A damping analysis of composite laminates using the closed form expression for the basic damping of Poisson's ratio

Various methods have been presented to obtain the effective damping of a symmetric laminated composite. In this paper, modified classical lamination theory based upon the elastic–viscoelastic correspondence principle was utilized by developing the basic damping of Poisson's ratio for accurately predicting the damping of laminated composite beams. The analysis involves an extension of the elastic–viscoelastic approach. Futhermore, Ni and Adams' theory was used for verifying the modified classical lamination theory. Six typical laminated composites with [±θ]_s,[0/θ]_s,[0/±θ/90]_s,[90/±θ/0]_s,[0/90/±θ]_s and [90/0/±θ]_s, stacking sequences were employed for this study. Numerical results have shown that damping values were in some difference among prediction methods over the particular range of fiber orientation.     

Role of matrix resin in delamination onset and growth in composite laminates

The effect of the matrix resin on the onset and growth of delamination in composite laminates has been investigated in this work. Two kinds of graphite/epoxy composite materials (T300/648-BF₃/MEA and T300/634-DDS) with quite different matrix properties have been used. The study was done on two different layups, [(±30)₃/90₂]_s and [(±45)₂/O₂/90₂]_s. Out-of-plane moiré interferometry and diiodomethane-enhanced X-radiography were used to detect delamination. A strength criterion for the onset of delaminatoin is proposed and an assessment made of the effect of matrix properties on delamination onset. A modified energy release rate model is presented for characterization of delamination growth emphasis being placed on assessing the behavior of delamination resistance curves and delamination growth rate. The results indicate that enhancement of matrix strength and ductility increases the critical loads for delamination onset and delamination resistance in the composite laminates under static loading, and significantly reduces the delamination growth rate under cyclic loading.     

Interfacial debonding in laminated titanium matrix composites

The results of an experimental program in which multiaxial loads were applied to [0₄] and [±45]_s silicon carbide/titanium (SiC/Ti) tubes are reviewed showing that stress coupling, matrix viscoplasticity (including room temperature creep) and fiber/matrix interfacial damage all contribute to nonlinear response and permanent strains in titanium matrix composites (TMC). A micromechanical model that explicitly considers the aforementioned phenomena is presented herein. The model assumes a periodic microstructure and uses finite elements to analyze a representative volume element. The composite is assumed to be in a state of generalized plane strain making it possible to discretize only a generic transverse plane while still being able to apply three-dimensional loading through appropriate boundary conditions. The response of laminated composites is predicted by incorporating the micromechanical results into nonlinear lamination theory. Predictions are presented to show the influence of the model parameters on the effective composite response of unidirectional [0₄] and angle-ply [±45]_s TMC laminates.     

The relation between compressive strength of carbon/epoxy fabrics and micro-tow geometry with various bias angles

In this paper compressive tests of carbon/epoxy (plain weave, 3k) fabric composites were performed to investigate the relation between compressive strength and various bias angles and shear angles. Compressive properties such as chord modulus and maximum strength of the fabric composite materials are essential to analyze the drape behaviour and estimate the quality of the final products. Various specimens with different bias and shear angles which were fabricated by using autoclave de-gassing moulding process were prepared to estimate the strength and chord modulus with respect to the bias and shear angle variations. The stacking sequences of the compressive test specimens are [0]_10T, [15]_10T, [30]_10T and [45]_10T for bias specimens and [±37]_10T, [±32]_10T, [±28]_10T, [±22]_10T for sheared specimens. Micro-tow structures were observed to correlate the fabric compressive strength with crimp angle. Anti-buckling rig was involved to prevent specimens from buckling during the compressive tests. The compressive test was performed with 1.3 mm/min strain rates. Compressive test results were compared with calculation results. Facture modes which were classified in two different modes were analyzed using microscopic observation.     

An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity

The failure characteristic of graphite polyetheretherketone (Gr/PEEK) under compression with a centrally located circular discontinuity was investigated through experimentation and a nonlinear ply-by-ply finite element technique. The stacking sequence of the laminates investigated were: [0 °₁₆], [90 °₁₆], [±45 °]_4S [0 °/90 °]_4S, and [0 °/ ± 45 0°/90 °]_2S. In the experimentation, [90 °]₁₆, [0 °/90 °]_4S, and [0 °/ ±45 °/90 °]_2S laminates, as well as three of the [0 °]₁₆, failed due to a crack that was normal to the loading direction and initiated from the edge of the hole progressing to the outer edges of the specimen. The [±45 °]_4S specimens failed to support the load due to an internal crack that originated from the hole's edge and then traveled at an angle of about 42% to the direction of loading. The finite element method used to analytically model the failure of Gr/PEEK accurately modeled the response of the specimens tested experimentally.     

Damage detection of surface cracks in composite laminates using modal analysis and strain energy method

This paper presents an approach to detect surface cracks in various composite laminates. Carbon/epoxy composite AS4/PEEK was used to fabricate laminated plates, [0]₁₆, [90]₁₆, [(0/90)₄]_S and [±45/0/90]_2S. Surface crack damage was created on one side of the plate using a laser cutting machine. Modal analysis was performed to obtain the mode shapes from both experimental and finite element analysis results. The mode shapes were then used to calculate strain energy using the differential quadrature method (DQM). Consequently, the strain energies of laminated plates before and after damaged were used to define a damage index which successfully identified the surface crack location.     

Dynamic pulse-buckling behavior of ‘quasi-ductile'' carbon/epoxy and E-glass/epoxy laminated composite beams

Dynamic pulse-buckling response of carbon/epoxy and E-glass/epoxy laminated composite beams with [(±67.5)_n]_s ply sequence, subject to axial impact was investigated experimentally and numerically. The laminated beams deformed like ductile metals, retaining a residual deformed shape after being axially impacted, exhibiting no obvious delamination. The ‘crest' deflection of the beams was found to be linearly proportional to the impact energy. The numerical investigation showed that the beams' top and bottom surfaces experienced stresses (transverse stress component) in excess of the tensile strength limits of the matrices.     

The buckling response of carbon fibre composite panels with reinforced cut-outs

This paper investigates the influence of cut-out diameter and reinforcement type upon the buckling stability of square CFRP panels. The study undertaken at Cranfield University in GB uses NASTRAN Finite Element Analysis (FEA) extensively for this investigation. The FEA results have been compared with results from practical tests and good agreement was found. Diagrams showing the influence of cut-out diameter, reinforcement lay up and thickness on the buckling stability of clamped or simply supported CFRP panels are presented. The results are shown for 2 mm thick ((± 45/0)_s)_s square CFRP panels with 30 mm wide reinforcement rings bonded around the central circular cut-outs. The panels are loaded in pure shear or in compression. The effect of reinforcement rings bonded to one or both sides of the panel has been investigated and shown in diagrams. The results presented can be used to find the optimum reinforcement type and thickness for square CFRP panels with central circular cut-outs.     

Optimization of composite plates with piezoelectric stiffener-actuators under in-plane compressive loads

Stiffeners which are used to strengthen a plate can be constructed of piezoceramic materials and subsequently used as piezo actuators to improve the load carrying capacity of the plate. In the present study, a fibre composite plate with initial imperfections and under in-plane compressive loads is studied with a view towards minimizing its deflection using the piezo actuators and the fibre orientations. Piezoceramic stiffeners are bonded symmetrically on the top and bottom of the plate and deployed as actuators. Two cases of electric fields, namely, the in-phase and out-of-phase voltages are applied to the actuators. The presence of initial deflections leads to deformation under the in-plane compressive loads which should be less than the critical buckling load. Two cases of initial imperfections are considered, and the first one is the deterministic initial deflections which are known a priori and as such they are given as input parameters for the problem. In the second case the initial deflections are uncertain and they have to be obtained according to a given criterion. In the present study they are determined to produce the least favourable initial deflection (largest deflection) at a given point and the solution is obtained by convex modelling. The effect of the actuators, the ply angles and the voltage are studied and their effects on the transverse deflection are investigated. A performance index involving the L₂ norm of the deflections is minimized using the piezo effect and as well as the ply angles the optimal values of which are determined for various problem parameters.     

The dynamic elastic buckling of a circular arch with finite displacements and initial imperfections

The equilibrium equations for elastic circular arches are established using the principle of virtual work. The nonlinear partial differential equations of motion are solved using a finite difference method (Park's method for time difference). The dynamic stability of a hinged and a clamped elastic circular arch with a uniform step load is analysed with finite deformations and initial geometric imperfections. Results show that the buckling mode varies with the value of the arch half angle, θ₀. The boundary condition and initial imperfection amplitude also effect the buckling mode. A nearly perfect arch usually buckling with a “direct” buckling form, while an imperfect arch with an “indirect” buckling form. The effect of θ₀ on the ratio p_d/p_s (p_d is the dynamic critical load and p_s the static critical load) is shown for different initial imperfections and different boundary conditions.     

铺层顺序对复合材料薄壁圆管轴向压溃吸能特性的影响研究

采用仿真和试验相结合的方法探讨复合材料薄壁圆管在准静态轴向压缩载荷下的失效吸能特性和吸能机理。首先,建立复合材料薄壁圆管"层合壳"有限元模型,通过显式动力学方法求解其在准静态轴向载荷下的压溃失效力学行为。仿真与试验结果在圆管轴向压溃变形过程、初始峰值载荷、平均压溃载荷及比吸能等主要吸能参数上具有很好的一致性,验证了"层合壳"复合材料圆管有限元模型和建模方法的有效性。其次,采用解析模型与仿真分析方法分别对[0/90]_3s、[0/90/0₂/90₂]_s、[0₃/90₃]_s三种不同铺层顺序的复合材料圆管的屈曲载荷与吸能特性进行了对比,进一步分析了铺层顺序对圆管失效吸能特性的影响。研究表明,0°与90°铺层交替程度对复合材料圆管的吸能特性影响较大,保证纤维失效方式在结构宏观失效中占主导地位能够提高材料失效吸收能量。     

复合材料开孔层板压缩渐进损伤试验

为研究碳纤维增强树脂基复合材料开孔层板在压缩加载过程中的损伤起始、演化方式和损伤特点,采用微距拍摄、逐级加载超声C扫描、X光扫描和扫描电子显微镜观测4种观测手段对国产CCF300/5228A[45/0/-45/90]4s、[452/02/-452/902]2s、[454/04/-454/904]s3种铺层方式的开孔层板进行了压缩试验研究。对压缩载荷作用下开孔层板的损伤起始和损伤演化进行了观察和对比。对试验中观测到的纤维微屈曲、纤维挤出、孔边开裂和分层扩展等现象之间的关系进行了分析和说明。试验结果表明:压缩载荷下45°和90°铺层相邻位置为层板易分层位置,含45°和90°铺层相邻位置的开孔层板渐进损伤过程较为明显:开孔层板在压缩载荷下较早出现损伤,损伤的起始和演化缓解了孔边应力集中,促使压缩应变能在孔边逐步释放,推迟开孔层板压缩破坏的发生,提高层板压缩承载能力。研究结果可为材料结构损伤容限设计提供依据。     

复合材料波纹梁冲击试验与数值模拟

为了探究复合材料波纹梁的吸能性能,针对铺层形式分别为[(±45)3/(0,90)/(±45)3]、[(±45)8]和[(±45)7]的3种复合材料波纹梁元件,进行了动态冲击试验,得到了吸能载荷-位移曲线,并对其损伤破坏形貌进行了分析。以连续损伤力学为基础,结合改进的Hashin损伤判定准则以及损伤演化规律,提出了针对波纹梁耐撞性损伤分析的刚度退化模型,并基于有限元软件平台开发了适用于波纹梁渐进损伤分析的子程序。对3种不同结构形式的波纹梁进行了渐进失效数值分析,模拟得到了能量评估参数比吸能(SEA)和平均载荷值,并将模拟结果与试验结果进行了对比分析。比较分析了不同薄弱环节复合材料波纹梁的吸能能力。结果表明:波纹梁在冲击载荷作用下发生了渐进压溃失效;平均压溃载荷的相对误差不超过12%,能够满足工程应用要求;薄弱环节的设置需综合考虑复合材料性能和铺层方式等因素。     

Analysis of cracks emanating from a circular hole in [0n/90m]s laminates under various boundary conditions

This paper investigates the problem of cracks emanating from a circular hole in an orthotropic finite plate under various boundary conditions. Three types of boundary conditions, that is, stress conditions, displacement conditions and their combinations are considered. Analysis is based on stress functions satisfying the stress free conditions along the crack. The coefficients of stress functions are determined from boundary conditions by using a modified mapping-collocation method. Then, the stress intensity factors are detennined from the coefficients of stress function. Numerical calculations are performed for various finite configurations of [0_n/90_m]_s laminates. The results indicate a strong dependence of the stress intensity factor on the material orthotropy, geometry and boundary conditions.     

Analysis of stiffness reduction of cracked cross-ply laminates

Stiffness reduction of cracked [0°_m/90°_n]_s laminates is analyzed by variational methods on the basis of the principle of minimum complementary energy. For this purpose admissible stress systems are constructed which satisfy equilibrium and all boundary and interface conditions. The optimal stress field is then determined by minimization of complementary energy. The analysis allows for crack interaction and random crack distribution. Results are given for Young's modulus, shear modulus and Poisson's ratio. Young's modulus results are in excellent agreement with experimental data for [[0°/90°₃]]_s glass/epoxy laminate.     

Magneto-elastic interchange in ferromagnetic alloys

The internal friction δ, exchange integral A, magnetocrystalline anisotropic constant K_I and saturation magnetization M_s of Fe–Cr–Al and Fe–Cr–Al–Si alloys annealed at 1373 and 1473 K are measured. The energy density and volume fraction of domain walls (DWs) of these alloys are calculated based on the theories of ferromagnetism and the magnetic parameters measured. The physical process of irreversible movement of 90° DWs is suggested. The results indicate the dissipated elastic energy per unit volume due to the irreversible movements of 90° DWs is equal in value to the energy density of DWs, that is γ_w/δ_w=λ_sE/2. It is an effect of magneto-elastic interchange in ferromagnetic alloys.     

Pyrolytic Trifluoromethylation of [76]-, [78]-, [84]-, and Aza[60]Fullerenes with Silver Trifluoroacetate; Evidence for Coordination of Fullerenes to Silver

Pyrolytic trifluoromethylation of [76], [78], [84], and aza[60]fullerenes with silver trifluoroacetate at 300°C results in extensive polyaddition of up to 18, 18, 20 and 20 CF₃ groups, respectively. In contrast to trifluoromethylation of [60]- and [70]fullerenes that give a full range of derivatives ranging upwards from C_n(CF₃)₂, [76]-, [78]-, and [84]-fullerenes only give C_n(CF₃)_6-18 derivatives, largely in the 10-12 CF₃ range; reaction with [76]fullerene is accompanied by formation of C₆₀(CF₃)₆ attributed to cage fragmentation. For aza[60]fullerene the hexa-addition level dominates, in contrast to its other reactions which give predominantly penta-addition products. All the compounds showed peaks at 1256±2 and 1180-1190 cm^-1, due to the CF₃ group, and peaks in this region are shown also by the soluble extract obtained on trifluoromethylation of nanotubes. As in trifluoromethylation of [60]- and [70]-fullerenes, the products obtained initially are involatile, attributed to formation os silver complexes; these are decomposed on subsequent solution in toluene. Mixed isomeric trifluoromethylated C₆₀F₈ derivatives viz. C₆₀F₇CF₃, C₆₀F₆(FG₃)₂, C₆₀F₅(CF₃)₃ and C₆₀F₄(CF₃)₄, and C₆₀F₄CF₃CF₂CF₃ (a C₆₀F₆ derivative) have been isolated from fluorination of [60]fullerene with MnF₃/K₂NilF₆ at 510°C.     

Buckling characteristics and layup optimization of long laminated composite cylindrical shells subjected to combined loads using lamination parameters

The buckling characteristics and layup optimization of long laminated composite cylindrical shells subjected to combined loads of axial compression and torsion are examined on the basis of Flügge’s theory. In the buckling analysis of long laminated composite cylindrical shells, 12 lamination parameters are introduced and used as design variables for layup optimization. Applying a variational approach, the feasible region in the design space of the 12 lamination parameters is numerically obtained. The buckling characteristics are discussed in the design space of the 12 lamination parameters. In the layup optimization, the optimum lamination parameters for maximizing the buckling loads and the laminate configurations for realizing the optimum lamination parameters are determined by mathematical programming methods. It is found that in case of combined loads of axial compression and torsion, the optimum laminate configurations are unsymmetric.     

Study of interaction curves for composite laminate subjected to in-plane uniaxial and shear loadings

In this study an attempt has been made to incorporate the effect of transverse shear on the stability of moderately thick/very thick composite laminated plates under in-plane compressive and shear loading using a Simple Higher Order Shear Deformation Theory based on four unknown displacement functions (u₀,v₀,w_b,w_s) instead of five which is commonly used in most of the higher order theories. The finite element method is employed to study the initial buckling load of laminated plates. The change in initial buckling response of thick rectangular antisymmetric laminates with respect to the fibre orientation angle has been studied. The interaction curves (between N_x and N_xy for different parameters of the laminates) are studied in detail.     

Determination of fracture energy and tensile cohesive strength in Mode I delamination of angle-ply laminated composites

The energy release rate in delamination of angle-ply laminated double cantilever composite beam specimens was calculated using the compliance equation, and interlaminar cohesive strengths were obtained. Instead of the traditional approach of a beam on an elastic foundation, a second-order shear-thickness deformation beam theory (SSTDBT) was considered. The equilibrium equations were obtained using the principle of minimum total potential energy and the system of ordinary differential equations were solved analytically. The problem was solved for [0°]₆ , [±30°]₅, and [±45°]₅ laminates with mid-plane delaminations and the results were verified using experimental evidence available in the literature.