Optimization of shear-deformable laminated plates under buckling and strength criteria

A shear deformable laminated theory is used to study the optimal design of rectangular plates under biaxial compressive loads. Such loads lead to plate failure by buckling or material failure which corresponds to the violation of the selected strength criterion. The minimum of the two loads (buckling load or material failure load) determines the critical failure load for a given set of problem parameters. At the optimum values of the ply angles, buckling or both failure criteria may be operational depending on the laminate thickness. The present study investigates the effect of laminate thickness on the optimal design and gives numerical results for symmetrically laminated angle-ply plates.     

Optimum design of fiber-reinforced composite cylindrical skirts for solid rocket cases subjected to buckling and overstressing constraints

In order to increase the flight range of aerospace vehicles and the efficiency of solid rocket motors, designers attempt to reduce the weight of solid rocket motors. A skirt is a potential element for weight reduction in rocket motors as it leads to reduction of the total weight of solid rocket motor. Due to its significance for solid rocket motors, the objective of this paper is to investigate the optimal design of a fiber-reinforced composite cylindrical skirt subjected to a buckling strength constraint and an overstressing strength constraint under aerodynamic torque and axial thrust. The present optimal design problem involve in determining the best laminate configuration to minimize the weight of the cylindrical skirt. To find the optimal solution accurately and quickly, the hybrid genetic algorithm (HGA) is employed in this work. Buckling strength and overstressing strength of the fiber-reinforced composite cylindrical skirt are analyzed using classical laminate theory and elastic stability theory of thin shells. The Tsai-Wu failure criterion is employed to assess the first ply failure, and an overstressing load level factor is introduced to describe the failure strength. In addition, a buckling load factor is introduced to describe the buckling strength. Due to the critical issue of buckling strength, the effects of the design parameters on the buckling strength are investigated in this work. Finally, a practical design example of the proposed fiber-reinforced composite cylindrical skirt is investigated using the present analysis procedure. Results reveal that the fiber-reinforced composite cylindrical skirt laminated symmetrically with both cross-ply layers [0/90°] and angle-ply layers [+45/−45°] can sustain a great buckling load. Furthermore, the buckling strength of the skirt shell laminated with equal-hybrid between the angle-ply layers and the cross-ply layers is greater than that of the skirt shell laminated with over-weighted hybrid between the angle-ply layers and the cross-ply layers. Results provide a valuable reference for designers of aerospace vehicles.     

复合材料层合板螺栓连接失效的数值模拟

基于二维有限元模型, 对复合材料层合板螺栓连接的破坏失效问题利用刚度降低的方法来模拟损伤演化过程。在ABAQUS 有限元软件中加入损伤子程序对螺栓连接强度和失效模式进行数值计算。计算结果表明, 该方法能够较好地反映和符合实验结果。对计算结果分析发现, 对于正交铺层, 剪切非线性不明显, 非线性和线性分析得到的计算结果差别比较小; 而对于角铺层, 剪切效应比较显著, 非线性和线性分析两种计算结果差别很大, 而且非线性分析比较适合于角铺层层合板的计算。配合间隙的大小对挤压强度会产生很大的影响, 随着配合间隙的增大, 连接强度大大降低。对于不同的配合间隙, 出现严重损伤的位置不同。间隙小时, 在远离螺栓孔中心线处损伤最大; 间隙大时, 损伤在靠近螺栓孔中心线位置最为严重; 间隙越大, 损伤峰值越高。      

Through-thickness compressive strength of a carbon/epoxy composite laminate

As carbon-fiber-reinforced composite materials are increasingly used for heavy-duty self-lubricating bearings, their through-thickness compressive strength (TTCS) has become an important parameter because the TTCS depends on the weave type and stacking sequence of laminates regardless of their tribological properties.In this work, the TTCS of a carbon/epoxy composite bearing material was measured with respect to weave type, stacking sequence, and direction of cut from the laminate. The tests showed that, for unidirectional laminate, cylindrical specimens resulted in the most reliable data of TTCS. However, for woven fabric laminate, cubic specimens with the edge length greater than twice the repeating unit gave reliable results.     

Analysis of the strength and fracture behaviour of unidirectional and angle-ply graphite-aluminium composites

The tensile behaviour of unidirectional and [±]_s angle-ply P100 graphite-reinforced 6061-Al composites was determined as a function of the angle () between the fibre and the applied load. The experimentally determined values of the elastic modulus and tensile strength of the composites are compared with those predicted from classical laminate theory. The measured elastic modulus values agreed with theoretical values, but the strength of the [\+-\gq]_s angle-ply composites was substantially greater than predicted. The discrepancy between experiment and theory is attributed to the stress required to fail the fibre ply/separator foil interface present in the angle-ply composites. The composite failure modes are also documented, and it is shown that the separator foils of the angle-ply composites shift the transition from tensile to shear failure to greater values of\gq relative to the off-axis unidirectional composites.     

碳纤维增强树脂基复合材料组分疲劳强度表征

对微观力学失效（Micro-mechanics of failure,MMF）理论的应用做了扩展,将其用于分析连续纤维增强树脂基（FRP）复合材料的三维复杂结构的疲劳强度。基于MMF理论,建立了连续FRP复合材料层合板疲劳强度表征方法。分别对碳纤维/树脂（UTS50/E51）复合材料单向层合板进行静载和疲劳试验,得到层合板的基本力学性能和宏观强度指标;对UTS50/E51层合板组分疲劳强度进行了表征,得到了纤维和树脂的拉伸、压缩MMF疲劳特征参量S-lgN曲线,为MMF方法应用于连续纤维增强复合材料层合板结构的疲劳强度分析提供了判断依据。使用建立的方法对UTS50/E51多向层合板的拉伸疲劳强度进行了分析,并将预测结果与试验结果进行对比。     

考虑横向剪切变形的反对称角铺设层合板的弯曲

本文对考虑横向剪切变形的反对称角铺设复合材料层合板弯曲问题进行了理论分析,得到了简化分层理论的封闭形式解。在由位能变分原理得到一般方程的基础上引入合理假设,得到了适合本问题的求解方程。在用简化的分层理论对典型算例进行数值计算的同时,也用经典层合板理论和一阶剪切变形理论进行了计算,一并与相关文献的三维精确解加以比较,结果表明,简化分层理论可以有效地应用于反对称角铺设层合板的弯曲问题。      

The failure of layered ceramics in bending and tension

In this paper, a brief review is presented of previous work describing the failure behaviour of simple layered ceramics in bending. Modelling work has demonstrated that this behaviour can be accurately and simply predicted. Based on this work, an optimum relation between laminate variables, such as interfacial toughness, layer thickness and failure strength, is proposed. This work is then extended to predict failure behaviour in tension. The model is described and the predicted failure behaviour presented. Based on these predictions, simple methods of improving failure behaviour through promoting delamination are discussed. A similar expression to that derived for bending is presented for optimum laminate structure. Of particular interest is the effect of very thin layers (< 10μm) on laminate failure behaviour. It is shown that enormous potential exists for very high strength, reliable, failure-resistant structures through control of interfacial properties. The effect of incorporating layers of different stiffness, thickness and strength is also investigated. It is proposed that the failure behaviour can be controlled somewhat using this approach. Comparison of predictions with experiment shows good agreement. The potential for changing the failure mode from progressive delamination to multiple layer cracking is also discussed. The results of the modelling suggest that the latter approach does not appear inherently suitable for a high-temperature composite.     

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.     

基于新修正偶应力理论的斜交铺设层合Kirchhoff板模型与尺度效应

基于新修正偶应力理论, 建立了只含有1个尺度参数的复合材料斜交铺设层合Kirchhoff板模型, 并分析了铺设角对尺度效应的影响。采用虚功原理推导了任意铺设角的层合Kirchhoff板的弯曲方程和边界条件。通过新模型给出了四边简支反对称角铺设微尺度层合Kirchhoff板的解析解。结果表明:细观尺度各向异性层合板的尺度效应并不仅仅受其几何尺寸的影响, 还受铺设角的影响;铺设角对尺度效应可能产生非常显著的影响。      

基于连续损伤力学的复合材料单剪螺栓连接强度估算策略

针对中国缺少T800级复合材料螺栓连接设计参数的问题,发展一种综合连续损伤力学（CDM）和工程算法的单剪连接强度估算策略,以替代试验,降低研究周期和成本。在该强度估算策略中,首先建立试件的CDM有限元模型,通过数值模拟得到单剪螺栓连接的设计参数,包括单剪挤压强度修正系数、无缺口层合板拉伸强度和应力集中减缓因子等。随后根据上述参数,建立工程算法,估算复合材料单剪螺栓连接的最终挤压强度。结果表明:通过该策略得到的T800级复合材料螺栓连接设计参数和强度估算结果与试验结果有较好的一致性,说明该强度估算策略的可行性。      

结合改进单胞模型的单钉双剪层合板螺栓连接结构挤压性能的多尺度表征分析

为提高螺栓连接层合板结构的可靠性和承载能力,基于ABAQUS软件及用户子程序(USDFLD),结合改进的单胞模型,建立了考虑组分材料失效的多尺度数值模型。利用该模型表征分析了单钉双剪层合板螺栓连接结构的力学性能,研究了铺层形式及几何尺寸对连接结构性能的影响。该模型的预报结果与试验结果吻合较好。结果表明:准各向同性层合板螺栓连接结构的挤压强度高于正交各向异性层合板连接结构的挤压强度,前者的失效模式为挤压失效,后者为剪出失效,该模式导致结构承载能力降低,设计中应避免。层合板边径比大于3时,不同宽径比连接结构的挤压强度趋近稳定值;但相同边径比的连接结构,其挤压强度随宽径比的增大而增大,连接结构设计时应给予考虑。      

Critical thrust force at delamination propagation during drilling of angle-ply laminates

A new formulation for the critical thrust force necessary to propagate the delamination generated during the drilling operation of an antisymmetric angle-ply laminate is proposed by modeling the delamination zone as an elliptical shape. The critical thrust force is analytically derived with the consideration of bending, twisting and mid-plane extension of the delamination zone. And then to maximize the critical thrust force, the optimal design of an angle-ply laminate is performed to find the optimal number of fiber per millimeter, optimum diameter of fiber and optimum lamination angle using ADS (Automated Design Synthesis).     

Beam analysis of angle-ply laminate end-notched flexure specimens

Analysis and experiments on quasi-unidirectional and angle-ply laminate end-notched flexure specimens are presented. The analysis is based on laminated beam theory incorporating first-order shear deformation theory. Compliance and strain-energy release rate determined for relatively thin unidirectional and angle-ply laminate ENF specimens were in good agreement with a previous classical plate theory formulation. For thicker laminates, however, effects of shear deformation on the compliance of the ENF specimen become significant. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminate ENF specimens was conducted. Specifically, [0]₆, [±30]₅ and [±45]₅ laminates with mid-plane delaminations were considered. Experimental compliance data agreed well with analytical predictions. The fracture toughness increased with increased angle θ at the ±θ interface. This is attributed to the fracture work associated with the debonding of transversely oriented fiber bundles in the quasi-unidirectional plies. The angle-ply laminates displayed more yarn debonding than the quasi-unidirectional laminate. For all laminates it was observed that the crack propagated in a non-uniform manner which is correlated with elastic coupling effects with cracked regions of the laminate beams.     

基于断裂韧性预报复合材料层合板的开孔拉伸强度

开孔层合板的强度预报往往取决于孔边的临界长度,它不仅与材料性能,而且与铺层、孔径都有关。本文基于线弹性断裂力学,提出了一种预报对称铺层层合板开孔拉伸强度的新方法,只需提供正交层合板的断裂韧性和无缺口层合板的拉伸强度,显著降低对实验数据的依赖性。首先,将临界长度表作为层合板断裂韧性和无缺口拉伸强度的函数,再通过正交层合板[90/0]_8s的紧凑拉伸试验和虚拟裂纹闭合技术,确定出0°层断裂韧性,进而计算得到任意对称铺层层合板的断裂韧性。本文测试了T300/7901层合板[0/±45/90]_2s和[0/±30/±60/90]_s的开孔拉伸强度,孔径分别为3 mm、6 mm和9 mm。理论预报结果与试验值吻合较好,最大误差为15.2%,满足工程应用需求。      

Residual strength prediction of composite materials: Random spectrum loading

The goal of this project is to identify if and how load order impacts residual strength in an E-glass/vinyl ester composite laminate subjected to variable amplitude fatigue loading. This paper presents results for constant amplitude loading data which, are used to fit parameters for a phenomenological model that can then applied to the spectrum loading cases. The residual strength distribution shape, in addition to median values, is modeled using Weibull statistics. Three cases are run experimentally and modeled for a 735,641 cycle spectrum containing 22 stress levels. The first two are ordered block loading, from highest stress to lowest and from lowest stress to the highest. In both cases, the model predicts the resulting residual strength distribution very accurately. A final case where the entire spectrum was randomized produced unexpected results with every specimen failing after 200,000-400,000 cycles while the model predicts identical residual strength when compared with the block loading case. This work points to a dire need for focus on developing a better understanding of load order impacts in design of composite structures based on constant amplitude fatigue tests.     

Fracture mechanics and optimization — a useful tool for fibre-reinforced composite design

This paper will demonstrate the application of fracture mechanics and optimization techniques for the optimum design of fibre-reinforced composite laminates (FRC). First, a boundary-value problem of a cracked composite laminate is solved within the framework of linear elastic fracture mechanics (LEFM). The solution relates the stress intensity factor at a crack tip and the crack-induced interfacial stresses to the laminate configuration. These results are then used in two types of the optimum design of fibre-reinforced composite laminates. In the first type of optimum design, namely a crack-insensitive design of the laminate, the crack driving force and interfacial principal tensile stress are both minimized by using single- and multicriterion optimization techniques. The second type of optimum design involves in situ strength design of multidirectional angle-ply laminates. In this case, a set of in situ strength parameters are proposed based on theoretical analysis and experimental observations. This optimization problem is a min {max} one and non-differentiable. A proper treatment of the non-differentiability is introduced and the min {max} optimization problem is converted into a differentiable single-criterion one using the bound-formulation technique. All the optimization problems are solved by non-linear mathematical programming. The results show that optimization can greatly enhance the load carrying capacity of the laminates.     

Compressive strength of composite laminates following free edge impact

Barely Visible Impact Damage (BVID) can occur when laminated composite material is subject to free edge impact loads in the plane of the laminate and can result in a significant reduction in compressive strength caused by buckle-driven delamination. This paper will report on a semi-analytical fracture mechanics model that predicts the Compression After Impact (CAI) strength of composite laminates subject to in-plane free edge impact. Compression testing has been undertaken on three impacted coupons in order to validate the theoretical results. Analytical results are shown to be on average within 10% of experimental values for the strain at which propagation of damage occurs.     

Stress and strength analysis of composite joints using direct boundary element method

In this paper, the stress distribution and the strength of bolted joints of orthotropic composite plates under uniform loading are investigated. A direct boundary element method with quadratic isoparametric elements in conjunction with a fundamental solution derived by Rizzo and Shippy¹ is used. Plates with rigid bolts are treated as two-dimensional plane stress problems, and the bolt size is considered to be identical to the hole dimension. The prediction of the laminate strength is based on the Yamada-Sun² failure criterion. Some numerical results for various edge distances and material properties are presented for illustrative purposes.     

The effect of fiber volume fraction on filament wound composite pressure vessel strength

This paper is a continuation of previous research reported in Ref. [1]. The previous paper discussed the relationship between fiber volume fraction in filament wound composite vessels and failure pressure. This research included a design of experiment investigation of manufacturing and design variables that affect composite vessel quality and strength. Statistical analysis of the data shows that composite vessel strength was affected by the manufacturing and design variables. In general, it was found that the laminate stacking sequence, winding tension, winding-tension gradient, winding time, and the interaction between winding-tension gradient and winding time significantly affected composite strength. The mechanism responsible for increases in composite strength was related to the strong correlation between fiber volume fraction in the composite and vessel strength. Cylinders with high-fiber volume in the hoop layers tended to deliver high-fiber strength. This paper further examines the relationship between fiber volume fraction and fiber strain to failure. Data from unidirectional strand tests and additional vessel tests are presented. A computer program that is based on the thermokinetics of the resin and processing conditions is used to calculate the fiber volume fraction distribution in the filament wound vessel. The strand's strength-versus-fiber volume data together with the computer program are used to predict composite vessel burst pressure. In general, good agreement with experimental data is observed.