Finite element analysis for the evaluation of the low-velocity impact response of a composite plate

The low-velocity impact responses of cross-ply CFRP composite plates are investigated experimentally and are simulated using the finite element code LS-DYNA. An experimental test was initially performed and two different modeling approaches were then employed to model the composite plates. In the first numerical modeling approach, solid elements are utilized for the composite layers, whereas in the second, shell elements are used. The numerical model using the shell elements shows a good correlation with the experimental results, while the impact damage in the form of delamination is predicted more precisely using solid elements.     

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.     

Low-velocity impact analysis of composite laminates using linearized contact law

Usually many researchers have used the modified Hertzian contact law or experimental static indentation law to analyze impact response of composite laminates subjected to low-velocity impact. In this study, physical meaning of the analytical method using the laws was investigated and the difference between the analytical results obtained using the two laws was also investigated. Furthermore parametric study on contact coefficient and exponent of the contact law was performed. Finally it could be shown that linearized contact law could be well applied to the low-velocity impact analysis of composite laminates. If this concept is used, any general-purpose finite element method software can be used to solve impact problem without direct developing any FEM code by each researcher. In this paper, some analytical results analyzed using a general-purpose commercial FEM software were also presented.     

LOW-VELOCITY IMPACT RESPONSE OF COMPOSITE LAMINATES CONSIDERING HIGHER-ORDER SHEAR DEFORMATION AND LARGE DEFLECTION

SUMMARY

Low-velocity impact responses of composite laminates are investigated analytically and experimentally. In analytical research, the finite element analyses based on various plate theories and three-dimensional thoeory are performed. For experimental research, a drop weight type impact test system is used. In geometrical non-linear analysis, a displacement field considering higher-order shear deformation and large deflection of the laminate is assumed and the finite element formulation is derived. The modified Hertzian contact law is incorporated into the finite element program to evaluate contact force. Numerical results including impact force histories, deflections, dynamic strains in the laminate from the impact response analysis are presented and compared with the experimental results from impact test. The results of the investigation indicate that higher-order shear deformation and large deflection effects should be considered to accurately describe the low-velocity impact response including interlaminar shear stress of the laminate.     

Predicting low-velocity impact damage on a stiffened composite panel

An intralaminar damage model, based on a continuum damage mechanics approach, is presented to model the damage mechanisms occurring in carbon fibre composite structures incorporating fibre tensile and compressive breakage, matrix tensile and compressive fracture, and shear failure. The damage model, together with interface elements for capturing interlaminar failure, is implemented in a finite element package and used in a detailed finite element model to simulate the response of a stiffened composite panel to low-velocity impact. Contact algorithms and friction between delaminated plies were included, to better simulate the impact event. Analyses were executed on a high performance computer (HPC) cluster to reduce the actual time required for this detailed numerical analysis. Numerical results relating to the various observed interlaminar damage mechanisms, delamination initiation and propagation, as well as the model’s ability to capture post-impact permanent indentation in the panel are discussed. Very good agreement was achieved with experimentally obtained data of energy absorbed and impactor force versus time. The extent of damage predicted around the impact site also corresponded well with the damage detected by non destructive evaluation of the tested panel.     

Analytical and numerical analysis of 3D grid-reinforced orthotropic composite structures

A comprehensive micromechanical investigation of 3D periodic composite structures reinforced with a grid of orthotropic reinforcements is undertaken. Two different modeling techniques are presented; one is based on the asymptotic homogenization method and the other is a numerical model based on the finite element technique. The asymptotic homogenization model transforms the original boundary value problem into a simpler one characterized by effective coefficients which are shown to depend only on the geometric and material parameters of a periodicity cell. The model is applied to various 3D grid-reinforced structures with generally orthotropic constituent materials. Analytical formula for the effective elastic coefficients are derived, and it is shown that they converge to earlier published results in much simpler case of 2D grid reinforced structures with isotropic constituent materials. A finite element model is subsequently developed and used to examine the aforementioned periodic grid-reinforced orthotropic structures. The deformations from the finite element simulations are used to extract the elastic and shear moduli of the structures. The results of the asymptotic homogenization analysis are compared to those pertaining to their finite element counterparts and a very good agreement is shown between these two approaches. A comparison of the two modeling techniques readily reveals that the asymptotic homogenization model is appreciably faster in its implementation (without a significant loss of accuracy) and thus is readily amenable to preliminary design of a given 3D grid-reinforced composite structure. The finite element model however, is more accurate and predicts all of the effective elastic coefficients. Thus, the engineer facing a particular design application, could perform a preliminary design (selection of type, number and spatial orientation of the reinforcements) and then fine tune the final structure by using the finite element model.     

缝合复合材料低速冲击损伤研究

通过三维动力学有限元法,采用空间杆单元来描述缝线,结合试验系统地研究了缝合复合材料的低速冲击损伤问题。采用修正的赫兹接触定律计算冲击接触力,NewMark直接积分法求解运动方程,求解冲击过程中的应力应变;在Chang和Hou等的分层扩展准则基础上,提出一修正的分层扩展准则并考虑纤维断裂,建立了分析低速冲击损伤面积的方法;对相同铺层的缝合与未缝合复合材料层板进行了低速冲击试验。分析结果与实验结果具有良好的一致性,证明本文中提出的修正的分层扩展准则是正确的。计算及试验结果均表明,在相同冲击能量作用下,缝合使冲击损伤面积明显减小。      

Rapid simulation of impacts on composite sandwich panels inducing barely visible damage

The finite element based design tool, CODAC, has been developed for efficiently simulating the impact behavior of sandwich structures consisting of two composite face sheets and a compliant core. To achieve a rapid and accurate stress analysis, three-layered finite shell elements are used. A number of macromechanical damage models are implemented to model damage onset and damage growth.

The transient impact analysis is assessed via an experimental impact test program on honeycomb sandwich panels. Force–time histories and damage sizes are examined. The influence of distinct damage and degradation models on the impact response is analyzed. Results show that the presented time-efficient methodology is capable of accurately modeling core failure behavior and rapidly simulating low-velocity impacts which induce barely visible damage.     

弹性压头与复合材料层合梁间的弹性接触分析

冲击器与复合材料接触性态的研究是复合材料低速冲击响应研究的关键.本文采用处理弹性接触问题的有限元混合法研究了弹性压头与复合材料层合梁间的弹性接触问题.用数值算例讨论了静力接触定律和压头弹性、层合梁铺设方式及摩擦等因素对接触内力和层合梁内部层间应力大小和分布的影响,得到一些有益的结论.     

Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model

A numerical model for simulating the process of low-velocity impact damage in composite laminates using the finite element method is presented in this paper, i.e. Part I of this two part series on the study of impact. In this model, the 9-node Lagrangian element of the Mindlin plate with consideration of large deformation analysis is employed. To analyze the transient response of the laminated plates, a modified Newmark time integration algorithm previously proposed by the authors is adopted here. We also proved that the impact process between a rigid ball and laminated plates is a stiff system, therefore a kind of A(α) stable method has been advocated here to solve the motion equation of the rigid ball. Furthermore, various types of damages including delamination, matrix cracking and fiber breakage, etc. and their mutual influences are modeled and investigated in detail. To overcome the difficulty of numerical oscillation or instability in the analysis of the dynamic contact problem between delaminated layers using the traditional penalty methods, we have employed dynamic spring constraints to simulate the contact effect, which are added to the numerical model by a kind of continuous penalty function. Moreover, an effective technique to calculate the strain energy release rate based on the Mindlin plate model is proposed, which can attain high precision. Finally, some techniques of adaptive analyses have been realized for improving the computational efficiency. Based on this model, a program has been developed for numerically simulating the damage process of cross-ply fiber-reinforced carbon/epoxy composite laminates under low-velocity impact load. In Part II, this numerical model will be verified by comparing with the experimental results. Also the impact damage will be investigated in detail using this numerical approach.     

Interlaminar stresses in laminated composite plates, cylindrical/spherical shell panels damaged by low-velocity impact

Prediction of damage caused by low-velocity impact in laminated composite plate cylindrical/spherical shell panels is an important problem faced by designers using composites. Not only the in-plane stresses but also the interlaminar normal and shear stresses play a role in estimating the damage caused. The work reported here is an effort in getting better predictions of damage in composite plate cylindrical/spherical shell panels subjected to low-velocity impact.

The low-velocity impact problem is treated as a quasi-static problem. First, the in-plane stresses are calculated by 2-D nonlinear finite element analysis using a 48 degrees of freedom laminated composite shell element. The damage analysis is then carried out using a Tsai-Wu quadratic failure criterion and a maximum stress criteria. Interlaminar normal and shear stresses are predicted after taking into account the in-plane damage caused by low-velocity impact. The interlaminar stresses are obtained by integrating the 3-D equations of equilibrium through the thickness. The deformed geometry is taken into account in the third equation of equilibrium (in the thickness direction). After evaluating the formulation and the computer program developed for correctness, the interlaminar stresses are predicted for composite plates/shell panels which are damaged by low-velocity impact.     

An Experimental Method for Dynamic Delamination Analysis of Composite Materials by Impact Bending

An improved experimental method for characterizing dynamic delamination growth in composite structures has been developed and verified using high speed photography and explicit finite element simulation. The method is based on a three-point bending device. End notch flexure carbon fiber composite beam specimens were subjected to both quasi-static and impact rates of Mode II loading. The experimental results showed no significant strain rate dependency of the delamination fracture toughness. This important result complements the scarce and conflicting data available in the literature, and serves as a reference for calibration of numerical modeling strategies.     

Low-velocity impact and residual tensile strength analysis to carbon fiber composite laminates

In this paper, low-velocity impact characteristics and residual tensile strength of carbon fiber composite laminates are investigated by experimentally and numerically. Low-velocity impact tests and residual tensile strength tests are performed using an instrumented drop-weight machine (Instron 9250HV) and static test machine (Instron 5569), respectively. The finite element (FE) software, ABAQUS/Explicit is employed to simulate low-velocity impact characteristics and predict residual tensile strength of carbon fiber composites laminates. These numerical investigations create a user-defined material subroutine (VUMAT) to enhance the damage simulation which includes Hashin and Yeh failure criteria. The impact contact force and the tensile strength are accurately estimated using the present method. Two different tensile damage modes after different impact energies are observed. The degradation of residual tensile strengths can be divided to three stages for different impact energies, and amplitudes of degradation are affected by stacking sequences.     

The finite element analysis of composite laminates and shell structures subjected to low velocity impact

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection. The impact response of the structure is proportional to the impactor velocity.     

Damage evaluation and strain monitoring for composite cylinders using tin-coated FBG sensors under low-velocity impacts

Background/purposeThe impact-induced damage of composite structures induced by low-velocity impacts were evaluated to verify the damage evaluation concept using the “memory effects” of tin-coated FBG sensors.MethodsLow-velocity impact tests for the composite cylinder with tin-coated FBG sensors were performed at three impact energies. Hoop ring tests for the composite cylinder including impact-induced damage were additionally undertaken in order to measure the burst pressure and to study the parameter correlations. The test results were compared with the numerical results obtained by a finite element analysis (FEA) based on a continuum damage mechanics (CDM) considering damage model. The parameter correlations among the impact parameters and the residual strains induced by tin-coated FBG sensors were investigated based on the tests results.ResultsImpact behaviors obtained by the tests and the numerical simulation were agreed well. It was found that tin-coated FBG sensors can monitor the strain of the composite cylinder under low-velocity impacts and their strain monitoring capability is comparable to that of normally used FBG sensors. The residual strains of tin-coated FBG sensors were correlated with the impact parameters such as the impact energy, the sensing position of the sensors, and the burst pressure of the composite cylinder.ConclusionThe correlations among the residual strains and the parameters proved the damage evaluation concept for composite cylinders using the “memory effects” of tin-coated FBG sensors under low-velocity impact conditions; that is, the impact-induced damage, impact location, and burst pressure can be inversely evaluated by referring to the correlations.     

Low-Velocity Impact Damage Simulation of Biaxial Warp-Knitted Flexible Composite with Simplified Microstructure Model

Applied Composite Materials - In this paper, the low-velocity impact deformation behavior of biaxial warp-knitted flexible composite was investigated. A simplified finite element model (FEM) of the...     

Hybrid approach in bird strike damage prediction on aeronautical composite structures

This paper deals with the problem of numerical prediction of bird strike induced damage on aeronautical structures. The problem of soft body impacts has been tackled by applying a hybrid Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. Eulerian modeling of the bird impactor resulted in a more realistic behavior of bird material during impact, which has lead to an enhanced response of the impacted structure. The work presented in this paper is focused on damage modeling in composite items of aeronautical structures. The bird impactor model and damage modeling approaches have been validated by comparison with experimental gas gun results available in the open literature, while the complete damage prediction procedure has been demonstrated on a complex airplane flap structure finite element model.     

Hybrid approach in bird strike damage prediction on aeronautical composite structures

This paper deals with the problem of numerical prediction of bird strike induced damage on aeronautical structures. The problem of soft body impacts has been tackled by applying a hybrid Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. Eulerian modeling of the bird impactor resulted in a more realistic behavior of bird material during impact, which has lead to an enhanced response of the impacted structure. The work presented in this paper is focused on damage modeling in composite items of aeronautical structures. The bird impactor model and damage modeling approaches have been validated by comparison with experimental gas gun results available in the open literature, while the complete damage prediction procedure has been demonstrated on a complex airplane flap structure finite element model.     

Impact analysis of composite laminates with multiple delaminations

This paper concerns with the transient response of composite laminates with multiple delaminations subjected to low-velocity impact by a rigid ball. The finite element method based on the Mindlin plate theory is employed to describe the motion and deformation of the laminates. A Hertzian-type indentation law is adopted to calculate the impact force between the laminates and the rigid ball. To deal with the dynamic contacts between delaminated layers effectively, a modified Lagrange multiplier technique is employed. For multi-body dynamic contacts, the computation of contact force between delaminated layers is addressed. Numerical results provide much information for understanding the impact phenomenon of the composite laminates with multiple delaminations.     

Finite element calculation of 4-step 3-dimensional braided composite under ballistic perforation

The ballistic perforation test results of 4-step 3-dimensional (3D) braided Twaron^®/epoxy composites, which were subjected to impact by conically cylindrical steel projectile, are presented. The residual velocities of projectile perforated composites target at various strike velocities were measured and also compared with that from finite element calculation. ‘Fiber inclination model’ for 3D textile composites was adopted to decompose the 3D braided composite at quasi-microstructure level for the geometrical modeling in preprocessor of FEM. The material modeling was also based on this simplified model. The finite element code of Ls-Dyna was used to simulate the impact interaction between projectile and inclined lamina. The residual velocity of projectile perforating the entire 3D braided composite can be calculated from the sum of kinetic energy loss of the projectile that obtained from FEM. From the simulation of ballistic penetration process and comparison between numerical results and experimental results, it proves that the analysis scheme of quasi-microstructure level in this paper is valid and reasonable. The simplified method in this paper could be extended to model other kinds of 3D textile composites under ballistic impact.