含单分层损伤复合材料层合梁的动力屈曲研究

采用有限差分（FDM）方法求解了含初始缺陷和单个分层损伤复合材料层合梁的轴向刚性质量块撞击的脉冲动力屈曲问题。基于Hamilton原理导出了考虑所有惯性影响以及一阶横向剪切变形（FSDT）影响时单个分层损伤复合材料梁的非线性动力屈曲控制方程；采用B—R准则判断梁动力屈曲时刻，同时确定刚性质量块的临界冲击速度。重点研究脱层、冲击速度、初始几何缺陷等因素对复合材料层合梁脉冲动力屈曲的影响。     

Influence of Shock Pre‐Compression Stress and Tensile Strain Rate on the Spall Behaviour of Mild Steel

Abstract: A series of plate‐impact spall experiments were conducted to investigate the influence of shock pre‐compression stress and tensile strain rates on the dynamic tensile fracture (or spall) behaviour of shocked mild steel. The shock pre‐compression stress amplitude and tensile strain rate were controlled independently to ensure that only one single‐loading parameter varied for each experiment. A push–pull type velocity interferometer system for any reflector (VISAR) was used to measure the free surface velocity profiles of samples. It is observed from experimental results that the influence of shock pre‐compression stress amplitude on the spall strength is less significant in the range attained in these experiments, whereas with increasing tensile strain rate, an evident 65% increase of spall strength is determined in the present tensile strain rate range of 10⁴ to 10⁶ s^?1. VISAR data are compared with finite‐difference calculations employing a modified damage function model with a percolation–relaxation function, and a good agreement between the calculation and the experiments was obtained. Preliminary simulation results also revealed that a critical damage exists, which physically corresponds to the critical intervoid ligament distance for triggering the onset of void coalescence, and may be regarded as a material parameter for describing the dynamic tensile fracture and independent of the loading conditions.     

Effect of shear and rotary inertia on dynamic fracture of a beam or plate in tensile loading

The dynamic fracture response of a long beam of brittle material subjected to tensile loading is studied. If the magnitude of the applied tensile loading is increased to a critical value, a crack will propagate from one of the longitudinal surfaces of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the tensile loading and the induced bending moment at the fracturing section is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the bending moment effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded. The results also apply for plane strain fracture of a plate in tensile loading provided the value of the elastic modulus is appropriately modified.     

An experimental and numerical study of the dynamic response of a free–free aluminum beam under high velocity transverse impact

Experiments and numerical simulations on the dynamic behavior of free–free aluminum beams subjected to high velocity transverse impact were performed using single-stage light gas gun and nonlinear finite element program, LS-DYNA. A cylindrical free–free beam with a diameter of 30 mm is impacted symmetrically and asymmetrically by a cylindrical aluminum projectile with a diameter of 10 mm in the present experiment. The lengths of the beam and projectile are 150 mm and 20 mm, respectively. It is shown that the responses of free–free beam include elastic–plastic deformation, structural failure and fragmentation. The number of fragments, the local deformation and the mass dissipation of the free–free beam increase linearly with the increase of the initial impact velocity of the projectile. However, the non-dimensional velocity at the central point of the free–free beam decreases with the increase of the initial impact velocity of the projectile and is independent of the impact location. It is found that the dependence of the kinetic energy of the free–free beam on the impact velocity of the projectile is similar to the dependence of the maximum velocity at the central point of the beam on the impact velocity of the projectile. Energy partitions are further predicted. For example, when impact velocity is 400 m/s, the ratio of kinetic energy of the beam to impact energy is 3.3 J while the ratios due to plastic energy dissipation and fragmentation are 15 J and 54% respectively. The rest remains in projectile. It is found that the energy partitions in high velocity impact case are nearly independent of impact location, which is different from those subjected to low velocity impact.     

Approximate elastic-plastic analysis of the static and impact behaviour of polymer composite sandwich beams

An elastic-plastic beam bending model has been developed to simulate the post-upper skin failure energy absorption behaviour of polymer composite sandwich beams under three-point bending. The beam skins consist of woven and chopped strand glass, while the core is a resin impregnated non-woven polyester material known as Coremat. A polyester resin was used for the construction. The theoretical model consists of a central hinge dominated by a crushing core and tensile elastic strains in the lower skin. Experimental measurements of the non-linear force-deflection characteristics for the beam are compared to the theoretical predictions from the model, and it is shown that the shear crushing of the core has an important effect on the behaviour of the beam. The model shows that the most important material properties are the lower skin tensile failure strain and the core crushing strength. Dynamic effects are included in the model in the form of a strain rate dependence of the core crushing stress and the strain rate dependence of the failure strain in the lower skin. The increase in material strength with strain rate gives rise to an improved energy absorption capacity for the beam under impact loading.     

High-velocity plate impact of metal foams

The ballistic impact of a massive, effectively 1-D plate on an initially stationary foam layer is considered. It is shown that four discrete velocity regimes must be considered. Two of these regimes are of major interest for ballistic impact studies. Regime 2 considers the case when the initial velocity of the plate is lower than the sound velocity of the constitutive material of the foam, but higher than the linear sound velocity of foam. Regime 3 considers the case when the initial plate velocity is lower than the linear sound velocity of the foam; but remains higher than the effective sound velocity for a perturbation in which the amplitude lies in the so-called “plateau region” of the static stress–strain diagram.Analytical solutions for dynamic deformation and energy absorption of foam materials under the plate impact condition for Regimes 2 and 3 are developed. It has been shown that in both cases, a compressive shock wave appears. The physical difference between these two regimes entails not only the creation of a shock front associated with the collapsing foam, but also an acoustic precursor in the case of Regime 3. As a result, the efficiency of energy absorption in Regime 2 depends only on the initial density of the foam, the density of the constitutive material of the foam, and the areal mass of the impacting plate, whereas the efficiency of energy absorption for Regime 3 also depends on the Mach number and the critical stress of the foam.Numerical plate impact simulations have been carried out in impact Regime 2. Explicit finite element analysis is performed using LS-DYNA 960. The time history of dynamic deformation and energy of the impact plate is presented. The numerical prediction is found to be in good agreement with the analytical results.     

Influences of tensile and bending strains on the critical current in multifilamentary Nb3Sn composites processed by Nb tube method

The critical current degradation of multifilamentary Nb₃Sn superconducting composites strained mechanically at room temperature has been investigated. The experimental results show that the effects of the Nb₃Sn layer thickness and the specimen wire structure, such as monolithic and stranded cable on critical current degradation, are appreciable for the specimens strained by bending stress, but are not for specimens strained by tensile stress. The results of the critical current degradation by tensile strain were discussed, based on the stress-strain characteristics of the composites.It was clarified that the critical strain in the case of applying tensile and bending stresses simultaneously at room temperature lay around the line which was drawn from the point of the critical tensile strain to that of the critical bending strain, when the ordinate was tensile strain and the abscissa was bending strain.     

Deformation and tearing of clamped work-hardening beams subjected to impulsive loading

An approximate theoretical analysis, based on a power law stress-strain relationship throughout, is presented herein to examine the behaviour of clamped beams subjected to uniformly distributed impulsive loads, which represents an extension of the previous study. In particular, the rupture (tensile tearing) of the beams under impulsive loading is predicted by an effective strain failure criterion which takes into consideration the influence of the transverse shear on the axial tensile strain. It is found that the present theoretical predictions are in good agreement with the experimental observations in terms of the maximum permanent transverse displacement and the critical input impulse causing beam tensile tearing failure when material strain rate sensitivity is taken into account.     

Compressional behaviour of carbon fibres

The axial compressive strain to failure of various types of PAN-based carbon fibres was measured by applying small and defined compressive loads to single filaments which have been bonded to a rectangular polymer cantilever beam and parallel to its long edge. By monitoring the Raman frequencies along the fibre with the 2 m laser probe of a Raman microscope, the critical compressive strain required for first fibre failure could be assessed and the residual load that each type of fibre supported after first failure, could be measured. Estimates of the compressive moduli for all fibres could, also, be obtained by considering the dependence of the Raman frequency upon compressive strain in the elastic region. The critical compressive strain to failure was found to decrease with fibre modulus and its value was, approximately, equal to 50% of the tensile fracture strain. However, for some low-modulus fibres the compressive strain to failure was found to approach the tensile fracture strain. The initial compressive moduli of high-modulus fibres were estimated to decrease up to a maximum of 10% with respect to their tensile moduli, whereas more significant reductions were found in the case of intermediate and low-modulus fibres.     

冲击载荷下复合材料层合杆的动力屈曲

研究复合材料层合杆被一质量块以某一速度沿轴向进行碰撞而导致的动力屈曲现象,采用不同的横向剪切理论,并用差分方法对杆的动力屈曲方程进行求解。文中考察了冲击块质量、初挠度、应力波、横向剪切等因素对临界冲击速度以及屈曲模态的影响。     

低速冲击下RC梁的动态响应和破坏机理研究

考虑材料非线性和应变率相关性等因素的影响,运用LS_DYNA非线性有限元软件对RC梁横向低速冲击试验进行了数值模拟,从动态损伤扩展、冲击能量转化等方面研究了RC梁的冲击响应过程和破坏机理。结果表明:RC梁的冲击响应过程可分为局部响应、整体响应和回弹变形三个阶段;RC梁的损伤主要发生在局部响应阶段,梁体变形主要发生在整体响应阶段;局部响应阶段的冲击力完全由梁体惯性力平衡,整体响应阶段的变形模式和截面弯矩分布与刚塑性模型基本相同;受拉钢筋变形耗能是RC梁最主要的冲击耗能机制。     

考虑应变梯度效应的三点弯梁模型解析研究--第二部分:局部化带的位移及转角

基于梯度塑性理论,分析了应变软化及真实裂纹扩展阶段的局部化带的张拉位移和转角。在弹性阶段,可以由弹性理论来确定二者的关系。真实裂纹出现后,利用平衡条件、几何条件及梯度以来的应变软化本构关系,得到了真实裂纹长度与局部化带长度的关系。当真实裂纹刚出现时,局部化带长度达到最大值。在任何阶段,局部化带到中性轴的距离单调降低,局部化带的张拉位移和转角受梁深、带宽、弹模及下降模量等的影响。弹模及下降模量越大,带宽越小,则局部化带的张拉位移和转角都增加。而且,在前两个阶段,张拉位移都线性增加,但在后两个阶段,转角都非线性增加。     

An experimental study on the dynamic axial plastic buckling of cylindrical shells

This paper deals with an experimental study on the dynamic plastic post-buckling behaviour of a stationary AMΓ aluminium alloy cylindrical shell under axial impact. According to current theory, it is believed that within a certain velocity range, the shell will buckle in a uniform axisymmetrical sinusoidal mode. However, we found that when the impact velocity is less than a certain critical value V_c1, the shell will exhibit only uniform plastic deformation in both the axial and radial directions and does not produce the sinusoidal waves. On the other hand, when the impact velocity exceeds another critical value V_c2, the shell will change from the axisymmetric mode into a nonuniform type of large deformation, the number of waves decreases slightly and the shell begins to lose its load-carrying capacity. Experimental results on cylinders with three different thicknesses are presented and discussed. An approximate theoretical formula for estimating V_c2 based on strain rate reversal is also given.     

Interfacial crack propagation in a thin viscoelastic film bonded to an elastic substrate

Edge decohesion along the interface of a thin viscoelastic film bonded to an elastic substrate under tensile residual stresses is considered. The tensile residual stress in the film is replaced by a combination of edge loads, and an explicit relation of strain energy with respect to time is obtained through simple beam analysis. The strain energy function is discretized into time steps which are assumed to be very small so that the dissipation effects over the time steps can be neglected. The energy release rate is then calculated using a Griffith type energy balance. An analytical model is developed to predict the crack growth and its velocity. Extent of crack growth along the interface is prediced based on a fracture criteria. The analytical predictions are compared with results from a viscoelastic finite element analysis.     

A combined experimental and numerical approach to study ballistic impact response of S2-glass fiber/toughened epoxy composite beams

A combined experimental and 3D dynamic nonlinear finite element (FE) approach was adopted to study damage in composite beams subject to ballistic impact using a high-speed gas gun. The time-histories of dynamic strains induced during impact were recorded using strain gages mounted on the front of the composite beam specimen. During ballistic impact tests, the impact velocity was also measured. The commercially available 3D dynamic nonlinear FE code, LS-DYNA, modified with a proposed user-defined nonlinear-orthotropic damage model, was then used to simulate the experimental results. In addition, LS-DYNA with the Chang–Chang linear-orthotropic damage model was also used for comparison. Good agreement between experimental and FE results was found from the comparisons of dynamic strain and damage patterns. Once the proposed nonlinear-orthotropic damage model was verified by experimental results, further FE simulations were conducted to predict the ballistic limit velocity (V₅₀) using either the number of damaged layer approach or a numerically established relation between the projectile impact velocity versus residual velocity or energy similar to the classical Lambert–Jonas equation for metals.     

The effects of strain rate and CCVC interfacial layer on mechanical behaviours of CALL

In this paper, the loading and loading-unloading tests of CALL and CALL (CCVC) under tensile impact have been carried out by a self-designed Rotating Circular Disk Tensile impact Apparatus. The quasi-static tension and short beam bending tests are performed on the Shimadzu-5000 testing apparatus. Experiment results show that both CALL and CALL (CCVC) have positive hybrid effect. Under quasi-static tension, the two composites have no obvious yielding until fracture, but have an obvious yielding point on the dynamic tensile stress-strain curves. The dynamic unstable fracture strain is about three times the static unstable fracture strain. The interlaminar shear strength (ISS) of CALL (CCVC) is 10 more than that of CALL. At the same time, the tensile strength and unstable fracture strain of CALL (CCVC) are also higher than that of CALL. In this paper, some conclusions are also drawn from the SEM observation of the fracture specimen surfaces.     

PA6/POE-g-MAH共混物在缺口冲击与缺口拉伸实验中的脆韧转变

用缺口冲击和缺口拉伸实验研究PA6/POE-g-MAH共混物的脆韧转变。结果显示,POE-g-MAH含量对共混物脆韧转变的影响主要是POE-g-MAH含量对裂尖局部应变速率的影响。在缺口冲击和缺口拉伸实验中,随着POE-g-MAH含量增加,裂尖附近参与变形的范围增大,导致局部应变速率降低。当局部应变速率降低至某临界值时,材料的断裂发生脆韧转变。在缺口拉伸实验中,随着拉伸速度增加,PA6/POE-g-MAH共混物发生脆韧转变的POE-g-MAH含量增加。这可能是拉伸速度与POE-g-MAH含量对PA6/POE-g-MAH共混物裂尖局部应变速率共同影响的结果。     

Dynamic response of top-down cracked asphalt concrete pavement under a half-sinusoidal impact load

A 3D finite element analysis model of cracked asphalt pavement is established by the FEM software ABAQUS. Based on dynamics mechanics, fracture mechanics and finite element theory, this paper studies the influence of various vehicle speeds, crack location, crack depth, damping ratio etc. on the dynamic response. The results show that the surface deflection, the maximum tensile strain at the bottom of the asphalt layer, and the maximum shear stress of the asphalt layer decreased with the increase in vehicle velocity when there is no crack in the pavement. No matter where the transverse position of the crack is the stress intensity factors increase with the increase in crack depth and decrease exponentially with the increase in longitudinal distance between the vehicle center and the crack. In the case of the crack locating in the center of wheel clearance, the surface deflection increases with the crack depth increasing. But if the crack is at the edge of the wheel track, there will be a critical vehicle velocity where the surface deflection is smaller than the asphalt pavement without crack if the vehicle velocity is above it. The maximum tensile strain at the bottom of the asphalt layer and the maximum shear stress of the asphalt layer are also smaller than the asphalt pavement without crack. The maximum tensile strain and the maximum shear stress decrease with the damping ratio increasing. So the increase in damping ratio can help to alleviate the propagation of cracks.     

Dynamic response of clamped sandwich beam with aluminium alloy foam core subjected to impact loading

The dynamic response of clamped sandwich beam with aluminium alloy open-cell foam core subjected to impact loading is investigated in the paper. The face sheet and the core of the sandwich beam have the different thickness. And the sandwich beam is impacted by a steel projectile in the mid-span. The impact force is recorded by using accelerometer. The results show that tensile crack and core shear are the dominant failure modes. And the impact velocity and the thickness of the face sheet and the foam core have a significant influence on the failure modes and the impact forces. Combining with the inertia effect and experimental results, the failure mechanisms of the sandwich beams are discussed. The thickness of the foam core plays an important role in the failure mechanism of the sandwich beam. In present paper, the failure of the sandwich beam with a thin core is dominated by the bending moment, while the sandwich beam with a thick core fails by bending deformation in the front face sheet and the bottom face sheet in opposite direction due to the plastic hinges in the front face sheet.     

Numerical study of spalling in an aluminum alloy 7020-T6

Planar impact experiment is frequently used to investigate dynamic fracture of materials, particularly the spall phenomenon. Spalling is caused by the superposition of rarefaction waves reflected from free surfaces and the spall zone is found in the interior of the target. Behavior of materials in this kind of experiment is strongly affected by the stress level, time of loading and temperature. The rate and temperature effects are closely related to the thermally activated micromechanical processes [1]. Thus, in a stressed body the creation of new fracture surfaces frequently occurs with the assistance of thermal activation. For a more detailed study, it is therefore necessary to take into account the physical aspects of spalling, including dynamic plasticity and temperature coupling. This paper reports the numerical analysis performed using a finite element FE code by implementation of a cumulative fracture criterion proposed in [2] where the apparent energy of activation for spalling depends on stress, temperature and load history. Initially, a series of calculations have been run for the purely elastic case to analyze the minimum critical impact velocity needed to obtain the spall stress and it has been determined to be a function of the critical time of loading. Such analysis is of great value in designing experiments that are relatively expensive. Next, a viscoplastic constitutive relation together with the cumulative criterion, and the equation of heat conduction have been implemented in a FE code. The set of relations takes into account strain hardening, strain rate sensitivity and temperature. This series of FE calculations have been performed in order to take into account, changes of temperature due to volume dilatation as well as conversion of plastic work into heat. In addition to spalling, the free surface velocity–time profiles have been calculated for a number of impact velocities. Specific variations of the free surface velocity indicates the creation of a new fracture surface inside the target plate. The two sets of FE calculations reported in this paper led to some discussion on the influence of physical parameters on spall mechanics.