Size effects in the mechanical behavior of cellular materials

Effective mechanical properties of cellular materials depend strongly on the specimen size to the cell size ratio. Experimental studies performed on aluminium foams show that under uniaxial compression, the stiffness of these materials falls below the corresponding bulk value, when the ratio of the specimen size to the cell size is small. Conversely, in the case of simple shear and indentation, the overall stiffness rises above the bulk value. Classical continuum theory, lacking a length scale, cannot explain this size dependent mechanical behaviour. One way to account for these size effects is to explicitly model the discrete cellular morphology. We performed shear, compression and bending tests using discrete models, for hexagonal (regular and irregular) microstructures. Even though discrete models give a very good agreement with the experiments, they are computationally expensive for complex microstructures, especially in three dimensions. To overcome this, one can use a generalized continuum theory, such as Cosserat continuum theory, which incorporates a material length scale. We fit the Cosserat elastic constants of the models by comparing the discrete calculations with the analytical Cosserat continuum solutions in terms of macroscopic properties. We critically address the limitations of the Cosserat continuum theory.     

The mechanical response of Rohacell foams at different length scales

The quasi-static mechanical response of polymethacrylimide (PMI) foams of density ranging from 50 to 200 kg m⁻³ is investigated in order to provide experimental data to inspire and validate numerical constitutive models for the response of polymer foams. The macroscopic mechanical response is characterised by conducting quasi-static compression, tension, shear and indentation experiments, whereas microscopic deformation mechanisms are identified by conducting in situ SEM observations during static compression and tension tests; it is shown that foams of low density collapse by cell wall buckling while foams of high density undergo plastic cell-wall bending. As a result, both the elastic and plastic macroscopic response of the foam display a tension/compression asymmetry.     

Room‐Temperature Mechanical Properties of V20Nb20Mo20Ta20W20 High‐Entropy Alloy

Refractory high‐entropy alloys (HEAs) have shown promising high temperature strengths, while their mechanical behaviors at room temperature are rarely reported. In this work, the room‐temperature mechanical properties of V₂₀Nb₂₀Mo₂₀Ta₂₀W₂₀ refractory HEA under various different loading modes including tension, compression, bending, shear loading, and microhardness are investigated. The results show that this alloy exhibits very high compressive strength but quite low strengths under tension, bending, and shear loading, similar to the conventional brittle materials. However, pronounced plasticity and slip bands are observed in compression samples, and no indentation cracking is observed in low‐load microhardness tests, which indicate the potential ability of plastic deformation in this refractory HEA. The present work suggests that the microstructure or composition of this HEA should be carefully tailored before its practical usage to suppress its large tendency for cracking and eventually improve its ductility and strength under tension.

     

Strength and toughness of barium titanate ceramics

The effect of processing variables on the mechanical and electrical properties of holmium-doped barium titanate ceramics with a positive temperature coefficient of resistance has been investigated. This paper contains details of the tests used to measure the mechanical properties of ceramics prepared using four compositional mixes. Two methods of measuring strength were used: diametral compression of disc samples and four-point bending of beam specimens. Fracture toughness was also evaluated using two methods: the failure of single edge-notched (SEN) beams under four-point loading and cracking from a surface indentation with a diamond pyramid indentor. Values of strength ranged from 18 to 82 MPa for the four materials when measured by the diametral compression test. This compared with a range of 35–79 MPa for the same materials tested in pure bending. Fracture toughness values ranged from 0.65 to 0.95 MPa m^1/2 for the SEN specimens and from 1 to 1.8 MPa m^1/2 using the indentation technique on the same samples.     

The effect of core thickness on the flexural behaviour of aluminium foam sandwich structures

The effect of core thickness on the deformation mechanism of an aluminium foam core/thermoplastic composite facing sandwich structure under 4-point bending was investigated. Full field strain analysis and visual observations show a number of failure mechanisms between the different core thicknesses. High strain concentrations were observed in each sample thickness corresponding to the particular region of failure. The thinner samples exhibited skin wrinkling and fracture, and some core cracking and crushing while the thicker samples failed due to core indentation. Increasing the skin thickness eliminated the incidence of core indentation. Instead, significant core shear cracking was observed.     

Damage and fracture of a cross woven C/SiC composite subject to compression loading

In order to understand the mechanical behaviours of ceramic matrix composites under various loading conditions, the compression stress-strain behaviour of a cross woven C/SiC ceramic matrix composite was characterized in terms of damage and fracture mechanisms, which were observed by scanning electron microscope (SEM) on a side-polished sample. The compression stress-strain curve was found to consist of two stages. The first stage, which extends to about 300 MPa, covers linear elastic deformation with a compression modulus of 140 GPa. The second stage starts with the occurrence of compression damage modes, which include ply delamination, bundle separation and transverse bundle cracking. Depending on the local structure of the sample, the second stage of the stress-strain curve can be either mostly linear or non-linear. The fracture of the composite under compression is by kinking, shearing and bending fracture of fibre bundles individually or in groups, forming a macroscopic shear band in the sample.     

Effects of statistics of cell’s size and shape irregularity on mechanical properties of 2D and 3D Voronoi foams

In the study of the mechanical properties of metallic foam, the relative density (or porosity) and the average size of cells are two key parameters of the meso-geometry, but it is also well known experimentally that the two parameters alone are not enough since the mechanical properties of metallic foams are different even with the same initial relative density and average cell size. In this paper, we have classified the irregularity of cells into two types to describe polygonal and polyhedral cells in 2D and 3D metallic foams, which are called size irregularity and shape irregularity, respectively. The former reflects the deviation of the size of a cell from the average cell size in the foam and the latter reflects the deviation of the shape of a cell from a circle with the same area (2D) or a globe with the same volume (3D). With the two kinds of definitions, effects of the irregularity of cells in aluminum foam on mechanical properties are investigated using the Voronoi tessellation technique and the finite element method. The well- designed 2D and 3D Voronoi models are constructed, of which the statistic distributions of size and shape irregularity are presented. The compression simulations of Voronoi-based models indicate that the yield stress of metallic foam is seldom affected by the size irregularity, but significantly affected by the shape irregularity. The more regular the foams, the higher will be their yield plateau at constant overall relative density and average cell size.     

维氏压痕对常压固相烧结碳化硅陶瓷材料力学性能的影响

为了研究维氏压痕裂纹对常压固相烧结碳化硅陶瓷(SSiC)材料力学性能的影响, 通过扫描电镜观察了0.1~100 N的压痕载荷下产生的表面裂纹及裂纹剖面的状况, 并测试了相应载荷下的力学性质, 探讨了压痕法测量SSiC材料硬度、韧性等力学性质的适当压力载荷. 结果表明, SSiC材料压痕裂纹起始的临界压力载荷介于0.1~0.2 N; 当压痕载荷小于0.5 N时, 裂纹尺寸小于5 μm, SSiC材料的平均弯曲强度受影响程度较小. 此外, 当压痕载荷为10 N以上时, 压痕法测得的维氏硬度值趋近定值, 且所得到的裂纹是半圆形裂纹, 因此, 10 N为采用压痕法准确测量SSiC材料硬度及韧性的最低压痕载荷值.     

高孔隙度可再生骨支架仿真与实验研究

目的 确定单元体与股骨的最佳孔隙度骨支架结构。方法 通过扫描电镜分析选区激光熔化(Selective laser melting,SLM)成形试样的微观结构;通过静力学模拟与实验分析不同孔隙度下标准结构与Voronoi多孔结构的压缩变形规律;通过生物力学仿真实验分析步态周期下标准结构与Voronoi多孔结构的应力分布情况。结果 在选区激光熔化成形的316L不锈钢微观组织中,均匀分布着细小的近六边形、伸长六边形的胞状结构和条柱状亚结构,受压时有利于分散应力,提高整体结构的稳定性;在压缩变形时,标准结构应力集中于垂直棱柱,易导致棱柱断裂引起试样倾斜;Voronoi结构连接杆的不均匀分布有利于分散应力,使Voronoi结构的最大等效应力(250.34 MPa)远低于标准结构(738.07 MPa),保证了整体受力均匀与结构稳定;在步态周期下,2种骨支架结构的应力随孔隙度的增加而增加,75%孔隙度的Voronoi结构具有更优异的承压能力与缓解应力屏蔽的作用。结论 通过模拟与试验分析,确定了单元体与股骨的最佳孔隙度及Voronoi结构优异的力学性能,验证了在步态周期下高孔隙度Voronoi骨支架结构的可靠性,为股骨置换手术提供了理论依据。     

Large shear strength enhancement of gamma-boron by normal compression

The effects of normal compression on the mechanical properties of boron phases have been investigated using the first principles. The results have shown that normal compression produces entirely different effects on gamma-boron and alpha-boron shear strengths. The three-center bonds connecting the B₂ dumbbell pair with the B₁₂ icosahedra in gamma-boron are greatly strengthened compared with the peculiar bonds in the alpha-boron, resulting in a 32% enhancement in gamma-boron shear strength. The current study provides an atomic understanding of the discrepancy between the theoretical and experimental indentation strength of gamma-boron.     

Mechanical Properties of TiN Coatings

It is difficult to measure the mechanical properties of physical vapor deposition coatings owing to their small layer thickness. This report describes a special four‐point bending device that makes it possible to determine quantitative critical tensile or compressive failure stresses and shear stresses in thin coatings. The bending test was also used to carry out measurements of hardness and critical loads (scratch test) under stress, excluding other influences such as microstructure changes. The material parameters determined form the basis of a finite element model of the indentation process, and this offers new possibilities for mechanical characterization of coated materials.     

Boron-assisted transformation to rod-like graphitic carbons from multi-walled carbon nanotubes in boron-mixed multi-walled carbon nanotube solids

We produced boron-mixed multi-walled carbon nanotube solids (B-mixed MWCNT solids) by heating and pressing the powder of purified MWCNTs mixed with 1, 5, and 10 wt % boron in the temperature range 1400-1800 °C every 200 °C under a constant pressure of 20 MPa in vacuo, and investigated the influence of boron addition on nanotube structure and the mechanical and electrical properties of the resulting B-mixed MWCNT solids. The structure of the prepared material was characterized by scanning electron microscopy equipped with energy-dispersive X-ray spectroscopy, high-resolution transmission electron microscopy-electron energy loss spectroscopy, Raman scattering spectroscopy, and X-ray diffraction, and their mechanical properties and conductivity were measured using a mechanical and Vickers indentation tester and an electric resistor, respectively. It is notable that part of the nanotubes in the B-mixed MWCNT solids solidified at 1800 °C had dramatically changed into rod-like graphitic carbons (RLGCs). The occupancy distribution of RLGCs increased with increasing boron contents. However, boron was not detected in the energy-loss near-edge structure spectrum of RLGCs. Furthermore, RLGCs were not observed in the boron-unmixed sample treated with the same solidified condition, indicating that adding boron causes a remarkable ability to transform the phase of MWCNT. Transformation from MWCNTs to RLGCs resulted in increased specific bending strength and modulus, Vickers hardness, and electrical conductivity of B-mixed MWCNT solids with increasing boron content and solidified temperature.     

Mechanics of balsa (Ochroma pyramidale) wood

Balsa wood is one of the preferred core materials in structural sandwich panels, in applications ranging from wind turbine blades to boats and aircraft. Here, we investigate the mechanical behavior of balsa as a function of density, which varies from roughly 60 to 380 kg/m³. In axial compression, bending, and torsion, the elastic modulus and strength increase linearly with density while in radial compression, the modulus and strength vary nonlinearly. Models relating the mechanical properties to the cellular structure and to the density, based on deformation and failure mechanisms, are described. Finally, wood cell-wall properties are determined by extrapolating the mechanical data for balsa, and are compared with the reduced modulus and hardness of the cell wall measured by nanoindentation.     

Mechanical response of cellular solids: Role of cellular topology and microstructural irregularity

Rapid advance in additive manufacturing techniques promises that, in the near future, the fabrication of functional cellular structures will be achieved with desired cellular microstructures tailored to specific application in mind. In this perspective, it is essential to develop a detailed understanding of the relationship between mechanical response and cellular microstructure. The present study reports on the results of a series of computational experiments that explore the effect topology and microstructural irregularity (or non-periodicity) on overall mechanical response of cellular solids. Compressive response of various 2D topologies such as honeycombs, stochastic Voronoi foams as well as tetragonal and triangular lattice structures have been investigated as functions of quantitative irregularity parameters. The fundamental issues addressed are (i) uniqueness of mechanical response in irregular microstructures, and effects of (ii) specimen size, (iii) boundary morphology, (iv) cellular topology, and (v) microstructural irregularity on mechanical response.     

Microhardness studies of chain-extended PE: II. Creep behaviour and temperature dependence

The variation of hardness with indentation time has been investigated for chain-extended polyethylene (PE), other PE samples crystallised under different conditions and paraffins. Hardness is shown to decrease with indentation time for all the samples investigated according to a power-law. Chain-extended PE, produced by high pressure crystallization or annealing, flows at the lowest rate under the indenter of all the PE samples considered. On the other hand, paraffins creep at the highest rate. Creep behaviour depends markedly on the crystal thickness of the material. The mechanical properties at long indentation times seem to be determined primarily by the deformation modes of the crystals. The temperature dependence of hardness and that of the creep behaviour has also been investigated. In chain-extended PE, the softening of the sample and the higher rate of creep with increasing temperature are discussed in terms of the thermal expansion of the unit cell.     

Effect of Zn content on microstructure and mechanical performance in Bi1.8Sr2Ca2Cu3.2−xZnxO10+δ glass ceramic

In this study, we have investigated the effects of Zn doping on structural and mechanical properties of Bi_1.8Sr₂Ca₂Cu_3.2?xZn_xO_10+δ ceramic samples with x = 0.0, 0.1, 0.5, 1.0. The prepared samples were characterized by using scanning electron microscope (SEM), energy dispersive spectroscopy (EDS), X-ray powder diffractometer (XRD) and static microhardness indenter. Surface morphology, orientation of grains and elemental composition analysis of the samples were investigated by SEM and EDS measurements, respectively. Texturing and lattice parameters a, b and c were determined from the XRD measurements. In this work we focused on Vickers microhardness measurements in order to characterize the mechanical properties. Experimental results of Vickers microhardness measurements were analyzed by using Meyer’s law, the elastic/plastic deformation model, proportional sample resistance model (PSR), modified PSR model, Hays–Kendall (HK) approach and indentation induced cracking (IIC) model. According to the obtained results, HK approach is the most suitable model for the CZn00 sample showing indentation size effect behavior and IIC Model is the most suitable model for the CZn01, CZn05 and CZn10 samples showing reverse indentation size effect behavior.     

含泡沫铝芯的复合板弯曲疲劳行为的研究

应用表面位移原位分析技术对由泡沫金属铝芯和金属面板组成的三层复合板在循环弯曲载荷条件下的损伤行为进行了观察和研究。循环弯曲载荷条件下复合板失效的基本方式是表面凹陷（Indentation，ID）和泡沫铝内芯切断（Coreshear，CS）。凹陷型失效是与加载压头接触的复合板表面局部压缩密切相关，该处沿垂直方向的压缩应变最大。内芯切断型失效是泡沫铝内芯中切应变最大的区域发生的剪切破坏。在疲劳应力比R=0时，复合板凹陷型失效的疲劳极限高于内芯切断型失效的疲劳极限。     

Fabrication methods for auxetic foams

Auxetic materials have a negative Poisson's ratio, that is, they expand laterally when stretched longitudinally. Negative Poisson's ratio is an unusual property that affects many of the mechanical properties of the material, such as indentation resistance, compression, shear stiffness, and certain aspects of the dynamic performance. The unusual mechanical properties of auxetic foams are attributed to the deformation characteristics of re-entrant microstructures. One way of obtaining negative Poisson's ratio is by using a re-entrant cell structure. Auxetic foam was fabricated from a conventional polymeric foam. The fabrication method for making both small and large auxetic foam specimens is described. This revised version was published online in November 2006 with corrections to the Cover Date.     

Effective elastic properties of auxetic microstructures: anisotropy and structural applications

Materials presenting a negative Poisson’s ratio (auxetics) have drawn attention for the past two decades, especially in the field of lightweight composite structures and cellular media. Studies have shown that auxeticity may result in higher shear modulus, indentation toughness and acoustic damping. In this work, three auxetic periodic microstructures based on 2D geometries are considered for being used as sandwich-core materials. Elastic moduli are computed for each microstructure by using finite elements combined with periodic homogenization technique. Anisotropy of elastic properties is investigated in and out-of-plane. Comparison is made between auxetics and the classical honeycomb cell. A new 3D auxetic lattice is proposed for volumic applications. Cylindrical and spherical elastic indentation tests are simulated in order to conclude on the applicability of such materials to structures. Proof is made that under certain conditions, auxetics can be competitive with honeycomb cells in terms of indentation strength. Their relatively soft response in tension can be compensated, in some situations, by high shear moduli.