Texture development and plastic anisotropy of B.C.C. strain hardening sheet metals

A Taylor-like polycrystal model is adopted here to investigate the plastic behavior of body centered cubic (b.c.c.) sheet metals under plane-strain compression and the subsequent in-plane biaxial stretching conditions. The <111> pencil glide system is chosen for the slip mechanism for b.c.c. sheet metals. The {110} <111> and {112} <111> slip systems are also considered. Plane-strain compression is used to simulate the cold rolling processes of a low-carbon steel sheet. Based on the polycrystal model, pole figures for the sheet metal after plane-strain compression are obtained and compared with the corresponding experimental results. Also, the simulated plane-strain stress—strain relations are compared with the corresponding experimental results. For the sheet metal subjected to the subsequent in-plane biaxial stretching and shear, plastic potential surfaces are determined at a given small amount of plastic work. With the assumption of the equivalence of the plastic potential and the yield function with normality flow, the yield surfaces based on the simulations for the sheet metal are compared with those based on several phenomenological planar anisotropic yield criteria. The effects of the slip system and the magnitude of plastic work on the shape and size of the yield surfaces are shown. The plastic anisotropy of the sheet metal is investigated in terms of the uniaxial yield stresses in different planar orientations and the corresponding values of the anisotropy parameter R, defined as the ratio of the width plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial tensile loading. The uniaxial yield stresses and the values of R at different planar orientations from the polycrystal model can be fitted well by a yield function recently proposed by Barlat et al. (1997b).     

Experimental Study of the Dynamic Flexural Strength of Concrete

In this paper, we analyze the increase in the dynamic flexural strength of concrete according to strain rate. A simple beam with center-point loading and a classical electro-mechanical testing machine are used to determine the static flexural strength. The dynamic measurements are conducted using a split Hopkinson pressure bar (SHPB) device in the same three-point bending configuration. The outer faces of the beams are instrumented with strain gauges to record the extreme tensile strains. Moreover, full-field displacement measurements are obtained using digital image correlation (DIC) on images recorded by a very high-speed camera. The strain gauge and DIC measurements are compared and used to determine the onset of failure and to evaluate the rate-related tensile strength. Several tests are performed at strain rates in the range from 1/s to 15/s. As expected, a significant increase in the flexural tensile strength with strain-rate is observed, which is consistent with results from the literature.     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

A simple model of the mechanical behavior of ceramic-like materials

This paper presents a macroscopic mechanical theory for ceramic-like materials undergoing isothermal deformations. The proposed model describes an elastic brittle material which is damageable only under tensile loading. The damage lowers the elastic stiffness in traction simulating hence the softening and the fracture (zero stillness) of the material. The basic idea is to consider the continuum as a mixture of two phases—a linear elastic phase and a masonry phase (which shows a linear elastic behavior under compression but cannot hold tractive loads at all). The damage is then related to the volume fraction β of the clastic constituent. The constitutive relations are derived from macroscopic thermodynamics with the volume fraction β and its gradient β taken as state variables.     

On tensile instabilities and ellipticity loss in fiber-reinforced incompressible non-linearly elastic solids

Loss of ellipticity and associated failure in fiber-reinforced non-linearly elastic solids is examined for uniaxial plane deformations. We consider separately fiber reinforcement that either endows the material with additional stiffness only in the fiber direction or introduces additional stiffness under shear deformations. In the first case it is shown that loss of ellipticity under tensile loading in the fiber direction corresponds to a turning point of the nominal stress and requires concavity of the Cauchy stress–stretch curve. For the second example loss of ellipticity occurs after the nominal stress maximum and prior to a turning point of the Cauchy stress.     

Loaded and unloaded optical response of polyester model materials

The optical behavior of mixtures of rigid and flexible polyester resins when loaded and unloaded under constant strain-rate and varying test temperature are characterized. New evidence about the photoplastic method of analyzing deformed but unloaded models is presented through experiments with tensile or compressive uniaxial specimens, diametrically compressed disks and beams under pure bending, which were analyzed during loading, unloading and after being unloaded.     

Compression-shear failure of cementitious materials with oblique weak layers

Compressive/shear failure and strain-softening behavior of a bi-material system consisting of two different mortar compositions are studied. The bulk part of the bi-material specimen was made from the stronger mortar and was cast first, and then an oblique weak layer made from the weaker mortar was introduced in the middle of the specimen. By controlling the weak layer angle, thickness and strength, the compressive/shear failure characteristics and Mode-II shear strain-softening behavior have been determined. A bi-linear strain-softening model is proposed to consider both the Mode-II shear strain-softening behavior and the influence of friction due to compression. A linear softening law for the first part of the bi-linear model is sufficient to describe the softening curve after the peak load, but the second linear ‘softening’ relation is required to explain the influence of friction on the load and displacement curve. With the bi-linear model the Mode-II fracture energy G^f-ll can be separated from the frictional energy dissipation. It is also found that two different frictional coefficients exist if a load and displacement curve has distinct softening and pure frictional regions.     

Constitutive equations in finite viscoplasticity of semicrystalline polymers

Three series of uniaxial tensile tests with constant strain rates are performed at room temperature on isotactic polypropylene and two commercial grades of low-density polyethylene with different molecular weights. Constitutive equations are derived for the viscoplastic behavior of semicrystalline polymers at finite strains. A polymer is treated as an equivalent network of strands bridged by permanent junctions. Two types of junctions are introduced: affine whose micro-deformation coincides with the macro-deformation of a polymer, and non-affine that slide with respect to their reference positions. The elastic response of the network is attributed to elongation of strands, whereas its viscoplastic behavior is associated with sliding of junctions. The rate of sliding is proportional to the average stress in strands linked to non-affine junctions. Stress–strain relations in finite viscoplasticity of semicrystalline polymers are developed by using the laws of thermodynamics. The constitutive equations are applied to the analysis of uniaxial tension, uniaxial compression and simple shear of an incompressible medium. These relations involve three adjustable parameters that are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. It is revealed that the viscoplastic response of low-density polyethylene in simple shear is strongly affected by its molecular weight.     

Mullins�� effect in semicrystalline polymers: experiments and?modeling

Experimental data are reported on isotactic polypropylene in uniaxial cyclic tensile tests with various maximum strains at room temperature. It is demonstrated that polypropylene reveals all characteristic features (hysteresis of energy, damage accumulation, and strain-hardening) of the Mullins effect. Constitutive equations are derived for the viscoplastic behavior of semicrystalline polymers at three-dimensional deformations with small strains. Adjustable parameters in the stress?Cstrain relations are found by fitting the observations. Numerical simulation shows that the model adequately predicts the viscoplastic response of polypropylene in uniaxial and biaxial cyclic tests.     

Supersonic flow of dusty gas over blunt bodies

The results are given of a numerical investigation of the flow of dusty gas over the complete front surface of a sphere. The flow conditions are varied over a wide range in which the state of the gas suspension in the shock layer changes from a frozen to an equilibrium state. The phenomenological approach [5] is used to derive the system of equations describing the behavior of the two-phase medium. The system of conservation equations for the gas—solid-particle mixture is closed by means of relations that generalize the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 73–77, May–June, 1982.     

Bending of Nonthin Transversally Isotropic Plates with Curvilinear Openings

The problem on the spatial stress–strain state of a nonthin transversally isotropic plate with a curvilinear nearly circular opening is considered. The plate is assumed to be subject to bending moments on the opening contour and at infinity. To solve the problem, it is proposed to make mutual use of two well-know methods — expansion of the displacement and stress components into Fourier series in Legendre polynomials of the thickness coordinate and boundary-shape perturbation. The equations and recurrent relations necessary for solution of the problem in an arbitrary approximation are presented     

Geometric and material nonlinear analysis of tensegrity structures

A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stress-strain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.     

Interparticle movement and the mechanical behavior of extruded powder aluminum at elevated temperature

This paper proposes a model and a mechanism for explaining the mechanical behavior of extruded powder aluminum at elevated temperature. This behavior is significantly different from that of ingot-cast and drawn aluminum which is subjected to the same tests. Powder aluminum exhibits a strain-softening effect which is evident in a decrease of stress with increasing strain in uniaxial test specimens when the experiment proceeds into the postyield region. Similar behavior is observed in the shear response during biaxial tension-torsion loading. For these tests, the shear stress is additionally reduced with increased axial extension. A model and mechanism are proposed, based on the relative motion of the extruded aluminum particles, to explain this effect. Equations are derived which relate the axial and shear stresses and strains. These equations are fitted to data obtained in a matrix of experiments, which include combined loadings from uniaxial tension to simple shear. Results are presented graphically and are in good agreement with the proposed models.     

A non-linear viscoelastic model for ceramics at high temperatures

High-temperature mechanical behavior of ceramics is characterized by non-linear rate dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to rupture. Moreover, rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the non-linear, asymmetric time-dependent behavior, a new non-linear viscoelastic model is proposed. Non-linearity and asymmetry are introduced in the volumetric component. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Non-linear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of rupture lives. Numerical simulation results compare well with results of four-point bending experiments.     

金属材料的强度与应力-应变关系的球压入测试方法

压入法获取材料单轴应力-应变关系和抗拉强度对服役结构完整性评价有重要的基础意义.假定材料均匀连续、各向同性、应力应变关系符合Hollomon律,基于能量等效假定,即代表性体积单元(representativevolume element, RVE)的vonMises等效和有效变形域内能量中值等效假定,本文提出了关联材料载荷、深度、球压头直径和Hollomon律的四参数半解析球压入(semi-analyticalspherical indentation,SSI)模型.通过球压入载荷-深度试验关系获得材料的应力-应变关系和抗拉强度.考虑压入过程中的损伤效应,针对金属材料提出了用于球压入测试的材料弹性模量修正模型.对11种延性金属材料完成了球压入试验,采用本文提出的球压入试验方法测到的弹性模量、应力-应变关系和抗拉强度与单轴拉伸试验结果吻合良好.      

Finite viscoelasticity and viscoplasticity of semicrystalline polymers

Observations are reported on low-density polyethylene in uniaxial tensile and compressive tests with various strain rates and in tensile and compressive relaxation tests with various strains. A constitutive model is developed for the time-dependent response of a semicrystalline polymer at arbitrary three-dimensional deformations with finite strains. A polymer is treated as an equivalent network of chains bridged by junctions (entanglements between chains in the amorphous phase and physical cross-links at the lamellar surfaces). Its viscoelastic behavior is associated with separation of active strands from temporary junctions and merging of dangling strands with the inhomogeneous network. The viscoplastic response is attributed to sliding of junctions between chains with respect to their reference positions. Constitutive equations are derived by using the laws of thermodynamics. The stress–strain relations involve 6 material constants that are found by matching the observations.      

A plasticity and anisotropic damage model for plain concrete

A plastic-damage constitutive model for plain concrete is developed in this work. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. Moreover, in order to account for different effects under tensile and compressive loadings, two damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. Stiffness recovery caused by crack opening/closing is also incorporated. The strain equivalence hypothesis is used in deriving the constitutive equations such that the strains in the effective (undamaged) and damaged configurations are set equal. This leads to a decoupled algorithm for the effective stress computation and the damage evolution. It is also shown that the proposed constitutive relations comply with the laws of thermodynamics. A detailed numerical algorithm is coded using the user subroutine UMAT and then implemented in the advanced finite element program ABAQUS. The numerical simulations are shown for uniaxial and biaxial tension and compression. The results show very good correlation with the experimental data.     

Thermo-viscoelastic and viscoplastic behavior of high-density polyethylene

Observations are reported on high-density polyethylene in uniaxial tensile tests with constant strain rates and relaxation tests at various temperatures ranging from 25 to 90 °C. A constitutive model is derived for the nonlinear viscoelastic and viscoplastic behavior of semi-crystalline polymers at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. It is demonstrated that (i) the model correctly approximates the observations and (ii) material parameters are independent of strain rate and change consistently with temperature.     

Experimental techniques for testing unstiffened plates in compression and bending

We present details of a dual-actuator rig developed for testing rectangular plates supported on three sides, with the remaining (longitudinal) edge free, under combined uniaxial compression and in-plane bending. Particular attention is given to ensuring a constant strain gradient at the loaded ends, as opposed to a constant load eccentricity, in order to determine the post-buckling behavior and ultimate load and moment capacities of unstiffened thin-walled elements. Strain gradients varying from pure compression to pure bending are facilitated. Attention is also given to ensuring simply supported boundary conditions, and the methods used for anchoring the tensile stresses that develop at the loaded edges as a result of large plate deflections. Details of the methods for controlling the applied displacements are given, for which a system of four laser displacement devices was employed in order to achieve the required strain gradient. The operation of the rig is verified against established theoretical solutions.     

缝纫复合材料单向板面内力学性能的试验研究

对缝纫复合材料单向板在单向拉伸载荷作用下的面内力学性能进行试验研究,给出了缝纫密度、缝纫线直径对复合材料单向板面内拉伸强度的影响规律.研究发现复合材料的破坏模式与缝纫密度有关,对于中低密度缝纫的单向板其破坏模式为纤维断裂,而对于高密度缝纫的单向板其破坏模式为复合材料撕裂破坏.并从复合材料细观结构层次上揭示了破坏模式和拉伸强度与缝纫密度之间的内在关系.