Hygrothermal effects on structural stiffness and structural damping of laminated composites

In this paper the hygrothermal effects on structural stiffness and damping of laminated composites are investigated. Since the hygrothermal influence on properties of composite materials is primarily matrix dominated, we first determine experimentally the effects of temperature and moisture on the storage modulus, Poisson's ratio and material damping of the epoxy matrix. With the experimentally determined properties of the epoxy material, we then determine the complex moduli (E _L ^* ,E _T ^* ,G _LT ^* andv _LT ^* ) of unidirectional glass-epoxy and graphite-epoxy composites. The structural stiffness (extensional and flexural) and damping of symmetric angle-ply laminates of glass-epoxy and graphite-epoxy are then investigated both analytically and experimentally for temperatues of 20° C and 80° C, respectively. Three moisture contents which are the dry, saturated and a non-uniform moisture gradient states corresponding to each temperature case are considered. Numerical and limited experimental results show that the effects of moisture on the real part ofA ₁₁ ^* ,A ₆₆ ^* ,D ₁₁ ^* andD ₆₆ ^* at room temperature, 20° C, are negligible for all the considered cases. But as temperature increases, the moisture and temperature combined influence induces significant changes in the complex stiffnessA ₁₁ ^* A ₆₆ ^* ,D ₁₁ ^* , andD ₆₆ ^* especially for the matrix dominated terms.     

Prediction of material damping of laminated polymer matrix composites

In this study the material damping of laminated composites is derived analytically. The derivation is based on the classical lamination theory in which there are eighteen material constants in the constitutive equations of laminated composites. Six of them are the extensional stiffnesses designated by [A] six of them are the coupling stiffnesses designated by [B] and the remaining six are the flexural stiffnesses designated by [D]. The derivation of damping of [A], [B] and [D] is achieved by first expressing [A], [B] and [D] in terms of the stiffness matrix [Q]^(k) andh _k of each lamina and then using the relations ofQ _ij ^(k) in terms of the four basic engineering constantsE _L,E _T, G_LT andv _LT. Next we apply elastic and viscoelastic correspondence principle by replacingE _L,E _T...by the corresponding complex modulusE _L ^*,E _T ^*,..., and [A] by [A]^*, [B] by [B]^* and [D] by [D]^* and then equate the real parts and the imaginary parts respectively. Thus we have expressedA _ij ,A _y ,B _ij ,B _ij , andD _ij in terms of the material damping _L ^(k) and _T ^(k)...of each lamina. The damping _L ^(k), _T ^(k)...have been derived analytically by the authors in their earlier publications. Numerical results of extensional damping l _ij =A _ij /A _ij coupling dampingc _ij =B _ij /B _ij and flexural damping F _ij =D _ij /D _ij are presented as functions of a number of parameters such as fibre aspect ratiol/d, fibre orientation , and stacking sequence of the laminate.     

Influence of bending-twisting and extension-bending coupling on damping of laminated composites

This paper describes a three-dimensional finite element-strain energy method for characterizing vibration coupling effects on damping of laminated composites. The analysis was performed on graphite-epoxy laminated cantilever beams in two stacking sequences: (i) 12-ply symmetric laminates [12()], and (ii) 12-ply antisymmetric laminates [6()/6(–)]. Thus, the effects of vibration coupling between bending and twisting in symmetric laminates, and between extension and bending in antisymmetric laminates on damping were studied. A modal strain energy method was applied in a finite-element formulation to solve for the natural frequencies, mode shapes and energy dissipation of the laminates. The coupling energy dissipation was separated from the non-coupling energy dissipation by the decomposition of the total energy dissipation in order to study its contribution to damping. The results of the first three modes, which includes two flexural modes and one torsional mode, are presented. The resulting torsional damping data are generally higher than the flexural damping data. The coupling effects on damping in flexural modes were found to be more significant than those in torsional modes, and such effects appear to be dependent upon the fibre angle and the vibration mode of interest. The coupling effects appear to increase damping in flexural modes, and were found to be maximized at a fibre angle around 30°. The non-coupling energy dissipation was found to be more dominant for the flexural modes at a fibre angle of 90°, and it appears to be more dominant at a fibre angle of 0° in torsional modes, however.     

The vibration damping of laminated plates

A method previously developed for determination of elastic and damping parameters of orthotropic plates (McIntyre, M. E. and Woodhouse, J., Acta Metall., 1988, 36, 1397–1416) was applied to laminated composite plates. The necessary theory is summarised, and the predictions of laminate theory compared with experimental results for three CFRP laminated plates with different constructions. It is also shown that laminate theory can be inverted, to obtain the ply properties from measurements on the laminated plate. This can sometimes afford a good way to obtain the necessary calibration data on the material properties of the plies.     

基于弹性-黏弹性对应原理的复合材料层合板模态阻尼预测:理论及其有限元实现

提出一种利用通用有限元软件求解复合材料结构模态阻尼的有限元方法。该方法基于扩展弹性-黏弹性对应原理,定义出具有频率依存性的黏弹性复合材料复刚度矩阵,并借助ABAQUS提供的二次开发接口UMAT将其编入求解器中,结合复特征值法求解任意铺层层合板的模态阻尼。与已有的理论方法相比,本模型的计算结果更为接近实验数据。从而验证了本文提出的数值分析方法的有效性和精确性,为利用ABAQUS软件分析各向异性材料阻尼提供了一条有效途径。     

高阻尼铝基复合材料的研究

采用包套挤压法制备了高阻尼6061Al/SiCp/ 石墨混杂金属基复合材料,并对所制备的复合材料的金相组织、力学和阻尼特性进行了初步分析。包套挤压法制备的6061Al/SiCp/石墨混杂金属基复合中增强增阻颗粒分布均匀,其体积分数可精确控制。SiC颗粒作为增强剂能够增大复合材料的强度和刚度,而石墨粉作为增阻剂可以提高复合材料的阻尼特性。试验结果表明,能够应用包套挤压法制备力学性能和阻尼特性符合定要求的新型结构－功能材料－6061Al/SiCp/石墨混杂金属基复合材料。     

Analytical modelling of laminated composites

A significant number of research papers has been published on the analytical modelling of composite laminates over the past 20 years. The drive for more accurate analysis has led us to techniques which have become computationally more and more burdensome, while the engineering world continues to use simple, first-older shear deformable plate theory as its primary tool. This paper presents a unique approach to the analysis of thick laminated composites by presenting two simple finite element methods. The first uses the Predictor Corrector technique to extend the simple Mindlin type element to achieve greater accuracy, and the second develops a new Least Squares element which can approximate a C¹ continuous element. The Least Squares element has the capability to incorporate a simplified higher order basis into a piecewise continuous displacement field creating an accurate, yet computationally simple, element. These two methods have the potential to upgrade analysis methods significantly with little additional computational cost. It is hoped that this work can instigate further research into efficient modelling of composite laminates.     

Active damping of geometrically nonlinear vibrations of laminated composite plates using vertically reinforced 1-3 piezoelectric composites

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated composite plates using vertically reinforced 1-3 piezoelectric composite (PZC) as the material of the constraining layer of the ACLD treatment. The Von Kármán type nonlinear strain-displacement relations and the first-order shear deformation theory (FSDT) are used for deriving the coupled electromechanical nonlinear finite element model. The Golla?CHughes?CMcTavish (GHM) method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the cross-ply and antisymmetric angle-ply plates for suppressing the geometrically nonlinear transient vibrations of the plates.     

Elastic stability of thick circular plates under three-dimensional states of stress

Summary The stability of three-dimensional thick circular elastic plates subjected to outside forces and displacements is analysed. The problems are investigated using the equilibrium method. The stability criterion is obtained from the condition of the existence of a non-zero perturbation from the buckled state. Discussing the obtained criteria, it is found that the critical forces in the plane of the plate are affected in a completely different manner by a constant-directional lateral compression field and by a uniform lateral hydrostatic pressure.

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Zusammenfassung Die Stabilität dicker, elastischer Kreisplatten unter äußeren Lasten und Verschiebungen wird mittels der Gleichgewichtsmethode untersucht. Das Stabilitätskriterium ergibt sich aus der Existenz einer im ausgebeulten Zustand möglichen, von Null verschiedenen Störung. Die Diskussion der erhaltenen Kriterien zeigt, daß die kritischen Lasten durch eine richtungskonstante seitliche Kompression und durch einen konstanten hydrostatischen Druck in vollkommen verschiedener Weise beeinflußt werden.

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The results of the present paper were obtained in the course of research conducted under NASA Grand NSG-420, and constitute part of a dissertation submitted to the New York University, New York 53, NY.

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With 3 Figures     

The preparation of laminated ceramic composites using paint technology

Ceramic paints comprising ceramic powder, dispersant, resin and solvent were prepared by high speed mixing. The powders were alumina and alumina with 20 vol% zirconia. Alternate layers of paint having thicknesses of 20–30 m were deposited by the random deposition of droplets from a conventional paint spray gun operating on compressed air. Laminates of up to 1 mm were produced. The microstructure of the multilayer ceramic wafers produced by drying, thermolysis and sintering is reported. The method avoids the thermolamination step associated with tape casting and allows laminates to be prepared on contoured fugitive substrates.     

The formation of residual stresses in laminated thermoplastic composites

The means by which residual stresses are generated in continuous carbon-fibre-reinforced thermoplastic composites are reviewed, with specific attention to the macroscopic stresses which form on a ply-to-ply level. Different means for their estimation are assessed, and approximate stress levels are defined for a variety of materials. The capacity for stress relaxation to occur during processing is examined, and it is shown that little useful stress-relieving ability can be promoted in such systems.     

Design procedure for reducing the stress concentration around circular holes in laminated composites

The stress concentration around a hole in a laminated composite may be decreased by increasing the thickness (bonding of two-dimensional panels) in this area. The problem may be described as an infinite orthotropic membrane with a finite circular orthotropic inclusion (ring) and a circular hole in the middle of the ring under arbitrary in-plane loading. A method for calculation of the stress concentration at the edge of the hole is presented. The method is based on the analytical solution for the case of an infinite inclusion. The finite dimensions of the inclusion are taken into account by means of a correction coefficient which is established empirically by processing a large amount of finite element results.     

Interfiber/interlaminar failure of composites under multi-axial states of stress

Unidirectional and textile carbon/epoxy composites were characterized under multi-axial states of stress. In-plane and through-thickness tensile, compressive, and shear tests were conducted at various orientations with the principal material axes. The stress–strain behavior, failure modes, and strengths were recorded. Results were compared with three types of failure criteria in three dimensions, limit criteria (maximum stress), fully interactive criteria (Tsai-Hill, Tsai-Wu), and failure mode based and partially interactive criteria (Hashin–Rotem, Sun, NU). The latter, a new interfiber/interlaminar failure theory developed by the authors, was found to be in excellent agreement with experimental results, especially in cases involving interfiber/interlaminar shear and compression. Of special note was the failure mode in transverse compression, where the failure plane was not predictable by conventional composite failure theories. The orientation of the failure plane was more in line with predictions by a Mohr–Coulomb failure model.     

Flexural behaviour of hybrid laminated composites

The present paper studies the flexural behaviour of hand manufactured hybrid laminated composites with a hemp natural fibre/polypropylene core and two glass fibres/polypropylene surface layers at each side of the specimen. When compared with full glass fibres reinforced polypropylene laminates, the hybrid composites have economical, ecological and recycling advantages and also specific fatigue strength benefits. Static and fatigue tests were performed in three point bending for both laminates to evaluate flexural strength properties and fatigue behaviour. Fatigue damage was measured in terms of the stiffness loss. Failure sites and mechanisms were evaluated through microscopy studies and a 3D numerical analysis using finite element method.     

Interlaminar shear fracture of laminated composites

The interlaminar fracture toughness in mode II and mode III of a number of advanced composites was studied using beam type test specimens and scanning electron microscopy. Special emphasis was placed on elucidating the material aspects of the fracture process and on quantifying the effect of matrix on fracture energy.The fracture energy in mode II was independent of crack extension while that for mode III exhibited a rather probablistic resistance behavior that was attributed to the effect of fiber bridging. The initiation fracture energy, considered here the true measure of G _IIIC , coincided with G _IIC . For either mode, the interlaminar region ahead of the crack tip exhibited considerable plastic deformations, the severity that is believed to control the laminate toughness. The interlaminar fracture energy in shear, hereby denoted as G _SC (=G _IIC =G _IIIC ), was accurately predicted from a straightforward adhesive joint fracture test provided the adhesive thickness coincide with the thickness of the interlaminar resin layer.

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Résumé On a étudié la rupture par décollement en mode II et en mode III de plusieurs composites évolués, en utilisant des éprouvettes en forme de barreaux et la microscopie électronique à balayage.Un accent particulier a été placé sur la solution d'aspects liés au matériau, portant sur le processus de rupture et sur la quantification des effets de la matrice sur l'énergie de rupture.On a trouvé que l'énergie de rupture en mode II est indépendante de la longueur de fissuration tandis que, pour le Mode III, elle fait état d'un comportement de résistance de caractère plutôt probabilité, attribué à l'effet de pontage entre les fibres.L'énergie d'amorçage de la rupture, que l'on considère ici comme la vraie mesure de G _IIIC , coïncide avec G _IIC .Pour les deux modes de sollicitation, la région de séparation en avant de l'éxtrémité de la fissure fait état d'une déformation plastique importante, dont on pense qu'elle contrôle sérieusement la ténacité due composite.L'énergie de rupture entre couches en cisaillement, que l'on appelle ici G _SC (=G _IIC =G _IIC ), a pu être prédite avec exactitude par des essais de rupture de joints collés, pour autant que l'épaisseur de l'adhésif coïncide de avec celle de la couche de résine entre deux plans du colaminé.

     

Interface corner stress states: plasticity effects

When a butt joint fails, failure often initiates in the region where the interface intersects the stress-free edge. Asymptotic solutions for the stress field found at this type of interface corner are presented for an idealized butt joint with rigid adherends and a thin, essentially semi-infinite, adhesive bond. Linear elastic, power law hardening, and perfectly plastic adhesive models are considered. A stress singularity of type Kr(<0) exists when the adhesive is either linear elastic or power law hardening. The impact of material properties on the order of the stress singularity and the effect of load level and bond thickness on the value of the interface corner stress intensity factor K are detailed. Slip theory is used to determined the asymptotic, interface corner stress field for a perfectly plastic adhesive. This solution indicates that there is a high level of hydrostatic tension, equal to 1.5 _y , in the yielded material along the interface. The three asymptotic solutions are used to construct interface normal stress distributions that closely approximate full, finite element results for an idealization butt joint when small scale yielding conditions apply.