Damping and Mechanical Properties of Cocured Composite Laminates with Embedded Perforate Viscoelastic Layer

The composite laminates with embedded acrylonitrile butadiene rubber （NBR） layer were fabricated by cocuring process. The embedded layers were perforated with a series of small holes to allow resin to flow through the damping layer and completely couple the structure to improve bending stiffness and interlaminar shearing strength of these cocured composite laminates. The damping, bending stiffness and shearing strength of these composite laminates with different perforation diameters were investigated. The experimental results show that increasing the perforation diameter leads to significant decreases in damping and significant increase in bending stiffness up to an area ratio of 7.065%. The area ratio here is defined as the ratio of perforation area to the total damping area. Beyond the area ratio of 7.065%, increasing the diameter to an area ratio of 50.24% results in only a slight variation in damping and bending stiffness. Moreover, increasing the perforation diameter does not always increase the shearing strength of the embedded viscoelastic layer. The shearing strength of embedded viscoelastic layer increases only when the area ratio is greater than 19.625%; instead, it will decrease.

FATIGUE LIFE PREDICTION THEORY OF COMPOSITE LAMINATES AND EXPERIMENTAL VERIFICATION

According to traditional phenomenological fatigue methodology and moderncontinuum damage mechanics theory, dual fatigue cumulative damage rules to predict fatigue damageformation and propagation lives of the notched composite laminates are presented. A 3-dimensionaldamage constitutive equation of anisotropic composites is also established. Damage strain energyrelease rate is interpreted as a driving force of the fatigue delamination damage propagation. A newdamage evolution equation and a damage propagation σ_a-σ_m-N~* surface (stress amplitude-meanstress-life surface) are derived. Hence, using the method above, the fatigue life of compositecomponents can be predicted. Finally, theoretically predicted results are compared with experimentaldata. It is found that the deviation of theoretic prediction from experimental results is about22%.

Multi-objective Optimization of Co-cured Composite Laminates with Embedded Viscoelastic Damping Layer

Presented herein is a methodology for the multi-objective optimization of damping and bending stiffness of cocoured composite laminates with embedded viscoelastic damping layer. The embedded viscoelastic damping layer is perforated with a series of small holes, and the ratio of the perforation area to the total damping area is the design variable of the methodology. The multi-objective optimization is converted into a single-objective problem by an evaluation function which is a liner weigh sum of the two sub-objective functions. The proposed methodology was carried out to determine the optimal perforation area ratios of two viscoelstic layers with different perforation distance embedded in two composite plates. Both the optimal perforation area ratios are approximate to 2.2%. However, the objective value of the plate with greater perforation distance in embedded viscoelatic layer is much greater.

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.

Analytical solutions to edge effect of composite laminates based on symplectic dual system

In the symplectic space composed of the original variables,displacements,and their dual variables,stresses,the symplectic solution for the composite laminates based on the Pipes-Pagano model is established in this paper.In contrast to the traditional technique using only one kind of variables,the symplectic dual variables include displacement components as well as stress components.Therefore,the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously.After being introduced into the symplectic dual system,the uniform schemes,such as the separation of variables and symplectic eigenfunction expansion method,can be implemented conveniently to analyze composite laminate problems.An analytical solution for the free edge effect of composite laminates is obtained,showing the effectiveness of the symplectic dual method in analyzing composite laminates.

ON THE DESCRIPTION OF ANISOTROPIC DAMAGE IN COMPOSITE LAMINATES

A general anisotropic damage theory of cracked laminates is formulated here.The deformation of composite laminates is composed of matrix elastic strains,pseudo-elastic damage strains due to cracking and permanent damage strains due to interlaminar slip.The surface of damage initiation is constructed accord- ing to the concept of linear elastic fracture mechanics for the virgin material.After the initial damage,a pesudo-elastic damage can be used to describe the damage behaviour if interlaminar slip is negligible.Damage evolution,load induced anisotropy and interlaminar-intralaminar interaction for composite laminates are exam- ined;the latter can perturb the normality structure of damage strain rate.Explicit expressions are given for pseudo-elastic (or secant) moduli of the damaging composite laminates,under a non-interacting assumption imposed on the cracks between different families.

Research on Fixture's Effect on Properties of Single-Shear Bolt Jointed Composite Laminates Structure

The testing on the bearing strength of single-shear bolt jointed composite laminates structure is done.And the effect of the fixture on the testing results is analyzed. Then a macro-micro multi-scale analytical model combined with the improved"Generalized Method of Cells( GMC) "is developed,which is used to predict the macro bearing strength and to characterize the micro constitute material failure of the bolt jointed composite laminates structure. Both the contact conditions at the bolt/hole boundary and the contact conditions at the specimen/fixture boundary,progressive damage,and the material properties degradation are all taken account into the analytical model. Thus,the numerical simulation results agree well with the experimental results.Finally,the effect of the fixture on the testing results is characterized. The results show that the incomplete contaction between the fixture and the specimen or the lack of the lateral constraint on the specimen will affect the limited bearing strength and the offset bearing strength of the bolt jointed composite laminates structure. In addition,the lower support rigid of the fixture will affect the rigid of the bolt jointed composite laminates structure.

Effects of Lay-up Types of Out-of-autoclave Prepregs on Preparation Quality of L-shape Composite Laminates

Effects of layer quantities and stacking sequences on L-shape composite manufacturing qualities in using OOA(out-of-autoclave)prepregs were studied.The mechanisms of air evacuated in 5 kinds of lay-ups were revealed by image analysis of cut surfaces and thickness measurements.Results show that air in OOA prepregs is evacuated in two ways.Most of the air is forced out of layers directly by vacuum before air accesses in prepregs closed.Very little entrapped air moves perpendicularly to outer layers under hydrostatic resin pressure.When a laminate contains less than 16 layers,voids can hardly be found in layers.When a laminate contains more than 16 layers,voids cannot be expelled completely during the window of vertical movement.As for stacking sequences,the synergetic effect of slip function and nest function determines the thickness and voids content of laminates.Results show that the average of single layer thickness of unidirectional layers is the lowest,and the average of single layer thickness of quasi-isotropic layers is the highest.The voids content of quasi isotropic is the highest,which is consistent with the theoretical analysis.

Analysis of vibration attenuation characteristics of large thickness carbon fiber composite laminates

The vibration attenuation and damping characteristics of carbon fiber reinforced composite laminates with different thicknesses were investigated by hammering experiments under free boundary constraints in different directions.The dynamic signal testing and analysis system is applied to collect and analyze the vibration signals of the composite specimens,and combine the self-spectrum analysis and logarithmic decay method to identify the fundamental frequencies of different specimens and calculate the damping ratios of different directions of the specimens.The results showed that the overall stiffness of the specimen increased with the increase of the specimen thickness,and when the thickness of the sample increases from 24mm to 32mm,the fundamental frequency increases by 35.1%,the vibration showed the same vibration attenuation and energy dissipation characteristics in the 0°and 90°directions of the specimen,compared with the specimen in the 45°direction,which was less likely to be excited and had poorer vibration attenuation ability,while the upper and lower surfaces of the same specimen showed slightly different attenuation characteristics to the vibration,the maximum difference of damping capacity between top and bottom surfaces of CFRP plates is about 70%.

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

CONSTITUTIVE RELATION AND STIFFNESS DEGRADATION OF CRACKED ANISOTROPIC COMPOSITE LAMINATES(II)─DETERMINATION OF RESOLVED STIFFNESS AND INVESTIGATION OF STIFFNESS DEGRADATION FOR CRACKED LAMINATES

The study on properly degradation of damaged,.onlj,osile laminates is extendedto anisotropic laminates with matrix cracking. In (II) of the paper, a solution forpartitioned stiffness is given to complete the constitutive relations developed in (I) Thestiffness degradation in cracked laminates is calculated and the results arediscussed.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

Effects of Sinusoidal Vibration of Crystallization Roller on Composite Microstructure of Ti/Al Laminated Composites by Twin-Roll Casting

A new,innovative vibration cast-rolling technology of “electromagnetic stirring+dendrite breaking+asynchronous rolling” was proposed with the adoption of sinusoidal vibration of crystallization roller to prepare Ti/Al laminated composites,and the effect of sinusoidal vibration of crystallization roller on composite microstructure was investigated in detail.The results show that the metallurgical bonding of titanium and aluminum is realized by mesh interweaving and mosaic meshing,instead of transition bonding by forming metal compound layer.The meshing depth between titanium and aluminum layers (6.6μm) of cast-rolling materials with strong vibration of crystallization roller (amplitude 0.87 mm,vibration frequency 25 Hz) is doubled compared with that of traditional cast-rolling materials (3.1μm),and the composite interfacial strength(27.0 N/mm) is twice as high as that of traditional cast-rolling materials (14.9 N/mm).This is because with the action of high-speed superposition of strong tension along the rolling direction,strong pressure along the width direction and rolling force,the composite linearity evolves from "straight line" with traditional casting-rolling to "curved line",and the depth and number of cracks in the interface increases greatly compared with those with traditional cast-rolling,which leads to the deep expansion of the meshing area between interfacial layers and promotes the stable enhancement of composite quality.

PREDICTIVE APPROACH TO FAILURE OF COMPOSITE LAMINATES WITH EQUIVALENT CONSTRAINT MODEL

This work established a new analytical model based upon the equivalent constraint model （ECM） to constitute an available predictive approach for analyzing the ultimate strength and simulating the stress/strain response of general symmetric laminates subjected to combined loading, by taking into account the effect of matrix cracking. The ECM was adopted to mainly predict the in-plane stiffness reduction of the damaged laminate. Basic consideration that progressive matrix cracking provokes a re-distribution of the stress fields on each lamina within laminates, which greatly deteriorates the stress distributed in the primary load-bearing lamina and leads to the final failure of the laminates, is introduced for the construction of the failure criterion. The effects of lamina properties, lay-up configurations and loading conditions on the behaviors of the laminates were examined in this paper. A comparison of numerical results obtained from the established model and other existed models and published experimental data was presented for different material systems. The theory predictions demonstrated great match with the experimental observations investigated in this study.

Analytical solution methods for eigenbuckling of symmetric cross-ply composite laminates

Based on the first-order shear deformation theory, this paper explores the analytical methods for eigenbuckling of symmetric cross-ply rectangular composite laminates with a pair of parallel edges simply supported and the remaining two edges arbitrarily constrained. The main contribution of present paper lies in two aspects： one is to present a simple and effective analytical method, namely, the separation-of-variables method, which can generate the closed-form buckling solutions without any computational difficulty; the other is to incorporate the accurate computation method of exponential matrix into the state space technique to avoid the inevitable numerically illconditioned problems reported in several literatures. The results obtained via both analytical methods are identical, and a good agreement with their counterparts in literature is observed. The separation-of-variables method can generate exact solutions within 1 s, which is impossible if the state space method is employed. Besides, the combination of the accurate computation method of exponential matrix and the state space method greatly improves the computational efficiency and gives correct results compared with the straightforward use of state space method.

Progressive damage behaviors of woven composite laminates subjected to LVI, TAI and CAI

This paper seeks to deal with progressive damage behaviors of woven composite laminates subjected to low-velocity impact(LVI),tension-after-impact(TAI)and compression-afterimpact(CAI).The LVI,TAI and CAI tests were conducted on woven carbon fibre lamina3238 A/CF3052 and woven glass fibre lamina 3238 A/EW250 F,and the time-dependent LVI contact force and deflection curves,static TAI and CAI load versus displacement curves were determined and discussed.A modified progressive damage model was presented for explicit dynamic LVI and implicit static TAI and CAI analysis by using basic material properties and geometrical dimensions,and progressive damage LVI,TAI and CAI behaviors of woven composite laminates were simulated,demonstrating a good correlation between simulations and experiments.

Multiaxial fatigue life prediction of composite laminates

A study of composite laminates under tension–torsion biaxial loading is presented.The focus is placed on fatigue lives of composite laminates under different tension–torsion biaxial fatigue loading paths.A macro-meso model used to predict multiaxial fatigue life of composite laminates is also presented in this paper.Firstly,a macro-scale 3 D RVE corresponding to composite laminates is established to determine strain components in the material principal direction of each layer for each biaxial stress ratio.Secondly,a meso-scale 3 D RVE corresponding to each layer with fibers distributed randomly is established,with progressive damage prediction method,biaxial strength of composite laminates can be predicted,and the final failure layer can be confirmed.Thirdly,select any one of fatigue loading path at which the final failure of composite laminates is fiber failure(matrix failure)to establish the reference curve for fiber(matrix).Finally,with reference curve,fatigue life of composite laminates under any biaxial loading path can be predicted.And numerical results show good agreements with experimental data.

THERMOELASTICITY ANALYSIS OF FINITE COMPOSITE LAMINATES WEAKENED BY MULTIPLE ELLIPTICAL HOLES

A finite composite laminate weakened by multiple elliptical holes of arbitrarydistribution, arbitrary orientation and arbitrary dimension, is treated as an anisotropic,finite multiple connected thin plate. Using the complex potential method in planetheory of heat conduction and elastictiy of an anisotropic body, the analytical solutionof a finite composite laminated plate subjected io arbitrary mechanical and thermalloads with multiple elliptical holes is. obtained by means of the Faber series expansion,mapping and the least square boundary collocation technique. The effects of someparameters on the thermostress distribution are studied in detail. Some conclusions aredrawn.