A novel solution of rectangular composite laminates under oblique low-velocity impacts

An analytical solution for the responses of composite laminates under oblique low-velocity impacts is presented for a cross-ply,orthotropic,and rectangular plate under oblique low-velocity impacts.The plate is under simply-supported edge conditions,and the dynamic displacement field is expressed in a mixed form by in-plane double Fourier series and cubic polynomials through the thickness as 12 variables for each layer.A system of modified Lagrange equations is derived with all interface constraints.The Hertz and Cattaneo-Mindlin theories are used to solve for the normal and tangential contact forces during the impacts.By further discretizing in the time domain,the oblique impact problem is solved iteratively.While the numerical results clearly show the influence of impact velocity,stacking sequence,mechanical parameters,and geometric parameters,the proposed analytical approach could serve as a theoretical basis for the laminate analysis and design when it is under low-velocity impacts.

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.

Low-velocity Impact Damage Analysis of Composite Laminates Using Self-adapting Delamination Element Method

On the basis ofa 2D 4-node Mindlin shell element method, a novel self-adapting delamination finite element method is presented, which is developed to model the delamination damage of composite laminates. In the method, the sublaminate elements are generated automatically when the delamination damage occurs or extends. Thus, the complex process and state of delamination damage can be simulated practically with high efficiency for both analysis and modeling. Based on the self-adapting delamination method, linear dynamic finite element damage analysis is performed to simulate the low-velocity impact damage process of three types of mixed woven composite laminates. Taking the frictional force among sublaminations during delaminating and the transverse normal stress into account, the analytical results are consistent with those of the experimental data.

FATIGUE LIFE PREDICTION METHOD FOR IMPACTED LAMINATES

The existing models are established based on the fatigue behavior of impacted laminates.It makes them unsuitable for the general use.So,a general 3-D progressive damage fatigue life prediction method for impacted laminates is developed based on the progressive damage theory and the fatigue behavior of unimpacted unidirectional plies.The model can predict the fatigue life of laminated composites with different ply parameters,geometry,impact damage,and fatigue loading conditions.In order to obtain the impact damage information in the case that no impact test data is available,a whole damage process analysis method for laminated composites under the impact loading and the fatigue loading is analyzed.The predicted damage statuses of composite laminates can be used to analyze the post-impact fatigue life.A parametric modeling program is developed to predict the impact damage process and the fatigue life of impacted laminates based on the whole damage process analysis method.The most relative error between the prediction and the test results is 7.78%.

PROGRESSIVE FAILURE ANALYSIS OF LAMINATED COMPOSITES WITH TRANSVERSE SHEAR EFFECTS

This paper deals with the progressive failure analysis of composite laminates. Triangular elements which include the transverse shear effects are us.d for the stress analysis. A new method for the calculation of the shear correction factors is presented. Several failure criteria are used to check the first ply failure and distinguish the laminate failure modes into fiber breakage or buckling, matrix cracking and delamination. After the failure is detected, the stiffness of the failed ply is modified according to the failure modes. The ultimate strength of the laminate is obtained by an iterative way. Several examples are given in the paper for stress analysis and progressive failure analysis of composite laminates.

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.

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.

Preparation, structure and properties of Mg/Al laminated metal composites fabricated by roll-bonding, a review

Laminated metal composites(LMCs) are a unique composite material and have great application prospects in automobiles, ships, aircraft,and other manufacturing industries. As lightweight materials, the Mg/Al LMCs are expected to combine the advantages of both Mg and Al alloys to broaden their application prospects. Roll-bonding is the most popular process for the fabrication of Mg/Al LMCs due to high production efficiency and good product quality stability. The roll-bonding process involves the deformation of the substrates and the formation of the interfacial diffusion layer. The latter will directly determine the interface bonding strength of Mg/Al LMCs. Bonding strength is very sensitive to the thickness of the reaction layer in the diffusion layer. When the thickness of the reaction layer exceeds 5 μm, the bonding strength decreases sharply. Therefore, controlling the thickness of the reaction layer is very important for the design of rolling parameters.The latest research also showed that the addition of intermediate layer metal and the construction of three-dimensional interfaces can further improve the interface bonding strength. How to apply these methods to roll-bonding is the focus of future research. Recently, a new rolling technique, corrugated roll/plat roll rolling+flat roll/flat roll rolling has been developed to fabricate Mg/Al LMCs. It can effectively promote the deformation of the hard layer and generate a wavy interface, resulting in the enhancement of the bonding quality and rolling quality.In the current review, the effects of rolling parameters and subsequent annealing on the interface structure of Mg/Al LMCs were elaborated in detail. The application of some special rolling techniques in the preparation of Mg/Al LMCs was also summarized. The latest research results on the relationship between interface structure and mechanical properties of Mg/Al LMCs were reviewed. Finally, further research directions in this field were proposed.

Formation mechanism and growth kinetics of TiAl_(3) phase in cold-rolled Ti/Al laminated composites during annealing

Cold-rolled Ti/Al laminated composites were annealed at 525−625℃for 0−128 h,and the interfacial microstructure evolution was investigated.The results indicate that only the TiAl_(3) phase was formed at the Ti/Al interface;most of TiAl_(3) grains were fine equiaxed with average sizes ranging from hundreds of nanometers to several microns and the TiAl_(3) grain size increased with increasing annealing time and/or temperature,but the effect of annealing temperature on the TiAl_(3) grain size was far greater than that of annealing time.The growth of the TiAl_(3) phase consisted of two stages.The initial stage was governed by chemical reaction with a reaction activation energy of 195.75 kJ/mol,and the reaction rate constant of the TiAl_(3) phase was larger as the Ti/Al interface was bonded with fresh surfaces.At the second stage,the growth was governed by diffusion,the diffusion activation energy was 33.69 kJ/mol,and the diffusion growth rate constant of the TiAl_(3) phase was mainly determined by the grain boundary diffusion owing to the smaller TiAl_(3) grain size.

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.

Effect of SACMA and QMW Test Methods on Compressive Properties of Composite Laminates after Low Velocity Impact

Experimental studies on the compressive behavior of composite laminates after low velocity impact was carried out with two test methods.One is SACMA Standard,and the other is a small dimensional specimen test method.Impact damage distributions,compressive failure process after impact,quasi static indentation and compression of laminates with a hole were brought into comparison between these two test methods.The results showed that there is a great difference between these two test methods.Compressive behavior of laminates after impact varies with different test methods.Residual compressive strength of laminates after low velocity impact measured with SACMA Standard can reflect stiffness properties of composite resins more wholely than that measured with the other method can do.Small dimensional specimen test method should be improved on as an experimental standard of compressive strength after impact.

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.

Microstructure and mechanical properties of bio-inspired Cf/Ti/Mg laminated composites

Inspired by an old fish skin structure,the Cf/Ti/Mg laminated composites were fabricated by squeeze casting technology.No porous or voids were found in final composite,and carbon fiber was uniformly dispersed in Mg matrix.Furthermore,the addition of net-shaped Ti adsorbed Al element and facilitated the nucleation of Mg_(17)Al_(12)nearby Ti.The reaction product Al_(4)C_(3)was found at the Cf and AZ91 interface.Mechanical tests indicate that the introduction of Ti could greatly improve the toughness of Cf/Mg composites.

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.

FRACTURAL PROCESS AND TOUGHENING MECHANISM OF LAMINATED CERAMIC COMPOSITES

Based on the model of multi-layer beam and the assumption of micro-inhomogeneity of material, the 3D fractural characteristics of laminated ceramic composites have been studied with numerical simulation. Under three-point bending load, crack initiation, coalescence, propagation, tuning off in the weak interface and final rupture have been simulated. The spatial distribution and evolution process of acoustic emission are also presented in the paper. The simulation verifies the primary mechanism of the weak interface inducing the crack to expand along there and absorbing the fractural energy. The disciplinary significance of the effect of strength and properties of material on the toughness and strength of laminated ceramic composites is, therefore, discussed in this paper.

DELAMINATION FORMATION AND DELAMINATION PROPAGATION OF COMPOSITE LAMINATES UNDER COMPRESSIVE FATIGUE LOADING

Fatigue tests of the smooth composite laminates and the notched composite laminates under compressive cyclic loading have been carried out. The damage mechanism is discussed and analyzed. Damage evolution is monitored using stiffness decay. From these tests, it is found that the initial delamination occurs at the free boundary of smooth specimens, or the notch boundary of notched specimens, subjected to the compression-compression cyclic load. A point of view in relation to two-phases of compression fatigue delamination of composites is proposed, namely, compression-compression delamination consists of the delamination formation phase and the delamination propagation, and there is a 'damage transition point' to separate this two-phases. Furthermore, an empirical modulus degradation formula and its parameters fitting method are presented. According to the test data handling results, it is shown that this formula is univocal and can fit the test data conveniently. In addition, two kinds of new anti-buckling devices are designed for these tests. At last, the E-N curves, the D-N curves and the S-N curve of the smooth carbon fiber reinforced composite laminates of T300/648C are determined to predict the fatigue life of the notched composite laminate. And the E-N curve of the notched specimens at the given load ratio R = 10 and minimum load Pmin = -0.45 kN is also measured to verify the estimated result of fatigue life.

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.

Suppression of thermal postbuckling and nonlinear panel flutter motions of variable stiffness composite laminates using piezoelectric actuators

Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbuckling and nonlinear panel flutter motions of VSCLs,a full-order numerical model is developed based on the linear quadratic regulator(LQR)algorithm in control theory,the classical laminate plate theory(CLPT)considering von Kármán geometrical nonlinearity,and the first-order Piston theory.The critical buckling temperature and the critical aerodynamic pressure of VSCLs are parametrically investigated.The location and shape of piezoelectric actuators for optimal control of the dynamic responses of VSCLs are determined through comparing the norms of feedback control gain(NFCG).Numerical simulations show that the temperature field has a great effect on aeroelastic tailoring of VSCLs;the curvilinear fiber path of VSCLs can significantly affect the optimal location and shape of piezoelectric actuator for flutter suppression;the unstable panel flutter and the thermal postbuckling deflection can be suppressed effectively through optimal design of piezoelectric patches.

Microstructure and mechanical behavior of Ti/Cu/Ti laminated composites produced by corrugated and flat rolling

Ti/Cu/Ti laminated composites were fabricated by corrugated rolling(CR) and flat rolling(FR) method.Microstructure and mechanical properties of CR and FR laminated composites were investigated by scanning electron microscopy, numerical simulation methods, peel and tensile examinations. The effect of CR and FR was comparatively analyzed. The results showed that the CR and FR laminated composites exhibited different effective plastic strain distributions of the Ti layer and Cu layer at the interface. The recrystallization texture, prismatic texture and pyramidal texture were developed in the Ti layer by CR, while the R-Goss texture and shear texture were developed in the Cu layer by CR. The typical deformation texture components were developed in the Ti layer and Cu layer of FR laminated composites. The CR laminated composites had higher bond strength, tensile strength and ductility.