Low Velocity Impact Analysis Research Articles

Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates

A nonlinear analysis is presented for impact response of carbon nanotube-reinforced composite (CNTRC) structures under thermal conditions. Two plate configurations (i.e., single-layer and sandwich plates) are considered, and the nanotube reinforcement is either uniformly-distributed or functionally-graded in the plate thickness direction. The material properties of nanotube reinforced composites are estimated using micromechanical models. The equations of motion are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity, and the thermal effects are included by considering the nanotube reinforced composites as temperature-dependent. The equations of motion are solved with a two-step perturbation technique, and the initial stresses caused by either the thermal or in-plane edge loads as in-plane boundary conditions are introduced. The influences of material property gradient, volume fraction distribution, temperature change, initial stress, initial velocity of the impactor, and core-to-face sheet thickness ratio on impact response of plate structures are discussed. The analysis presented can help better understand the nonlinear impact response of functionally-graded materials and facilitate design and optimization of nanocomposite structures against impact and under thermal and other environments.

Static and low-velocity impact on mechanical behaviors of foam sandwiched composites with different ply angles face sheets

The current studies give a brief account of analysis of static and low-velocity impact on foam sandwiched composites comprising composite faces from carbon/epoxy and cores from Rohacell (polymethacrylimide). The face sheets consist of four different stacking sequences as unidirectional, cross-ply, angle-ply and quasi-isotropic, which were fabricated by using hand lay-up process. Later, the composite panels were subjected to quasi-static and low-velocity impact loading using MTS and an instrumented Drop-Weight Machine (Instron 9250HV), respectively. The load-displacement curves have been obtained to characterize the failure mechanisms in the face sheets and the core. Impact parameters were evaluated and compared for different types of sandwich structures. Failure modes were studied by sectioning the samples at the impact location and observing under optical microscope. The results evaluated from static test have shown that the unidirectional have the highest peak load. However, the dynamic test data indicated that the foam sandwich with unidirectional face sheet have lowest peak load, lowest displacement at peak load and minimum energy absorption. It has also been observed that largest damage size, highest penetration depth and shear cracking have been experienced by unidirectional as compared to cross-ply, angle-ply and quasi-isotropic face sheets.

A new finite element model for low-velocity impact analysis of sandwich beams subjected to multiple projectiles

In this paper, a new finite element formulation is presented for high-order impact analysis of sandwich beams with any boundary conditions subjected to simultaneous multiple small projectiles. The contact of the projectiles may occur on arbitrary places on both faces of the beam. Hamilton’s principle is used for driving the governing partial differential equations of motion. The effect of each projectile is modeled by a one degree of freedom spring-mass system with variable stiffness by assuming the Hertzian contact law. The appropriate elemental matrices are derived for a sandwich beam element that carrying four sprung masses on both face sheets. Based on the presented formulation, an FE code is developed using the Newmark method with direct iteration process. The various cases are used to validate the predictions of the presented higher order theory and FE formulation shows good agreement with available results in the open literature and exact solution. Furthermore, numerical examples are presented to investigate effects of various parameters on the response of the structure.

A micromechanical approach for semi-analytical low-velocity impact analysis of a bidirectional functionally graded circular plate resting on an elastic foundation

All the rare investigations made on low velocity impact analysis of the functionally graded plates have employed the simple rule of mixture that may lead to inconsistent results in some circumstances, e.g., when the Poisson ratios of the constituent materials are quite different. On the other hand, these researches have been performed either by purely using a commercial finite element software or employing the conventional Hertz-type contact laws that are valid only if the overall plate flexibility is ignored. In the present paper, it is mainly focused on four novelties: (i) description of the apparent stiffness of the contact region of the plate based on the micromechanical Mori-Tanaka model for two-directional variations of the material properties of the functionally graded plates, (ii) employing an enhanced contact model, considering the micromechanics-based material model and plate and foundation compliances, (iii) evaluation effects of the foundation stiffness on the apparent impact stiffness and the plate responses, and (iv) using a weighted residual semi-analytical solution procedure and an iterative updating scheme to solve the nonlinear governing equations. Presence of the elastic foundation has caused very interesting, unexpected but reasonable behaviors to be observed.

항공기 적용 샌드위치 복합재 구조의 충격 손상 거동 연구

본 연구에서는 복합재 샌드위치 적층판의 저속 충격 해석을 수행하였다. 샌드위치 구조 형상의 스킨은 탄소/에폭시(Carbon-Epoxy) 재질이 채택되었고 코어(Core)의 재질은 폼(Foam)이 적용되었다. 연구의 타당성을 입증하기 위해 관련 문헌에서의 연구 결과에서 제시한 실험 결과와 유한 요소 해석 결과의 비교가 선행되었다. 타당성 검증을 바탕으로 본 연구에서 손상이 시작되는 충격체의 속도를 평가하고, 예측된 충격 속도에서 충격 거동을 분석하기위해 유한요소법을 이용하여 충격 해석을 수행하였다. 샌드위치 복합재 적층판의 충격 해석 결과 예측된 충격 속도에서 손상이 발생함을 확인하였다. 최종 시편 시험 결과와 수치 해석 결과의 비교 값이 잘 일치함을 확인하였다. In this study, low velocity impact analysis on composite sandwich structure was performed. Sandwich structure configuration is made of Carbon-Epoxy face sheets and foam cores. For validating study, the results of an experimental and a finite element method analysis were compared previously. From the finite element method analysis results of sandwich panel, it was confirmed that the results of analysis was reasonable. Impactor velocity to initiate damage was estimated, and in order to investigate the damage at the predicted velocity, impact analysis using finite element method was performed. According to the impact analysis results of sandwich panel, it was confirmed that the damage was generated at the estimated impact velocity. Finally, The comparison of the numerical results with those measured by the experiment showed good agreement.

Assessment of different higher order theories for low-velocity impact analysis of fibre-metal laminate cylindrical shells

Assessment of different higher order shell theories for low-velocity impact response analysis of simply-supported fibre-metal laminate circular cylindrical shells is achieved. A new two-degree-of-freedom spring-mass model is adapted and used for contact force history estimation. The Fourier series method is used to solve the governing equations of fibre-metal laminate shell. The mechanical behaviour of fibre-metal laminate is assumed to be elastic. The impact behaviour is assumed to be quasi-static. In order to investigate the effect of the thickness flexibility on the impact response analysis of fibre-metal laminate cylindrical shells, different 2D and 3D higher order shell theories are evaluated. Also, effects of some parameters including metal volume fraction and fibre-metal laminate layup on the impact response are investigated. The results indicate that regardless of the fibre-metal laminate layup, as the value of metal volume fraction increases, the influence of the thickness flexibility on the impact response of fibre-metal laminate cylindrical shells is more significant. Also, as the metal volume fraction increases, the impulse (area under contact force–time) remains almost unchanged. In fact, the fundamental frequency of the shell governs both the peak value of the contact force as well as the contact duration. It is shown that Al/G 2/1 is the best layup to minimise the shell deflections due to impact load and to maximise the fundamental frequency.

Numerical Analysis of Low Velocity Impact on Laminated Composite Plates

A numerical investigation is performed to study the behaviour of a composite plate under low velocity impact. The finite element simulation is performed to investigate the stress distribution during the impact on the laminated composite plate. The effectiveness of the developed numerical model is investigated by comparing the results in terms the transverse-deflection and stress, longitudinal stress and impact duration with those of available literature. Various parametric studies are performed to study the effect of boundary conditions, thickness of the laminate, impactor mass and velocity and composite lay-up sequence on stress variation of the composite laminate. It is concluded that the stresses are distributed symmetrically along the bottom and top layers irrespective of the boundary conditions. Furthermore, it is shown that the maximum tensile stress is yielded at the bottom layer while the maximum compressive stress is yielded at the top layer of the laminated composite plate. Symmetric variation in in-plane shear stress distribution is also observed. It is also shown that the thickness of the composite plate plays an important role on the deflection of the plate. It is further shown that depending on the boundary conditions considered, the significant variation of shear stress is observed along the shear plane with respect to the mass and velocity of the impactor and the lay –up configuration.

Nonlinear eccentric low-velocity impact analysis of a highly prestressed FGM rectangular plate, using a refined contact law

In the present paper, a nonlinear analysis is presented for response prediction of a low-velocity eccentric impact between a functionally graded rectangular plate and a rigid sphere or a projectile with a spherical nose. Some of the novelties of the present paper are (i) considering the more general case of eccentric impact, (ii) investigating effects of the initial in-plane loads on the impact responses of the functionally graded plates, especially for compressive loads that are comparable but not equal to the buckling loads, (iii) using a contact law that incorporates influences of the transverse variations of the material properties of the substrate layers and the plate thickness, and (iv) using nonlinear strain-displacement relations instead of using the traditional infinitesimal deformations assumption for assessment of influences of the initial preloads. Due to using von Karman strain-displacement relations and a nonlinear contact law, the governing equations are highly nonlinear. For this reason, an iterative solution scheme is employed. A sensitivity analysis is performed to investigate influences of the specifications of the plate and the indenter, the eccentric value, and the in-plane preloads on the indentation and force time histories. Results reveal that due to the resulting increase in the contact force, slightly higher damages may be expected for impacted FGM plates subjected to initial compressive in-plane loads.

Low-Velocity Impact and Residual Burst-Pressure Analysis of Cylindrical Composite Pressure Vessels

Low-Velocity Impact and Residual Burst-Pressure Analysis of Cylindrical Composite Pressure Vessels

Composite damage model based on continuum damage mechanics and low velocity impact analysis of composite plates

A composite damage model based on continuum damage mechanics (CDMs) is proposed for the progressive damage analysis of a composite structure. The damage progressive law that considers the Weibull distribution of the composite strength was employed in the damage model. The nonlinear shear behavior of the composites was also considered. Also, a simple model that considers the irreversible strain due to the damage was proposed. The damage model was implemented in the user material subroutine of the ABAQUS/explicit program, VUMAT. Low velocity impact tests of the graphite/epoxy composite plates were also performed in a range of impact energies. The impact energies were classified into three levels based on the impact damage and impact behavior. The impact analyses of the composite plate were performed using the ABAQUS/explicit program with the developed composite damage model. The impact response and impact damage from the numerical analyses were comparable with those of test results.

Nonlinear low-velocity impact response analysis of a radially preloaded two-directional-functionally graded circular plate: A refined contact stiffness approach

The available rare publications on low-velocity impact analysis of the functionally graded plates have mainly been performed using commercial finite element softwares and discrete models for variations of the material properties. In the present research, nonlinear low-velocity impact analysis of two-directionally-graded circular plates under radial preloads is presented. Some of the novelties of the present research are: (a) the problem is treated based on a complete formulation and accurately modeling of variations of the material properties, (b) considering a functionally graded material whose properties vary in both radial and transverse directions, (c) considering influence of the initial compressive/extensional radial loads, (d) using nonlinear von Karman-type strain–displacement relations for evaluating effects of the radial preloads, (e) employing a refined contact law that accounts for the material heterogeneity and plate thickness, and (f) using a Galerkin-type solution procedure to achieve more accurate results. Therefore, results may be used for radially-graded and transversely-graded circular plates as special cases. The nonlinear governing equations are solved employing an iterative numerical procedure during each Newmark’s time integration step. A comprehensive sensitivity analysis including effects of various material heterogeneity, geometric, and motion parameters is accomplished.

Strain rate dependent low velocity impact response of layerwise 3D-reinforced composite structures

The performance evaluation of a novel layerwise 3D-reinforced glass–fibre composite material under low velocity impact loading conditions is presented. Firstly, strain rate dependent material properties are determined, for which the experimental procedure is explained in detail on the example of polypropylene and epoxy matrix based composite configurations. The gained orthotropic property-profile provides the input parameters for a numerical low velocity impact analysis of a demonstrator structure. This complex shaped bucket structure, manufactured within a VARTM process, is subjected to various impact scenarios, for which a fully instrumented drop tower testing rig has been designed and utilised. The numerical results are compared with the experimentally observed impact response. The predictive capability of the proposed multidisciplinary evaluation approach for composites subjected to impact loading conditions is finally discussed.

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.

Low velocity impact analysis of laminated composite plates using a 3D elasticity based layerwise FEM

A three-dimensional elasticity based approach coupled with layerwise laminated plate theory are employed to conduct low velocity impact analyses of general fiber reinforced laminated composite plates. The computation algorithm is finite element method. A computer code named IMPLW3D (Impact response, 3D elasticity based layerwise approach) is developed for the purpose. Hertzian nonlinear contact law models the contact forces between the rigid projectile and the laminated plate. The convergence, stability and accuracy of the algorithm are verified by solving different examples. The results predicted by the IMPLW3D code are compared with those developed by the ABAQUS software and the available solutions from open literature. Finally, the effects of the impact velocity, mass of the impactor, anisotropic material properties on the impact response are examined.

Quasi-Static and Low-Velocity Impact Response of Fully Backed or Simply Supported Sandwich Beams

The present paper describes analysis of low-velocity transverse impact on sandwich beam, with composite faces from Eglass/epoxy and cores from Polyurethane or PVC. Boundary conditions are fully backed rigid or simply supported. This research is based on a step by step study to generate more reliable impact results. Indentation of laminated beam, indentation of sandwich beams, and three-point loading have been analyzed with existing theories and modeled with the FE code ABAQUS, also their results are compared with experimental results. In quasi-static three-point bending, energy is consumed through three mechanisms: indentation of laminated beam, indentation of sandwich beam, and bending of sandwich beam. Impact on fully backed specimen is modeled in two cases of impactor energies using mass spring model of SDOF (single-degree-of-freedom) and indentation stiffness, lower energy of impactor for elastic indentation of sandwich beams, and higher energy for indentation in plastic area. TDOF (two-degree-of-freedom) with flexural and contact stiffnesses are used for impact on simply supported beams. Impacts are simulated by ABAQUS, as well. Results can describe response of beam and impactor displacements in terms of core and faces thicknesses, core material, and impactor energies for static and impact results. The experimental results are in good agreement with the analytical and FE analyses.

Low-velocity impact analysis of composite laminates under initial in-plane load

In this paper, low-velocity impact response and damage of composite laminates is analytically investigated. A modified displacement field of the plate considering initially loaded in-plane strain is proposed. From the displacement field, a finite element equation on the structural behavior of composite laminate is newly induced and a computational program is coded. Numerical results using the FEM code is compared with the numerical ones from reference. Additional numerical analysis is performed on another impact condition, and the effect of initial in-plane load is investigated. Potential delamination damage area in the first inter-ply surface from the bottom of the laminate is approximately estimated, and the effect of the initial in-plane load and the impact condition are also investigated. Consequently, it may be concluded that the initial in-plane load of the laminate does not affect so much on the impact damage area of the laminate.

Failure analysis of low velocity impact on thin composite laminates: Experimental and numerical approaches

Abstract The dynamic behavior of composite laminates is very complex because there are many concurrent phenomena during composite laminate failure under impact load. Fiber breakage, delaminations, matrix cracking, plastic deformations due to contact and large displacements are some effects which should be considered when a structure made from composite material is impacted by a foreign object. Thus, an investigation of the low velocity impact on laminated composite thin disks of epoxy resin reinforced by carbon fiber is presented. The influence of stacking sequence and energy impact was investigated using load–time histories, displacement–time histories and energy–time histories as well as images from NDE. Indentation tests results were compared to dynamic results, verifying the inertia effects when thin composite laminate was impacted by foreign object with low velocity. Finite element analysis (FEA) was developed, using Hill’s model and material models implemented by UMAT (User Material Subroutine) into software ABAQUS™, in order to simulate the failure mechanisms under indentation tests.

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.

Analysis of Low-Velocity Impact on Composite Sandwich Panels Using an Assumed Strain Solid Element

Low-velocity impact on composite sandwich panels has been investigated. The contact force is computed from a proposed modified Hertzian contact law. In the proposed contact law, the exponent is adjusted and the through-the-thickness elastic constant of honeycomb core is reduced properly to approximately predict the measured contact force-time history during the impact. The equivalent transverse elastic constant is calculated from the rule of mixture. Nonlinear equation to calculate the contact force is solved by the Newton-Raphson method and time integration is done by the Newmark-beta method. A finite element program for the low-velocity impact analysis is coded by implementing these techniques and an 18-node assumed strain solid element. Behaviors of composite sandwich panels subjected to low-velocity impact are analyzed for various cases with different geometry and lay-ups. It has been found that the present code with the proposed contact law can predict measured contact forces and contact times for most cases within reasonable error bounds, especially for thick sandwich plates.

가정변형률 솔리드 요소를 이용한 복합재 샌드위치 평판의 저속충격 해석

본 논문에서는 저속충격을 받는 복합재 샌드위치 평판의 동적 거동에 관한 연구를 수행하였다. 접촉 하중의 산출을 위해서 Hertz의 접촉법칙을 새로이 수정하는 방법을 제시했는데, 지수를 줄이는 방법과 심재의 두께방향의 탄성계수의 값을 줄여 등가 탄성계수를 계산하는 방법을 사용했다. 접촉하중을 산출하는 비선형 방정식은 Newton-Raphson 방법을 사용하여 계산하였고, 시간적분에는 Newmark-beta 방법을 사용하였다. 이러한 기법과 18절점 가정변형률 솔리드 요소를 적용하여 저속충격 해석용 유한요소 프로그램을 개발했다. 이 프로그램을 이용하여 다양한 복합재 샌드위치 평판의 저속충격에 대한 동적 거동을 해석하였다. 제안된 접촉법칙을 적용한 해석결과를 분석하여 볼 때, 대부분의 경우에서 접촉하중과 접촉시간이 실험결과와 대체로 일치함을 확인하였다. Low-velocity impact on composite sandwich panel has been investigated. Contact force is computed from a proposed modified Hertzian contact law. The Hertzian contact law is constructed by adjusting numerical value of the exponent and reducing the through-the- thickness elastic constant of honeycomb core. The equivalent transverse elastic constant is calculated from the rule of mixture. Nonlinear equation to calculate the contact force is solved by the Newton-Raphson method and time integration is done by the Newmark-beta method. A finite element program for the low-velocity impact analysis is coded by implementing these techniques and an 18-node assumed strain solid element. Behaviors of composite sandwich panels subjected to low-velocity impact are analyzed for various cases with different geometry and lay-ups. It has been found that the present code with the proposed contact law can predict measured contact forces and contact times for most cases within reasonable error bounds.