Damage tolerance of fully orthotropic laminates in compression

The compression after impact (CAI) strength of fully orthotropic composite laminates with up to 21 plies is presented, as analysed by an existing strip model. Candidate layups, which can be symmetric, anti-symmetric or non-symmetric, are preselected to exhibit no elastic coupling response, with manufacturing rules applied. These criteria, along with the use of a simple surrogate sublaminate buckling model, were chosen to allow analysis of all feasible laminates in the design space without excessive computation time. Results indicate that although the inclusion of non-symmetric layups in the design space does not give benefits with respect to maximum achievable damage tolerance, these laminates can exhibit damage tolerance close to that of an anti-symmetric design for some ply counts, and better than symmetric solutions in most cases. It is also noted that in some instances increasing the number of plies in a laminate can actually reduce the highest achievable threshold load for damage tolerance, as a result of the large influence Poisson’s ratio has on sublaminate buckling. Average errors in the surrogate model were low in all cases, with maximum non-conservative errors less than 1%. The surrogate buckling model reduced computational time by over 99% when compared to the fully exhaustive search.     

A micro-to-meso sublaminate model for the viscoelastic analysis of thick-section multi-layered FRP composite structures

Classical ply-by-ply analysis of multi-layered thick-section composite structures with tens of layers through the cross-section is often impractical, especially when material nonlinearity and time-dependent effects are included. This study introduces an integrated micromechanical-sublaminate modeling approach for the nonlinear viscoelastic analysis of thick-section and multi-layered composite structures. The sublaminate model is used to generate three-dimensional (3D) effective nonlinear responses at through-thickness material integration points with given spatial variations of strains determined from the trial strain increments of the standard displacement-based finite-element (FE). The number of material integration points is determined by the resolution of the FE discretization of the composite structure. The sublaminate model at a selected material point represents the effective nonlinear continuum behavior in its neighborhood using the 3D lamination theory with uniform in-plane strain and out-of-plane stress patterns through the representative layers. Therefore, the sublaminate has first-order stress and strain paths and cannot recognize the local sequence of the layers. While this approach is very effective approximation especially in the case of a very large number of repeating layers using relatively few elements (integration points) through the thickness, it cannot be used to represent the interlaminar stresses or bending/extension/twisting coupling effects within a sublaminate. A previously developed micromechanical model by the authors for a nonlinear viscoelastic unidirectional lamina is used for each layer in the sublaminate. The proposed modeling approach is first calibrated and verified against creep tests on off-axis glass/epoxy performed by Lou and Schapery (J. Compos. Mater. 5:208–271, 1971). Analyses for different thick-section laminated structures are presented using the integrated sublaminate with both shell and 3D continuum elements. The proposed 3D nonlinear time-dependent sublaminate model is computationally efficient and robust in analyzing multi-layered composite structures having large number of plies.     

复合材料圆柱壳轴压屈曲性能分析

对完整复合材料圆柱壳轴向压缩性能进行了试验研究,得到了圆柱壳结构的破坏载荷和各测量点的载荷-应变曲线,通过分析得出结构的破坏形式为屈曲破坏。利用ANSYS有限元软件建立了模型,对复合材料圆柱壳进行屈曲分析,将有限元计算的结构变形和屈曲载荷与试验结果进行对比,计算结果与试验结果一致,验证了模型的有效性。利用建立的有限元模型,分析了开口尺寸和铺层角度对含矩形开口的复合材料圆柱壳屈曲载荷的影响。在开口处加装复合材料口盖对结构进行补强,补强后的柱壳结构满足强度设计要求。     

A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites

In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.     

以复合材料层合板为面板的夹层板稳定性分析

本文构造了一个考虑面板抗弯刚度及耦合刚度的三角形复合材料夹层板单元,对复合材料夹层板的总体稳定性进行了计算和分析,讨论了面板铺设、夹心与面板厚度比对临界载荷的影响。本文还导出了复合材料夹层板内力与应变的关系式,分析并指出了即使夹层板总体铺设为对称铺设时忽略面板耦合刚度对临界载荷带来的影响。      

模态缺陷条件下复合材料柱形壳屈曲特性

为了开展多模态缺陷条件下复合材料柱形壳的屈曲特性研究,进行了理想柱形壳在轴压工况下的线性屈曲分析,得出前50阶屈曲失稳模式,即模态缺陷;基于弧长法研究不同模态缺陷条件下复合材料柱形壳的非线性屈曲特性;将有限元分析结果、NASA SP-8007规范计算结果与Bisagni试验结果作对比分析。结果表明:对于轴压柱形壳屈曲问题,第1阶模态缺陷不是最差缺陷,在第1阶模态缺陷条件下求出的非线性屈曲载荷比试验值高出较多;高阶模态缺陷条件下的复合材料柱形壳非线性屈曲计算结果与试验结果最为吻合,两者相差较少;屈曲载荷下降受缺陷形状、幅值双重影响,复合材料柱形壳屈曲计算需考虑多模态问题;NASA求出的屈曲载荷非常保守,低于试验值较多,用NASA方法进行复合材料柱形壳的设计,往往会导致结构笨重、材料浪费、性能降低。     

Efficient techniques for predicting viscoelastic behavior of sublaminates

Even for linear elastic behavior, stress analysis of thick laminated composites can be very computation intensive if every lamina is modeled discretely. In such cases, modeling of individual lamina is impractical and the homogenization method for sublaminates becomes essential. In the current work, 3D homogenization formulas for an elastic sublaminate, which were derived by the authors in previous work, were utilized to determine the 3D effective properties for a viscoelastic sublaminate. The properties were determined by three methods that exploited the 3D elastic homogenization formulas: (i) quasi-elastic method, (ii) correspondence principle, and (iii) direct time integration of the incremental viscoelastic equations. The finite element method with discrete modeling of the plies was used to obtain reference solutions. The effective viscoelastic properties obtained using the three methods based on the elastic homogenization formulas were in very good agreement with the reference solution. Among these methods, the quasi-elastic method was found to be both accurate and the simplest method in determining the effective properties. The methods were also used to predict the stress response of a sublaminate to different strain histories. The direct time integration method using the 3D elastic homogenization formulas performs accurately and efficiently for this problem.     

RTM整体成型复合材料翼盒的固有模态及稳定性

采用基于水溶性型芯的RTM成型技术制备了整体化的复合材料翼盒, 并对翼盒进行了自由振动模态试验; 采用三维壳单元, 建立了翼盒固有模态及稳定性有限元分析模型, 该模型分析的翼盒固有模态与试验结果吻合很好, 验证了有限元模型的有效性; 为研究翼盒固有模态及稳定性的铺层效应, 采用该模型分析计算了4种铺层方案的翼盒的固有模态及稳定性。研究结果表明: 对称铺层蒙皮有利于提高翼盒轴向压缩与轴向扭转屈曲载荷及固有频率, 而不利于面外弯曲和弯扭组合情况; 腹板减薄和增加腹板45°铺层均不利于提高, 甚至会大幅度降低屈曲载荷及固有频率, 弯扭组合加载最容易导致失稳。     

复合材料双曲率壳屈曲和后屈曲的非线性有限元研究

基于 ABAQUS软件分析平台 , 采用非线性有限元法研究了横向载荷作用下复合材料双曲率壳的屈曲和后屈曲行为。通过在有限元模型中引入 Tsai2Wu失效准则 , 预测了复合材料双曲率壳的初始失效及渐进破坏过程 , 数值结果和试验数据吻合较好 , 表明了该模型的合理有效性 , 并详细讨论了各种参数对屈曲和后屈曲行为的影响。经分析复合材料双曲率加筋壳在均布压载和剪力联合作用下的屈曲和后屈曲行为 , 得到了屈曲载荷的拟合曲线 , 研究表明顺剪力的存在有利于提高屈曲载荷。     

Delamination tolerance studies in laminated composite panels

Determination of levels of tolerance in delaminated composite panels is an important issue in composite structures technology. The primary intention is to analyse delaminated composite panels and estimate Strain Energy Release Rate (SERR) parameters at the delamination front to feed into acceptability criteria. Large deformation analysis is necessary to cater for excessive rotational deformations in the delaminated sublaminate. Modified Virtual Crack Closure Integral (MVCCI) is used to estimate all the three SERR components at the delamination front from the finite element output containing displacements, strains and stresses. The applied loading conditions are particularly critical and compressive loading on the panel could lead to buckling of the delaminated sublaminate and consequent growth of delamination. Numerical results are presented for circular delamination of various sizes and delamination at various interfaces (varying depth-wise location) between the base- and the sub-laminates. Numerical data are also presented on the effect of bi-axial loading and in particular on compressive loading in both directions. The results can be used to estimate delamination tolerance at various depths (or at various interfaces) in the laminate.     

Local Buckling Prediction for Large Wind Turbine Blades

Local buckling is a typical failure mode of large scale composite wind turbine blades. A procedure for predicting the onset and location of local buckling of composite wind turbine blades under aerodynamic loads is proposed in this paper. This procedure is distinct from its counterparts in adopting the pressure distributions obtained from Computational Fluid Dynamics (CFD) calculations as the loads. The finite element method is employed to investigate local buckling resistance of the composite blade. To address the mismatch between the unstructured CFD grids of the blade surface and the finite shell elements used during the buckling analysis, an interpolation code is developed, allowing mapping the pressure computed by using CFD to the finite element model. With the well documented National Renewable Energy Laboratory phase VI wind turbine blade, the procedure is demonstrated to be capable of yielding satisfactory results. Comparison with results obtained by using the blade surface pressure distributions calculated using a simple method is also conducted.     

Buckling strength of GFRP under-water vehicles

The paper is concerned with the structural response of a composite shell structure intended as a model of an under-water vehicle for service in sea environment. The main objective of the research is the prediction of the collapse pressure using both analytical expressions and linear or non-linear numerical analysis and the following comparison with the experimental pressure obtained in off-shore tests. The structure is composed of three basic parts with regular geometry: a cylindrical part (with the following geometrical properties: R/t=30.5, L/R=2 being the internal radius 305 mm, the length 610 mm and the thickness 10 mm) and two conical and spherical end-closures with the same thickness. The cylindrical shell was made up of 7 plies of E-glass woven roving with polyester resin. Various structural analyses were conducted before performing the experiment in the sea to verify the reliability of the analytical and numerical tools. Firstly the entire model was analysed to predict the nature of the collapse (material failure or elastic buckling) and it was stated that the collapse was due to elastic buckling of the cylindrical part. Consequently, the attention was focused on this component and approximation formulae for the evaluation of the linear buckling pressure of isotropic and composite cylindrical shells were used together with finite element models. Afterward the study was enlarged to consider the effects of the recorded geometric imperfections into a non-linear buckling analysis. The collapse pressures were compared to the design values derived from the available recommendations and to the experimental result obtained in an off-shore test (1.3 MPa).     

复合载荷作用变刚度复合材料回转壳屈曲优化

通过曲线纤维轨迹设计,变刚度复合材料回转壳将拥有比常刚度（直线纤维）回转壳更好的抗屈曲稳定性,为此,研究了复合载荷作用下曲线纤维铺层形式和几何参数对变刚度复合材料回转壳屈曲性能的影响规律。首先根据回转壳横截面圆弧变化改进曲线纤维角度线性描述方法,建立了变刚度复合材料回转壳的参数化有限元模型;其次,结合序列二次响应面方法和回转壳屈曲优化模型,搭建了复合材料回转壳曲线纤维轨迹优化的设计流程;最后,以准各向同性铺层复合材料回转壳为比较基准,对弯扭载荷作用变刚度圆柱壳和轴压、弯矩和扭矩分别作用变刚度椭圆柱壳在不同铺层方式、不同几何参数下的屈曲性能进行了优化比较。结果表明:弯扭载荷作用下,变刚度圆柱壳的屈曲性能随弯矩载荷占比增加而提高,且均好于准各向同性圆柱壳,但扭矩载荷占优时,优化常刚度圆柱壳的屈曲性能更具有优势;不同载荷作用下,具有较小截面方向比的变刚度椭圆柱壳屈曲性能要明显好于对应的准各向同性椭圆柱壳,且横截面越接近圆形,曲线纤维对椭圆柱壳屈曲性能的改善越弱。      

开口及边界条件对复合材料三分之一柱面壳压缩屈曲性能的影响

研究了完整、开口周边加强及开口加口盖3种型式的复合材料三分之一柱面壳的压缩屈曲性能,考查了3种典型复合材料柱面壳的轴压屈曲强度,分析了开口及口盖对柱面壳压缩稳定性的影响.结果表明:开口大大降低了柱面壳的轴压屈曲强度;口盖可以部分恢复其强度,但很难达到开口之前的水平.进行了开口加口盖经编织物铺层三分之一柱面壳轴向压缩试验,其轴压屈曲强度比用平面织物制造的相同结构的降低很多.为了探究其轴压屈曲强度比同类结构偏低很多的原因,进行了非均匀加载复合材料柱面壳模型有限元分析.结果表明:柱面壳边界不均匀加载会降低其承载能力,根据柱面壳刚度分布制定边界载荷可以提高其承载能力.     

Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading

A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.     

The influence of mechanical couplings on the compressive stability of anti-symmetric angle-ply laminates

The compressive stability of anti-symmetric angle-ply laminated plates with particular reference to the degrading influence of membrane–flexural coupling is reported in this paper. The degree of membrane–flexural coupling in the laminated composite plates is varied, essentially, by altering the ply-angle and the number of plies in the laminated stack for a given composite material system. The coupled compressive buckling solutions are determined in the paper using the finite strip method of analysis and the buckling displacement fields of the strip formulation are those which are able to provide zero in-plane normal movement at the edge boundaries of the laminated plates.

Results are given for anti-symmetric angle-ply laminated plates subjected to uniaxial compression and these have been obtained from fully converged finite strip structural models. Validation of the finite strip formulation is indicated in the paper through comparisons with exact solutions where appropriate. Increasing the number of plies in the laminated system is seen to reduce the degree of coupling and the critical stress levels are noted to tend towards the plate orthotropic solutions. The ply-angle corresponding to the optimised buckling stress for any particular laminate is noted in the paper to be influenced by the support boundary conditions at the plates unloaded edges. For any particular laminate the minimum critical buckling stress and corresponding natural half-wavelength of the buckling mode are shown to be highly sensitive to ply-angle variation.

Some post-buckling results are presented in the paper and these have been determined using the finite element method of analysis. The influence of membrane–flexural coupling is shown to be significant throughout the compressive post-buckling history of the laminated plates. The optimised ply-angle with regard to the critical compressive buckling stress of square simply supported anti-symmetric angle-ply laminates is shown to be less effective in the post-buckling range with regard to post-buckled compressional stiffness.     

Nonlinear buckling analysis of hygrothermoelastic composite shell panels using finite element method

Hygrothermal stresses due to the change in environmental condition may induce buckling and dynamic instability in the composite shell structures. In the present investigation, the hygrothermoelastic buckling behavior of laminated composite shells are numerically simulated using geometrically nonlinear finite element method. The orthogonal curvilinear coordinate is used for modeling a general doubly curved deep or shallow shell surface. The geometrically nonlinear finite element formulation is based on general nonlinear strain–displacement relations in the orthogonal curvilinear coordinate system. The present theory can be applicable to thin and moderately thick shells. The mechanical linear and nonlinear stiffnesses, and the nonmechanical nonlinear geometric stiffness matrices and the hygrothermal load vector are presented. It is also observed that during the present numerical solution of nonlinear equilibrium equation, in order to construct the nonlinear stiffness matrices for the first load step, the initial deformation can be assumed as zero or any computer generated small random number or the properly scaled fundamental buckling mode shape. To verify the present formulations and finite element code, the present results are compared well with those available in the open literature. Parametric studies such as thickness ratio and shallowness ratio on buckling are performed for spherical, truncated conical and cylindrical composite shell panels. The buckling behavior and deflection shapes are characterized by multiple wrinkles along unreinforced direction at higher moisture concentrations or temperature rise.     

Optimisation of hybrid high-modulus/high-strength carbon fibre reinforced plastic composite drive shafts

This study deals with the optimisation of hybrid composite drive shafts operating at subcritical or supercritical speeds, using a genetic algorithm. A formulation for the flexural vibrations of a composite drive shaft mounted on viscoelastic supports including shear effects is developed. In particular, an analytic stability criterion is developed to ensure the integrity of the system in the supercritical regime. Then it is shown that the torsional strength can be computed with the maximum stress criterion. A shell method is developed for computing drive shaft torsional buckling. The optimisation of a helicopter tail rotor driveline is then performed. In particular, original hybrid shafts consisting of high-modulus and high-strength carbon fibre reinforced epoxy plies were studied. The solutions obtained using the method presented here made it possible to greatly decrease the number of shafts and the weight of the driveline under subcritical conditions, and even more under supercritical conditions. This study yielded some general rules for designing an optimum composite shaft without any need for optimisation algorithms.