In-plane Impact Research Articles

OS0907 ハニカム構造の面内衝撃挙動に及ぼすライン充填セルの影響(OS09-02 材料・構造の衝撃問題2,OS09材料・構造の衝撃問題(1))

セルがライン状に充填されたハニカム構造体の面内圧縮挙動を有限要素解析により明らかにした.充填されたセルはライン状に配置されており,ハニカム構造体はライン状に配置された充填セルによって複数のセル領域で構成される.ハニカム構造体が圧縮されるとそれぞれのセル領域は独立に変形し,その結果,面内圧縮挙動に充填セルの影響が生じた.ライン状の充填セルを持つハニカムモデルの衝撃エネルギ吸収量は,充填されていない場合よりも増加することが明らかとなった.

Dynamic investigation of a functionally graded layered structure with a crack crossing the interface

The dynamic response of a functionally graded layered structure with a crack crossing the interface is analyzed. The in-plane impact loading condition is considered. By using the Laplace and Fourier integral transforms, singular integral equation method and residue theory, the present problem is reduced to a singular integral equation in the Laplace transform domain. The influences of Young’s modulus ratio, thickness ratio, and crack length and location on the dynamic stress intensity factors (DSIFs) are investigated. Particularly, the DSIFs corresponding to different crack locations are shown in the case when the crack center moves from one layer to another layer through the interface. The peak and static values and overshoot characteristics of the DSIFs are analyzed. It is found that these values typically exhibit kinking behavior when the crack tips arrive at the interface. This study is different from previous other investigations in the following respects: (1) the dynamic response of a crack crossing the interface of a functionally graded structure is studied analytically, which has hardly been done in the past and (2) the present model can be reduced to some important problems, such as a functionally graded coating-substrate structure with a crack in the graded coating or homogeneous substrate or one intersecting the interface.

2138 一部セルを充填したハニカムの動的挙動(S12-3 複合材料・複合組織,S12 先端材料システムの強度・機能評価とメゾメカニックス)

In this research, in-plane impact behaviors of the honeycomb structures randomly filled into some cells with stiff inclusions were analyzed by finite element (FE) analysis. Effect of random arrangement of inclusions on deformation processes and in-plane impact behavior of honeycomb structure was considered. During deformation processes of the models, growth of shear bands were disturbed by inclusions and cell region surrounded by inclusions did not deformed. Average stress increased and densification strain decreased with increasing fraction of inclusions. The honeycomb with 50% cells filled by the inclusions could not be deformed. Some models below 25% fraction of inclusions had higher absorbed energy than that of model with no inclusion and the others show lower ones.

Transient response of a center crack in a functionally graded piezoelectric strip under electromechanical impact

The dynamic fracture problem for a functionally graded piezoelectric strip containing a center crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the medium vary continuously in the thickness direction, and that the strip is under in-plane mechanical and electric impact loadings. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the material nonhomogeneity and the loading combination.

Transient response of interface cracks between dissimilar magneto-electro-elastic strips under out-of-plane mechanical and in-plane magneto-electrical impact loads

Using the integral transform and the Cauchy singular integral equation methods, the problem of interface cracks between dissimilar magneto-electro-elastic strips under out-of-plane mechanical and in-plane magneto-electrical impacts is investigated. The magneto-electric permeable boundary condition on the crack surfaces is adopted. The number of the interface cracks is arbitrary. The field intensity factors and energy release rates are derived and discussed. The effects of the crack configuration and the main constitutive parameters of the magneto-electro-elastic materials on the dynamic response are examined. Results show that the dynamic energy release rates (DERRs) as the crack extension force are quite equivalent to the dynamic stress intensity factors (DSIFs) for magneto-electric permeable interface cracks. The DERRs may be retarded or accelerated by specifying different combinations of material parameters. In addition, the parameters of the crack configuration, including the ratio of the strip width to the crack length, the ratio of the widths for different strips, and the distances between two cracks, exert a considerable influence on the DERRs. The results seem useful for design of the magneto-electro-elastic composite structures and devices of high performance.

The transient response of a crack in a functionally graded strip under an in‐plane impact load

AbstractThe transient response of a functionally graded strip with an embedded or edge crack perpendicular to the boundary is studied under an in‐plane impact load. By means of integral transform methods, the present problem is changed into a singular integral equation which can be solved numerically in the Laplace domain. It is found that the singular terms for the edge crack are different from those for the embedded crack. The influences of parameters such as the nonhomogeneity constant and the geometry parameters on the dynamic stress intensity factors (DSIFs) are studied.

The transient fracture behavior for a functionally graded layered structure subjected to an in-plane impact load

The transient fracture behavior of a functionally graded layered structure subjected to an in-plane impact load is investigated. The studied structure is composed of two homogeneous layers and a functionally graded interlayer with a crack perpendicular to the boundaries. The impact load is applied on the face of the crack. Fourier transform and Laplace transform methods are used to formulate the present problem in terms of a singular integral equation in Laplace transform domain. Considering variations of parameters such as the nonhomogeneity constant, the thickness ratio and the crack length, the dynamic stress intensity factors (DSIFs) in time domain are studied and some meaningful conclusions are obtained.

Dynamic behaviour and energy absorption of 1D and 2D regularly packed cells

This paper summarises the studies of dynamic behaviour and energy absorption performance of the following regularly packed cell systems under axial (in 1D cases) or in-plane (in 2D cases) impact loading: 1D and 2D ring systems, a chain of type II cells, and a 2D honeycomb block. Under impact loading, these packed cells exhibit complicated dynamic behaviour, such as localisation and propagation of the deformation, the dependence of deformation mode on the impact velocity, significant effect of lateral inertia displayed by type II cells, and so on. It is revealed that the early response of these packed cells is dominated by the collision between the striker and the impinged end of the packed cells. Since the dynamic deformation mode of these regularly packed cells is notably affected by the impact velocity, while different deformation modes often lead to different energy absorption capacity and failure mechanisms, particular attention is paid to the determination of mode transition velocities.

Scaling impacted structures

The problem of non-scalability of structures under impact loads caused by strain-rate effects is solved in this article by properly correcting the impact velocity. The technique relies on the use of an alternative dimensionless basis, together with a mathematical model which allows the calculation of a correction factor for the impact velocity. This new velocity, when applied to the model, makes it to assure the satisfaction of the scaling laws. The indirect similitude method detailed here is applied to two strain-rate sensitive structures, a double plate under in-plane impact and a beam subjected to a blast load. The results show a very good agreement so that the model and a prototype made from strain rate sensitive materials behave the same.

Scaling impacted structures

Summary The problem of non-scalability of structures under impact loads caused by strainrate effects is solved in this article by properly correcting the impact velocity. The technique relies on the use of an alternative dimensionless basis, together with a mathematical model which allows the calculation of a correction factor for the impact velocity. This new velocity, when applied to the model, makes it to assure the satisfaction of the scaling laws. The indirect similitude method detailed here is applied to two strain-rate sensitive structures, a double plate under in-plane impact and a beam subjected to a blast load. The results show a very good agreement so that the model and a prototype made from strain rate sensitive materials behave the same.

Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface - Part I: Static problem

The static crack problem of a functionally graded coating-substrate structure with an internal or edge crack perpendicular to the interface is investigated under an in-plane load. The structure is made up of a functionally graded coating with an internal or edge crack and a homogeneous substrate of finite thickness. The material properties are assumed to vary continuously from the coating to the substrate. By use of Fourier transform method, the mixed boundary value problem is reduced to a singular integral equation which can be solved numerically. During the analysis, a higher-order term is obtained in the asymptotic analysis of the singular kernel to improve the convergence efficiency of numerical integrals. The influences of material constants and the geometry parameters on the stress intensity factors (SIFs) are studied. In Part II of this paper, the transient response of the structure subjected to an in-plane impact is investigated.

Nonlinear dynamic buckling of stiffened plates under in-plane impact load.

This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton's principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained form Budiansky-Roth criterion.

The dynamic fracture behavior of a functionally graded coating–substrate system

The dynamic fracture behavior of a functionally graded coating–substrate system with an internal crack perpendicular to the interface is studied under an in-plane impact load. The structure consists of a functionally graded coating and a semi-infinite homogeneous substrate. The crack is located in the functionally graded coating. The mixed boundary value problem is formulated analytically by use of integral transform techniques and singular integral equation. The influences of material constants and the geometry parameters on the dynamic stress intensity factors (SIFs) are studied.

Transient response of sandwiched piezoelectric strip with crack normal to interface under impact

The dynamic electromechanical response of a cracked piezoelectric strip is considered. The strip is sandwiched between two layers of elastic materials. Antiplane mechanical and inplane electric impact loads are applied. The crack is oriented normally to the interfaces. Based on the superposition principle and integral transform techniques, the problem is reduced to the solutions of singular integral equations. An internal crack and a crack terminated at interface are examined. Numerical calculations are made for the variations of the dynamic energy density factors versus time while the geometric parameters are changed.

Impact response of an anti-plane crack in a FGPM bonded to a homogeneous piezoelectric strip

A finite crack under transient anti-plane shear loads in a functionally graded piezoelectric material (FGPM) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential functions along the thickness of the strip, and that the two layered strips is under combined anti-plane shear mechanical and in-plane electrical impact loads. The analysis is conducted on the electrically unified crack boundary condition. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Fredholm integral equations of the second kind in the Laplace transform domain. Then, a numerical Laplace inversion is performed and the dynamic intensities are obtained as functions of time and geometric parameters, which are displayed graphically.

Dynamic buckling of elastic–plastic square tubes under axial impact—I: stress wave propagation phenomenon

The speeds of the stress waves that can propagate in an elastic–plastic medium with isotropic linear strain hardening in a plane stress state are obtained in order to analyse the influence of the transient deformation process on the initiation of buckling in square tubes under axial impact. The kinematic conditions across a surface of discontinuity were employed to obtain the stress wave propagation speeds for an initial condition [ v x ]= V 0. It is shown that the plastic wave speeds depend on the stress state and on the direction of wave propagation. The material hardening properties have a stronger effect on the speed of the slow plastic wave, while the shear stress affects both the speeds of the fast and slow plastic waves. The magnitude of the instantaneously applied in-plane load [ σ xx ] at t=0, which results from an impact in the direction (n x=1, n y=0) , is obtained as a function of the initial velocity V 0 when using the differential relationships along the characteristics. A numerical simulation of an in-plane impact on a finite plate by a large mass with an initial velocity shows that the predicted stress wave speeds from the theoretical analysis agree with the speed of the propagation of the plastic zone in the plate. It is shown that the initial buckling pattern forms within a sustained axial plastic flow and remains unchanged when large displacements develop. Therefore, it is concluded that the transient process in elastic–plastic plates subjected to an in-plane impact plays a significant role for the formation of the final buckling shape and this process can be analysed using estimates for the stress wave speeds obtained for an elastic–plastic medium in a plane stress state.

In-plane dynamic crushing of honeycomb. Part I: crush band initiation and wave trapping

In this paper the dynamics of crush band initiation and wave trapping that result from in-plane impact on a honeycomb are analysed using finite element simulations. The honeycomb structures were loaded in compression at the top surface with a prescribed velocity. Two different boundary conditions were considered; these produced an approximation to a state of uniaxial stress or uniaxial strain at an early state of deformation. The simulations proved that elastic wave propagation had an important effect on crush band initiation, since loading and unloading parts of the compressive wave can reinforce or delay crushing, respectively. Stress enhancement with increasing impact speed is mainly due to translational micro-inertia and not due to micro-rotational inertia. This effect is stronger for uniaxial strain than for uniaxial stress. For the specific case examined here, stress enhancement begins for uniaxial strain at an impact speed of about 1.0 m/ s whereas for uniaxial stress it begins at about 10.0 m/ s . For the analysed honeycomb the simulation showed for both boundary conditions the existence of a critical impact velocity, so that for impact speeds larger than this critical speed a crush band initiated at the impact surface. For much smaller speeds the location of the initial crush band was determined by the distribution and extent of initial imperfections. In the case of uniaxial stress an analytical estimate of the critical impact speed was derived using the theory of wave trapping. The critical speed depends only on the ratio of the length of the ribbon wall to the length of the thinner inclined wall and the material properties of the constituent material. For the aluminium honeycomb investigated in this paper, wave trapping is predicted to occur for impact speeds greater than 7.6 m/ s which is close to the critical speed calculated with the finite element simulations.

Dynamic fracture behavior of a cracked piezoelectric half space under anti-plane mechanical and in-plane electric impact

The dynamic response of a cracked piezoelectric half-space under anti-plane mechanical and in-plane electric impacting loads is investigated in the present paper. In the study, the crack is assumed parallel to the free surface of the half-space. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Cauchy-type singular integral equations in the Laplace transform domain, which are solved numerically. Then, a numerical Laplace inversion is performed and the dynamic stress and electric displacement factors are obtained as functions of time and geometry parameters. The dynamic energy release rate is derived for piezoelectric materials in terms of the electroelastic intensities and is displayed graphically.

Dynamic buckling of thin isotropic plates subjected to in-plane impact

The dynamic stability behaviour of imperfect simply supported plates subjected to in-plane pulse loading is investigated. For the calculation of dynamic buckling loads a stress failure criterion is applied. The large-deflection plate equations are solved by a Galerkin method by using Navier's double Fourier series. In this paper the dynamic load factor (DLF) is redefined and plots that are useful for the design of plate structures are presented. Parametric studies are performed in which the influences of the pulse duration, shock function, imperfection, geometric dimensions and limit stress of the material are discussed. Comparison between the dynamic buckling loads, which are obtained by the commonly used criterion of Budiansky and Hutchinson [Proceedings of the 11th International Congress of Applied Mechanics (1964) 636], and the dynamic elastic limit loads, which are computed by the stress failure criterion, shows that the latter criterion is more useful for the design of lightweight structures.

Local elastodynamic stresses in the unit cell of a woven fabric composite

A theoretical study of the local elastodynamic stresses of woven fabric composites under dynamic loadings is presented in this article. The analysis focuses on the unit cell of an orthogonal woven fabric composite, which is composed of two sets of mutually orthogonal yarns of either the same fiber (nonhybrid fabric) or different fibers (hybrid fabric) in a matrix material. Using the mosaic model for simplifying woven fabric composites and a shear lag approach to account for the inter-yarn deformation, a one-dimensional analysis has been developed to predict the local elastodynamic and elastostatic behavior. The initial and boundary value problems are formulated and then solved using Laplace transforms. Closed form solutions of the dynamic displacements and stresses in each yarn and the bond shearing stresses at the interfaces between adjacent yarns are obtained in the time domain for any type of in-plane impact loadings. When time tends to infinity, the dynamic solutions approach to their corresponding static solutions, which are also developed in this article. Solutions of certain special cases are identical to those reported in the literature. Lastly, the dynamic stresses and bond shearing stresses of plain weave composites subjected to step uniform impacts are presented and discussed as an example of the general analytical model.