Strength modeling of brittle materials with two- and three-dimensional pore structures

Strength under compression of highly porous aerated autoclaved concrete was modeled by means of Finite Element Analysis of the porous microstructure. The complex microstructure of aerated autoclaved concrete is characterized by three hierarchical levels of pores. Strength and failure behaviour is controlled by large artificial air pores (AAP) with a mean diameter of 0.5–3 mm. Stress distribution in the brittle matrix material under external load was calculated by FEA for different pore arrangements. Based on the stress distribution multiaxial Weibull Theory was used to predict failure probability with regard to the porous microstructure. Two- and three-dimensional ordered pore arrangements show an exponential decrease of strength with porosity in the range of 0–0.4, depending on the Weibull parameter m of the matrix material. Strength vs. porosity relation differs significantly for pore structures with simple cubic and body centered cubic pore arrangements. The compatibility of two-dimensional with three-dimensional models is examined.     

Fabrication of Lotus‐type Porous Metals and their Physical Properties

Lotus‐type porous metals whose long cylindrical pores are aligned in one direction were fabricated by unidirectional solidification in a pressurized gas atmosphere. The pores are formed as a result of precipitation of supersaturated gas when liquid metal is solidified. The lotus‐type porous metals with homogeneous size and porosity of the evolved pores produced by a mould casting technique are limited to the metals with high thermal conductivity. On the other hand, the pores with inhomogeneous pore size and porosity are evolved for metals and alloys with low thermal conductivity such as stainless steel. In order to obtain uniform pore size and porosity, a new “continuous zone melting technique” was developed to fabricate long rod‐ and plate‐shape porous metals and alloys even with low thermal conductivity. Mechanical properties of tensile and compressive strength of lotus‐type porous metals and alloys are described together with internal friction, elasticity, thermal conductivity and sound absorption characteristics. All the physical properties exhibit significant anisotropy. Lotus‐type porous iron fabricated using a pressurized nitrogen gas instead of hydrogen exhibits superior strength.     

Anisotropic compressive properties of porous copper produced by unidirectional solidification

Porous copper whose long cylindrical pores are aligned in one direction has been fabricated by unidirectional solidification of the melt in a mixture gas of hydrogen and argon. The compressive yield strength of the porous copper with the cylindrical pores orientated parallel to the compression direction decreases linearly with increasing porosity. For the porous copper whose pore axes are perpendicular to the compressive direction, the compressive yield strength slightly decreases in the porosity range up to 30% and then decreases significantly with increasing porosity. The compressive stress–strain curves depend on the compressive direction with respect to the pore direction, which are due to the stress concentration around the pores and the buckling of the copper between the pores. From two different types of stress–strain curve, the energy absorption capacity of the porous copper with the pores parallel to the compressive direction is higher than that perpendicular to the compressive direction at a given porosity.     

Strength and pore morphology of porous aluminum and porous copper with directional pores deformed by equal channel angular extrusion

Porous aluminum with a porosity of 17.6% and porous copper with a porosity of 39.7% (the pores of both aluminum and copper were cylindrical and oriented in one direction) were deformed by equal channel angular extrusion using a 150° die with sequential 180° rotations (route C), and the mechanical strength and pore morphology after the extrusions were investigated. In the case of porous aluminum with low porosity, the pores were collapsed by the extrusions that were both parallel and perpendicular to the orientation direction of the pores. In contrast, the porosity of porous copper decreased slightly after extrusions that were parallel to the orientation direction of the pores, and the pores thus remained even after four extrusions. The yield strength after the second extrusion was 7.3 times greater than it was before the extrusion, even though there was a decrease in porosity of only 8%. On the other hand, almost all the pores of the porous copper collapsed after the fourth extrusion, when the extrusion direction was perpendicular to the orientation direction of the pores. Thus, the yield stress cannot be enhanced without being accompanied by progressive densification.     

叔丁醇基凝胶注模工艺制备轻质、高强莫来石多孔陶瓷

以叔丁醇为成型溶剂, 莫来石粉为起始原料, 采用凝胶注模成型方法制备出轻质、高强莫来石多孔陶瓷. 莫来石多孔陶瓷中的孔隙形成于干燥过程中叔丁醇的快速挥发, 孔隙分布均匀且相互连通. 随烧结温度升高, 气孔率、开气孔率和比表面积分别由77.8%、76.0%和10.39m²/g下降到67.6%、65.5%和4.26m²/g, 而抗压强度则由3.29MPa显著提高到32.36MPa, 材料孔径大小受烧结温度影响较小, 孔径尺寸呈单峰分布, 且几乎所有的气孔都为开口气孔, 透气度与孔径尺寸具有一致的变化关系. 莫来石多孔陶瓷在高气孔率条件下仍然保持高强度的主要原因是材料中均匀的孔隙结构、孔径尺寸小且相对集中、以及因烧结颈的形成在空间上所表现出的一种颗粒搭接骨架结构.     

Effects of pores on shear bands in metallic glasses: A molecular dynamics study

The effects of nanoscale pores on the strength and ductility of porous Cu₄₆Zr₅₄ metallic glasses during nanoindentation and uniaxial compression tests are modelled and investigated using molecular dynamics (MD) simulations. In the MD simulations, atomistic amorphous samples were digitally prepared through fast quenching from the liquid states of copper and zirconium alloy. In both of the nanoindentation and uniaxial compression simulations, shear transformation zones and shear bands are observed through the local deviatoric shear strains in the samples. The results show that the existence of pores causes strain concentrations and greatly promotes the initialization and propagation of shear bands. Importantly, only pores reaching critical size can effectively facilitate the formation of multiple shear bands. It is also observed that hardening occurs through pore annihilation and the shear band stops in porous metallic glasses.     

Preparation of 3-D regenerated fibroin scaffolds with freeze drying method and freeze drying/foaming technique

Although three-dimensional fibroin scaffolds have been prepared with freeze drying method, the porosity and pore sizes still can not satisfy the requirement of tissue engineering. In this article, fibroin porous scaffold with high porosity and > 100μm diameter interconnected pores was firstly prepared with freeze drying method through adjusting fibroin concentration. The morphology of different scaffolds lyophilized from different fibroin concentration was observed by SEM. A novel freeze drying improved method, freeze drying/foaming technique, was also devised to prepare fibroin scaffolds at different fibroin concentrations. Using the said method, the porosity and pore size of fibroin scaffolds prepared from 12% concentration were 85.8 ± 4% and 109 ± 20 μm respectively with yield strength up to 450 ± 6 KPa while the porosity and pore size of fibroin scaffolds prepared from 8% concentration were 96.9 ± 3.6% and 120 ± 30 μm respectively with yield strength up to 30 ± 1 KPa. The freeze drying/foaming technique produced scaffolds with a useful combination of high yield strength, interconnected pores, and pore sizes greater than 100 μm in diameter. Through adjusting fibroin concentration and thawing time, the porosity, pore sizes and mechanical properties could be controlled to satisfy the different requirements of tissue engineering. The results suggested that fibroin scaffolds prepared with the above methods could be formed for utility in biomaterial application.     

多孔PZT95/5铁电陶瓷的机械性能和铁电性能研究

采用添加造孔剂的方法制备多孔锆钛酸铅(PZT95/5)铁电陶瓷, 研究了孔结构包括孔隙率、孔径及孔形状对多孔PZT95/5陶瓷机械性能和电性能的影响及机理, 并揭示多孔PZT95/5陶瓷微观结构、机械性能和铁电性能的内在联系。研究表明: 孔隙率的增加降低了多孔PZT95/5陶瓷的声阻抗, 改善了陶瓷与封装材料的声阻抗匹配. 孔隙率增加, 多孔PZT95/5陶瓷的屈服应力和剩余极化强度降低, 矫顽场强增大。孔结构对多孔PZT95/5陶瓷屈服应力的影响可由应力集中理论解释; 多孔PZT95/5陶瓷剩余极化强度随孔结构的变化可用内应力结合空间电荷理论加以解释。     

Synthesis and structural control of Fe-based porous layer on Fe substrate for joining with resin parts using combustion reaction

A porous Fe/TiB₂ composite layer was synthesized on an Fe substrate by a powder metallurgy process using combustion reactions among Fe, Ti, and B to achieve Fe/resin joints through interpenetrating phase layers. The effects of Fe particle size and the blending ratio of the raw powder mixture on the porous structure, roughness of the top surface of the porous layer, and adhesiveness between the porous layer and Fe substrate were investigated. The peak temperature measured with a thermocouple increased with increasing Fe particle size and blending ratio of Ti and B. An increase in the peak temperature does not affect the porosity of the porous layer. Higher peak temperatures increase the pore size and change the pore morphology from open to semi-closed (although pores are not completely isolated). The change in pore morphology prevents the exposure of pores on the top surface of the porous layer, resulting in decreasing surface roughness. Moreover, an increase in the maximum temperature promotes bonding between the Fe substrate and porous layer. These results are discussed in view of the thermodynamic assessment using the calculated equilibrium phase diagram.     

Porous NiTi by creep expansion of argon-filled pores

NiTi powders are densified in the presence of argon gas, whose initial pressure is varied between 1 and 33 atm, to create NiTi billets containing isolated Ar-filled pores. Upon vacuum annealing, the pressurized pores expand by creep of the surrounding NiTi matrix at rates which are in agreement with a simple analytical model up to 16% porosity. Beyond this porosity, foaming becomes very slow, as pores connect with each other and with the specimen surface where the gas escapes. This is due to failure of previous NiTi powder boundaries weakened by oxides insoluble in NiTi; this mechanism does not occur in Ti foams which dissolve their oxides at high temperature, allowing higher levels of pore expansion and foam porosity. NiTi with 10–16% porosity exhibits Young's moduli of 48–57 GPa, and may be useful for high-strength, low stiffness biomedical implants with superelastic or shape-memory properties.     

Thermal shock resistance of the porous Al2O3/ZrO2 ceramics prepared by gelcasting

Porous Al₂O₃/ZrO₂ ceramics with porosity varying from 6% to 50% were fabricated by gelcasting using polystyrene (PS) as pore-forming agent. The effects of sintering temperature on porosity, strength as well as pore size were investigated. The flexural strength of these porous ceramics at room temperature significantly decreases as the porosity increases. Thermal shock resistance of these ceramics was improved by increasing the porosity. Both the critical difference temperature (ΔT_c) and residual strength of high porosity ceramics were higher than those of low porosity ceramics. These improvements can be attributed to the pores in the specimens which relax the thermal shock stress and arrest the propagation of microcracks effectively, which is confirmed by XRD analysis of specimens which encountered different thermal shock temperature difference.     

Fabrication, properties and application of porous metals with directional pores

This paper reviews the recent development of fabrication methods, various properties of porous metals with directional pores and its applications. This porous metals are fabricated by unidirectional solidification in pressurized gas atmosphere such as hydrogen, nitrogen and oxygen. The pores are evolved from insoluble gas when the melt metal dissolving the gas is solidified. The nucleation and growth mechanism of the directional pores in metals are discussed in comparison with a model experiment of carbon dioxide pores in ice. Three fabrication techniques, mold casting, continuous zone melting and continuous casting techniques, are introduced. The latter two techniques can control the solidification velocity and the last one possesses a merit for mass production. The porosity and pore size are able to be controlled by solidification velocity and ambient gas pressure, while the pore direction can be controlled by solidification direction. Not only metals and alloys but also intermetallic compounds, semiconductors and ceramics can be produced by this method. Anisotropy in the mechanical and physical properties is resulted from anisotropic pore morphology. The experimental results on the anisotropy in the elastic property and electrical conductivity are consistent with those calculated with an effective-mean-field theory. The anisotropic behaviors of tensile, compressive and fatigue strength are explained in terms of the dependence of stress concentration on the pore orientation. This porous metals exhibit good sound absorption and vibration-damping properties. Several possible applications are in progress for heat sink, golf putter, biomaterials and so on.     

Macroscopic response and microstructure evolution in viscoplastic polycrystals with pressurized pores

This paper presents a finite-strain homogenization model for the macroscopic behavior of porous polycrystals containing pressurized pores that are randomly distributed in a polycrystalline matrix. The porous polycrystal is modeled as a three-scale composite, where the pore size is taken to be much larger than the grain size, and the grains are described by single-crystal viscoplasticity. The instantaneous macroscopic response and corresponding field statistics in the material are determined using a generalization of the recently developed iterated second-order homogenization method, which employs the effective behavior of a linear comparison composite to estimate that of the nonlinear composite by means of a suitably designed variational approximation. Moreover, consistent evolution laws are derived for the pore pressure, pore geometry, and the underlying texture for the polycrystalline matrix. The model is then used to investigate porous ice polycrystals under a wide range of loading conditions. It is found that the pore pressure evolution has a strong effect on the material’s response under compressive loadings. More specifically, the macroscopic response of the porous polycrystals can be categorized into three different regimes: (i) a texture-controlled regime at low triaxialities, where the materials behave like solid polycrystals; (ii) a porosity-controlled regime at high triaxialities, where the materials behave like porous untextured materials; and (iii) a transition regime at intermediate triaxialities, where the materials exhibit a more complex behavior. This work highlights the importance of accounting for the interplay between porosity and matrix texture evolution in describing the constitutive response of porous polycrystals undergoing finite deformations.

     

Ti-C含量对多孔TiC/FeAl复合材料孔型结构和力学性能的影响

以尿素为造孔剂,利用自蔓延高温合成技术制备了多孔TiC/FeAl复合材料,主要考察了Ti-C含量（质量分数为15wt%~35wt%）对多孔TiC/FeAl复合材料孔型结构和压缩性能的影响。当Ti-C含量不高于25wt%时,多孔TiC/FeAl复合材料由毫米孔和孔壁微孔组成规则的复合孔型结构。相互连通的毫米孔产生于尿素颗粒的挥发和液相迁移;微孔尺寸为10~50 μm,产生于Fe-Al-Ti-C粉末的自蔓延过程,孔径随Ti-C含量的增加而增大。通过调整尿素的体积分数,多孔TiC/FeAl复合材料的孔隙率可控制在56.64%~85.35%。当Ti-C含量不高于25wt%时,多孔TiC/FeAl复合材料的抗压强度随Ti-C含量的增加而增大。当Ti-C含量高于25wt%时,多孔TiC/FeAl复合材料壁面微孔形状很不规则,且抗压强度下降。孔隙率约为64.3%时,多孔Fe-Al金属间化合物和TiC/FeAl复合材料（Ti-C含量为25wt%）的抗压强度分别为20.03 MPa和66.68 MPa,对应的应变值分别为4.77%和8.21%。另外,多孔TiC/FeAl复合材料的压缩性能可用Gibson-Ashby模型来解释。     

A coupled discrete element‐finite difference approach for modeling mechanical response of fluid‐saturated porous materials

A model of fluid‐saturated poroelastic medium was developed based on a combination of the discrete element method and grid method. The developed model adequately accounts for the deformation, fracture, and multiscale internal structure of a porous solid skeleton. The multiscale porous structure is taken into account implicitly by assigning the porosity and permeability values for the enclosing skeleton, which determine the rate of filtration of a fluid. Macroscopic pores and voids are taken into account explicitly by specifying the computational domain geometry. The relationship between the stress–strain state of the solid skeleton and pore fluid pressure is described in the approximations of simply deformable discrete element and Biot's model of poroelasticity. The developed model was applied to study the mechanical response of fluid‐saturated samples of brittle material. Based on simulation results, we constructed a generalized logistic dependence of uniaxial compressive strength on loading rate, mechanical properties of fluid and enclosing skeleton, and on sample dimensions. The logistic form of the generalized dependence of strength of fluid‐saturated elastic–brittle porous materials is due to the competition of two interrelated processes, such as pore fluid pressure increase under solid skeleton compression and fluid outflow from the enclosing skeleton to the environment. Copyright © 2015 John Wiley & Sons, Ltd.     

Study on β-TCP Coated Porous Mg as a Bone Tissue Engineering Scaffold Material

Three-dimensional honeycomb-structured magnesium (Mg) scaffolds with interconnected pores of accurately controlled pore size and porosity were fabricated by laser perforation technique. Biodegradable and bioactive β- tricalcium phosphate (β-TCP) coatings were prepared on the porous Mg to further improve its biocompatibility, and the biodegradation mechanism was simply evaluated in vitro. It was found that the mechanical properties of this type of porous Mg significantly depended on its porosity. Elastic modulus and compressive strength similar to human bones could be obtained for the porous Mg with porosity of 42.6%-51%. It was observed that the human osteosarcoma cells (UMR106) were well adhered and proliferated on the surface of the β- TCP coated porous Mg, which indicates that the β-TCP coated porous Mg is promising to be a bone tissue engineering scaffold material.     

Preparation and properties of a new porous ceramic material used in clean energy field

At high temperature, the oxide redox reactions of ceria can split H₂O and CO₂ to produce H₂ and CO, so porous ceria with high temperature resistance and high specific surface area has an important foreground in clean energy applications. In this work, a reticulated porous ceria ceramic material with interconnected porous structure was prepared by the impregnation technique using organic polyurethane sponges as template. The influences of pretreated sponge, dipping time length, pore size and sintering temperature on the porosity and strength of the porous ceria ceramics were systematically studied. With the increasing sintering temperature, the glass phase occurred and led to an increase in strength, but an decrease in porosity. Eventually, we analyzed the relationships between porosity and strength of these porous materials, aiming to provide theoretical and practical references for its application in clean-energy field.     

Effects of porosity and pore distribution on static strength properties of porous zirconia

Bulk porosity, along with size and spatial distribution of pores, play key roles in strength of porous ceramics, as reported in a study on porous alumina. Hence, a fracture mechanics procedure was proposed to evaluate their strength by presuming that behavior of pore distribution is equivalent to that of crack distribution, and each pore is surrounded by virtual crack. In contrast to alumina, zirconia has distinct spherical‐shaped pores. Moreover, its strength properties vary with stabilizing additives. In this research, strength properties of yttria‐stabilized zirconia ceramics were studied to verify applicability of the procedure proposed for simulating strength of porous ceramics. The effect of pore characteristics on static strength properties was determined experimentally and confirmed by Monte‐Carlo simulations. It was revealed that simulated strength coincided with experimental results within a narrow scatter band, ie, factor of 2^1/2. Therefore, the proposed procedure was found to be appropriate for estimating strength of porous zirconia.     

Elastoplastic mechanics of porous materials with varied inner pressures

A micromechanics model and a computational homogenization method were developed to examine the macroscopic elastoplasticity and yield behavior of closed-cell porous materials with varied inner gas pressures. For the uniaxial stress–strain relation of the porous material, the micromechanics model coincides well with the numerical homogenization, especially for the case of relatively low porosity and gas pressures. The effects of the combination of the different gas pressures on the uniaxial stress–strain curve, the nominal Poisson’s ratio, yield surface and initial yield strength of the material are systematically investigated. The multiple gas pressures can induce the tension–compression asymmetry of the uniaxial stress–strain curves and the nominal Poisson’s ratio of nonlinear deformation. In particular it is shown that when the multiple gas pressures coincide, the yield surface of the porous material with inner gas pressures can be simply obtained from that of the porous material without inner pressures by a shift along the negative direction of the hydrostatic stress axis. However, when the multiple pressures are different, in addition to a translation along the hydrostatic axis, the yield surface undergoes a change in shape and size, and the maximal equivalent stress is lowered by a difference in gas pressures. Furthermore, the multiple gas pressures have a significant effect to reduce the yield strength of the closed cell porous materials.