饱和岩石滞弹性弛豫机理的实验研究

通过Metravib热机械分析仪,用正弦波加载方式,模拟地震波的传播。实验时固定静载为100N,正弦波动载荷恒为60N,将总载荷控制在屈服点以下。在温度为-50℃~90℃,升温速率保持在1℃/分,频率为5Hz~400Hz的条件下,对饱和泵油彭山砂岩和遂宁砂岩样品进行单轴循环加载实验,获得饱和泵油彭山砂岩和遂宁砂岩的衰减、虚模量、实模量、波速与温度和频率以及动载荷的关系。以此研究了饱和多孔岩石的衰减和虚模量、杨氏模量和弹性波波速随温度和频率的动态响应。取得了随频率增高,饱和多孔岩石的衰减峰和虚模量峰的峰位向高温方向移动的热激活弛豫机制。杨氏模量和弹性波波速随温度升高而下降,随频率增高而增大,具有频散效应;杨氏模量和弹性波波速随动载荷振幅的增大而降低。这些结果与低频共振的驻波实验取得了同样的热激活弛豫规律,说明热激活弛豫规律具有一定的普适性。     

A procedure for estimating Young’s modulus of textured polycrystalline materials

In this study, a procedure for estimating Young’s modulus of textured and non-textured polycrystalline materials was examined based on finite element analyses, which were performed using three-dimensional polycrystalline finite element models of a random structure, generated using the Voronoi tessellation. Firstly, the local stress/strain distribution and its influence on macroscopic elastic properties were evaluated. Then, the statistical relationship between Young’s modulus obtained from the finite element analyses and averaged Young’s modulus of all grains evaluated based on Voigt’s or Reuss’ model was investigated. It was revealed that the local stress/strain in the polycrystalline body is affected by crystal orientation and deformation constraint caused by adjacent grains, whereas only the crystal orientation affects Young’s modulus of the polycrystalline body when the number of grains is large enough. It was also shown that Young’s modulus correlates well with the averaged Young’s modulus of all grains, in which the size of grains is considered in the averaging. Finally, a procedure for estimating Young’s modulus of textured and non-textured materials was proposed. Young’s modulus of various materials can be estimated from the elastic constants of single crystal and the distribution of crystal orientation and size of grains, which can be obtained by using electron backscatter diffraction (EBSD).     

Characterization of mechanical properties of aluminum cast alloy at elevated temperature

The tensile response, the low cycle fatigue(LCF) resistance, and the creep behavior of an aluminum(Al) cast alloy are studied at ambient and elevated temperatures.A non-contact real-time optical extensometer based on the digital image correlation(DIC)is developed to achieve strain measurements without damage to the specimen. The optical extensometer is validated and used to monitor dynamic strains during the mechanical experiments. Results show that Young's modulus of the cast alloy decreases with the increasing temperature, and the percentage elongation to fracture at 100℃ is the lowest over the temperature range evaluated from 25℃ to 300℃. In the LCF test, the fatigue strength coefficient decreases, whereas the fatigue strength exponent increases with the rising temperature. The fatigue ductility coefficient and exponent reach maximum values at 100℃. As expected, the resistance to creep decreases with the increasing temperature and changes from 200℃ to 300℃.     

Measurement of Elastic Properties of Epoxy Molding Compound by Single Cylindrical Configuration with Embedded Fiber Bragg Grating Sensor

We propose a novel experimental method, based on a fiber Bragg grating (FBG) sensor, to measure the elastic properties of epoxy molding compound (EMC) from a single specimen configuration. The FBG sensor is embedded in the center of a cylindrical EMC specimen, and deforms together with the EMC. The Bragg wavelength (BW) shifts are documented during compressive and hydrostatic loadings. Young’s modulus and bulk modulus are determined from the BW shifts using the relationships between the elastic constants and the BW shift. Two major developments to accommodate the unique requirements of EMC testing include: (1) a large mechanical pressure to be applied during curing; and (2) a very high gas pressure required for hydrostatic testing. The shear modulus and Poisson’s ratio are calculated from the two measured constants to provide a complete set of elastic properties of EMC.     

Large In-plane Deformation Mapping and Determination of Young’s Modulus of Rubber Using Scanner-Based Digital Image Correlation

Experimental Techniques - We propose a novel scanner-based digital image correlation (DIC) method to determine the full-field in-plane displacement as well as the Young’s modulus of...     

Parameters controlling fracture resistance in functionally graded materials under mode I loading

In this investigation the fracture behavior of functionally graded materials (FGMs) was studied by means of experiments carried out on model polymer-based FGMs. Model graded materials were manufactured by selective ultraviolet irradiation of ECO [poly(ethylene carbon monoxide)], a photo-sensitive ductile copolymer that becomes more brittle and stiffer under exposure to ultraviolet light. The mechanical response of the graded material was characterized using uniaxial tensile tests. Single edge notched tension graded ECO specimens possessing different spatial variations of Young’s modulus, failure stress and failure strain were tested under remote opening loading. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material. The measured displacement field was then used to extract fracture parameters such as stress intensity factor and T-stress, and thus construct resistance curves for crack growth in the FGMs. For this loading configuration it was found that the nonsingular T-stress term in the asymptotic expansion for stresses needs to be accounted for in order to accurately measure the fracture resistance in FGMs. In addition, the influence of local failure properties (i.e., failure stress and failure strain) on crack growth resistance was investigated in detail. It was found that depending on the combined effects of the spatial variation of these two failure parameters, regardless of the spatial variation of the Young’s modulus, the FGM fracture resistance can either increase, decrease or remain constant with continued crack growth.     

An inverse problem in film/substrate indentation: extracting both the Young’s modulus and thickness of films

In an indentation test, the effective Young’s modulus of a film/substrate bilayer heterostructure varies with the indentation depth, a phenomenon known as the substrate effect. In previous studies investigating this, only the Young’s modulus of the film was unknown. Once the effective Young’s modulus of a film/substrate structure is determined at a given contact depth, the Young’s modulus of the film can be uniquely determined, i.e., there is a one-to-one relation between the Young’s modulus of the film and the film/substrate effective Young’s modulus. However, at times it is extremely challenging or even impossible to measure the film thickness. Furthermore, the precise definition of the layer/film thickness for a two-dimensional material can be problematic. In the current study, therefore, the thickness of the film and its Young’s modulus are treated as two unknowns that must be determined. Unlike the case with one unknown, there are infinite combinations of film thickness and Young’s modulus which can yield the same effective Young’s modulus for the film/substrate. An inverse problem is formulated and solved to extract the Young’s modulus and thickness of the film from the indentation depth-load curve. The accuracy and robustness of the inverse problem-solving method are also demonstrated.     

基于高速3D-DIC技术的砂岩动力特性粒径效应研究

利用分离式霍普金森压杆（SHPB）,对粗砂岩、中等粒径砂岩和细砂岩进行了应变率为69～83 s–1的动态单轴抗压实验,研究了粒径尺寸效应对砂岩动力特性的影响。通过三维数字图像相关（3D-DIC）技术分析高速摄像图像,获得了砂岩的实时应变场,据此分析了动态荷载下3种粒径砂岩的动力变形特性和裂纹开展行为。结果表明,砂岩弹性应变储能可逆释放的临界应变率随着粒径的减小而升高,动态压缩强度随着粒径减小而增大,动态强度应变率敏感度则与强度规律相反。相较于静态条件下,中等粒径砂岩和细砂岩的动态弹性模量增长了2～3倍,粗砂岩的动态弹性模量增长达5倍以上。细砂岩的动态泊松比相较于静态提高了约25%,中等粒径砂岩的动态泊松比约为静态时的70%。动态裂纹首先出现于试件内部,然后传播至表面,呈现出应变局部化,动态荷载下岩石裂纹的孕育和扩展相比静态条件下均有所提前,其中细砂岩在动态荷载条件下的归一化裂纹起裂阈值仅为峰值强度的10%。微观分析表明,矿物粒径大小和黏土矿物含量分别在砂岩的动力力学性质和裂纹开展行为方面发挥主要作用。     

Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration

In this paper, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated. Nonlinearities due to large-amplitude shell motion are considered using the Donnell’s nonlinear shallow-shell theory, with account taken of the effect of viscous structure damping. The dynamic Young’s modulus which varies with vibrational frequency of the laminated composite shell is considered. An improved nonlinear model, which needs not to introduce the Airy stress function, is employed to study the nonlinear forced vibrations of the present shells. The system is discretized by Galerkin’s method while a model involving two degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. The stability of analytical steady-state solutions is analyzed. Results obtained with analytical method are compared with numerical simulation. The agreement between them bespeaks the validity of the method developed in this paper. The effects of rotating speed and some other parameters on the nonlinear dynamic response of the system are also investigated.     

Young’s modulus prediction of hexagonal nanosheets and nanotubes based on dimensional analysis and atomistic simulations

The present work investigates Young’s modulus of hexagonal nanosheets and nanotubes based on dimensional analysis and molecular mechanics. Using second derivatives of the strain energy density revealed from molecular dynamics simulations at 0 K (i.e., molecular mechanics) with harmonic potentials for various combinations of force constants, Young’s modulus have been computed for single-walled armchair and zigzag nanotubes of different radii. This parametric study with the aid of dimensional analysis allows explicitly establishing Young’s modulus of (n, n) armchair and (n, 0) zigzag nanotubes as functions of the force constants, bond length and chiral index n. Proposed formulae are applied to estimate Young’s modulus of graphene, boron nitride, silicon carbide sheets and their nanotubes. The accuracy of the proposed formulae are verified and discussed with available data in the literature for these three sheets and their nanotubes.     

大理岩动态拉伸强度及弹性模量的SHPB实验研究

提出了获取脆性材料动态拉伸强度及弹性模量的实验步骤及相关记录数据的分析方法。利用直径为100mm的分离式Hopkinson压杆径向冲击巴西圆盘和平台巴西圆盘试样,测试了大理岩在高应变率加载下的动态力学性能。应力波加载下动态劈裂拉伸圆盘在试样中心产生了约45/s的拉伸应变率。分析了实验的有效性并考虑了试样两个端面应力波波形差异的影响以提高实验结果的精度。结果表明准静态下的公式可适用于动态劈裂拉伸实验;大理岩的动态拉伸强度及弹性模量比静态时有明显的增加。     

Strength and fracture toughness of heterogeneous blocks with joint lognormal modulus and failure strain

We obtain analytical approximations to the probability distribution of the fracture strengths of notched one-dimensional rods and two-dimensional plates in which the stiffness (Young’s modulus) and strength (failure strain) of the material vary as jointly lognormal random fields. The fracture strength of the specimen is measured by the elongation, load, and toughness at two critical stages: when fracture initiates at the notch tip and, in the 2D case, when fracture propagates through the entire specimen. This is an extension of a previous study on the elastic and fracture properties of systems with random Young’s modulus and deterministic material strength (Dimas et al., 2015a). For 1D rods our approach is analytical and builds upon the ANOVA decomposition technique of (Dimas et al., 2015b). In 2D we use a semi-analytical model to derive the fracture initiation strengths and regressions fitted to simulation data for the effect of crack arrest during fracture propagation. Results are validated through Monte Carlo simulation. Randomness of the material strength affects in various ways the mean and median values of the initial strengths, their log-variances, and log-correlations. Under low spatial correlation, material strength variability can significantly increase the effect of crack arrest, causing ultimate failure to be a more predictable and less brittle failure mode than fracture initiation. These insights could be used to guide design of more fracture resistant composites, and add to the design features that enhance material performance.     

On the verification and validation of a spring fabric for modeling parachute inflation

A mesoscale spring–mass model is used to mimic fabric surface motion. Through coupling with an incompressible fluid solver, the spring–mass model is applied to the simulation of the dynamic phenomenon of parachute inflation. A presentation of a verification and validation efforts is included. The present model is shown to be numerically convergent under the constraints that the summation of point masses is constant and that both the tensile stiffness and the angular stiffness of the spring conform with the material׳s Young modulus and Poisson ratio. Complex validation simulations conclude the effort via drag force comparisons with experiments.     

Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media

The paper presents a three-dimensional solution to the equilibrium equations for linear elastic transversely isotropic inhomogeneous media. We assume that the material has constant Poisson’s ratios, and its Young’s and shear moduli have the same functional form of dependence on the co-ordinate normal to the plane of isotropy. We show, apparently for the first time, that stresses and displacements in such an inhomogeneous transversely isotropic elastic solid can be represented in terms of two displacement functions which satisfy the second- and fourth-order partial differential equations. We examine and discuss key aspects of the new representation; they include the relationship between the new displacement functions and Plevako’s solution for isotropic inhomogeneous material with constant Poisson’s ratio as well as the application of the new representation to some important classes of three-dimensional elasticity problems. As an example, the displacement function is derived that can be used to determine stresses and displacements in an inhomogeneous transversely isotropic half-space which is subjected to a concentrated force normal to a free surface and applied at the origin (Boussinesq’s problem).     

Measurement of Temperature-Dependent Young’s Modulus at a Strain Rate for a Molding Compound by Nanoindentation

The mechanical properties of a molding compound on a packaged integrated circuit (IC) were measured by spherical nanoindentation using a 50 μm radius diamond tip. The molding compound is a heterogeneous material, consisting of assorted diameters of glass beads embedded in an epoxy. Statistical analysis was conducted to determine the representative volume element (RVE) size for a nanoindentation grid. Nanoindentation was made on the RVE to determine the effective viscoelastic properties. The relaxation functions were converted to temperature-dependent Young’s modulus at a given strain rate at several elevated temperatures. The Young’s modulus values at a given strain rate from nanoindentation were found to be in a good agreement with the corresponding data obtained from tensile samples at or below 90 °C. However, the values from nanoindentation were significantly lower than the data obtained from tensile samples when the temperature was near or higher than 110 °C, which is near the glass transition. The spatial distribution of the Young’s modulus at a given strain rate was determined using nanoindentation with a Berkovich tip. The spatial variation of the Young’s modulus at a given strain rate is due to the difference in nanoindentation sites (glass beads, epoxy or the interphase region). A graphical map made from an optical micrograph agrees reasonably well with the nanoindentation results.     

Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates

This paper presents a three-dimensional elasticity solution for a simply supported, transversely isotropic functionally graded plate subjected to transverse loading, with Young’s moduli and the shear modulus varying exponentially through the thickness and Poisson’s ratios being constant. The approach makes use of the recently developed displacement functions for inhomogeneous transversely isotropic media. Dependence of stress and displacement fields in the plate on the inhomogeneity ratio, geometry and degree of anisotropy is examined and discussed. The developed three-dimensional solution for transversely isotropic functionally graded plate is validated through comparison with the available three-dimensional solutions for isotropic functionally graded plates, as well as the classical and higher-order plate theories.     

Novel Technique for Static and Dynamic Shear Testing of Ti6Al4V Sheet

Few shear test techniques exist that cover the range of strain rates from static to dynamic. In this work, a novel specimen geometry is presented that can be used for the characterisation of the shear behaviour of sheet metals over a wide range of strain rates using traditional tensile test devices. The main objectives during the development of the shear specimen have been 1) obtaining a homogeneous stress state with low stress triaxiality in the zone of the specimen subjected to shear and 2) appropriateness for dynamic testing. Additionally, avoiding premature specimen failure due to edge effects was aimed at. Most dimensional and practical constraints arose from the dynamic test in which the specimen is loaded by mechanical waves in a split Hopkinson tensile bar device. Design of the specimen geometry is based on finite element simulations using ABAQUS/Explicit. The behaviour of the specimen is compared with the more commonly used simple shear specimen with clamped grips. Advantages of the new technique are shown. The technique is applied to Ti6Al4V sheet. During the high strain rate experiments high speed photography and digital image correlation are used to obtain the local shear strain in the specimen. Comparison of experimental and numerical results shows good correspondence.     

Influence of the spatial variation of Poisson’s ratio upon the elastic field in nonhomogeneous axisymmetric bodies

The effect of a nonconstant Poisson’s ratio upon the elastic field in functionally graded axisymmetric solids is analyzed. Both of the elastic coefficients, i.e. Young’s modulus and Poisson’s ratio, are permitted to vary in the radial direction. These elastic coefficients are considered to be functions of composition and are related on this basis. This allows a closed form solution for the stress function to be obtained. Two cases are discussed in this investigation: first, both Young’s modulus and Poisson’s ratio are allowed to vary across the radius and the effect of spatial variation of Poisson’s ratio upon the maximum radial displacement is investigated; secondly, Young’s modulus is taken as constant and the change in the maximum hoop stress resulting from a variable Poisson’s ratio is calculated.     

Internal Deformation Measurement and Force Chain Characterization of Mason Sand under Confined Compression using Incremental Digital Volume Correlation

The mechanical behavior of granular materials such as sand is not well understood due to its complex solid/fluid-like behavior. In this paper, Mason sand was investigated to determine the grain-level Young’s modulus and hardness by nanoindentation, and the mesoscale behavior through X-ray tomography of a sample in compression. Mason sand specimen was confined in a polycarbonate tube and compressed in the axial direction at ten axial compressive strains up to -21.8 % while its microstructures were observed. The mesoscale deformations were determined by incremental digital volume correlation of reconstructed volumetric images. A procedure for characterization of internal force chains is developed. The minor principal strains and their principal directions were obtained and used to determine the formation and evolution of force chains.     

Characterization of Anisotropic Polymeric Foam Under Static and Dynamic Loading

An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young??s and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., C _ij . An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10^?4 s^?1), intermediate (1 s^?1), and high (10³ s^?1) strain rates. A simple model proposed for the Young??s modulus of the foam was in very good agreement with the present and published experimental results.