复杂应力状态下三维纤维向应力公式及其应用研究  

Spacial filament stresses in fiber directions and application research in state of triaxial stress

作　　者：耿沛[1] 邢静忠[1] 陈晓霞[1] 

机构地区：[1]天津工业大学机械工程学院,天津300387

出　　处：《固体火箭技术》2016年第2期236-241,246,共7页Journal of Solid Rocket Technology

基　　金：浙江大学CAD&CG国家重点实验室开放课题(A1515);国家自然科学基金(11372220);国家自然科学基金(51575390);天津市应用基础与前沿技术研究计划一般项目(14JCYBJC19200)

摘　　要：为解决二维纤维向应力公式在计算三向应力状态时出现的偏差,推导出三维纤维向应力公式。利用正轴和偏轴坐标系下的应力和应变的坐标变换,导出正轴和偏轴的应力-应变关系。利用对称均衡铺设层的应力和变形关系,求解得到三向应力状态下的纤维应力公式。其退化情况等同于现有二维公式;用于厚壁筒模型时,本公式与其三维公式完全一致。采用ANSYS软件的SOLID191层合单元建立有内胆的纤维缠绕厚壁筒模型,计算内外压作用下的应力分布及强度比。对比表明,本公式的计算结果与有限元结果一致。研究发现,在复杂应力状态下,三维应力公式可给出更准确的计算结果;基于二维应力公式的纤维层强度比小于三维公式的结果。本公式为Tsai-Wu等复杂应力状态下失效准则的强度计算奠定理论基础。三维纤维应力公式不仅适用于厚壁柱形容器等结构,而且适用于任意对称均衡铺设的纤维增强复合材料结构的应力和强度计算。In order to reduce the deviation of the two-dimensional （2D） fiber stresses formulae in calculating the three-dimen- sional （3D） stresses, 3D fiber stresses formulae were present. Using the coordinate transformation of stress-strain in on-axis and off- axis coordinate systems, the on-axis and off-axis stress-strain relationship was given. Based on the relationship of forces equilibrium and deformation consistency between the global unit and the alternate-ply, 3D fiber stresses formulae were derived analytically. The degradation is equivalent to the 2D formulae in the references, and the 3D formulae in the thick-walled cylinder model. Finite ele- ment models （FEMs） of filament winding thick-walled cylinder were built in ANSYS software by layered element SOLID191, and numeric results were calculated and analyzed under internal pressure, and both internal and external pressure, respectively. Perfect agreement of fiber stresses in fiber directions and strength ratio between the FEMs and the theory was achieved. It is found that the 3D fiber stresses formulae give more accurate stresses results and lower strength ratio than 2D formulae in triaxial stress state. The formulae in the paper give a theoretical basis for Tsai-Wu failure criteria in triaxial stress state. The 3D fiber stresses formula applies to the stresses and strength ratio calculation of thick-walled cylindrical structure, and any structures made of symmetrical alternate-ply fiber reinforced composite material.

关 键 词：纤维向应力 正交各向异性 强度比 失效准则 有限元分析 

分 类 号：V438[航空宇航科学与技术—航空宇航推进理论与工程]