Experimental studies on the yield behavior of ductile and brittle aluminum foams

Specimen size effects are a major cause of the unreliability of foam models in finite element codes. Here, the modified Arcan apparatus is used to investigate the biaxial yielding of ductile and brittle Al foams. This apparatus subjects a central section of a “butterfly-shaped” specimen to a uniform state of plane stress. The stresses have local maxima at the central section, thus ensuring that yielding occurs there. A yield envelope, which directly relates to the crushing process, can then be determined. Size effects are introduced when using conventional methods such as tri-axial or plate-shear tests. In such tests, averages of stress and strain are measured. These measures do not represent the actual yield event, because foam's internal structure is inhomogeneous and so is the deformation field. Strain localization and failure can occur at any weak layer of cells in the bulk. In this study, we have performed a series of biaxial tests on isotropic Alporas and anisotropic Hydro closed-cell Al foams of approximately equal densities. Alporas failed locally by a ductile phenomenon of progressive crushing of cells. It also possessed uniaxial strength asymmetry. Hydro specimens parallel and perpendicular to ‘foam rise’ were investigated. The Hydro foam developed a local, characteristic brittle crack at loads in the vicinity of the yield point. Phenomenological yield surfaces, which incorporate these features are obtained for the foams, and show dependence on both the deviatoric and hydrostatic stresses. We also provide expressions for the shear and hydrostatic strengths in terms of the uniaxial strengths. Finally, the size-independence of the yield surface is verified using the uniaxial compression of tapered specimens.     

高温下轻质泡沫铝动态力学性能实验

对传统的分离式Hopkinson压杆装置加以改进,设计了一种长杆直接撞击Hopkinson杆的实验方案,检测出低波阻抗材料在高温动态加载下的应力均匀性。对轻质泡沫铝材料的实验表明,在同一撞击速度下,温度越高,试件两端的应力均匀性越差,增加温度与提高撞击速度均会导致泡沫铝材料冲击端与支撑端的应力不均匀性。根据高温下应力均匀性的实验结果,确定高温下试件均匀变形对应的冲击速度,再通过传统的分离式Hopkinson压杆实验得出泡沫铝在高温动态下的力学性能。     

泡沫铝泡孔动态变形特性研究

在SHPB实验中采用应变冻结法将试件冻结于设定的压缩应变,然后观察内部泡孔的变形情况并讨论其变形机理。分别对同一相对密度(40%)、不同基体材料的两种泡沫铝以及两种相对密度(19%和8%)、相同基体材料的泡沫铝进行实验,讨论了基体材料的本构关系、泡沫的相对密度对变形模式的影响。利用ANSYS/LS DYNA软件对泡沫铝在动态压缩时泡孔的变形进行数值模拟计算,进一步说明泡沫铝泡孔变形的模式与基体材料本构关系及相对密度的关系。     

DYNAMIC PROPERTIES OF AL-ALLOY FOAM BEAM DAMAGED BY COMPRESSIVE FATIGUE

The permanent residual strain in aluminum （Al） alloy foams induced by compressive fatigue gradually increases with the increasing number of loading cycles. Consequently, the progressive shortening of Al-alloy foam degrades the dynamic material performance by the failure and ratcheting of multi-cells in the foam. In this paper, the dynamic properties of Al-alloy foams damaged by compressive fatigue were studied. The beam specimens with various residual strains were made by cyclic compression-compression stress. The dynamic bending modulus and loss factor were evaluated by using a beam transfer function method. As a result, the dynamic bending stiffness of Al-alloy foam turned out to be decreased due to damage while the loss factor was improved because of the increasing energy dissipation of such factors as cracked cell walls formed during the shortening process of the foam. The loss factor shows a manifest dependence on the fatigue residual strain.     

Strength and stiffness of sandwich beams in bending

This investigation is concerned with the experimental versus analytical correlation of the mechanical properties of sandwich-beam specimens. Such sandwich structures are commonly employed in the aircraft industry. Four-point and three-point load tests were conducted on a large number of sandwich-beam specimens, fabricated by using fiber-glass reinforced plastics (both unidirectional and woven-glass cloth) and DTD 685 aluminum alloy for the facings with aluminum honeycomb core and polyurethane foam cores and the indigenously available Araldite as the bonding medium between the core and the facings.The flexural stiffness of the composite sandwich specimens used in this investigation compared favorably with theoretical predictions. The shear stiffness was found to be about 55 percent and 45 percent of the theoretically predicted values for FRP (fiberglass-reinforced-plastic) cloth and FRP unidirectional laminates with aluminum honeycomb core sandwich, respectively. The failure load as determined by experiments was less than the theoretically predicted safe load. There was a loss of strength as well as a steep decrease in the failure load in the case of low density foam core.It was concluded that FRP facing plates with aluminum honeycomb core sandwich structure may be preferred to similar aluminum-alloy facing sandwich construction if high flexural stiffness and shear stiffness properties are required at less cost and weight. Indigenously available Araldite was quite satisfactory for bonding the core to the facings.This investigation has confirmed the importance of experiments in the field of sandwich structures which can effectively replace other conventional uneconomical structural or machine members which are currently in use.     

数字图像相关方法在闭孔泡沫铝压缩试验中的应用

为了了解相对密度与胞孔结构对闭孔泡沫铝力学性能的影响,本文采用放大成像及数字图像相关技术对两种不同密度的泡沫纯铝试样进行了实验研究.利用数字图像相关方法对泡沫纯铝变形前后的图像进行相关计算,获得了弹性范围内静态压缩情况下闭孔泡沫铝材料表面的全场变形及局部孔结构的变形,同时根据试验结果计算了试件的名义弹性模量.实验结果表明泡沫铝整体孔结构的变形与泡沫金属材料相对密度有关,而单个孔结构的变形主要与孔壁面光滑程度和皱褶有关.实验结果还表明图像相关方法能够有效地应用于闭孔泡沫金属的力学性测量和评估的研究.     

Deformation rate effects on failure modes of open-cell Al foams and textile cellular materials

The compressive behavior of open-cell aluminum alloy foam and stainless steel woven textile core materials have been investigated at three different deformation rate regimes. Quasi-static compressive tests were performed using a miniature loading frame, intermediate rates were achieved using a stored energy Kolsky bar, and high strain rate tests were performed using a light gas gun.In agreement with previous studies on foam materials, the strain rate was not found to have a significant effect on the plateau stress of metallic foams. For all the tests, real time imaging of the specimen combined with digital image correlation analysis allowed the determination of local deformation fields and failure modes. For the Kolsky bar tests, the deformations in the foam specimen were found to be more distributed than for the quasi-static test, which is attributed to moderate inertia effects. The differences in failure mode are more dramatic for the gas gun experiments, where a full compaction shock wave is generated at the impact surface. The stresses in front and behind the shock wave front were determined by means of direct and reverse gas gun impact tests, i.e., stationary and launched specimen, respectively. A one-dimensional shock wave model based on an idealized foam behavior is employed to gain insight into the stress history measurements. We show that the predictions of the model are consistent with the experimental observations. Woven textile materials exhibited moderate dependence of strength on the deformation rate in comparison with open-cell foam 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。     

Alloying effects on dislocation substructure evolution of aluminum alloys

The constitutive response of aluminum alloys is controlled by the evolution of dislocation substructure including mobile and forest dislocation density, cell size distribution and morphology, and misorientation angle between neighboring cells. The present study focuses upon the small strain regime and compares the measured microstructural evolution of 3003, 5005, and 6022 aluminum alloys during deformation. Room temperature tensile deformation experiments were performed on industrially manufactured specimens of each alloy and the evolving microstructure was compared with the mechanical response. The dislocation structure evolution was characterized using transmission electron microscopy and orientation imaging of deformed specimens. It was observed that structural evolution is a function of lattice orientation and the character of neighboring grains. In general, the dislocation cell size and misorientation angle between dislocation cells evolves systematically with deformation at relatively small strain levels.     

Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength.     

冲击条件下泡沫铝的细观变形特征分析

利用SHPB-高速摄影机系统,拍摄到了泡沫铝细观结构在SHPB冲击过程中的变形,分析了试件 的应变分布及破坏模式。研究表明,泡沫铝试件在SHPB冲击过程中应变分布是不均匀的,试件两端的应变 和应变率远大于中间部分的应变和应变率,即在SHPB实验过程中泡沫铝试件不能严格满足均匀性变形假 定。因此,需要考虑对用SHPB方法测量泡沫金属动态力学性能方法进行必要的修正。     

通孔泡沫铝的动态压缩行为

在SHPB装置上对渗流法制备的通孔泡沫铝进行了动态压缩实验,研究了相对密度为0.341~0.419的通孔泡沫铝在10-3~2000 s-1应变率范围内的压缩响应特征和应变率相关性,并用扫描电镜（scanning electron microscope,SEM)分析了泡沫铝的压缩变形特征。实验结果表明,通孔泡沫铝有明显应变率效应,随应变率上升,泡沫铝流动应力提高。SEM观察结果揭示,在动态压缩下,通孔泡沫铝宏观上均匀变形,微观变形机制以泡孔横向伸展坍塌为主。     

Aluminum foam-polymer hybrid structures (APM aluminum foam) in compression testing

The Advanced Pore Morphology (APM) process, a new method for production of aluminum foam-polymer hybrid materials, is described. Small volume aluminum foam spheres are produced first and then adhesively joined in a separate process step to realize an APM foam part. Detailed information on mechanical properties of this new hybrid material is given. Results of uniaxial and hydrostatic compression tests are summarized and evaluated to show how typical parameters characterizing material and process such as spatial arrangement, size and density of the foam elements influence the global properties. Two levels of the hierarchical architecture of the material are evaluated—namely the individual foam spheres and the hybrid structure. Variation of adhesives and adhesive coating thickness used in bonding the spheres in conjunction with study of unbonded specimens provides additional insight in the influence of this bond. First estimates on density dependence of mechanical properties are derived from the experimental data. Distinctive differences between APM and conventional aluminum foams are qualitatively explained. Throughout the study, AlSi7 aluminum foam produced from chemically identical precursor material according to the powder metallurgical FOAMINAL^® process is included as reference material.     

基于数字图像相关方法对冲击载荷下泡沫铝全场变形过程的测试

应用分离式霍普金森压杆(以下简称SHPB)和高速摄影装置研究了冲击载荷下泡沫铝试件全场变形的测量方法。使用SHPB对泡沫铝试件进行冲击压缩实验,同时用高速摄影装置对实验过程进行全程跟踪拍摄。将得到的高速摄影图像采用数字图像相关方法进行分析,由此可得到冲击压缩过程中泡沫铝试件全场应变的分布和变化规律。此研究揭示了冲击载荷下泡沫铝试件局部化变形的发展过程,为研究泡沫铝在不同冲击载荷下不同变形模式的内在机制提供了新的可靠的方法。     

不同应变率下泡沫铝的形变和力学性能

对低密度泡沫铝在不同变形率下的形变和力学性能进行了系统的试验研究。结果表明:（1）沿剪切方向骨架首先塌陷,即变形的局部化是低应变率下块体泡沫铝的主要变形特征;（2）在不同应变率下泡沫铝表现出体积应变基本上随工程应变呈线性变化,在低应变率下泊松比随轴向应变呈幂次关系增加,但在高应变率下泊松比随塑性应变增加,从一峰值降低并趋于稳定;（3）低应变率下泡沫铝材料塑性变形均匀,而高应变率下剪切变形较大;（4）泡沫铝材料的强度对应变率不很明显,但随塑性应变增加,它的率敏感性增加。     

Sensitivity of the shear gage to normal strains

This paper documents an experimental study that was conducted to demonstrate the sensitivity of the shear gage to the presence of normal strains. The shear gage is a specially designed strain gage rosette that measures the average shear strain in the test section of notched specimens such as the losipescu, Arcan and compact shear specimens. These specimens can have complicated stress states with high shear and normal strain gradients. To evaluate the sensitivity of the shear gage to normal strains, shear gages were tested on an Arcan specimen. The Arcan specimen is a notched specimen that can be loaded in pure shear (90 deg), pure tension (0 deg) and at intermediate 15- deg increments. The shear modulus for an aluminum specimen was determined at each of these loading angles. It was found that the gages display nearly zero sensitivity to normal strains ( _x, _y). Moiré interferometry was used to document the shear and normal strain distributions in the test section and to provide an independent method for determining the average shear strain. These results reinforce the robust nature of testing with the shear gage.     

不同冲击速度下泡沫铝变形和应力的不均匀性

利用常规Hopkinson杆实验装置和改进的Hopkinson杆实验装置对泡沫铝试件进行冲击压缩实验,同时用高速摄影装置对实验过程进行全程跟踪拍摄。通过改变冲击速度,观测到了3种不同的变形模式。将得到的高速摄影图像用数字图像相关方法进行分析,讨论了3种模式下全场应变不同的发展过程,并依此讨论应力的不均匀性,为研究不同冲击速度下变形不均匀对泡沫铝动态力学行为的影响提供了新的方法。     

Study on Deformation of Polycrystalline Aluminum Alloy Using Moiré Interferometry

Polycrystalline aluminum alloy is manufactured by annealing, compared to the width of the specimen, the size of the grains can not be omitted, which makes the specimen anisotropic. Under uniaxial tension, the deformation field is inhomogeneous. In this study, moiré interferometry is successfully applied to measure the deformation of the polycrystalline specimen. The experimental results presented the stress versus strain responses of the marked grains in different orientations and different shapes. By using fringe centering method, the strain distributions under certain load in the centers and on the boundaries of the grains are analyzed.     

Plastic constraint considerations at the prediction of wide plate failure behaviour from small scale testing, like c.o.d. determinations in s.e.n.b.-specimens

The stress intensity factor, crack opening displacement, J-integral, etc. will depend, besides on load, reduced (physical) cracklength and dimensions also on the plastic constraint situation near the crack tip. Assumedly their critical values are also dependent on this, which can imply an appreciable quantitative consequence for uniaxial gross stresses larger than (2/3) Y, as elaborated. This might interfere when trying to predict large sale behaviour of notched plates from small scale behaviour of specimens with the same thickness, as this presumbly does not guarantee equal plastic constraint. An average plastic constraint factor (p.c.f.) estimate for contained plastic flow can be indicated from simultaneous readings of s.i.f. or c.o.d. and gross stress during loading and its decrease followed. This allows to predict the failure conditions at the end of the experiment, provided the dependence of critical c.o.d. on this p.c.f. was previously determined. For arbitrary notched specimens a priori predictions of failure from the known critical c.o.d./p.c.f.-curve can be envisaged, using analytical and numerical evaluations of p.c.f. development at loading. The transition temperature concept is discussed with respect to the p.c.f. The failure prognosis for wide plate testing from small scale testing is reconsidered for deformation controlled loading: for contained plastic flow an alternative for the design-curve is suggested, using the deformation of the gauge length of the specimen defined as the distance between the localisations of load application. Finally the allowable deformation of plates, indicated for the required load in absence of a defect, is analysed for plates with a defect present.     

Simulation of the densification of real open-celled foam microstructures

Ubiquitous in nature and finding applications in engineering systems, cellular solids are an increasingly important class of materials. Foams are an important subclass of cellular solids with applications as packing materials and energy absorbers due to their unique properties. A better understanding of foam mechanical properties and their dependence on microstructural details would facilitate manufacture of tailored materials and development of constitutive models for their bulk response. Numerical simulation of these materials, while offering great promise toward furthering understanding, has also served to convincingly demonstrate the inherent complexity and associated modeling challenges.The large range of deformations which foams are subjected to in routine engineering applications is a fundamental source of complication in modeling the details of foam deformation on the scale of foam struts. It requires accurate handling of large material deformations and complex contact mechanics, both well established numerical challenges. A further complication is the replication of complex foam microstructure geometry in numerical simulations. Here various advantages of certain particle methods, in particular their compatibility with the determination of three-dimensional geometry via X-ray microtomography, are exploited to simulate the compression of “real” foam microstructures into densification. With attention paid to representative volume element size, predictions are made regarding bulk response, dynamic effects, and deformed microstructural character, for real polymeric, open-cell foams. These predictions include a negative Poisson's ratio in the stress plateau, and increased difficulty in removing residual porosity during densification.