAFEEZ F. Variation-based cracked laminate analysis revisited and fundamentally extended[J]. International Journal of Solids and Structures, 2009, 46(20): 3505-3515.
[19] VINOGRADOV V, HASHIN Z. Variational analysis of cracked angle-ply laminates[J]. Composites Science and Technology, 2010, 70(4): 638-646.
[20] HAJIKAZEMI M, SADR M H, HOSSEINI-TOUDESHKY H, et al. Thermo-elastic constants of cracked symmetric laminates: a refined variational approach[J]. International Journal of Mechanical Sciences, 2014, 89: 47-57.
[21] HUANG Z Q, ZHOU J C, HE X Q, et al. Variational analysis for angle-ply laminates with matrix cracks[J]. International Journal of Solids and Structures, 2014, 51(21-22): 3669-3678.
[22] HUANG Z Q, HE X Q. Stress distributions and mechanical properties of laminates[θ_m/90_n] _S with closed and open cracks in shear loading[J]. International Journal of Solids and Structures, 2017, 118: 97-108.
[23] NUISMER R J, TAN S C. Constitutive relations of a cracked composite lamina[J]. Journal of Composite Materials, 1988, 22(4): 306-321.
[24] TAN S C, NUISMER R J. A theory for progressive matrix cracking in composite laminates[J]. Journal of Composite Materials, 1989, 23(10): 1029-1047.
[25] LUNDMARK P, VARNA J. Crack face sliding effect on stiffness of laminates with ply cracks[J]. Composites Science and Technology, 2006, 66(10): 1444-1454.
[26] HASHIN Z. The spherical inclusion with imperfect interface[J]. Journal of Applied Mechanics, 1991, 58(2): 444-449.
[27] HASHIN Z. Thin interphase/imperfect interface in elasticity with application to coated fiber composites[J]. Journal of the Mechanics and Physics of Solids, 2002, 50(12): 2509-2537.
[28] WÜRKNER M, BERGER H, GABBERT U. Numerical study of effective elastic properties of fiber reinforced composites with rhombic cell arrangements and imperfect interface[J]. International Journal of Engineering Science, 2013, 63: 1-9.
[29] WÜRKNER M, BERGER H, GABBERT U. Numerical investigations of effective properties of fiber reinforced composites with parallelogram arrangements and imperfect interface[J]. Composite Structures, 2014, 116: 388-394.
[30] HUANG Z Q, HE X Q, LIEW K M. A sensitive interval of imperfect interface parameters based on the analysis of general solution for anisotropic matrix containing an elliptic inhomogeneity[J]. International Journal of Solids and Structures, 2015, 73: 67-77.
[31] YU H Y. A new dislocation-like model for imperfect interfaces and their effect on load transfer[J]. Composites Part A: Applied Science and Manufacturing, 1998, 29(9-10): 1057-1062.
[32] HUANG Z Q, NIE G H, CHAN C K. Solution of the plane problem for anisotropic media containing an elliptic inhomogeneity with dislocation-like interface[J]. Acta Mechanica, 2013, 224(11): 2863-2880.