Evolution of mechanical properties for a dual-phase steel subjected to different loading paths

The evolution of the mechanical properties of a dual-phase (DP590) steel sheet after being prestrained by uniaxial tension, plane strain and equal biaxial stretching was investigated. Specimens were first loaded using the three prestraining modes. Then, from the prestrained specimens, a few sub-sized samples were machined along the rolling direction and the transverse direction for further uniaxial tension testing. Six loading paths were provided. Equal biaxial stretching was performed using a cruciform specimen. The evolution of work hardening performance, elastic modulus, yield stress and tensile stress under the six loading paths were discussed in detail. The results indicate that loading paths can affect the latent work hardening performances, strain hardenability, yield stress and tensile stress evolution as well as the elastic modulus decrease during plastic deformation. The uniaxial tension–uniaxial tension path results in a cross-softening phenomenon, the largest yield stress enhancement and a mild maximum tensile stress increase. The equal biaxial stretching-uniaxial tension path leads to a cross-hardening phenomenon, the least yield stress enhancement and the largest tensile strength increase maximum tensile strength. The elastic modulus of DP590 steel not only changes with the accumulated plastic strain but also varies with the loading paths. The largest decrease of the elastic modulus equal biaxial stretching–uniaxial tension can reach 12.7% beyond 8% equivalent strain, which is 5.2% greater than that in the monotonic uniaxial tension path.     

基于能量原理的岩样单轴压缩剪切破坏失稳判据

利用能量原理对倾斜的剪切带-带外弹性岩石构成的系统的稳定性进行了研究。单轴压缩岩样沿轴向的变形被分解为两部分,带外弹性岩石压缩引起的变形和剪切带错动引起的变形。后者与剪切带的相对剪切变形具有简单的几何关系。系统的总势能由剪切带的弹性及耗散势能和带外弹性岩石对剪切带所作的外力功构成。剪切带的弹性及耗散势能与剪切带的体积有关系。剪切带的尺寸由梯度塑性理论确定。将系统的总势能对相对剪切变形求一阶导数(等于零),得到了弹性岩石的平衡条件。将总势能对相对剪切变形求二阶导数(小于零),得到了系统的失稳判据。它综合反映了岩石材料弹性及应变软化阶段本构参数(弹性模量及软化模量)、剪切带之外弹性岩石的尺寸、剪切带的尺寸及系统的结构形式(剪切带倾角)对系统稳定性的影响。失稳判据比以往所得到的失稳判据更严格,更精确,更具有广泛意义。     

Pressure and temperature dependence of elastic properties of lanthanum gallogermanate glasses

The hydrostatic and the uniaxial pressure, and the temperature dependence of elastic properties of a series of lanthanum gallogermanate glasses were determined by ultrasonic pulse-echo techniques. The experimental results are used to obtain the complete set of second- and third-order elastic constants of these glasses. The normal behavior of negative temperature dependence and positive pressure dependence of the ultrasonic velocities were observed in these glasses. The pressure derivative of shear and bulk moduli, and the longitudinal and shear acoustic mode Gruneisen parameters are all positive for these glasses.     

Elastic anisotropy and low-temperature thermal expansion in the shape memory alloy Cu-Al-Zn

Cu-based shape memory alloys are known for their technologically important pseudo-elastic and shapememory properties, which are intimately associated with the martensitic transformation. A combination of deformation theory and finite-strain elasticity theory has been employed to arrive at the expressions for higher order elastic constants of Cu-Al-Zn based on Keating's approach. The second- and third-order elastic constants are in good agreement with the measurements. The aggregate elastic properties like bulk modulus, pressure derivatives, mode Grüneisen parameters of the elastic waves, low temperature limit of thermal expansion, and the Anderson-Grüneisen parameter are also presented.     

Hyper-elastic constitutive equations of conjugate stresses and strain tensors for the Seth-Hill strain measures

The use of hypo-elastic constitutive equations for large strains in nonlinear finite element applications usually requires special considerations. For example, the strain does not tend to zero upon unloading in some elastic loading-unloading closed cycles. Furthermore, these equations are based on objective material time rate tensors, which require incrementally objective algorithms for numerical applications and integration. Hyper-elastic constitutive equations on the other hand do not require such considerations. However, their behaviour for large elastic strains is important and may differ in tension and compression. In the present work, Hyper-elastic constitutive equations for the Seth-Hill strains and their conjugate stresses are explored as a natural generalisation of Hook’s law for finite elastic deformations. Based on the uniaxial and simple shear tests, the response of the material for different constitutive equations is examined. Together with an objective rate model, the effect of different constitutive laws on Cauchy stress components is compared. It is shown that the constitutive equation based on logarithmic strain and its conjugate stress gives results closer to that of the rate model. In addition, the use of Biot stress-strain pairs for a bar element results in an elastic spring which obeys the Hook’s law even for large deformations and has the same behaviour in both tension and compression. The effect of the constitutive equation on the volume change of the material has also been considered here.     

Elastic theory for the deformation of a solid or layered spheroid under axisymmetric loading

The theory for the deformations of a spheroidal particle is of great scientific interest in numerous physical and biological problems ranging from fracture analysis of plain solids to the compression of biological cells in an atomic force microscope or during micropipette aspiration. Using a formulation in terms of Papkovich–Neuber potentials, we derive the deformations of a prolate, elastic spheroid under known axisymmetric loading. The internal stresses to which the object is subjected are deduced from Hooke’s law of elasticity in prolate spheroidal coordinates. The generalisation to layered spheroids with viscoelastic properties is also discussed. Since for isotropic objects the surface displacements and stresses are directly related by the elastic modulus and Poisson’s ratio alone, the presented, closed-form, analytical solutions may be applied to deduce these important elastic constants from standard stress-deformation experiments. We illustrate the versatility of the findings by analysing the surface displacements and stress states of spheroids with small and large aspect ratios in the presence of both normal and shear surface tractions. Of particular interest in this study is the influence of Poisson’s ratio on the deformation of a near-spherical particle, for instance a soft cancer cell, which is subjected to surface stresses of the kind that can be found in optical traps, like the optical stretcher.     

Nonlinear elastic equation of state of solids subjected to uniaxial homogeneous loading

Applying the finite deformation theory to a solid, which possesses either cubic or isotropic symmetry at stress-free natural state and is subsequently loaded homogeneously in uniaxial direction, one obtains a stress (or strain) dependence of the Young's modulus, Poisson's ratio, and a volume (or density) change, together with a nonlinear elastic relation between stress and strain. These are all expressed in terms of the second and third order elastic constants of the solid material. These expressions are illustrated with examples of cubic silicon crystal, isotropic carbon steel, Pyrex glass, and polystyrene at the relaxed state.     

Mechanical behaviour analysis of buried pressure pipeline crossing ground settlement zone

Numerical simulation model of buried pipeline crossing ground settlement zone was established considering pipeline–soil interaction. Mechanical behaviour of the buried pipeline was investigated, and effects of ground settlement, pipeline parameters and surrounding soil parameters on mechanical behaviour of the buried pipeline were discussed. These results show that there are two high stress areas on both sides of the dividing plane. High stress areas are oval on the top and bottom of the pipeline. Z-shape bending deformation appears under the action of ground settlement. In ground settlement zone, axial strain on the top of the pipeline is compression strain, and axial strain on the bottom of the pipeline is tension strain. On the contrary, they are tension strain and compression strain respectively in no settlement zone. Bending deformation, axial strain and plastic strain of the buried pipeline increase with the increase in ground settlement. Von Mises stress, high stress area, axial strain and plastic strain of the buried pipeline increase with the increasing diameter-thick ratio and internal pressure, but they decrease with the increase in buried depth. Diameter-thick ratio and internal pressure have a small effect on the bending deformation of the buried pipeline. Bending deformation decreases with the increase in buried depth in ground settlement zone. Von Mises stress and high stress area increase with the increasing surrounding soil’s elasticity modulus and cohesion, but they increase first and then decrease with the increase in Poisson’s ratio. Bending deformation of the pipeline in no settlement zone increases with the increase in elasticity modulus and Poisson’s ratio, but it is affected little by the cohesion. Axial strain and plastic strain have a bigger relationship with the elasticity modulus and Poisson’s ratio. Axial strain and plastic strain of the buried pipeline increase with the increase in cohesion, and the change rates increase with the increase in ground settlement.     

Triaxial compression deformation for artificial frozen clay with thermal gradient

In order to study the deformation characteristics of artificial frozen soil with thermal gradient, such as the stress-strain relationship, a series of triaxial compression tests for frozen clay had been conducted by K₀DCGF (K₀ consolidation, freezing with non-uniform temperature under loading) method and GFC (freezing with non-uniform temperature, isotropic consolidation) method at various consolidation pressures and thermal gradients. Stress-strain curves in K₀DCGF test present strain softening during shearing process and the elastic strain is approximately 0.001;but which present the strain hardening characteristics in GFC tests and the elastic strain is approximately 0.01. The elastic modulus and peak stress for frozen clay decrease as the thermal gradient increased at different consolidation pressure both in K₀DCGF test and GFC test. The peak stress and elastic modulus in K₀DCGF test are significant independent on the pressure melting and crushing phenomena occurring in GFC test. To describe the shear deformation characteristics for frozen clay with thermal gradient, the exponent and power equations considering the correction equation on thermal gradient and model parameters from frozen clay with uniform temperature are developed .The results indicated that the proposed equations can reproduce the shear deformation well both in K₀DCGF test and GFC test.     

The Elastic Constants and Anisotropy of Superconducting MgCNi3 and CdCNi3 Under Different Pressure

The second-order elastic constants (SOECs) and third-order elastic constants (TOECs) of MgCNi₃ and CdCNi₃ are presented by using first-principles methods combined with homogeneous deformation theory. The Voigt–Reuss–Hill (VRH) approximation are used to calculate the bulk modulus B, shear modulus G, averaged Young’s modulus E and Poisson’s ratio ν for polycrystals and these effective modulus are consistent with the experiments. The SOECs under different pressure of MgCNi₃ and CdCNi₃ are also obtained based on the TOECs. Furthermore, the Zener anisotropy factor, Chung–Buessem anisotropy index, and the universal anisotropy index are used to describe the anisotropy of MgCNi₃ and CdCNi₃. The anisotropy of Young’s modulus of single-crystal under different pressure is also presented.     

Elastic properties and sound velocities of silicane/graphane hybrids

Using ab initio density functional theory, the effect of hydrogen arrangement on the elastic properties of silicene–graphene hybrid is studied. Mechanical stability, elastic constants and sound velocities of pure and five configurations of hydrogenated SiC sheet, namely, chair, table, boat, zigzag and armchair, are explicitly examined. To reveal the anisotropic properties of the six structures, the polar plots of Young’s modulus, Poisson ratio and acoustic waves speed are given. Compared to graphene, it is shown that all the isotropic systems are less stiffer with lower in-plane Young’s modulus and stronger with their larger Poisson ratio, moreover, their compressional and shear waves propagate faster. The analysis of linear elastic behavior shows that the armchair configuration has an auxetic structure. The result of this work could be used for the design of future silicane–graphane based nanodevices with potentially large technological impact in nanomechanics.     

岩样单轴压缩峰后泊松比理论研究

研究了单轴压缩岩样应变软化阶段侧向应变与轴向应变的比值(峰后泊松比)的变化规律。岩样的塑性变形假设根源于塑性应变局部化。岩样的轴向及侧向变形被分别分为两部分:弹性变形(由虎克定律描述)及由局部化引起的塑性变形(由梯度塑性理论及几何关系确定)。应变软化阶段的轴向应变-侧向应变曲线、轴向应力-轴向应变曲线及轴向应力-侧向应变曲线都得到了实验验证。在峰值强度时,峰后泊松比等于峰前泊松比。当压缩应力降至零时,峰后泊松比达到临界值。该临界值可能比峰前泊松比大,也可能比它小。峰后泊松比还和试件尺寸有关,这与峰前泊松不同。峰后泊松比与轴向压应力之间的关系可能是一条直线,也可能是上凸的,或上凹的。这取决于岩石的本构参数(弹性模量、剪切及软化模量、剪切带宽度及峰前泊松比)、试件的结构尺寸(试件宽度及高度)及剪切带倾角之间的关系。     

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

A local constitutive model for anisotropic granular materials is introduced and applied to isobaric (homogeneous) axial-symmetric deformation. The simplified model (in the coordinate system of the bi-axial box) involves only scalar values for hydrostatic and shear stresses, for the volumetric and shear strains as well as for the new ingredient, the anisotropy modulus. The non-linear constitutive evolution equations that relate stress and anisotropy to strain are inspired by observations from discrete element method (DEM) simulations. For the sake of simplicity, parameters like the bulk and shear modulus are set to constants, while the shear stress ratio and the anisotropy evolve with different rates to their critical state limit values when shear deformations become large. When applied to isobaric deformation in the bi-axial geometry, the model shows ratcheting under cyclic loading. Fast and slow evolution of the anisotropy modulus with strain. Lead to dilatancy and contractancy, respectively. Furthermore, anisotropy acts such that it works “against” the strain/stress, e.g., a compressive strain builds up anisotropy that creates additional stress acting against further compression.     

Acoustoelastic response of polycrystalline aggregates exhibiting transverse isotropy

Acoustoelasticity is an ultrasonic technique which has been used for the determination of active and residual stresses in common structural materials. This paper examines the effect of texture on the acoustoelastic response in polycrystalline bodies. In particular materials which are transversely isotropic aggregates of cubic crystals are studied. The second- and third-order elastic constants of the polycrystal are derived from the elastic properties of the constituent crystals, and the crystalline orientation relative to the body's symmetry axis. The acoustoelastic relations between velocity and deformation are then presented for the aggregate. Finally, evaluation of the acoustoelastic response for several ideal textures using data for aluminum single crystals shows that the response is highly dependent on the texture.     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。     

Incremental constitutive equation for large strain elasto plasticity

Starting from the standard theory with intermediate configuration for finite deformations of an isotropic elasto-plastic material with isotropic hardening, rate type constitutive equations are obtained. The small elastic strain approximation is then discussed and it is shown that, in this approximation, these equations reduce to Hill's formalism of large strain elasto-plasticity obtained from the classical Prandtl-Reuss relations of infinitesimal plasticity by substituting for the infinitesimal strain rate, stress and stress rate respectively the rate of deformation tensor, the Cauchy stress tensor and the Jaumann stress rate tensor. The limiting case of perfect plasticity is also investigated.     

含孔隙混凝土复合材料有效力学性能研究

混凝土、岩石等工程材料是典型的多孔介质材料,孔隙或微裂纹的存在对材料的弹性模量及强度等力学参数产生很大影响。该文基于三相球模型确定了含孔隙复合材料的有效体积模量,提出采用空心圆柱形杆模型推导得到了含孔隙复合材料有效剪切模量的理论公式,并在各向同性材料的假设条件下确定了材料的有效弹性模量及泊松比;推导并得到了含孔隙材料的有效抗拉、抗压强度及有效抗剪强度与孔隙率之间的定量关系公式,并进一步得到了含孔基质在达到有效强度时的临界应变与孔隙率之间的定量关系。结果表明该文方法能较好的预测含孔混凝土材料的有效力学性能,且公式简单,易于应用。     

First-Principles Calculations on Structure,Elastic and Thermodynamic Properties of Al2X （X=Sc,Y） under Pressure

To understand deeply the structural,elastic and thermodynamic characteristics of Al 2 X (X= Sc,Y) compounds in C15 type (space number 227) Cu 2 Mg structure,we have performed ab-initio density functional theory within the local density approximation (LDA) and the generalized gradient approximation (GGA).The thermodynamic properties of the considered structures are obtained through the quasi-harmonic Debye model.We have presented the results on the basic physical parameters,such as the lattice constant,bulk modulus,pressure derivative of bulk modulus,second-order elastic constants,Zener anisotropy factor,Poisson s ratio,Young s modulus,and isotropic shear modulus.In order to gain further information,the pressure-and temperature-dependent behaviour of the volume,bulk modulus,thermal expansion coefficient,heat capacity,entropy,Debye temperature and Gru¨neisen parameter were also evaluated over a pressure range of 0-20 GPa for Al 2 Sc and 0-17 GPa for Al 2 Y compound and a wide temperature range of 0-2000 K for both compounds.The obtained results were compared with the other reported values.     

Characterization of close-celled cellular aluminum alloys

The deformation behaviour of two different types of aluminium alloy foam are studied under tension, compression, shear and hydrostatic pressure. Foams having closed cells are processed via batch casting, whereas foams with semi-open cells are processed by negative pressure infiltration. The influence of relative foam density, cell structure and cell orientation on the stiffness and strength of foams is studied; the deformation mechanisms are analysed by using video imaging and SEM (scanning electronic microscope). The measured dependence of stiffness and strength upon relative foam density are compared with analytical predictions. The measured stress versus strain curves along different loading paths are compared with predictions from a phenomenological constitutive model. It is found that the deformations of both types of foams are dominated by cell wall bending, attributed to various process induced imperfections in the cellualr structure. The closed cell foam is found to be isotropic, whereas the semi-open cell foam shows strong anisotropy.