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.

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.

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.

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.

Inter-well internal resonance analysis of rectangular asymmetric cross-ply bistable composite laminated cantilever shell under transverse foundation excitation

The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.

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.

DAMAGE PROGRESSIVE MODEL OF COMPRESSION OFCOMPOSITE LAMINATES AFTER LOW VELOCITY IMPACT

Compressive properties of composite laminates after low velocity impact are one of the most serious circumstances that must be taken into account in damage tolerance design of composite structures. In order to investigate compressive properties of composite laminates after low velocity impact, three dimensional dynamic finite element method (FEM) was used to simulate low-velocity impact damage of 2 kinds of composite laminates firstly. Damage distributions and projective damage areas of the laminates were predicted under two impact energy levels. The analyzed damage after impact was considered to be the initial damage of the laminates under compressive loads. Then three dimensional static FEM was used to simulate the compressive failure process and to calculate residual compressive strengths of the impact damaged laminates. It is achieved to simulate the whole process from initial low-velocity impact damage to final compressive failure of composite laminates. Compared with experimental results, it shows that the numerical predicting results agree with the test results fairly well.

Damage Detection and Material Property Reconstruction of Composite Laminates Using Laser Ultrasonic Technique

Laser ultrasonic technique has received increasing attentions in the past decade due to its contactless nature and a wide range of applications have been reported. In this review,applications of laser ultrasonic technique developed at Nanjing University of Aeronautics and Astronautics(NUAA)as well as elsewhere for non-destructive testing in composite laminates are presented. The principles of generating and detecting in a laser ultrasonic system are introduced,three different system configurations are also introduced with each configuration's advantages and disadvantages explained. More importantly,two major applications developed at NUAA for composite laminates are presented including damage detection,stiffness reconstruction and fatigue life prediction. Both applications are realized by a fixed-point PZT sensor and scanning pulse laser based on the linear reciprocal theorem. Analytical method and numerical models are employed and developed to realize the functionalities.

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.

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.

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.

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.

Mechanical property of single-bolted composite laminates

In order to investigate the effects of different geometrical parameters and pretightening loads on failure mode and bearing strength,a large number of single-bolted T300/QY8911 composite laminates were tested under static tension load.Box-plot was used to extract the singular testing values of bearing strength and effective statistical values were obtained.T-test method of independent samples was used to study how much pretightening loads influence bearing strength.The results show that the geometrical parameters,such as ratios of width to hole diameter(w/d) and edge distance to hole diameter(e/d),remarkably influence failure mode and bearing strength.Net-section failure will occur when w/d is smaller than 4,and shear-out failure will occur when e/d is smaller than 2.Bearing failure or bearing and shear-out combined failure will occur when w/d is greater than 4 and e/d is greater than 2.There is an optimal combination of geometrical parameters to achieve the highest bearing strength.For most of specimens,pretightening loads do not explicitly influence bearing strength.

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.

Fatigue life prediction and experiment research for composite laminates with circular hole

Based on the fatigue prediction model of exponential function and Whitney-Nuismer(WN) criterion of static strength for the composite material laminate with a circular hole, the stress correct factor ( β ) was put forward and a new fatigue prediction model for composite material laminate was set up. T300/KH304, which is recently studied and is a high capability composite material, was used as the raw material. In order to gain the factor β , the fatigue experiments of the laminates with holes in different diameters and the same ratio of width to diameter were conducted. The fatigue analysis and tests of the laminates with a hole 5 mm in diameter are carried out at different stress levels, and the results meet the engineering requirement. The simple, prompt and practical method is provided for the prediction of S-N curve of composite laminate with a circular hole.

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.

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.