铝/硅橡胶复合材料动态压缩行为的研究

通过向开孔泡沫铝中填充硅橡胶而制备了铝 /硅橡胶复合材料 ,在Hopkinson压杆实验装置上对这种材料进行了动态压缩实验 ,分析了其动态压缩应力 应变响应特征 ,并与开孔结构泡沫铝的压缩行为进行了比较。结果表明 :铝 /硅橡胶复合材料的压缩应力 应变响应具有两个阶段的特征 ,即弹性和塑性变形阶段 ;这种复合材料具有较强的应变率效应 ,随应变率的提高 ,其屈服强度和流动应力显著上升。     

Energy absorption of an egg-box material

Conical frustra made from leaded gun-metal have been compressed axially. Collapse is either by a travelling plastic hinge or by tearing. An analytical model is developed for the travelling plastic hinge in a rigid, ideally plastic solid; its predictions are compared with the observed response, and with those of an axisymmetric finite element analysis. The travelling hinge mechanism is also observed in the compressive collapse of an egg-box material comprising a square array of conical frustra. Collapse mechanism maps are constructed for the egg-box material, and they show the regimes of dominance of elastic buckling, material tearing and the travelling plastic hinge. The maps are useful for selecting egg-box geometries that maximise the energy absorption per unit mass at any prescribed value of collapse stress. The optimisation indicates that the egg-box material has a similar energy absorption capacity to that of hexagonal honeycombs and is superior to that of metal foams.     

Structural response of pyramidal core sandwich columns

An experimental and analytical investigation is carried out to examine the in-plane compressive response of pyramidal truss core sandwich columns. The identified failure mechanisms include Euler buckling, shear buckling and face wrinkling. The operative mechanism is dependent on the properties of the bulk material and geometry of the sandwich columns and analytical formulae are derived for each of these modes. Failure maps are constructed for sandwich columns made from an elastic ideally-plastic material and AISI 304 stainless steel which has a strongly strain hardening response. Pyramidal core sandwich columns made from 304 stainless steel have been designed using these mechanism maps and the measured responses are compared with the analytical predictions. Finally, optimal single layer and multi-layer pyramidal sandwich column designs that minimize the weight for a given load carrying capacity are calculated using the developed analytical models for the failure of the sandwich columns. The results demonstrate that pyramidal core sandwich columns outperform the currently used hat-stiffened column design.     

Modeling the dynamic response of visco-elastic open-cell foams

This article introduces a mesoscopic formulation for modeling the dynamic response of visco-elastic, open-cell solid foams. The effective material response is obtained by enforcing on a representative 3D unit cell the principle of minimum action for dissipative systems. The resulting model accounts explicitly for the foam topology, the elastic and viscous properties of the cell wall, and the inertial effects arising from non-affine motion within the cells. The microinertial effects become significant in retarding the foam collapse during exceedingly high strain-rate loading. As an application example, a heterogenous case of compressive deformation at high strain rate is simulated utilizing the present model as a constitutive update in a non-linear finite element analysis code. This FEM simulation shows the ability of the model to capture the progressive foam collapse during the dynamic compression as observed in experimental studies. Using the microscopic model, the inertial and viscous strain-rate effects are investigated through the foam density, viscosity, and relative density. Based on the physics incorporated into the local cell model, we provide insight into the physical mechanisms responsible for the experimentally observed strain-rate effects on the behavior of dynamically loaded foam materials.     

On the crushing of aluminum open-cell foams: Part II analysis

Part II of this study is concerned with the modeling of all aspects of the compressive response and crushing of the open-cell Al foam studied in Part I. The foam microstructure is modeled using the regular cell of Kelvin with cell anisotropy and ligament geometry established by X-ray tomography. The ligaments are modeled as shear-deformable beams and the material is elastoplastic calibrated to the properties of the Al alloy base material. It is demonstrated that the initiation stress of measured responses is associated with a limit load instability that results from plastification of foam ligaments due to combined bending and axial compression. The periodicity of the Kelvin cell enables calculation of the initial elastic properties as well as the initiation stress with just a single fully periodic characteristic cell. The crushing response is evaluated by considering finite size 3D domains that allow localized deformation to develop. Localization is in the form of shear buckling that develops along the principal diagonals of the Kelvin cell foam. Localized crushing is arrested by contact between the ligaments of the buckled cells. Contact is approximated by limiting the amount a cell can collapse in the direction of the applied load. This arrests local collapse and causes it to spread to neighboring material at a nearly constant stress level as in the experiments. The stress picks up when the whole domain has crushed. Although the calculated collapse patterns differed from the more random ones observed in the experiments, the calculated force–displacement responses match very well the experimental ones in all aspects.     

On the crushing of aluminum open-cell foams: Part I. Experiments

This two-part study is concerned with the understanding and modeling of the compressive response of open-cell metallic foams. Part I presents experimental results from Al-6101-T6 foams of three different cell sizes with relative densities of about 8%. X-ray tomography is first used to characterize the geometry of the microstructure. The cells are irregular polyhedra of nearly uniform size that are somewhat elongated in one direction. The ligaments are nearly straight with convex, three-sided cross-sections and variable area distribution along their length. Foam specimens were compressed at slow displacement rates along the rise and transverse directions and the evolution of crushing in the specimens was monitored using X-ray tomography. In both directions, the response is initially nearly linear, terminating into a limit load that is followed by an extensive load plateau. At an average strain of about 55% the load increases monotonically again due to densification. The limit load is caused by plastification due to combined compression and bending of the ligaments. Beyond this point, cells start to buckle and collapse locally, forming bands that cover the full cross-section of the specimen. Contact of the collapsing cells arrests local deformation triggering collapse in neighboring cells. In this manner, crushing gradually spreads throughout the specimen and when this is achieved the load required for further deformation starts to rise. The initial elastic modulus, the stresses at the limit load and the plateau and the extent of the plateau have been measured as a function of relative density for both directions. The stress–displacement response in the transverse direction is generally somewhat lower than in the rise direction but the prevalent events were found to be similar in the two directions.     

Dynamic buckling of an inclined strut

The dynamic compressive response of a sandwich plate with a metallic corrugated core is predicted. The back face of the sandwich plate is held fixed whereas the front face is subjected to a uniform velocity, thereby compressing the core. Finite element analysis is performed to investigate the role of material inertia, strain hardening and strain rate hardening upon the dynamic collapse of the corrugated core. Three classes of collapse mode are identified as a function of impact velocity: (i) a three-hinge plastic buckling mode of wavelength equal to the strut length, similar to the quasi-static mode, (ii) a ‘buckle-wave’ regime involving inertia-mediated plastic buckling of wavelength less than that of the strut length, and (iii) a ‘stubbing’ regime, with shortening of the struts by local fattening at the front face. The presence of strain hardening reduces the regime of dominance of the stubbing mode. The influence of material strain rate sensitivity is evaluated by introducing strain rate dependent material properties representative of type 304 stainless steel. For this choice of material, strain rate sensitivity has a more minor influence than strain hardening, and consequently the dynamic collapse strength of a corrugated core is almost independent of structural dimension.     

Phenomenological modeling of the response of a dense colloidal suspension under dynamic squeezing flow

The split Hopkinson pressure bar experimental technique is used to evaluate the squeezing flow response of a concentrated, discontinuously thickening colloidal suspension of spherical silica particles loaded at high stresses/strain rates. These results provide insight into the transitional behavior of these materials, as well as the post-transitional response under compressive loading. A method of analyzing the strain and strain rate dependent behavior is presented to identify modes of material response (viscous, elastic, etc.). Experimental results are presented as stress–strain–strain rate plots and a surface fitting approach is used to develop a phenomenological model describing the overall response. From this model, it is possible to identify regions of elastic and viscous behavior using a gradient analysis approach. It was found that, after an initial period of viscous deformation, the suspension behaves like a viscoelastic material – this regime corresponds well with transition in which large clusters of particles percolate. This is followed by a third, viscous regime in which the material undergoes viscous deformation. At the highest stresses, a plateau region of plastic deformation has been identified. This approach and the conditions under which it may be applied are described in detail in the paper.     

On the compressive strength of open-cell metal foams with Kelvin and random cell structures

Two families of finite element models of anisotropic, aluminum alloy, open-cell foams are developed and their predictions of elastic properties and compressive strength are evaluated by direct comparison to experimental results. In the first family of models, the foams are idealized as anisotropic Kelvin cells loaded in the <100> direction and in the second family more realistic models, based on Surface Evolver simulations of random soap froth with N³ cells are constructed. In both cases the ligaments are straight but have nonuniform cross sectional area distributions that resemble those of the foams tested. The ligaments are modeled as shear deformable beams with elasto-plastic material behavior. The calculated compressive response starts with a linearly elastic regime. At higher stress levels, inelastic action causes a gradual reduction of the stiffness that eventually leads to a stress maximum, which represents the strength of the material. The periodicity of the Kelvin cell enables calculation of the compressive response up to the limit stress with just a single fully periodic characteristic cell. Beyond the limit stress, deformation localizes along the principal diagonals of the microstructure. Consequently beyond the limit stress the response is evaluated using finite size 3-D domains that allow the localization to develop. The random models consist of 3-D domains of 216, 512 or 1000 cells with periodicity conditions on the compressed ends but free on the sides. The compressive response is also characterized by a limit load instability but now the localization is disorganized resembling that observed in experiments. The foam elastic moduli and strengths obtained from both families of models are generally in very good agreement with the corresponding measurements. The random foam models yield 5–10% stiffer elastic moduli and slightly higher strengths than the Kelvin cell models. Necessary requirements for this high performance of the models are accurate representation of the material distribution in the ligaments and correct modeling of the nonlinear stress–strain response of the aluminum base material.     

Multi-scale Mechanical Characterization of Palmetto Wood using Digital Image Correlation to Develop a Template for Biologically-Inspired Polymer Composites

Palmetto wood is garnering growing interest as a template for creating biologically-inspired polymer composites due to its historical use as an energy absorbing material in protective structures. In this study, quasi-static three-point bend tests have been performed to characterize the mechanical behavior of Palmetto wood. Full-field deformation measurements are obtained using Digital Image Correlation (DIC) to elucidate on the strain fields associated with the mechanical response. By analyzing strain fields at multiple length scales, it is possible to study the more homogeneous mechanical behavior at the macro-scale associated with the global load-deformation response; while at the microscale the mechanical behavior is more inhomogeneous due to microstructural failure mechanisms. Thus, it was possible to determine that, despite the presence of discontinuous macro-fiber reinforcement, at the macro-scale the response is associated with classical bending and progressive failure processes that are adequately described by Weibull statistics proceeding from the tensile side of the specimen. At the microscale, however, the failure mechanisms giving rise to the macroscopic response consist of both shear-dominated debonding between the fiber and matrix, and inter-fiber matrix failure due to pore collapse. These microscale mechanisms are present in both the compressive and tensile regions of the specimen, most likely due to local macro-fiber bending, which is independent of the global bending state. The pore collapse mechanism observed during mechanical loading appears to improve the energy absorption of the matrix material, thereby, transferring less energy and shear strain to the macro-fiber-matrix interface for initiation of debonding. However, the pore collapse mechanism can also accumulate substantial shear strain, which results in matrix shear cracking. Through these complex failure mechanisms, Palmetto wood exhibits a high resistance to catastrophic failure after damage initiation, an observation that can be used as inspiration for creating new polymer composite materials.     

泡沫铝合金动态力学性能实验研究

利用分离式霍布金森压杆(SHPB)实验技术和MTS材料实验机对两组不同孔径、不同密度的开孔泡沫铝合金进行了准静态和动态压缩实验研究。实验结果表明:泡沫铝合金的静态和动态变形过程均具有泡沫材料变形的三个阶段特征。开孔泡沫铝合金的变形是均匀变化过程，并不出现局部的变形带。与相对密度对力学性能的影响相比，孔径大小的影响可以忽略不计。在考察的应变率范围内，屈服应力对应变率并不很敏感。     

Ratcheting and wrinkling of tubes due to axial cycling under internal pressure: Part II analysis

Part I presented a set of experiments in which pressurized tubes were cycled axially under stress control about a compressive mean stress. This loading history causes biaxial ratcheting involving compressive axial strain and expansion of the diameter of the tube. The compressive strain in turn induces the initiation and growth of axisymmetric wrinkles. Persistent cycling resulted in localization of the wrinkles and collapse. In Part II the problem is first modeled as a shell with initial axisymmetric imperfections while the biaxial ratcheting of the material is modeled using the Dafalias–Popov two-surface nonlinear kinematic hardening model. It is demonstrated that when suitably calibrated this modeling framework reproduces the prevalent ratcheting deformations and the evolution of wrinkling including the conditions at collapse accurately for all experiments. The calibrated model is then used to evaluate the ratcheting behavior of pipes under thermal-pressure cyclic loading histories experienced by axially restrained pipelines.     

Design sensitivity analysis for parameters affecting geometry,elastic–viscoplastic material constant and boundary condition by consistent tangent operator-based boundary element method

This paper presents a design sensitivity analysis method by the consistent tangent operator concept-based boundary element implicit algorithm. The design variables for sensitivity analysis include geometry parameters, elastic–viscoplastic material parameters and boundary condition parameters. Based on small strain theory, Perzyna’s elastic–viscoplastic material constitutive relation with a mixed hardening model and two flow functions is considered in the sensitivity analysis. The related elastic–viscoplastic radial return algorithm and the formula of elastic–viscoplastic consistent tangent operator are derived and discussed. Based on the direct differentiation approach, the incremental boundary integral equations and related algorithms for both geometric and elastic–viscoplastic sensitivity analysis are developed. A 2D boundary element program for geometry sensitivity, elastic–viscoplastic material constant sensitivity and boundary condition sensitivity has been developed. Comparison and discussion with the results of this paper, analytical solution and finite element code ANSYS for four plane strain numerical examples are presented finally.     

Compressive strength of edge-loaded corrugated board panels

Postbuckling strength of simply supported corrugated board panels subjected to edge compressive loading has been studied experimentally using a specially developed test fixture. Although the load versus out-of-plane displacement response was highly sensitive to the presence of initial imperfections in the panels, the collapse loads did not vary much, which is attributed to the stable postbuckling behavior of the plates. Thin plates collapsed at nearly twice the buckling load, while thick panels collapsed at loads below the elastic critical buckling load. Local buckling of the facing on the concave side of the buckled plate was observed at load levels close to the collapse load. The plate collapse was triggered by compressive failure of the facings that initiated at the unloaded edges. A simplified design analysis was derived based on approximate postbuckling analysis and compared with an existing design formula for corrugated board panels and boxes.     

弹体贯穿混凝土数值模拟的改进材料模型

研究混凝土结构在冲击载荷下的力学特性对武器以及防护结构的设计和评估具有重要意义,而合适的材料模型可以更准确地预测混凝土结构的力学行为和破坏模式。因此,本文中提出了一种改进的混凝土塑性损伤材料模型来描述其在冲击载荷下的力学响应。该改进模型考虑了压力-体积应变关系、应变率效应、洛德角效应和塑性损伤累积对混凝土材料力学特性的影响,并引入了一个与损伤相关的硬化/软化函数来描述压缩状态下的应变硬化和软化行为。随后,通过对3个独立的强度面进行线性插值得到了该改进模型的破坏强度面,并采用部分关联流动法则考虑了混凝土材料的体积膨胀特性。最后,开展了单个单元在不同加载条件下和弹体贯穿钢筋混凝土靶的数值模拟,验证了该改进模型的可行性、准确性以及预测性能提升。     

软质聚氨酯泡沫的动态压缩力学性能和本构模型

采用Instron 9350落锤试验机研究了中低应变率下软质聚氨酯泡沫的动态压缩力学性能,分析了其应力-应变响应特征和应变率敏感性,讨论了应变率对材料应变率敏感性指数和能量吸收特性的影响,并基于实验结果建立了可准确描述其压缩力学响应的率相关本构模型。结果表明,软质聚氨酯泡沫的静动态压缩应力-应变响应具有典型的三阶段特征,且呈现出明显的应变率强化效应。准静态加载下,材料具有较高的吸能效率但能量吸收值较小,应变率对最大吸能效率和比吸能的影响较小;动态加载下,随着应变率的增加,最大吸能效率显著减小而比吸能明显增大。考虑应变率影响的修正Sherwood-Frost模型和修正Avalle模型都能够很好地表征软质聚氨酯泡沫的静动态压缩应力-应变响应,但修正Avalle模型的参数较少,更便于工程应用。研究结果可为软质聚氨酯泡沫抗冲击结构的设计和优化提供指导。     

不同应变率下聚乙烯材料的压缩力学性能

为了研究聚乙烯材料在不同应变率下的压缩力学性能,通过准静态实验和动态实验获得聚乙烯材料不同应变率下的应力应变曲线,分析发现:聚乙烯的弹性模量和屈服强度随应变率增大而增大,具有明显的黏弹塑性;聚乙烯材料进入塑性阶段,其应力应变曲线在不同应变率下具有相近的变化趋势,即塑性切向模量近似相同。根据聚乙烯材料的压缩力学性能,建立了弹性区、屈服点和塑性区的分段本构模型。该模型的屈服点和塑性段与实验结果吻合较好,由于弹性段采用线弹性模型,与实验结果存在一定偏差,可近似描述材料的弹性行为。     

The Effect of Strain Rate,Specimen Geometry and Lubrication on Responses of Aluminium AA2024 in Uniaxial Compression Experiments

The ability to observe and quantify intrinsic material response to loading at different rates of strain has been improved by reducing the errors of mechanical characterisation in uniaxial compression experiments. In order to perform comparisons of the results from uniaxial compression tests used to characterise mechanical properties of aluminium alloys at different strain rates, it is necessary to reduce errors resulting from factors such as specimen design. In this study, the effects of strain rate, specimen geometry and lubrication on the compressive properties of aluminium AA2024 alloy were quantitatively investigated by measuring the mechanical behaviour of this alloy as functions of strain rate, specimen aspect ratio and lubrication condition. Both the deformation history and the failure mode were identified using low and ultrahigh speed photography. The interaction of factors influencing the measured stress-strain response was quantified, and suitable specimen aspect ratios for compression tests at different strain rates were identified.     

A numerical axisymmetric collapse analysis of viscoplastic cylindrical shells under axial compression

Circularcylindrical shells are frequently used as structural components because of their high strength and their ability to absorb energy during complete structural collapse. Total collapse analyses have mainly been based on experimental work and approaches inspired by this. However, in the last few years, powerful numerical tools have been available and numerical collapse analyses have become more attractive. This paper presents results from an axisymmetric numerical collapse analysis. The analysis is based on a finite rotation shell theory accounting for contact between the shell walls. The strains are assumed to remain small and the shell material is described by an elastic–viscoplastic model. The sensitivity of the collapse behaviour is demonstrated with respect to parameters such as initial imperfections, thickness of the shell, material parameters and rate of deformation. Comparisons between the results numerically obtained and approaches found in the literature are presented. Good agreement was found for the folding length of the developed collapse pattern whereas small differences between the mean crushing loads was observed. Furthermore, it was noted that the developed collapse pattern was strongly dependent on the strain hardening of the material.     

地震作用下基于响应敏感性的单层球面网壳冗余度分析方法研究

冗余特性是结构鲁棒性的重要组成部分,也是损伤情况下结构安全性的体现。在地震等动力荷载作用下单层球面网壳结构的倒塌模式由诸多因素决定,其中结构的冗余度是重要的影响因素。为合理评估地震作用下的结构冗余度,本文基于结构响应对单元材料弹性模量的敏感性提出地震作用下的结构构件冗余度评价方法,并对一星型网壳在地震作用下的弹性、弹塑性冗余度进行分析,以验证方法的有效性。结果表明,结构冗余度能够反映构件在结构中的重要性,冗余度值的大小是构件重要性的衡量指标,低冗余度构件是结构的关键构件。利用结构的冗余度分布,可以采取加强低冗余构件的措施,从而实现网壳结构倒塌模式的优化控制。