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.     

剪切和扭转工况下微纳米薄壁蜂窝的等效剪切模量计算

分别针对剪切和扭转两种工况给出了微纳米薄壁蜂窝等效剪切模量的解析计算方法.该方法综合考虑了由面板对芯层的约束导致的高度效应和当蜂窝胞壁厚度进入微纳米量级时引起的尺度效应.首先对蜂窝各胞壁选取了可反映面板约束以及受力状态的三角级数位移场,然后在本构关系中引入修正偶应力理论以描述尺度效应,最后应用能量均匀化方法求得蜂窝的等效剪切模量.以典型六边形蜂窝为例,给出了完整的计算过程和结果.与文献中的等效剪切模量结果进行对比,讨论了不同工况下等效剪切模量随芯层高度和胞壁厚度的变化趋势,以及高度效应和尺度效应之间的相互影响.     

Bending tests to estimate the axial force in slender beams with unknown boundary conditions

This paper presents a static method for the axial load identification of slender prismatic beams with uncertain length and unknown boundary conditions as is typical of struts and ties of truss structures or tie-rods of arches and vaults. The proposed method requires the knowledge of the beam flexural rigidity only. Flexural displacements or curvatures are measured at five cross sections of the beam subjected to an additional concentred lateral load. Unlike analogous dynamic methods, any set of experimental data may be used in the identification algorithm. The proposed algorithm is verified by means of many numerical and experimental tests on beams having different boundary conditions. Excellent estimates of the axial forces are obtained when the greatest possible distance between sensors is adopted, even if in the presence of high values of the axial forces very accurate displacement measurements are required.     

不同围压下含天然贯通节理岩石卸载破坏机理研究

二郎山特长高速公路隧道断裂带较多,受此影响,隧道开挖后岩爆灾害十分严重．从此隧道中取样制备成含天然贯通节理试件,进行常规单轴压缩室内试验,获取基本力学参数和破坏模式．本文以室内实验结果为依据,确定数值试验时所采用的岩石和节理的力学参数,利用RFPA软件开展数值试验,研究了不同围压同轴向荷载下卸掉围压诱发岩石失稳破坏机理．试验结果表明,五种不同围压(5、10、15、20、25 MPa)卸载后应力-应变曲线均呈“断崖式”跌落,试样均突然破坏,与现场岩爆情况吻合;受贯通节理影响,不同围压试样的具体破坏形态、声发射数量最大值出现时刻有所差异;在卸载阶段五种试样声发射累积数量都突然急剧增大．     

用动态光弹性法研究炮身膛线的脱落问题

本文利用动态光弹性法研究了炮膛膛线脱落的机理。用包含五条膛线的部分炮筒横截面或扇形平面模型,在六种不同的载荷状态下进行了实验。得到了不同载荷状态下,不同瞬时的等差线条纹图的系列照片,以及膛线根部不同瞬时的应力分布曲线。结果表明:当一条或相邻数条膛线顶端受到足够大的均布冲击载荷时,将在承载膛线两侧根部的应力极值点出现膛线脱落的起裂点,而形成八字形脱落;而对非均布的其它几种冲击载荷,膛线都不会出现八字形脱落。     

气动加载与振动激励耦合试验方法研究

飞机结构在飞行过程中同时承受气动载荷和振动载荷的联合作用,这两种载荷的耦合加载试验对于飞机结构成为一项重要的研究内容,所以有必要对此类试验的可行性及其耦合加载方式进行研究。此次试验以气囊加载静载/常规疲劳载荷状态下试件的振动响应测试为目的,设计符合试验要求的试件和整套试验装置。得到了气囊5种不同加载情况下试件振动响应变化情况,并对此试验结果进行了理论分析,得出以下结论:a)气囊模拟静载/常规疲劳载荷加载不会大幅改变结构本身振动特性,此耦合试验方法所模拟环境比较接近飞机结构真实载荷环境;b)加载气囊的个数、部位及加载力的不同对试件结构的振动响应有一定影响,应增加气囊蓄能器或在试验前进行分析以选择合理的加载点。     

基于有限元-时域分段自适应算法的围岩衬砌耦合渐进分析

以开挖时间、一衬时间、二衬时间划分时间区段,考虑围岩与衬砌为弹性/粘弹性介质,将围岩的“位移/应力释放不完全”、开挖等影响模拟为载荷的渐进释放,提出一个有限元-时域分段自适应算法,求解围岩衬砌耦合问题,并通过数值算例对算法进行了验证。所提方法给出了各时间区段的关联条件;可更准确描述各变量随时间的变化;同时将原时空耦合问题转化为一系列空间问题,并利用有限元方法递推求解;当步长变化时可通过自适应计算保证稳定的计算精度。此外,还建立了一个载荷渐进参数的反问题数值求解模型,并给出了相关算例。     

基于有限元-时域分段自适应算法的围岩衬砌耦合渐进分析

以开挖时间、一衬时间、二衬时间划分时间区段,考虑围岩与衬砌为弹性/粘弹性介质,将围岩的“位移/应力释放不完全”、开挖等影响模拟为载荷的渐进释放,提出一个有限元-时域分段自适应算法,求解围岩衬砌耦合问题,并通过数值算例对算法进行了验证.所提方法给出了各时间区段的关联条件;可更准确描述各变量随时间的变化;同时将原时空耦合问题转化为一系列空间问题,并利用有限元方法递推求解;当步长变化时可通过自适应计算保证稳定的计算精度.此外,还建立了一个载荷渐进参数的反问题数值求解模型,并给出了相关算例.     

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical buckling load. The present investigation may be of some help in further understanding the mechanical properties of MWNTs.     

Improved normalization method for ductile fracture toughness determination based on dimensionless load separation principle

This study successfully deals with the inhomogeneous dimension problem of load separation assumption, which is the theoretical basis of the normalization method. According to the dimensionless load separation principle, the normalization method has been improved by introducing a forcible blunting correction. With the improved normalization method, the J-resistance curves of five different metallic materials of CT and SEB specimens are estimated. The forcible blunting correction of initial crack size plays an important role in the J-resistance curve estimation, which is closely related to the strain hardening level of material. The higher level of strain hardening leads to a greater difference in JQ determined by different slopes of the blunting line.If the blunting line coefficient recommended by ASTM E1820-11 is used in the improved normalization method, it will lead to greater fracture resistance than that processed by the blunting line coefficient recommended by ISO 12135-2002. Therefore, the influence of the blunting line on the determination of JQ must be taken into full account in the fracture toughness assessment of metallic materials.     

Development of a load-cell compensation system

When a materials testing machine is used dynamically, the force recorded by the load cell may differ from that experienced by the specimen. This error is caused by the mass of the load string, usually the grip, between the specimen and the load cell.The equations of motion for a testing machine are developed and the parameters affecting the error are identified. A system is described which removes the inertia error from the load-cell output by measurement of the acceleration of the mass. The effectiveness of the technique is assessed by the use of strain-gaged reference specimens, of different stiffnesses, for comparison with the load-cell output. Two methods for calibrating the system are used and their merits assessed.     

VIBRATION ANALYSIS OF A BEAM WITH EMBEDDED SHAPE MEMORY ALLOY WIRES

In this study, analytical relations for evaluating the exact solution of natural fre- quency and mode shape of beams with embedded shape memory alloy （SMA） wires are presented. Beams are modeled according to Euler-Bernoulli, Timoshenko and third order beam （Reddy） the- ories. A relation is obtained for determining the effect of axial load generated by the recovery action of pre-strained SMA wires. By defining some dimensionless quantities~ the effect of different me- chanical properties on the frequencies and mode shapes of the system are carefully examined. The effect of axial load generated by SMA wires with buckling load and frequency jump is accurately studied.     

杆系结构静强度和疲劳失效机理及可靠性分析

根据疲劳载荷造成的疲劳累积损伤对结构极限承载力的影响情况,讨论了结构系统承载能力的可靠度计算方法,分析了结构系统中每一个单元在静载和疲劳载荷作用下的两种失效模式,并考虑了二者之间的相关性对该单元可靠性的影响,具体分析了结构系统在这两种载荷作用下的失效机理,给出了在这两种载荷作用下结构系统的可靠性分析方法. 算例表明,在不同的使用年限内,静载和疲劳载荷对结构系统可靠性的影响是不同的;在结构系统主要失效路径中既有单元静强度失效又有单元疲劳失效,这是符合结构系统使用真实情况的.     

Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites

The load transfer mechanisms and effective moduli of single-walled nanotube (SWNT) reinforced composites are studied using a continuum model. A “critical” fiber length is defined for full load transfer by numerically evaluating the strain-energy-changes for different fiber lengths. The effective longitudinal Young’s modulus and bulk modulus of the composite are derived. The effect of the interphase is also discussed. The results indicate the fiber length is critical both to the load transfer efficiency and effective moduli of the composite. The SWNT-matrix interphase plays an important role in load transfer efficiency but affects the effective moduli only slightly.     

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

The generalized differential quadrature method (GDQM) is employed to consider the free vibration and critical speed of moderately thick rotating laminated composite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton’s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points lying on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical technique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.     

Foam mechanics: nonlinear response of an elastic 3D-periodic microstructure

The compressive response of a 3D open-cell foam with periodic tetrakaidecahedral cells is studied through combined theoretical and numerical efforts. Under compressive loading the response is characterized by an extended load plateau following the relatively sharp rise to a maximum load. Several processes of loading have been simulated numerically using appropriately nonlinear kinematics. The onset of failure under macroscopic loading conditions is shown to be the reason of the load plateau. A failure surface is defined in macroscopic stress space by the onset of the first buckling-type instability encountered along proportional load paths. The analysis is carried out through two methods. The first one consists in increasing specimen size with periodic boundary conditions leading to the termed microfailure surface. The second one consists in considering both periodic and nonperiodic displacements variations on a minimum unit cell. The resulting failure surfaces are shown to coincide. Moreover, the postbuckling analysis has been carried out for two particular loadings: the uniaxial compression and the uniaxial deformation.     

Simulation of stochastic loads for fatigue experiments

A simple direct simulation method for stochastic fatigue-load generation is described in this paper. The simulation method is based on the assumption that only the peaks of the load process significantly affect the fatigue life. The method requires the conditional distribution functions of load ranges given the last peak values. Analytical estimates of these distribution functions are presented in the paper and compared with estimates based on a more accurate simulation method. In the more accurate simulation method samples at equidistant times are generated by approximating the stochastic load process by a Markov process. Two different spectra from two tubular joints in an offshore structure (one narrow banded and one wide banded) are considered in an example. The results show that the simple direct method is quite efficient and results in a simulation speed of about 3000 load cycles per second using a personal computer. Finally the proposed simulation method for fatigue-load generation is tested by comparing some fatigue damage measures obtained by the simulation methods.     

Thickness reduction rate of plastically compressed metal plate by hardened rollers

The rate at which a solid deforms permanently depends on the load history, geometry and material properties. When a metal plate is compressed between two hardened rollers, its thickness reduces continuously if the material elements are deformed beyond their elastic limits. Those near the region of contact will experience more distortion as compared with those interior to the plate. This effect is analyzed incrementally in time by the theory of plasticity coupled with the strain energy density criterion. Failure is examined by assuming that the location of crack initiation coincides with the maximum of the minimum strain energy density function, (dW/dV)_min^max, when reaching its critical value. This is found to occur at the center of the plate depending on the rate of deformation. An increase in plate thickness reduction without failure can be achieved by taking smaller loading steps. Displayed graphically are numerical results for five different load histories that provide useful insights into the rate dependent process of metal forming.     

Load enhancement effects by polymer-thickened oils in strip squeeze film flow

A modification to existing equipment is described which permits continuous squeeze-film flow to be obtained between parallel-sided strips of material rather than between disc-shaped surface. Squeeze film flow is simulated by having liquid move through one of the surfaces via an array of equispaced holes. The Squeeze-film behavior of a Newtonian base oil is first tested at temperatures of 24°C and 55°C. It is shwon that loads are in reasonable agreement with theretical predictions and that end effects (corrected by means of a guard ring) and fluid maldistribution effects are of small proporitons. At the very highest liquid flowrates, the rapid liquid flow through the holes may influence the measured load. The Polymer-thickened oils, representinhg 10 W/30 and 10 W/50 motor oils, are tested at temperatures of 24°C and 55°C. Both oils five marked load enhancement, compared with Newtonian oil under similar flow conditions, at the higher flowrates used. The 10 W/50 oil gives load enhancement of 76 per cent at 55°C, increasing rapidly with the simulated approach velocity. Fluid inertia effects in the squeeze film flow aslo increase the load significantly. The results confirm earlier data using disc-shaped surfaces; load enhancement is greater in the present work on strip squeeze films because the fluid deformation rates are greater (2000 s^t-1 in planar extention and 2 x 10⁵ s^t-1 in shear). It is suggested that the fuel consumption of cars could be improved by the development of elastic, shear stable oils of lower viscosity than those currently in use.