平面应变模具尺寸差对金属流变及其力能的影响

采用MARC/Superform有限元软件对平面应变压缩过程进行了二维有限元分析,分析了上下模具尺寸不相等时,对金属流变规律及其力能参数的影响.同时应用滑移线场理论对端部的滑移线场进行了分析,分析了金属的流动情况,进一步验证了有限元模拟结果的可靠性.研究结果显示:模具尺寸相等时,金属流动呈现对称分布;当上下两个模具尺寸不等时,金属流动呈现非对称分布,有剪切变形产生.而且随着模具尺寸差的增大,其交叉剪切变形越严重,总压力也增大,平均压力相对降低,这与异步轧制过程类似.所研究结果为异步轧制过程提供了一种新的物理模拟方法.     

Temperature changes during hot plane strain compression testing

Abstract

Detailed understanding of the flow stress and microstructural development during plane strain compression testing requires accurate knowledge of the time variation of temperature. A finite difference model of the temperature variations has been developed and implemented in a computer program on a PC, which can rapidly produce results for multideformation schedules. An outline and validation of the model is presented here; the validation exercise compares temperature records taken during a variety of plane strain compression tests with those generated by the model.     

Development of shear bands in dynamic plane strain compression of depleted uranium and tungsten blocks

We study the initiation and growth of shear bands in prismatic bodies of rectangular cross-section made of either depleted uranium or tungsten and deformed in plane strain compression at a nominal strain-rate of 5000 s⁻¹. It is assumed that defects are distributed symmetrically with respect to the two centroidal axes and each quadrant has up to 300 randomly distributed defects in the form of a weaker material; the flow stress for the weaker material in a quasistatic simple compression test is taken to be 5% lower than that for the original material. It is found that, in the deformed configuration, shear bands in depleted uranium blocks are inclined at approximately 42.5° counterclockwise from the horizontal axis, those in tungsten are inclined at nearly 135°. When shear bands initiate, the total compressive force required to deform the body drops sharply for the uranium blocks but gradually for the tungsten blocks. After a shear band has developed, dead zones form in both uranium and tungsten blocks; the size of the dead zone in the tungsten block is more than that in the uranium block. When the shear modulus for the tungsten is artificially changed so as to equal that for the uranium, the angle of inclination for the shear bands in tungsten blocks changes to that found for the uranium blocks. This suggests that the value of the shear modulus plays a noticeable role in the development of shear bands. We have also studied the effect, on the initiation of shear band, of modeling the defects as either very weak or very strong material.     

Dynamic shear band development in plane strain compression of a viscoplastic body containing a rigid inclusion

Summary We study the plane strain thermomechanical deformations of a viscoplastic body containing a rigid non-heat-conducting ellipsoidal inclusion at the center. Two different problems, one in which the major axis of the inclusion is parallel to the axis of compression and the other in which it is perpendicular to the loading axis are considered. In each case the deformations are presumed to be symmetric about the two centroidal axes and consequently deformations of a quarter of the block are analyzed. The material of the block is assumed to exhibit strain-rate hardening, but thermal softening. The applied load is such as to cause deformations of the block at an overall strain-rate of 5000 sec^–1. The rigid inclusion simulates the presence of second phase particles such as oxides or carbides in a steel and acts as a nucleus for the shear band.It is found that a shear band initiates near the tip of the inclusion and propagates along a line inclined at 45° to the horizontal axis. At a nominal strain of 0.25, the peak temperature rise near the tip of the vertically aligned inclusion equals 75% of that for the horizontally placed inclusion. The precipitous drop in the effective stress near the inclusion tip is followed somewhat later by a rapid rise in the maximum principal logarithmic strain there.     

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.     

An adaptive mesh refinement technique for the analysis of shear bands in plane strain compression of a thermoviscoplastic solid

We have developed an adaptive mesh refinement technique that generates elements such that the integral of the second invariant of the deviatoric strain-rate tensor over an element is nearly the same for all elements in the mesh. It is shown that the finite element meshes so generated are effective in resolving shear bands, which are narrow regions of intense plastic deformation that form in high strain-rate deformation of thermally softening viscoplastic materials. Here we assume that the body is deformed in plane strain compression at a nominal strain-rate of 5000 sec^-1, and model a material defect by introducing a temperature perturbation at the center of the block.     

Influence of voids on shear band instabilities under plane strain conditions

The effect of microscopic voids on the failure mechanism of a ductile material is investigated by considering an elastic-plastic medium containing a boubly periodic array of circular cylindrical voids. For this voided material under uniaxial or biaxial plane strain tension the state of stresses and deformations is determined numerically. Bifurcation away from the fundamental state of deformation is analysed with special interest in a repetitive pattern that represents the state of deformation inside a shear band. Both in the fundamental state and in the bifurcation analysis the interaction between voids and the details of the stress distribution around voids are fully accounted for. Comparison is made with the shear band instabilities predicted by a continuum model of a ductile porous medium. Based on the numerical results an adjustment is suggested for the approximate yield condition in this model of dilatant, pressure sensitive plastic behaviour.

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Résumé Les effets de lacunes microscopiques sur le mécanisme de la rupture d'un matériau ductile ont été étudiés en considérant un milieu élastoplastique comportant une double rangée périodique de lacunes circulaires cylindriques. Pour ce matériau soumis à une tension en état plan de déformations uniaxiales ou biaxiales, on détermine par voie numérique l'état des tensions et des déformations. On analyse une déviation par rapport à l'état fondamental des déformations en s'intéressant plus particulièrement à l'aspect répétifif représentant l'état de déformation à l'intérieur d'une bande de cisaillement. L'interaction entre les lacunes et les détails de la distribution des contraintes autour de ces lacunes sont pris en compte dans une approche fondamentale et dans l'analyse de la déviation. Une comparaison est établie avec les instabilités des bandes de cisaillement prédites par un modèle continu dans un milieu poreux ductile. En se basant sur les résultats numériques, on suggère un ajustement à la condition approchée de cédage dans ce modèle de comportement plastique en dilatation et sensible à la pression.

     

Probing into the strain induced anisotropy of Hostun RF loose sand

Several recent linear drained preloading histories with fixed direction were especially designed to study the effects of strain induced anisotropy of loose Hostun RF sand in the compression side of the classical triaxial plane. Nearly identical void ratio and a same initial isotropic stress state prior to the final undrained shearing in compression are the requirements of the experimental program to take into account only the deviatoric strain histories. The effects of previous deviatoric strain histories on the undrained response of loose Hostun RF sand are identified: mainly the progressive transformation of a contractive and unstable behaviour of very loose sand into a dilative and stable behaviour of dense-like sand by previous linear drained history, while remaining in the same state of loose density. Experimental data evidence the directional dependency of the initial gradient of the effective stress paths, independent of the length of the approaching linear stress paths; the large common non linear effective stress response up to the deviatoric stress peak; the progressive appearance of the dilatancy domain and the unexpected evolution of the undrained behaviour of loose and presheared sand. The paper provides new insights into the mechanisms of strain induced anisotropy of loose sand created by simple linear triaxial stress paths from an isotropic stress state.     

Effect of surface energy on the plastic behavior of crystalline thin films under plane strain constrained shear

In this work, a new continuum dislocation based model for crystal plasticity with surface energy effect is proposed. Based on the model, a thin film under plane constrained shear is considered. From the perspective of energy, the yield strength as a function of film thickness has been calculated which is achieved by comparing the energy due to elastic deformation, plastic deformation without surface energy and that with surface energy effect. According to the numerical results, the model including the impenetrable surface assumption can capture the surface dominated deformation mechanism for thin films of nanometer scale. In addition, the transition in dominant deformation mechanisms is also predicted for film thicknesses ranging from tens of nanometers to several microns.     

Heat generation in plane strain compression of a thin rigid plastic layer

This paper presents a theoretical investigation into heat generation in the continued quasi-static plane strain compression of a thin metal strip between two rigid, parallel perfectly rough dies. The strip material is rigid perfectly plastic. The length of the dies is supposed to be much larger than the current strip thickness. The plastic work rate approaches infinity in the vicinity of perfectly rough friction surfaces. Since the plastic work rate is involved in the heat conduction equation, this significantly adds to the difficulties of solutions of this equation. In particular, commercial finite element packages are not capable of solving such boundary value problems. The present approximate solution is given in Lagrangian coordinates. In this case, the original initial/boundary value problem reduces to the standard second initial/boundary value problem for the nonhomogeneous heat conduction equation. Therefore, the Green’s function is available in the literature. An example is presented to illustrate the general solution.     

Effect of kinematic hardening on the initiation and growth of shear bands in plane strain deformations of a thermoviscoplastic solid

Summary We study dynamic thermomechanical deformations of an elasto-viscoplastic body deformed in plane strain compression at a nominal strain-rate of 5 000 sec^–1. The boundaries of the block are assumed to be perfectly insulated. We model the thermoviscoplastic response of the material by the Brown-Kim-Anand constitutive relation in which the evolution of the microstructural changes is accounted for by two internal variables, viz. a scalar and a traceless symmetric second order tensor. The former accounts for the isotropic hardening of the material, and the latter for the kinematic hardening. We model a material defect by introducing a temperature perturbation in the stress-free reference configuration. It is found that the consideration of kinematic hardening does not change the qualitative nature of results.     

Correction of plane strain compression data for the effects of inhomogeneous deformation

Abstract

Plane strain compression tests to investigate the effects of heterogeneity of deformation on various initial specimen geometries have been carried out. Equations for correction of nominal strain and strain rate to slip line field strain and strain rate have been developed and applied to experimental flow stress-strain data. Investigation of the deformed specimens showed evidence of changing friction conditions during deformation, therefore a simple function allowing friction to change was applied. The corrections eliminate the geometry effect observed in the initial data and lead to modified constitutive equations for flow stress.     

Effect of texture and testing conditions on strain localization during cyclic deformation of copper polycrystals

Fatigue tests were performed on pure copper polycrystals with a crystallographic texture different from that produced by ‘standard’ thermomechanical treatments, which emphasize multi-slip 111–100 textures. The texture along the loading axis deviated by 10–15° from these two poles for the samples used here. The experiments were initiated by ramp loading as a mechanical pretreatment and the cyclic stress–strain curve (CSSC) was established by step tests using enough cycles at each step to insure saturation. Under these conditions, a plateau was observed in the CSSC at an appropriate stress level and in a reproducible fashion.     

Numerical modelling of the NGI-DSS test and cyclic threshold shear strain for degradation in sand

Ability of laboratory determination of a sand behaviour in static and dynamic loading conditions are influenced by (among other things): sample preparation, number of tests, size of strains, speed of loading and averaging of the errors during examination. Dynamic load per se causes accumulation of the pore water pressure and the phenomenon of stiffening-threshold-degradation which makes the understanding of the sand behaviour more difficult. The complex behaviour of granular material, i.e. sand, is caused by chemical and physical properties of individual particles and their mutual interaction. Obviously, these interrelationships could not be analysed on the basis of laboratory testing. One way to analyse it is numerically, with algorithm that takes into consideration the characteristics of individual particles as well as their interaction in the sand matrix. Discrete element method (DEM) is a numerical method which takes into consideration the discrete nature of sand and shape of particles and is used as an elementary research tool for sand behaviour. Program package PFC3D is based on DEM and allows the modelling of the laboratory equipment, materials and calibration of its micro-characteristics, based on experimental results. The research of cyclic threshold shear strain for degradation in sand includes observation and visualization of the sample preparation (creation of the material skeleton), pouring of the material (transition from liquid to meta-stable state), influence of the particle shape (interlocking, arching), consolidation (deformation of the skeleton) and development and braking of force chains through the sample. This paper explores the suitability of the selected numerical method for modelling of NGI-DSS device, calibration of the tested granular material (Nevada sand) and preparation of the sample for testing and presentation of the stiffening-threshold-degradation phenomenon.     

Effect of shear deformation on the elastica with axial strain

The problem of the elastica is generalized to include the effect if shear as well as axial strain. This leads to a non-linear two-point boundary-value problem composed of five first-order differential equations. At first the problem is linearized to study the way in which the bucking loads are modified by the combination of effects. For a simple column, the eigenvalues are found to be zeros of a third-order polynomial, and these are evaluated by a straightforward Newton–Raphson technique using a digital computer. The postbucking behaviour is then studied by using the computer and a ‘shooting’ method to solve the non-linear problem. For the special case of the prismatic column, graphs plotted by the computer are displayed to show the variation of load with both lateral and axial deflection for various combinations of axial compressibility and shear deformability. For one particular case, the deflected center line at various load levels is shown.     

Stress-induced anisotropy in sand under cyclic loading

The anisotropy of a granular material’s structure will influence its response to applied loads and deformations. Anisotropy can be either inherent (e.g. due to depositional process) or induced as a consequence of the applied stresses or strains. Discrete element simulations allow the interactions between individual particles to be explicitly simulated and the fabric can be quantified using a fabric tensor. The eigenvalues of this fabric tensor then give a measure of the anisotropy of the fabric. The coordination number is a particle scale scalar measure of the packing density of the material. The current study examines the evolution of the fabric of a granular material subject to cyclic loading, using two-dimensional discrete element method (DEM) simulations. Isotropic consolidation modifies and reduces the inherent anisotropy, but anisotropic consolidation can accentuate anisotropy. The ratio of the normal to shear spring stiffness at the particle contacts in the DEM model affects the evolution of anisotropy. Higher ratios reduce the degree of anisotropy induced by anisotropic consolidation. The anisotropy induced by cyclic loading depends on the amplitude of the loading cycles and the initial anisotropy.     

Influence of fabric shear and flow direction on void formation during resin transfer molding

In resin transfer molding, void type defect is one of common process problems, it degenerates the mechanical performances of the final products seriously. Void content prediction has become a research hotspot in RTM, while the void formation when the flow direction and the tow direction are not identical or the fabric is sheared has not been studied to date. In this paper, based on the analysis of the resin flow velocities inside and outside fiber tows, a mathematical model to describe the formation of micro- and meso-scale-voids has been developed. Particular attention has been paid on the influence of flow direction and fabric shear on the impregnation of the unit cell, so their effects on the generation and size of voids have been obtained. Experimental validation has been conducted by measuring the formation and size of voids, a good agreement between the model prediction and experimental results has been found.