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.     

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.     

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.     

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 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.     

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.     

预浸织物剪切变形时树脂细观分析模型

为了更好地研究在发生剪切变形时预浸织物材料的力学性能,建立了在像框剪切试验时未固化的树脂对织物发生剪切变形时的阻碍作用的细观分析模型.通过对材料的单胞进行分析,得到了织物单胞变形前、后各质点间的运动学关系,进而得到了树脂材料对整个织物单胞的阻力矩,即树脂的阻尼作用.此阻尼作用较好地说明了树脂在预浸织物材料中的作用.此外,通过树脂的流变试验得到其粘性系数,该粘度系数确定,即该材料的阻尼作用确定.     

Three dimensional fabric evolution of sheared sand

Granular particles undergo translation and rolling when they are sheared. This paper presents a three-dimensional (3D) experimental assessment of fabric evolution of sheared sand at the particle level. F-75 Ottawa sand specimen was tested under an axisymmetric triaxial loading condition. It measured 9.5?mm in diameter and 20?mm in height. The quantitative evaluation was conducted by analyzing 3D high-resolution x-ray synchrotron micro-tomography images of the specimen at eight axial strain levels. The analyses included visualization of particle translation and rotation, and quantification of fabric orientation as shearing continued. Representative individual particles were successfully tracked and visualized to assess the mode of interaction between them. This paper discusses fabric evolution and compares the evolution of particles within and outside the shear band as shearing continues. Changes in particle orientation distributions are presented using fabric histograms and fabric tensor.     

The shear properties of woven carbon fabric

This paper presents experimental and theoretical studies of the shearing properties of carbon plain weave fabrics and prepregs. The shearing characteristics of these materials are determined by the use of a picture frame shear rig which is loaded by a mechanical test machine. The shear force/angle curves are presented for the experiments conducted with the various test materials. A proposed shear model based on previous research which idealizes the fabric yarns as beam elements is presented. Using fabric geometric and material parameters, the model predicts the initial slip region of the fabric, as well as the more dominant elastic deformation range. Comparisons of the experimental and theoretical results were conducted to validate the model. A discussion of the findings from the analysis is also given, with particular focus relating to the accuracy, limitations and advantages offered by such a model. Results indicated that the slip model gives modestly accurate predictions, whilst the elastic modulus model showed very good correlation with experimental data.