Compressive response of circular cell polycarbonate honeycombs under inplane biaxial static and dynamic loading—Part II: simulations

The static and dynamic experimental results of a polycarbonate circular cell honeycomb subjected to inplane biaxial loading are simulated through numerical analysis using the finite element method. The experimental results were presented in Part I of this two part paper (Chung and Waas, Int. J. Impact Eng. (2001), in preparation). Through several comparisons between the experimental and numerical results, the biaxial inplane crushing mechanisms of the circular cell honeycomb material are studied. The finite element simulations are able to accurately capture the essential features observed and measured in the experiments.     

A theoretical and experimental study on metal hexagonal honeycomb crushing under quasi-static and low velocity impact loading

In the study of honeycomb crushing under quasi-static loading, two parameters are important; the mean crushing stress and the wavelength of the folding mode. On the other hand, the kinetic energy absorbed by the honeycomb is investigated in the impact loading. In this paper, through fully considering the cylindrical curvature effects and implementing the energy method, a new theoretical model for the estimation of the mean crushing stress and the wavelength of the folding mode of the metal hexagonal honeycomb is presented. Afterwards, developing this static model to the dynamic state, a theoretical model for study of the behavior of these energy absorbers, in the low velocity impact loading, is proposed and the required initial velocity of the impactor, for creation of the desired folding length in these structures, is determined, analytically. The presented theoretical models have been compared with experimental results obtained from experiments on three kinds of honeycomb with the various minor diameters and thicknesses of the cell walls under quasi-static and low velocity impact loading in the axial direction. Excellent correlation has been observed between the theoretical and experimental results.     

动静组合加载下不同负温人工冻结粉质黏土强度和变形特性分析

研究动静组合加载下不同负温冻土的强度和变形特性对提高冻土开挖破碎效率、确保冻土工程稳定具有重要的理论和工程意义.借助改进的分离式Hopkinson压杆试验系统,研究了不同负温下人工冻结粉质黏土的静态和动态应力-应变曲线、抗压强度、变形模量和破坏特征.试验结果表明:单轴动态压缩条件下,随着试验温度的降低,人工冻结粉质黏土...     

倾斜胞壁Nomex蜂窝芯压剪复合力学响应

成形具有一定曲率的夹层结构时,需要将蜂窝芯铣削成曲面形状,造成蜂窝胞壁呈一定倾角,进而降低蜂窝夹芯结构面外承载能力。为了定量化分析面外载荷作用下倾斜胞壁蜂窝芯的力学性能,建立了倾斜胞壁蜂窝芯面外压剪复合有限元模型,并通过设计专用Arcan夹具实现蜂窝芯的面外压剪复合加载,用于验证模型的有效性。对比仿真与实验结果,发现蜂窝芯压剪响应及胞壁变形模式吻合较好。利用验证的有限元模型对胞壁倾角范围为0°～40°的蜂窝芯在面外压剪复合载荷下的力学响应进行了研究,结果表明随着蜂窝胞壁倾角的增大,蜂窝芯面外承载能力逐渐降低;当胞壁倾斜角由0°增加到40°,初始应力峰值下降最大幅度为47.7%,平原阶段强度下降幅度为29%;进一步分析了倾斜胞壁蜂窝芯截面芯格尺寸与胞壁倾角的几何关系,将倾斜胞壁蜂窝芯等效为具有相同截面尺寸的垂直胞壁蜂窝芯,推导了倾斜胞壁蜂窝芯在面外压缩及剪切载荷作用下的坍塌强度,揭示了胞壁倾角对蜂窝芯坍塌强度影响机制。     

Mechanical behaviors of carbon fiber composite sandwich columns with three dimensional honeycomb cores under in-plane compression

Mechanical properties and failure modes of carbon fiber composite egg and pyramidal honeycombs cores under in plane compression were studied in the present paper. An interlocking method was developed for both kinds of three-dimensional honeycombs. Euler or core shear macro-buckling, face wrinkling, face inter-cell buckling, core member crushing and face sheet crushing were considered and theoretical relationships for predicting the failure load associated with each mode were presented. Failure mechanism maps were constructed to predict the failure of these composite sandwich panels subjected to in-plane compression. The response of the sandwich panels under axial compression was measured up to failure. The measured peak loads obtained in the experiments showed a good agreement with the analytical predictions. The finite element method was used to investigate the Euler buckling of sandwich beams made with two different honeycomb cores and the comparisons between two kinds of honeycomb cores were conducted.     

“Segment-wise model” for theoretical simulation of barely visible indentation damage in composite sandwich beams: Part II – Experimental verification and discussion

When localized transverse loading is applied to a sandwich structure, the facesheet locally deflects and the core crushes. A residual dent induced by the core crushing significantly degrades the mechanical properties of the sandwich structure. In a previous paper, the authors established a “segment-wise model” for theoretical simulation of barely visible indentation damage in honeycomb sandwich beams with composite facesheets. Honeycomb sandwich beam was divided into many segments based on the periodic shape of the honeycomb and complicated through-thickness characteristics of the core were integrated into each segment. In this paper, the new model is validated by experiments using specimens with different types of honeycomb cores. In addition, the damage growth mechanism under indentation load was clarified from the viewpoint of the reaction force from the core to the facesheet. The applicability of the model to other types of core materials is also discussed.     

Crack propagation velocities in bi-phase plates under static and dynamic loading

An investigation of the dependence of the crack-propagation velocity in complex bimaterial plates at different loading rates was undertaken. The specimens were fractured under the influence of both static and dynamic loadings and the crack-propagation velocities were detected by high speed photography with the optical method of caustics.The investigation was concentrated in detecting the influence that the different loading rates have on the fracture velocities in both phases of the plates and how this influence interferes—counteracting or superimposing—with the other factors that determine the crack propagation process in bi-material specimens. These factors are the effect of interface, the influence of the mechanical characteristics of each phase on the crack-propagation velocity etc.The results show that for constant and given material characteristics of the bi-phase plate the crack propagation velocity in the first (notched) phase tends to increase with increasing strain rates.The same is valid for the crack propagation velocity in the second phase, but only for the case when fracture occurs under the influence of a dynamic load. A significant discrepancy of the latter statement occurs, however, in the case of fracture under a continuously-increasing static load. In this case the crack-propagation velocity in the second phase reaches some remarkably high values, which are of the order of high strain-rate dynamic crack propagation velocities.In this way, the crack-arrest effect on the crack propagation velocity appears to be more significant in the case of a static loading than it is for the case of dynamic loading.     

冻融循环后粉煤灰陶粒混凝土定侧压下的强度和变形性能试验研究

利用混凝土静、动三轴试验系统,完成了粉煤灰陶粒混凝土立方体试件在4组不同冻融循环次数、4种恒定侧压下的双轴压压强度和变形性能试验。考察了不同侧压应力水平下试件的破坏形态和试件表面裂缝分布及走向特征。测量了4种侧压应力水平下的极限抗压强度及两个加载方向的应变值,并根据试验结果系统分析了定侧压下粉煤灰陶粒混凝土双轴压压极限强度和变形性能(包括峰值应变、应力-应变关系曲线、弹性模量)随冻融循环次数和侧压应力水平的变化规律,建立了考虑冻融循环次数和侧压应力水平的主应力空间的双轴压压强度准则,为寒冷海洋环境条件下粉煤灰陶粒混凝土结构在经受双轴压压荷载作用时的强度分析提供试验和理论依据。     

On the response of thin-walled CFRP composite tubular components subjected to static and dynamic axial compressive loading: experimental

In this work the crushing response and crashworthiness characteristics of thin-wall square FRP (fibre reinforced plastic) tubes that were impact tested at high compressive strain rate are compared to the response of the same tubes in static axial compressive loading. The material combination of the tested specimens was carbon fibres in the form of reinforcing woven fabric in epoxy resin, and the tested tubes were constructed trying three different laminate stacking sequences and fibre volume contents on approximately the same square cross-section. Comparison of the static and dynamic crushing characteristics is made by examining the collapse modes, the shape of the load–displacement curves, the peak and average compressive load and the absorbed amount of crushing energy in both loading cases. In addition, the influence of the tube geometry (axial length, aspect ratio and wall thickness), the laminate material properties-such as the fibre volume content and stacking sequence-and the compressive strain rate on the compressive response, the collapse modes, the size of the peak load and the energy absorbing capability of the thin-wall tubes is extensively analysed.     

Strain localization in circular honeycombs under in-plane biaxial quasi-static and low-velocity impact loading

Strain localization in a finite block of circular honeycomb is studied using a phenomenological approach based on the structural response of the honeycombs. The deformation modes characteristic for a circular honeycomb material under in-plane biaxial compression are identified from the experiments and described analytically for compression strains up to about 15%. It is concluded that the particular deformation modes depend on the local strain field, and modes with different dominant strains can co-exist inside a finite block subjected to equi-biaxial remote strains. The relationships between the local strain components for the development of these modes are determined. Using the proposed approach to the strain localization, it is shown that for equal remote strains applied to a finite block of honeycombs, larger remote stresses would occur when assuming homogeneous deformation inside the block in comparison to the calculated stress when the strain inhomogeneity takes place. A comparison between the theoretical and experimental results is made for a finite honeycomb block under quasi-static equi-biaxial compression.     

Biaxial cyclic deformation of an epoxy resin: Experiments and constitutive modeling

Biaxial (proportional and non-proportional) cyclic tests were conducted on thin-walled tubular specimens to investigate deformation behavior of an epoxy resin, Epon 826/Epi-Cure Curing Agent 9551. The focus was placed on the biaxial stress-strain response and their dependency on the load control mode, stress or strain range and loading path. Experimental results indicated that under strain-controlled equi-biaxial (proportional) cyclic loading, mean stress relaxation occurred in both axial and hoop directions, whereas under stress-controlled equi-biaxial cyclic loading, ratcheting strains accumulated in both principal directions. Under strain- or stress-controlled non-proportional cyclic loading, anisotropy in stress-strain responses was induced in both axial and hoop directions, and the axial and hoop hysteresis loops rotated in opposite directions. This was particularly evident at high stress or strain levels. The experimental results were further used to evaluate the predictive capabilities of a nonlinear viscoelastic constitutive model. Qualitative and quantitative comparison with the test data indicated a good agreement in predicting the complex stress-strain response under biaxial cyclic loading with various loading paths, applied stress or strain ranges and loading control modes.     

Theoretical prediction and numerical simulation of honeycomb structures with various cell specifications under axial loading

The axial crushing of honeycomb structures with various cell specifications is studied analytically and numerically. Based on the Super Folding Element theory, a new method for predicting the mean crushing stress of honeycomb structures with various cell specifications under axial loading is developed. In this new theoretical method, two types of simplified folding modes named SFM1 and SFM2 are proposed. The mean crushing stress and the folding wavelength for honeycomb structures with various cell specifications are then determined by a minimum principle. The effective crushing distance and the loading rate effect are both considered. In order to illustrate the effectiveness of the proposed approach, numerical simulations are carried out by employing the explicit finite element code LS-DYNA. The bond of the honeycomb panels is simulated by using a tie-break contact. It can be seen that the analytical solutions are in agreement with the numerical results as well as the Wizerbicki’s solutions.     

Numerical Study on Hybrid Tubes Subjected to Static and Dynamic Loading

The commercial finite element program LS-DYNA was employed to evaluate the response and energy absorbing capacity of cylindrical metal tubes that are externally wrapped with composite. The numerical simulation elucidated the crushing behaviors of these tubes under both quasi-static compression and axial dynamic impact loading. The effects of composite wall thickness, loading conditions and fiber ply orientation were examined. The stress–strain curves under different strain rates were used to determine the dynamic impact of strain rate effects on the metal. The results were compared with those of a simplified analytical model and the mean crushing force thus predicted agreed closely with the numerical simulations. The numerical results demonstrate that a wrapped composite can be utilized effectively to enhance the crushing characteristics and energy absorbing capacity of the tubes. Increasing the thickness of the composite increases the mean force and the specific energy absorption under both static and dynamic crushing. The ply pattern affects the energy absorption capacity and the failure mode of the metal tube and the composite material property is also significant in determining energy absorption efficiency.     

Modelling of fatigue lifetime under non-proportional multiaxial alternating loading

This paper presents two approaches to lifetime prediction under non‐proportional multiaxial alternating loading; a phenomenological approach using the Manson–Coffin relation and a microstructural approach. Both models have in common the use of a new multiaxiality factor. The data sets for the adaptation and validation of both models are taken from the authors' own experiments. In these tests, both the load paths and the phase shift are varied. The biaxial test apparatus allows for an application of fixed principal stress or strain directions even under non‐proportional loading. A fairly good agreement with our multiaxial lifetime results is obtained with both models. For an advanced assessment of the quality of the approaches used, the models are compared with several other well‐known models from the literature. An additive yardstick is used for the comparison of the different models.     

Behaviour of sandwich panels subjected to intense air blast – Part 1: Experiments

Tests that investigate the inelastic response of blast-loaded sandwich structures, comprising mild steel plates and aluminium alloy honeycomb cores, are reported. The “uniform” loading was generated by detonating a disc of explosive and directing the blast through a tube towards the target. Localised blast loading was generated by detonating discs of explosive in very close proximity to the test structure. The sandwich panels responded in a more efficient manner to the uniformly distributed loading, and hence the majority of the paper is concentrated on uniform loading response. The honeycomb sandwich results are compared to test results on structures with air as the core. The failure modes and interaction between the components are discussed. Three phases of interaction are identified for each sandwich structure, based upon deformation, contact, crushing and tearing responses of the sandwich components. The compromise between load transfer through the core and improved energy absorption is discussed.     

双轴动载作用下脆性裂纹扩展问题的近场动力学建模与分析

在双参数微极近场动力学弹脆性模型基础上,引入反映长程力尺寸效应的核函数修正项以提高定量计算精度和收敛稳定性。通过定量变形计算和双轴动载作用下含中心裂纹准脆性板的裂纹扩展过程模拟,验证了本文模型与算法。应用本文模型能准确反映动载作用下的裂纹起裂、扩展、分叉与二次分叉等现象。进一步分析了双轴动载作用下含不同倾角、不同间距平行双裂纹脆性板的破坏模式、起裂时间与承载能力,以及含不同倾角多裂纹脆性板的破坏机制。结果表明:初始裂纹倾角与间距对脆性板承载能力有显著影响,在平行双裂纹倾角一定时,间距越大脆性板承载能力越强;双轴动载作用下多裂纹扩展时,裂纹之间首先相互连接且无分叉,在初始裂纹连接贯通后向边界扩展时出现分叉及二次分叉。     

双轴载荷下复合材料十字型试样几何形状对中心测试区系数的影响

基于双轴拉伸载荷下复合材料十字型试样的设计特点,对比分析了不同几何形状的十字型试样在不同厚度比和载荷比条件下中心测试区应力集中系数和承力系数的变化规律,并开展了不同载荷比的双轴拉伸实验进行验证。研究表明:十字型试样中心测试区系数与载荷大小无关,与试样几何形状、厚度比及载荷比有关;等宽加载臂宽度越小、厚度比越大,应力集中系数越小,载荷比不同,应力集中系数也不同;一般而言,中心测试区承力系数随厚度比增加而增大,x向承力系数βx随载荷比增加呈非线性增大,y向承力系数βy随载荷比增加呈线性减小;在双轴拉伸载荷条件下,形状D十字型试样在载荷比f=4/1时中心测试区y向应力分量为负值,表现为压应力状态。     

负荷传感器试验的准静态加荷方法研究

通过对叠置加荷方式工作过程的分析，讨论了非静态加荷问题。由于传感器和仪表的静态性能与动态性能的差异、动态性能的离散性，以及测量过程中采样频率、采样间隔和数据处理等因素均会对试验的力值计量精度产生影响，因此采用非静态加荷方式进行负荷传感器负荷特性试验会产生测量误差。理论分析证明，采用非静态加荷方法提高试验工作效率、保证测量精度的关键在于加荷速度的控制和正确的采样与数据处理方法。本文提出了准静态加荷这一概念，并对准静态加荷方法的实现及其在负荷传感器试验中实施的可行性进行了理论和试验研究。结果表明，受技术条件的限制，动态加荷是不现实的，而准静态加荷确是可行的非静态加荷方法。它满足负荷传感器负荷特性试验中试验工作效率高、保证测量精度、容易实施和生产成本低的要求。     

Progressive damage analyses of angle‐ply laminates exhibiting free edge effects using continuum damage mechanics with layer‐wise finite element method

Capability of continuum damage mechanics (CDM) to predict the damage mechanism evolution of composite laminates has rarely been carried out, and most of the previous CDM works mainly focused on the overall response of the laminates. In this paper, progressive damage and overall response of the composite laminates under quasi‐static, monotonic increasing loading are investigated using three‐dimensional (3D) CDM implementation in a finite element method that is based on the layer‐wise laminate plate theory. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle‐ply composite laminates under quasi‐static loading that exhibit free edge effects is investigated. It is shown that using CDM global behaviour and various damage mechanisms affected by the complex nature of free edges can be qualitatively well predicted.     

Dynamic ice forces of slender vertical structures due to ice crushing

The dynamic ice forces and structure vibrations generated by crushing failure of ice sheet were investigated by full-scale tests conducted on a cylindrical compliant monopod platform in Bohai Bay, China. The load panels recorded three ice force modes distinguished by ice speed, which cause structure quasi-static, steady-state and random vibrations respectively. Based on the tests data, the physical process of dynamic ice forces in crushing failure was probed, by analysis of mechanical behaviour of ice under compressive loading related to relative loading speed of ice-structure interaction. It is proved that the three ice force modes takes place in loading speeds which make ice fail in ductile, ductile–brittle transition and brittle range respectively. In addition, the key problem from the structure design point of view involved in each ice force mode is discussed.